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- Reliability-Based Hybrid-ARQ Using Convolutional Codes
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Channel coding ( jstor ) Computer systems performance ( jstor ) Convolutional codes ( jstor ) Decryption ( jstor ) Error rates ( jstor ) Human error ( jstor ) Jammers ( jstor ) Jamming ( jstor ) Simulations ( jstor )
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RELIABILITY-BASED HYBRID-ARQ USING CONVOLUTIONAL CODES By ABHINAV ROONGTA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005 Copyright 2005 by Abhinav Roongta To my parents and my sister ACKNOWLEDGMENTS First I would like to thank and express my sincere gratitude to my advisor, Dr. John M. Shea. This work would not have been possible without his expertise, hard work and pa- tience. He guided me at each and every stage of my Ph.D. program and was always easily accessible. He read and revised all our conference papers and presentations and worked unlimited nights and weekends for our journal article. Besides being a great research advi- sor, I also wish to thank him for his excellent teaching in EEL 5544 and EEL 6550. The efforts that he put in his teaching, in his lectures and creating questions for the exam, really amazed me right from day one of 5544 when he gave the Monte-Hall problem. I would also like to thank Dr. Tan Wong, Dr. Yuguang Fang and Dr. Richard New- man for providing valuable input at the time of my Ph.D. proposal defense. Dr. Richard Newman read this dissertation from cover to cover and provided detailed feedback for im- proving it. I would also like to thank all the students in our lab, NEB 403-405. Thanks to Arun for helping me debug my code on several occasions and strengthening my belief that reliability-based hybrid ARQ is a practical solution; Jang-Wook for patiently answering my questions on jamming model and estimation; Deniz for giving me his LaTex templates and organizing the WING picnic; Sarva and Jianfeng for organizing the WING seminar. I would also like to thank Hongqiang Zhai for bringing me up to speed with network simu- lator (ns2). I also thank my friends Adrian and Brock for burning the midnight oil with me while coding adaptive signal processing algorithms in MATLAB. Together we managed to sail across the troubled waters of EEL 6814. I wish to thank certain "behind-the-scene" people who directly or indirectly con- tributed towards this dissertation. I thank Linda Kahila and Shannon Chillingworth in the ECE Graduate Student Services Office for advising on degree requirements, taking care of paper work and sending regular reminders regarding registration and fee payment deadlines. Thanks to them I never had to read the Graduate Student Handbook. Thanks to Janet Holman, our administrative secretary, for keeping the lab well stocked and doing the paper work for travel to conferences. I also thank all my "non-ECE" friends and my current and past apartment-mates for making life fun. Thanks to Abhudaya and Nitin, my current apartment-mates, for giving me ride to the lab on weekends. Together we survived the hurricanes in the Gatorland. Finally, I would like to thank my parents, Santosh and Madhu Roongta, and my sister Aastha to whom I owe everything. I have become what I am because of their sacrifices, blessings and unconditional love and support. Thank you! TABLE OF CONTENTS ACKNOWLEDGMENTS .. .... LIST OF TABLES ....... page . . . . . iv LIST OF FIGURE S . . . . . . . . . ABSTRACT .................. CHAPTER 1 INTRODUCTION ........... Previous Work on Hybrid ARQ Objective ...... Main Contributions ...... Outline of This Dissertation . 2 RELIABILITY-BASED HYBRID ARQ FOR NON-FADING CHAN- NELS WITHOUT INTERFERENCE .......... . .. 7 2.1 System M odel ........ ..... .. .. ........... 8 2.2 RB-HARQ using Convolutional Codes without Puncturing . 9 2.3 RB-HARQ with Variable Redundancy and Smaller Request Packet .12 2.4 RB-HARQ with RCPC Codes and Arithmetic Coding . ... 15 2.4.1 Error Probability Comparison of RB-HARQ with HARQ with RCPC codes .......... ...... ...... 19 2.4.2 Throughput Comparison of RB-HARQ with HARQ with RCPC codes . ......... ... .. ... 20 3 RELIABILITY-BASED HYBRID ARQ FOR PARTIAL-TIME JAM- MING CHANNELS ............................ 25 3.1 MAP Estimation Algorithms ... ............ 27 3.2 Maximum-Likelihood Estimation of Jammer Parameters . ... 30 3.3 Reliability-Based Hybrid ARQ Schemes ..... . ..... 31 3.3.1 Analysis of Probability of Packet Error for HARQ . .. 34 3.3.2 Size of retransmission-request packet .. . . 36 3.4 Performance of Estimation Algorithm .... ........ 39 3.5 Perform ance Results .... .................. ... 42 3.5.1 Packet error probabilities ... .......... 43 3.5.2 Throughput Results . . . . . 48 4 RELIABILITY-BASED HYBRID-ARQ FOR CSMA-CA-BASED WIRE- LESS NETW ORKS ............................ .. 54 4.1 Interference Modelling .. ............ .... 54 4.2 Non-Fading Channel Model . . . . 57 4.3 Performance of Reliability-Based Hybrid-ARQ in CSMA-CA- Based Networks . ..61 5 CONCLUSIONS AND DIRECTIONS FOR FUTURE WORK ....... 64 5.1 C conclusion . . .. . . . .. 64 5.2 Directions for Future Work ..................... 66 REFEREN CE S . . . . . . . . . 67 BIOGRAPHICAL SKETCH ............................. .. 71 LIST OF TABLES Table page 4.1 Simulation parameters in ns2 . . . . . . 56 4.2 Interference parameters obtained using simulation . . . 56 LIST OF FIGURES Figure page 2.1 Probability of bit error by reliability rank for rate 1/2, (5,7) convolutional c o d e . . . . . . . . . 8 2.2 System model for hybrid ARQ with convolutional codes. . . 9 2.3 Probability of bit error vs. Effective Eb/No for three retransmissions of 5.0% incremental redundancy each. . . . . 11 2.4 Reliability values for example packet of 1000 information bits. .. . 13 2.5 Reliability values, after elimination and smoothing for example packet of 1000 inform ation bits. . . . . . . 15 2.6 Average number of bit indices fedback (NF) and average number of information bits requested for retransmission (NR) vs. E,/No for RB- HARQ scheme . . . . . . . 16 2.7 Probability of bit error vs. Effective EbI/N for RB-HARQ scheme with variable redundancy and reduced retransmission-request packet .. . 17 2.8 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/7. . . . 20 2.9 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/7. . . . 21 2.10 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/3. . . . 22 2.11 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/3. . . . 23 2.12 Throughput comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/7. . . . 24 3.1 Communication scenario. . . . . . . 25 3.2 System m odel . . . . . . . . 26 3.3 Two-state Markov model for jammer. . . . . . 27 3.4 Probability of miss and false alarm of jammed symbols when all jamming parameters must be estimated in comparison to when all jamming parameters are known at E,/Nj = -3 dB. . . . 41 3.5 Probability of packet error for RB-HARQ(J) with estimation of jamming parameters or perfect CSI, p = 0.4 and E,/Nj = -3 dB. . . 42 3.6 Probability of packet error for RB-HARQ(J), Type-I HARQ and retrans- mission of a random set of symbols, p = 0.4 and E,/Nj = -3 dB. . 43 3.7 Probability of packet error for three retransmissions of RB-HARQ(J), p = 0.4 and E,/Nj = -3 dB . . . .. . . 45 3.8 Probability of packet error for different RB-HARQ schemes compared with Type-I HARQ and conventional HARQ, p = 0.4 and E,/Nj = 0 dB. 46 3.9 Probability of packet error for different RB-HARQ schemes, p = 0.4 and E,/Nj = 3 dB . . . . . . . 47 3.10 Probability of packet error for adaptive and fixed RB-HARQ, p = 0.4 and E /N j = -3 dB . . . . . . . 48 3.11 Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ, after 3 retransmissions at p = 0.4 and E,/Nj = -3 dB. .. 50 3.12 Throughput of adaptive RB-HARQ(R), RB-HARQ(J), Type-I HARQ and conventional (uniform) HARQ, p = 0.4 and Es/Nj = -3 dB. .. . 52 3.13 Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ as a function of p at E,/No = 0 dB, E,/Nj = -3 dB. . 53 4.1 Probability density function of the normalized power of the interfering packet . . . . . . . . 57 4.2 Effect of interference on probability of packet error for AWGN channel. 59 4.3 Throughput for Type-I HARQ with up to 2 retransmissions and PI = 1 .61 4.4 Throughput for RB-HARQ and Type-I HARQ with up to 2 retransmissions and AW GN channel . . . . . . . 62 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RELIABILITY-BASED HYBRID-ARQ USING CONVOLUTIONAL CODES By Abhinav Roongta August 2005 Chair: John M. Shea Major Department: Electrical and Computer Engineering In this work we develop selective-retransmission hybrid-ARQ protocols for commu- nication systems that use soft-input soft-output (SISO) decoders. The schemes that we propose are based on reliability-based hybrid-ARQ that use the estimated a posteriori probabilities at the output of the SISO decoder to adaptively determine the set of bits to be retransmitted in response to error detection. First we show the performance of the proposed scheme for nonfading additive white Gaussian noise channels without any interference. We begin by evaluating the performance of a simple reliability-based hybrid ARQ scheme that uses fixed rate convolutional codes in the forward channel and exploits their time-correlation properties to achieve smaller re- transmission requests. Then we extend our work where rate-compatible punctured convo- lutional (RCPC) codes are used in the forward channel and arithmetic coding is used in the feedback channel. We compare the performance of the proposed scheme with the common approach to hybrid-ARQ that uses punctured convolutional codes. The results show that the proposed RB-HARQ scheme achieves better performance than a hybrid-ARQ scheme that uses only RCPC codes. Next we extend our work to improve communication performance on partial-time jamming channels. For channels with partial-time jamming, we can extend our measure of reliability to incorporate not only aposteriori probability information but also estimates of the probability that a bit was jammed. We compare the performance of the proposed scheme with that of a conventional approach in which a predetermined set of bits is re- transmitted in response to a packet failure. The results show that RB-HARQ schemes can achieve better performance than the conventional approach. Next we extend our work to wireless networks that use carrier sense multiple access with collision avoidance (CSMA-CA). We first propose a new channel model that considers the packet errors due to channel noise as well as those due to interference from simulta- neous transmission by other nodes. The proposed channel model takes into account the fact that collisions may result in parts of a packet being corrupted while other parts are received without corruption. Therefore, the proposed channel model is more realistic than an AWGN channel model and can be used in a cross-layer design approach which consid- ers combining ARQ at the data link layer and channel coding at the physical layer. We also investigate the performance of a RB-HARQ technique for CSMA-CA-based wireless networks. CHAPTER 1 INTRODUCTION Automatic-repeat-request (ARQ) and forward-error-correction (FEC) are two basic techniques for controlling transmission errors in data communication systems [1,2]. Automatic- repeat-request schemes typically use a high-rate error-detecting code. They are simple and provide high system reliability. However, one severe drawback of ARQ systems is that their throughput efficiency falls rapidly with increasing channel-error rate. An FEC com- munication system uses a powerful error-correcting code to combat transmission errors. The throughput efficiency of such systems is maintained at a constant level (equal to the code rate) regardless of the channel error rate. The drawback of an FEC system is that it is difficult to achieve high system reliability and decoding is hard to implement. Thus, ARQ is often preferred over FEC for error control in data communication systems, such as packet-switching data networks and computer communication networks. Forward-error- correction is preferred over ARQ in communication systems where return channels are not available or retransmission is not possible for some reason. Hybrid-ARQ (HARQ) schemes that use a proper combination of ARQ and FEC can overcome the drawbacks of both ARQ and FEC schemes. Systems that use HARQ consist of an FEC subsystem contained within an ARQ system. The FEC subsystem reduces the frequency of retransmissions by correcting many common error patterns without retrans- mission, thus increasing the throughput of the system. When an uncorrectable error is de- tected, the ARQ system requests retransmission instead of passing the unreliably decoded message to the user. Thus HARQ systems provide higher reliability than an FEC system alone and higher throughput than the system with ARQ only. Hybrid-ARQ schemes are broadly classified into Type-I and Type-II hybrid-ARQ schemes. Type-I HARQ schemes use a code designed for simultaneous error correction and error detection. Therefore, the codes used in such schemes require more parity bits than a code used only for error detec- tion. This increases the overhead for each transmission. As a result, when the channel error rate is low, the type-I hybrid ARQ scheme has a lower throughput than its corresponding ARQ scheme. However, type-I HARQ schemes provide higher throughput than the cor- responding ARQ scheme when channel error rate is high because HARQ scheme's error- correction capability reduces the frequency of retransmissions. Type-II HARQ schemes are based on the concept that the parity check bits for error correction are sent to the receiver only when they are needed. 1.1 Previous Work on Hybrid ARQ The concept of type-II HARQ or the incremental-redundancy HARQ schemes was first introduced by Mandelbaum [3] and then extended by Metzner [4], Ancheta [5] and Lin and Yu [6]. In these schemes, a message is encoded using a code for error-detection only. If the receiver detects the presence of errors in a received codeword, it saves the erroneous message in a buffer and sends a NACK to the transmitter. The transmitter then transmits a block of parity-check bits formed based on the original message and an error- correcting and error-detecting code. When this parity block is received, it is used to correct the erroneous message stored in the buffer. In case the error correction is successful, the corrected message is delivered to the data sink. If the error correction is unsuccessful, the receiver requests a second retransmission, from the transmitter, which may be either the original codeword or again a parity block. Type-II HARQ scheme provides better perfor- mance than the type-I HARQ scheme if the code used for error correction and the retrans- mission strategy is properly chosen. Incremental-redundancy hybrid-ARQ schemes that use punctured convolutional codes and code combining were proposed by Hagenauer [7]. In these and other hybrid-ARQ schemes [1,2], the set of bits to be transmitted in response to error detection is a predetermined part of the ARQ algorithm. For example, consider the HARQ scheme proposed by Hagenauer [7] in which rate-compatible punctured convolu- tional (RCPC) codes are used. In this scheme if the higher rate codes are not sufficiently powerful to decode channel errors, a predetermined subset of the bits that were previously punctured is transmitted in order to decrease the code rate. Automatic-repeat-request has also been considered to improve the performance of wireless communications in the presence of interference. Hostile jamming can severely disrupt wireless communications. The typical responses to such disruptions are retransmis- sions through ARQ, ARQ with adaptation of the signaling parameters [8-12], and adapta- tion in the network layer [13-17]. The performance of Type-I hybrid-ARQ protocols in a slotted direct-sequence code-division multiple-access network operating in a hostile jam- ming environment was studied by Hanratty and Stuber [18]. The effect of jamming on throughput of HARQ protocol was also studied by Feldman and Levannier et al. [19,20]. Wilkins and Pursley [11] evaluated the performance of an adaptive rate coding system for channels with Rayleigh fading, partial-band interference, and thermal noise. It was shown that adaptive-rate coding systems provide significantly higher throughput than sys- tems that use fixed-rate coding. This is because adaptive-rate coding systems use a high- rate code, which gives high throughput rate, when channel conditions are good, and use a low-rate code only when necessary to combat a large amount of interference. Pursley and Wilkins [10] showed that it is beneficial to be able to change both the transmission power and the code rate in a slow-frequency hopping communication system. It was suggested that the code rate should be adapted based on the jammer parameters while the power level should be adapted based on signal-to-noise ratio. Most of the previous work identifies that adaptation is the key to responding to jam- ming. However, in each of these works, traditional ARQ is assumed. Although traditional ARQ is adaptive in the sense that retransmissions only occur when a packet is in error, it is non-adaptive in the sense that the response to a packet error is fixed: the entire packet should be retransmitted. Even if hybrid-ARQ is used, the response neither adapts to the reliability of the received packet nor to the set of symbols that was jammed. A reliability- based hybrid ARQ (RB-HARQ) algorithm that is truly adaptive was proposed by Shea [21]. In RB-HARQ, soft-input soft-output decoders are used to identify which bits in a received packet are unreliable, and retransmissions are requested for only those unreliable bits. By requesting information for the unreliable bits, the performance of the decoder can improve more quickly than if a fixed HARQ scheme is used. The performance of RB-HARQ using turbo codes and convolutional codes over AWGN channel was shown by Kim and Shea [22] and Roongta and Shea [23], respectively. Another RB-HARQ scheme that uses received packet reliability to optimize throughput over static and time-varying channels was inde- pendently proposed by Tripathi et al. [24]. All of the previous work on RB-HARQ [21-25] uses the magnitude of the log a posteriori probability (log-APP) ratio computed by the maximum aposteriori (MAP) [26] algorithm to identify the unreliable bits. 1.2 Objective The objective of this work is to develop selective-retransmission hybrid-ARQ pro- tocols that will efficiently use the soft-output available at the decoder and achieve better performance than the conventional HARQ schemes considered in different research stud- ies [3-20]. These protocols are aimed at improving the performance of wireless communi- cation systems that suffer from hostile interference. However, the protocols that we develop are general enough that they can be used for any communication system that uses soft-input soft-output (SISO) decoders. 1.3 Main Contributions In this work we propose and evaluate the performance of selective-retransmission hybrid-ARQ protocols that significantly improve the performance of communication sys- tems that use soft-input soft-output decoders In all of the previous work that uses ARQ [3- 20], the set of bits to be retransmitted is not adapted to the set of bits that are likely to be in error. The work presented here is unique in this sense. The proposed work uses a MAP decoding algorithm to identify bits that are likely to be in error. For communication sys- tems that suffer from hostile jamming, the proposed work uses iterative MAP algorithms to estimate the probabilities that a bit is jammed and in error. The retransmissions in the proposed hybrid-ARQ schemes are adapted to the the set of bits that are likely to be in error or jammed. The main contributions of this work are: We propose reliability-based hybrid-ARQ (RB-HARQ) for nonfading AWGN chan- nels without any interference. The proposed scheme adapts the retransmission to the set of unreliable bits identified using the log- APP for each information bit, uses rate-compatible punctured convolutional (RCPC) codes, with or without puncturing, in the forward channel, achieves small retransmission request packets by using simple arithmetic coding on the feedback channel, or using the time correlation properties of convolutional codes. This also adapts the size of retransmission to the channel conditions. We develop RB-HARQ to improve communication performance in a hostile amming environment. The proposed scheme uses the log-APP of the information bits and the log-APP ratio of jammer state to identify the unreliable bits, uses iterative MAP algorithms to estimate the probability that each bit is jammed as well as the reliability of each bit, adapts the retransmission based on the output of these MAP algorithms, and uses optimal run-length arithmetic coding or a suboptimal but less complex source coding to compress the retransmission request packet. We provide a performance comparison of the proposed RB-HARQ schemes with the conventional HARQ in which a predetermined set of bits is retransmitted. We propose a new channel model for ad-hoc wireless networks that not only consid- ers errors due to channel noise but also considers errors due to interference caused by simultaneous transmission by other nodes. 6 We propose a RB-HARQ technique for wireless networks that use carrier-sense mul- tiple access with collision avoidance (CSMA-CA) and investigate the performance of the proposed technique. 1.4 Outline of This Dissertation This dissertation is organized as follows. Chapter 1 gives the introduction to the work presented in this report. Chapter 2 presents the proposed work and evaluates its perfor- mance for nonfading additive white Gaussian noise channels without any interference. Chapter 3 presents the work for partial-time jamming channels. Chapter 4 presents a new channel model for ad-hoc wireless networks which can be used to design efficient HARQ protocols. In Chapter 5 we present conclusions and directions for future work. CHAPTER 2 RELIABILITY-BASED HYBRID ARQ FOR NON-FADING CHANNELS WITHOUT INTERFERENCE In this chapter, we propose and evaluate the performance of RB-HARQ techniques for nonfading AWGN channels without any interference. We also compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [7], which uses punctured convolutional codes. The RB-HARQ technique that we propose is motivated by an understanding of the decoding process and analysis of the error packets. We use the MAP algorithm [26] for the decoding of convolutional codes. For each information bit uk, the decoder computes the log aposteriori probability (log-APP) ratio [27] as follows ^) (P(uk +ly) L(uk) =log P(Uk 1Y) (2.1) P(Uk = -11y)) I where y is the received codeword in noise. When the decoder fails to decode a packet correctly, it is because the decoder has failed to find soft-decision log-APP values with the correct signs for some of the information bits in the packet. The bits that have soft-decision log-APP values with incorrect signs result in errors at the decoder output. Analysis of error packets reveals that the decoder can use the log-APP values to ac- curately identify the bits that prevent the packet from decoding correctly [21]. We refer to such bits as weak bits. To see this, consider a block of 1000 information bits encoded by a rate 1/2 convolutional code with generator polynomials 1 + D2 and 1 + D + D2 for transmission over an additive white Gaussian noise (AWGN) channel. For each error packet, rank the bits at the output of the convolutional decoder by the magnitude of their soft-decision log-APP values. The bit with the smallest soft-output is considered the least reliable (0), and the bit with the largest soft-output is considered most reliable (999). The probability of error for each bit by rank is shown in Figure 2.1. These results indicate that o 1 c 0.3 T) Eb No =0 dB .0 0.2 Eb/N = 1 dB b o 0.1 - 0 0 200 400 600 800 1000 Bit reliability (O=least reliable) Figure 2.1: Probability of bit error by reliability rank for rate 1/2, (5,7) convolutional code. the least reliable bits correspond to errors about 50% of the time, while very reliable bits are rarely in error. Thus the bits that have small log-APPs are likely to be the weak bits. The performance of the decoder is likely to improve if additional information about the weak bits can be used to improve their soft-decision estimates. 2.1 System Model The system model for the work presented in this chapter is shown in Figure 2.2. The communication system consists of the source radio S and the destination radio D linked by a data channel through which a packet of information is to be delivered from S to D. Convolutional codes are used for encoding the data bits in S. The encoded packet is then appropriately punctured to get the desired initial code rate. The resulting code bits are modulated using BPSK and then transmitted over an AWGN channel. The destination radio Source Radio Destination Radio Data Channel Encoder Modulator - Decoder Detector Feedback Source Channel Source Decoder Encoder S D Figure 2.2: System model for hybrid ARQ with convolutional codes. D attempts to decode the packet and sends a retransmission request through the feedback channel if an error is detected. D uses the magnitudes of the log-APPs to identify the least- reliable bits and constructs the retransmission-request packet, which contains a list of such bits. The source encoder in the destination radio D is used to compress the retransmission- request packet. The source radio S decodes the encoded retransmission-request packet and then retransmits the code bits corresponding to those requested information bits. To further clarify, for any requested information bit S transmits all the corresponding code bits irrespective of whether they were punctured in the initial transmission. Noisy versions of the retransmitted code bits are received at D and are added to any previously received values of the same code bits. In our study, we assume perfect error detection and the presence of a highly reliable feedback channel from D to S. Note that the source encoder in D and source decoder in S are only used for retransmission-request packets transmitted over the feedback channel. 2.2 RB-HARQ using Convolutional Codes without Puncturing We first investigate the performance of the RB-HARQ scheme without puncturing and without any source coding. We will use the results to determine the relative degradation of the approach to compressing the request packet, as discussed in the next section. For all the results in this section, the code used for transmission from S to D is a rate 1/2, constraint length K = 7 convolutional code with generator polynomials (in octal) 554 and 744. These results also apply if the feedback channel has a high capacity so that a large retransmission-request packet can be sent from D to S. The source S initially transmits the packet using a rate 1/2 convolutional code. If D fails to decode the packet correctly, it sends a retransmission-request packet containing a list of the positions of the 50 least- reliable information bits. In the work by Kim and Shea [22], S responds to the request packet by retransmitting the information bits. However, the code in their work [22] is a systematic turbo code, whereas the code we consider in this section is a nonsystematic convolutional code. Thus, for these results, S retransmits the two code bits corresponding to each of the positions identified by D. To further clarify, D is using the reliability of the information bits to identify weak sections in the code trellis and then requests new code information for those trellis sections. The received code symbols are combined with all previously received copies of those symbols. For BPSK transmission over an AWGN channel, the soft-outputs for the symbols can be added together. For the results presented in this section, each packet consists of 1000 information bits. Each retransmission request consists of a list of 50 bit positions, and S transmits 100 code bits in response to each request. This corresponds to 5% incremental redundancy per re- transmission. We consider the performance when the request and retransmission process can occur up to three times. Each retransmission effectively reduces the code rate and hence increases the EbI/N at the receiver. We account for this additional received energy by defining the effective Eb /N as the average Eb/No at the receiver, taking into account the average number of incremental redundancy transmissions per packet. The results in Fig- ure 2.3 show the probability of bit error for reliability-based hybrid-ARQ with the rate 1/2, constraint-length seven convolutional code. In Figure 2.3 we observe that to achieve a probability of bit error of less than 10-6, a system using RB-HARQ technique with three retransmissions of 5.0% incremental redundancy each requires 1.9 dB lower Eb/No than a system with no ARQ. Most of the performance has been gained after only two incremen- tal transmissions, and the third transmission only improves performance by approximately 10 0 No ARQ After 1st retransmission .... After 2nd retransmission -After 3rd retransmission 101 - 0 L. 2 10- S 10- 4111 L... 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Effective Eb / N (dB) Figure 2.3: Probability of bit error vs. Effective EbN\ for three retransmission of 5.0% incremental redundancy each. 0.1 dB. Further improvement in performance may be achieved by optimizing the number of bits retransmitted in each iteration. We note that for the technique presented in this section, the retransmission-request packet can be very large. Consider the following example. For a packet of 1000 informa- tion bits, each bit index can be represented by a ten-bit binary number. So, without any compression, the retransmission-request packet consisting of 50 least-reliable bit indices, 0 -\ 10-6-I-I-I-I-I-"-------I I I 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 will consist of 500 bits. Such a large retransmission-request packet will generally decrease the overall system throughput. In the next section, we present results for a variable redun- dancy RB-HARQ scheme which has a much smaller retransmission-request packet. 2.3 RB-HARQ with Variable Redundancy and Smaller Request Packet The RB-HARQ scheme that we present in this section has variable redundancy. As channel conditions improve, fewer bits are retransmitted. The scheme that we propose in here is based on two important observations during our simulations. The first observation, as shown in Figure 2.1, is that in any packet with errors, the bits that are in error have low reliability (magnitude of log-APP) values. The second observation is that in any packet with errors, the error events (the bits that are in error) are correlated in time. The results in Figure 2.4 illustrate the reliability values for each bit in an example packet that was decoded in error as a function of the bit index (position in the packet). The packet size is 1000 information bits, and it was transmitted over an AWGN channel using the rate 1/2 convolutional code with constraint length K = 7. The results in Figure 2.4 also indicate the bits that were in error. We observe from the figure that bits that are in error have low reliability values and occur in groups (time-correlated). There is one group of error bits around bit index 600 and another group of error bits around bit index 950. Based on the two observations made above, we modify the RB-HARQ technique pro- posed earlier. The system model remains the same as in Figure 2.2. Whenever the des- tination radio D fails to decode a packet correctly, it calculates a threshold 7 based on the reliability values of the bits in that packet. Then it performs an elimination opera- tion in which all the reliabilities greater than 7 are made zero. Following the elimination operation, D performs a smoothing operation as follows: L(u) = =-2 L(k+ (2.2) 5 In our study, the threshold 7 is calculated as follows: 7 = a + 0.1- p, (2.3) O 0 10 0 100 200 300 400 500 600 700 800 900 1000 Bit index Figure 2.4: Reliability values for example packet of 1000 information bits. where a is the minimum reliability value and the p is the average reliability value of the packet in consideration. We were guided by the following considerations while selecting the threshold in (2.3): (i) The threshold calculation should be computationally simple. (ii) The threshold should be large enough so that it is greater than the least reliability value because the bits with low reliabilities are the ones that are likely to be in error. (iii) The threshold should be small enough that the size of retransmission request packet is small and the number of bits retransmitted is not very large. The smoothing operation was performed using a rectangular window of length 5 as de- scribed by (2.2). Figure 2.5 shows the reliability values, after the elimination and smoothing operations were performed, for the packet with errors shown in Figure 2.4. We observe in Figure 2.5 that there are 5 windows (groups) of non-zero reliabilities in the entire packet. The destination radio, D, sends the first bit index and the last bit index, of each window, to S. The source S then retransmits the code bits, corresponding to all the information bits, in each of the window. Thus, the number of bit indices sent back from D to S is fewer than the number of information bits that are actually requested for retransmission. We define NF to be the average number of bit indices per retransmission-request packet sent from D to S. We also define NR to be the average number of information bits requested for retransmission for every packet in error. The results in Figure 2.6 show the above two quantities (NF and NR) at various values of the channel symbol energy-to-noise density ratio (E/,No). We observe that a large reduction in the size of retransmission- request packet has been obtained. For example, at -3 dB the average number of bit indices per retransmission-request packet (NF) is 9.1 whereas the average number of information bits requested per packet with errors (NR) is 139.5. At 2 dB, NF is 2.0 and NR is 11.0. We note that in the RB-HARQ technique presented in the previous section, all the bit indices had to be fed back ( NF NR) to the source radio. Thus we have obtained more than 80 percent reduction in the size of the retransmission-request packet. The scheme presented in this section has variable redundancy compared to fixed redundancy in the previous sec- tion. By doing this we are able to take advantage of better channel conditions. As Eb/No improves, we request fewer information bits and hence, fewer code bits are retransmitted. Hence, the redundancy decreases with increasing SNR, which leads to higher throughput. The results in Figure 2.7 show the probability of bit error for a system that uses RB- HARQ technique with variable redundancy and small retransmission-request packets. Fig- ure 2.7 shows that to achieve a probability of bit error of less than 10-6, a system using the above ARQ technique requires 1.7 dB lower Eb/No than a system with no ARQ. We note that this improvement in the system performance has been obtained by using a simple heuristic for calculation of threshold 7. System performance can be further improved by optimizing the threshold, packet size and the lenth and shape of the window used for the smoothing operation. The RB-HARQ scheme in this section performs about 0.2 dB worse 1.5 Reliability value Bits in error Q4- o 0.5 (U C II 0 100 200 300 400 500 600 700 800 900 1000 Bit index Figure 2.5: Reliability values, after elimination and smoothing for example packet of 1000 information bits. than the scheme in the previous section, but reduces the size of the retransmission-request packet by at least 80 percent at all signal to noise ratio (SNR) values. 2.4 RB-HARQ with RCPC Codes and Arithmetic Coding In this section we evaluate the performance of a RB-HARQ scheme that uses rate- compatible punctured convolutional (RCPC) codes in the forward channel and arithmetic coding in the feedback link. First we compare the performance of the proposed technique with a system without ARQ. Then in section 2.4.1 we compare the performance of the proposed technique with that of the HARQ technique that uses only RCPC codes. The performance is evaluated in terms of probability of bit error and probability of packet error. The results presented in this section illustrate the potential of RB-HARQ combined with 140 \ -0 ( -o 120 \ CU0) 100 U C () 0 \ N 80 \ R C C >7 20 N F IE S0 I II 0 4- -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 E / N (dB) Figure 2.6: Average number of bit indices fedback (NF) and average number of informa- tion bits requested for retransmission (NR) vs. Es/No for RB-HARQ scheme. RCPC codes. For all of the results presented in this chapter, the information packet trans- mitted from S to D is encoded using a convolutional code of rate 1/2, constraint length K = 3 with generator polynomials (in octal) 5 and 7. In this chapter, we present the results for a block size of 1000 information bits, including the tail bits. The first transmission for every packet is at rate higher than 1/2. This is achieved by puncturing the rate 1/2 code using the puncturing pattern specified in the work by Hagenauer [7]. If packet is received in error at D, it sends a retransmission request to S. In this work we consider the use of lossless arithmetic coding [28] to compress the retransmission-request packet. The source S initially transmits the packet using either a rate 2/3 or 4/7 convolutional code. If D fails to decode the packet correctly, it sends a retransmission-request packet containing a list of the positions of either 50 or 25 of the least-reliable information bits. The numbers 25 and the positions of either 50 or 25 of the least-reliable information bits. The numbers 25 and 100 No ARQ After 1st retransmission .... After 2nd retransmission After 3rd retransmission 10-1 10-2 0 4- 10-5 "\ lI 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Effective Eb / N (dB) Figure 2.7: Probability of bit error vs. Effective Eb/No for RB-HARQ scheme with vari- able redundancy and reduced retransmission-request packet 50 are chosen so that in the next section we can make a fair comparison between the pro- posed scheme and the HARQ scheme proposed by Hagenauer [7]. In studies that consider RB-HARQ based on turbo codes [21, 22], S responds to the request packet by retransmit- ting the information bits. However, the code in these studies [21,22] is a systematic turbo code, whereas the code we consider in this work is a nonsystematic convolutional code. Thus, for these results, S retransmits the two code bits corresponding to each of the posi- tions identified by D. To further clarify, D is using the reliability of the information bits to identify unreliable sections in the code trellis and then requests new code information for those trellis sections. The received code symbols are combined with all previously received \> \ \ \ 10-6r \ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Effective Eb / NO (dB) Figure 2.7: Probability of bit error vs. Effective Eb/No for RB-HARQ scheme with vari- able redundancy and reduced retransmission-request packet 50 are chosen so that in the next section we can make a fair comparison between the pro- posed scheme and the HARQ scheme proposed by Hagenauer [7]. In studies that consider RB-HARQ based on turbo codes [21,22], S responds to the request packet by retransmit- ting the information bits. However, the code in these studies [21,22] is a systematic turbo code, whereas the code we consider in this work is a nonsystematic convolutional code. Thus, for these results, S retransmits the two code bits corresponding to each of the posi- tions identified by D. To further clarify, D is using the reliability of the information bits to identify unreliable sections in the code trellis and then requests new code information for those trellis sections. The received code symbols are combined with all previously received copies of those symbols. For BPSK transmission over an AWGN channel, the soft-outputs for the symbols can be added together. For the results presented in this section, each packet consists of 1000 information bits, including the tail bits. For initial transmission rate 4/7, a total of 1750 (1000 7/4) coded bits per packet are transmitted in the first transmission. Each retransmission request consists of a list of 25 bit positions, and S transmits 50 code bits in response to each request. This corresponds to 2.5% incremental redundancy per retransmission. We consider the performance when the request and retransmission process can occur up to five times. Each retransmission effectively reduces the code rate. After five retransmissions, a total of 2000 (1750 + 50 5) coded bits are received at D. Thus the code rate after five retransmissions is 1/2. For initial transmission rate 2/3, a total of 1500 (1000 3/2) coded bits per packet are transmitted in the first transmission. Each retransmission request consists of a list of 50 bit positions and S transmits 100 code bits in response to each request. After five retransmissions, a total of 2000 (1500 + 100 5) coded bits are received at D, thus lowering the code rate to 1/2. Note that in this section, the size of the retransmission-request packet is not taken into account; the additional overhead from the request packet is considered in Section 2.4.2, where we evaluate the throughput. The results in Figure 2.8 and Figure 2.9 show the probability of bit error and prob- ability of packet error, respectively, as a function of the channel symbol energy-to-noise density ratio (E/,No). The initial code rate for these results is 4/7. In Figure 2.8 we observe that to achieve a probability of bit error of 10-6, a system using the proposed RB- HARQ technique with five retransmissions of 2.5% incremental redundancy each requires 3.2 dB lower E,/No than a system that uses rate 4/7 code with no ARQ. This is a signif- icant performance gain, and most of it has been achieved after only two retransmissions. It should be noted that the error curves indicate flooring at higher values of E/,No. The results in Figure 2.9 show that to achieve a probability of packet error of 10-3, a system using the proposed RB-HARQ technique with five retransmissions of 2.5% incremental re- dundancy each requires 3.5 dB lower E,/No than a system that uses rate 4/7 code with no ARQ. The results in Figure 2.10 and 2.11 show the probability of bit error and probability of packet error, respectively, for the initial code rate 2/3. In Figure 2.10 we observe that to achieve a probability of bit error of 10-5, a system using the proposed RB-HARQ tech- nique with five retransmissions of 5.0% incremental redundancy each requires 3.9 dB lower E,/No than a system that uses rate 2/3 code with no ARQ. In Figure 2.11 we observe that to achieve a probability of packet error of 10-2, a system using the proposed RB-HARQ technique with five retransmissions of 5.0% incremental redundancy each requires 3.7 dB lower E,/No than a system that uses rate 2/3 code with no ARQ. These results show that the proposed technique can significantly improve the performance of communication sys- tems where convolutional codes are used, provided there is a reliable feedback channel for retransmission-request packets. 2.4.1 Error Probability Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [7] (RCPC-HARQ). We compare the two schemes in terms of probability of bit error and probability of packet error. Results in Figures 2.10 and 2.11 show the performance comparison of the two schemes when the initial code rate is 2/3. Every packet is first transmitted using a rate 2/3 convolu- tional code. The RCPC-HARQ scheme, in response to a NACK, moves to a lower code rate by retransmitting 250 bits in each retransmission thus achieving rate 1/2 after two retrans- missions. The performance of the RCPC-HARQ scheme is shown in Figures 2.10 and 2.11 using solid lines. In the RB-HARQ scheme, that we propose, 100 bits are transmitted in a series of five retransmissions thus achieving a rate 1/2 after five retransmissions. The performance of the RB-HARQ scheme is shown in Figures 2.10 and 2.11 using dashed lines. In Figure 2.10 we observe that to achieve a probability of bit error of 10-6, the pro- posed RB-HARQ scheme requires 2 dB lower E1/No than the RCPC-HARQ scheme. In 100 first transmission rate 4/7 -0- first retransmission 10 -- second retransmission 10- --- third retransmission S-- fourth retransmission S-2 fifth retransmission 10-3 10- rate 1/2 10 -\ n 10 40- \\ \ 0 Z 10-4 0 :\\\ \ \ \ \ \ 2 \1 0 2 / 1/2 10 S\ \\ \ \ \ \ x 10-7 \\ \ 1-8 \1 0. 108 10-9 -3 -2 -1 0 1 2 3 4 5 E /N (dB) Figure 2.8: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 4/7. Figure 2.11 we observe that to achieve a probability of packet error of 10-3, the proposed RB-HARQ scheme requires 2 dB lower E,/No than the RCPC-HARQ scheme. Thus we conclude that the proposed scheme achieves significant performance improvement over the RCPC-HARQ scheme. Note that this gain is achieved at the cost of large retransmission- request packets and more retransmissions than in the RCPC-HARQ scheme. 2.4.2 Throughput Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the two schemes in terms of throughput. We do the performance comparison for the case when the initial code rate is 4/7. First let us consider the size of retransmission-request packet in the proposed scheme. As previously mentioned, the retransmission-request packet consists of the 25 least reliable bit positions. 100 10-1 \ S\ \ \ \ a \ \ \ \ o 1/2\re\ 10-4 \\ first transmission rate 4/7 \ \ -0- first retransmission \ 10-5 -u- second retransmission \ b S -- third retransmission ---- fourth retransmission -- fifth retransmission -6 rate 1/2 10-6 -- -3 -2 -1 0 1 2 3 4 5 Es /N (dB) Figure 2.9: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 4/7. For a packet of 1000 information bits, each bit position can be represented by a 10-bit index. Thus each retransmission-request packet consists of 250 bits if no source coding is used. However we can apply arithmetic coding to compress the retransmission-request packet. The way the compressed retransmission-request packet is generated is as follows. The destination radio D constructs an all-zero bit packet of size equal to the number of information bits in the transmitted packet. Thus for the results presented in this paper, D constructs a packet of 1000 bits. Then it places a one in the bit positions corresponding to the 25 least reliable bit positions. Thus the packet consists of 975 zeros and 25 ones. The arithmetic coding is then applied on this 1000 bit packet that consists of 975 zeros and 25 ones. Our results show that arithmetic coding produces compressed retransmission-request 100 10 10-2 10- 0 10-3 4/7 S:\ n 11/2 10-6 rate 2/3 \ \ O 10 -- first retransmission ' -0- second retransmission \ -1- third retransmission \ 1/2 S-A- fourth retransmission 10 -- fifth retransmission \ rate 4/7 -e- rate 1/2 10-9 -3 -2 -1 0 1 2 3 4 5 Es /N (dB) Figure 2.10: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 2/3. packets that have an average size of 190 bits thus achieving a compression ratio of 5.26 (1000/190). Thus by using arithmetic coding we are able to save 60 (250 minus 190) bits every time a retransmission-request packet is sent from D to S. Figure 2.12 illustrates the throughput of the RCPC-HARQ scheme proposed by Ha- genauer [7] and the RB-HARQ scheme proposed in this paper. We assume that when the limits of retransmission are reached for either HARQ scheme, the packet is retransmitted at the original rate and the HARQ process begins again. Then the throughput is defined as the ratio of the number of bits per packet to the expected number of coded bits that must be transmitted to achieve correct decoding of the packet. Thus, the throughput S is given by B S = -Ps, T 10 0 S a T 160-----_ \ ,- 2/3 \ q \ \ - \ \ A 10 -10-2 \ \ \ .o 1/2 0 _ \\ \ -010 third retransmission -A fourth retransmission -n- fifth retransmission rate 4/7\ o 3\ \ 05 10_4 -i \ \ \ S-- rate 1/23 10 6 -3 -2 -1 0 1 2 3 4 5 Es /N (dB) Figu re 2.11: Performance comparison of the proposed RB-HARQ scheme with the RCPC- ARQ sch eme with initial code rate 2/3. where B is the packet size in bits, T is the expected transmission emitted in both the diretransmissions by the HARQ process, and Ps is the probability of packet success by the end of the HARQ process. In our simulations, throughput is calculated as the ratio of number of information bits in packets that are decoded correctly to the total number of bits transmitted in both the directions. The throughput of the RCPC- HARQ scheme is illustrated by the curve labeled by RCPC-HARQ. The curves labeled RB-HARQ 2, 3 and 4 illustrate the performance of the proposed RB-HARQ schemes. For RB-HARQ2, th retransmission-request packet is sent without source coding. For RB- ARQ3 retransmission-request packet is sent with source encoding at D. RB-HARQ4 -e- rate 1/2 10-6 -3 -2 -1 0 1 2 3 4 5 Es/NO (dB) Figure 2.notes1: Performance comparisonughput of the proposed RB-HARQ scheme without taking into account retransmission-request packet. Thus, RB-HARQ4 can be interpreted as the throughput2/3. where B is the packet size in bits, T is the expected number of coded bits that are trans- mitted in both the directions by the HARQ process, and Ps is the probability of packet success by the end of the HARQ process. In our simulations, throughput is calculated as the ratio of number of information bits in packets that are decoded correctly to the total number of bits transmitted in both the directions. The throughput of the RCPC- HARQ scheme is illustrated by the curve labeled by RCPC-HARQ. The curves labeled RB-HARQ 2, 3 and 4 illustrate the performance of the proposed RB-HARQ schemes. For RB-HARQ2, the retransmission-request packet is sent without source coding. For RB- HARQ3, retransmission-request packet is sent with source encoding at D. RB-HARQ4 denotes the throughput of the proposed RB-HARQ scheme without taking into account retransmission-request packet. Thus, RB-HARQ4 can be interpreted as the throughput when the overhead on the retransmission request is not considered important, or RB- HARQ4 can be interpreted as a simple, loose upper bound on the throughput that can be achieved with any source coding algorithm. Results in Figure 2.12 show that the pro- posed scheme achieves significantly higher throughput at most signal to noise ratios. For example, at 0.0 dB the throughput (RCPC-HARQ) of the RCPC-HARQ scheme is approxi- mately 0.11 while the throughput of the proposed scheme with compressed retransmission- request packet (RB-HARQ3) is approximately 0.39. The results show that even if we send the retransmission-request packet without any source coding, we still achieve a higher throughput (RB-HARQ2) than the RCPC-HARQ scheme. 0.5 0.4 Q_ =0.3 o -- 0.2 0.1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 E /No (dB) Figure 2.12: Throughput comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 4/7. CHAPTER 3 RELIABILITY-BASED HYBRID ARQ FOR PARTIAL-TIME JAMMING CHANNELS In this chapter we extend the RB-HARQ technique to improve performance in a hos- tile jamming environment. Consider the communication scenario shown in Figure 3.1 in which the transmitter S is communicating with the receiver D in the presence of a partial- time jammer J. We consider an asymmetric situation in which the receiver (D) and the transmitter (S) experience different levels ofjamming. In particular, we focus on the sce- nario in which the receiver is experiencing high jamming levels compared to the transmitter. Source Destination Jammer Figure 3.1: Communication scenario. The system model for the above communication scenario is shown in Figure 3.2. We consider packetized communication in which packets at S are encoded using a convolu- tional code for transmission to D. Code symbols are modulated using BPSK and received in the presence of white Gaussian thermal noise and time-varying jamming. The jammer is modeled using a discrete-time two-state Markov model as shown in Figure 3.3. If at time k the jammer is in state 0, then the code symbol transmitted at time k is not jammed. State 1 indicates that the jammer is on and the code symbol is jammed. The proportion of time for which the jammer is active is specified as p, and E{Tj} represents the expected value of the time (in terms of number of code symbols) spent in the jamming state before returning to the unjammed state. The four transition probabilities pij, where i, j E {0, 1}, shown in Figure 3.3 can be calculated from p and E{Tj} using the following two equations. Pol p= 01 Pio + Poi E{Tj} = -- Pio Uk (3.1) (3.2) r - - - - - - Conv. BPSK 4 -- --Interleaver---- SEncoder I mod. IS Source decoder -L-_ __ --- Feedback channel D Source D Source encoder U k Interleaver I I Figure 3.2: System model. The power spectral density of the thermal noise is No/2. The jamming power spectral density (PSD) is Nj/2. However, as the jammer is only active for proportion p of all time, pol poo po Pl Figure 3.3: Two-state Markov model for jammer. the effective jamming PSD when the jammer is active is Nj/(2p). Thus, the total PSD of the noise (thermal noise and jammer noise) in state 1 is EZ No/2 + Nj/(2p). Let Es denote the energy per modulation symbol. Matched-filter reception is assumed. Then if the jammer is in state 1 at time k, the received symbol can be modeled by yk = Ck E + nk + Jk, (3.3) where Ck is the transmitted code symbol, which takes values from 1. Here, nk represents the contribution from thermal noise and is a zero-mean Gaussian random variable with variance ao = No/2. The jamming is modeled as a Gaussian random variable Jk that has zero mean and variance Nj/(2p). Thus the total variance of the noise plus jamming is given by oa = (No + p- Nj)/2. 3.1 MAP Estimation Algorithms The destination radio D uses MAP algorithms to estimate the jammer state for each received symbol and to decode the received packet. The use of the channel interleaver prevents the application of a single MAP algorithm to a hyper-trellis containing the states of the convolutional code and the jammer. Therefore we consider two MAP algorithms connected in a feedback loop, as shown in Figure 3.2. The estimation of the jammer state and impact on MAP decoding is considered briefly in Section 3.4 and in detail by Kang et al. and Moon et al. [29, 30]. We provide a brief review of these algorithms and their interaction, and then describe how they are impacted by the ARQ transmissions. Consider first the MAP algorithm for estimating the jammer state. In the absence of any channel side-information, the parameters of the jamming signal (p, E{Tj} and N,/2) can also be estimated using the Baum-Welch algorithm (cf. [29, 30]). We briefly consider the case where the parameters of the jamming signal are known, as it offers some insight into the processing used in this paper. At each time k, the destination D computes the log-APP ratio for the jammer state given the received codeword y, which is given by L(k) = 10 P(J =Oy) (3.4) where y is the received codeword in noise and jk E {0, 1} denotes the jammer state at time instant k. This calculation is performed using the BCJR algorithm [26] operating on the received symbols in the order in which they are transmitted. The branch metric connecting jammer state z' to jammer state z at time k is given by Fk(z', z) = p(z, ykz') = P(zz') -p(ykz', z) = P(zlz') [p(!1 z,Ck = +l)P(ck = +1Y) +p(yk I', Z, Ck = -1)P(Ck = -1 y)], (3.5) where yk and Ck represent the received and transmitted code symbols, respectively, at time k. Note that P(zlz') corresponds to one of the four transition probabilities shown in Fig- ure 3.3. The forward- and backward-looking state probabilities are determined in the usual way from the branch metrics. The probabilities P(ck = +1ly) and P(ck = -l|y) are set to 0.5 in the first iteration, and are updated in later iterations according to the a posteriori estimates produced by the MAP algorithm for decoding the message. The BCJR algorithm for the message computes the log-APP ratio For each informa- tion bit Uk given y, L )(u) lg( P(u 2 0.) L(UP(uk = + y) (3.6) uP(uk =-1y)) Note that this BCJR algorithm operates in the order of the original code symbols before interleaving (i.e., in the order of the deinterleaved received symbols). We assume the use of a rate 1/2 convolutional code. Then the metric for the branch connecting state s' to state S is 7k(s',s) = P(s s') -p(yl) s',s) p(y2) ',s), (3.7) where ykl) and y2) are the matched-filter outputs for the two code symbols corresponding to the kth message bit, Uk. Here P(s s') = P(uk) is the apriori probability of information bit Uk, which is taken to be 0.5. Note that p(ykl) s', s) and p(y 2) s', s) depend on whether the symbol is jammed. Let j'l) and j2) be the states of the jammer for the received code symbols y~l) and y), respectively, where j) = 1 if the symbol is jammed and ji) = 0 otherwise. Then P(y) s',s) p s', s, j) = )P(ji) = y) +p(y s', s,j )P = ly), (3.8) where we are approximating the probability of jamming as independent from symbol to symbol, although this will not be true for a finite interleaver. As explained previously, P(j) = 0 y) and P(jk) = 1 y) are estimated using the MAP algorithm for the jammer state. If the received packet is in error after decoding, D sends a retransmission-request packet to S through the feedback channel. In this paper, we assume perfect packet error detection and an error-free feedback channel. The retransmission-request packet contains information about the set of bits that are estimated to be unreliable. The set of unreliable bits is identified using the log-APPs for the jammer states and information bits, which are computed using (3.4) and (3.6), respectively. The source encoder at D is used to compress the retransmission request packet. S decodes the retransmission-request packet and then retransmits the requested set of code symbols. Noisy (and possibly jammed) versions of the retransmitted code symbols are received at the receiver and combined in an optimal manner with the previously received copies as follows. Let yk,l and yk,2 be the two received copies of the symbol Ck after the first and second transmission, respectively. The received log- likelihood ratio (LLR) for symbol ck is given by 2 2 L(yk) 2 Y-k, + 2-Yk,2 (3.9) Ork,l1 k,2 if the jamming state is known exactly. Here ok, is the variance of the noise plus jamming for the ith received copy of ck. If the jamming state is not known exactly, then L(yk) = [(YkllCk = )p(yk,2k = +) (3.10) p(yk,llCk = -l)p(yk,2 Ck = -1) where each of the four terms is averaged over the two possible jamming states as follows p(yk,ilck) p(yk,iCk,jk = O)p(jk = 0) +p(yk,i Ckjk = l)p(jk = 1), (3.11) where p(jk) is approximated by p(jk y). 3.2 Maximum-Likelihood Estimation of Jammer Parameters The MAP algorithms described previously need the estimates of the transition proba- bilities of the jammer model and the estimate of the jammer variance. Maximum-likelihood (ML) estimation of these parameters is briefly described in this section. The ML estimator for the transition probability from state z' to state z, given in the paper by Liporace [31], is as follows pz'z k= (3.12) EkN1 Ak-I(Z1 Ak-I(Z1) where N is the number of message bits in the packet and R is code rate. Here Ak(z') is the forward-looking state probability, Ak (z) is the backward-looking state probability, and Fk(z', z) [26] is the branch metric, The ML estimator for the variance of the noise when the jammer is in state 1 is given by [31] EN- Ak k k C2 k=1 A,(l )Ak(l) ~ML ~ (1) Yk (3.13) 3.3 Reliability-Based Hybrid ARQ Schemes Consider the packet error rate for coded communication in the presence of a partial- time jammer. Let T be the total number of information bits plus tail bits encoded with a rate k/n convolutional code. Then for soft-decision, maximum-likelihood (ML) decoding, an upper bound on the packet error probability is given by the following expression [32,33] f (n/k)T PI m where Ad is the number of error events of weight d and Pd is the pairwise error probability (PEP) for two codewords separated by Hamming distance d. Consider the performance of a system that does not employ ARQ. Assume that an ideal interleaver is used in which the jamming symbols at the input to the decoder experience independent jamming. Then the PEP is given by P(d /Q ( + d p)) (1 Pd- (3.15) d =0 -o di Here dl is the number of symbols that are jammed out of the total d symbols that make up the error event. As mentioned previously, O -= No/2, and ao2 = (No + p-'Nj)/2. An upper bound and good approximation for (3.15) is as follows [34]: ( d [( d (d z 21-1 d) (d\pd (lp)a-dd pd < Q ( 2) f xp [E ( 2) ) di 0d =O0 = Q V o(' 2 d,=o" (d) (peF)d, (1-_ p)ad (3.16) where E, E, No No + p-IN/ Then it is simple to show that the maximum term in the summation in (3.16) is for di = di,max, where [d [p(l p)] +1 d,max 1 + P(1 )e 1 For fixed E,/Nj and p, as E,/No increases dl,max d, and the performance will be dominated by the event that all d code symbols are jammed. Thus to ensure maximum asymptotic gain from a HARQ scheme, all jammed symbols should be retransmitted. At high E8/No, retransmitting unjammed symbols will provide a small performance gain, and thus the number of symbols to be retransmitted can be reduced by not retransmitting symbols that are unjammed. We use the MAP algorithm for the jammer state to estimate which symbols are jammed and the MAP algorithm for the message to estimate which bit decisions are reliable. We first consider RB-HARQ strategies that use this information to retransmit a fixed number of bits in response to a decoding error. By combining the two reliability measures, we propose several HARQ strategies that request retransmission for some set of bits that is determined to be unreliable. 1. In RB-HARQ(J), the destination only uses the jamming information L (jk) to decide which code symbols are jammed. In the absence of perfect jammer state information, a symbol is estimated to be jammed if L(jk |) > 0 and is estimated to be unjammed otherwise. The information about the set of code symbols is conveyed to the source, which retransmits the code symbols that are estimated to be jammed by the destina- tion. 2. In RB-HARQ(R), the destination only uses the reliability |L (uk)| to decide which information bits are unreliable. The information about the set of such unreliable information bits is conveyed to the source. The source then retransmits the code symbols corresponding to those information bits. 3. In RB-HARQ(R+J), the destination uses both \L(uk) and L(jk) to determine those information bits which have the least value of IL(uk) and also have one or both code symbols jammed. Information about the set of such information bits is conveyed to the source, which then retransmits the code symbols corresponding to such bits. We also consider an RB-HARQ scheme that adapts the number of bits to be retrans- mitted based on reliability information. In the RB-HARQ(R-A) scheme, the size of the retransmission is adapted based on the bit reliabilities IL(uk)\ of the bits in the packet. We use determine whether a bit should be retransmitted by comparing an estimate of the probability of error for the bit to a target bit error probability. For example, packet error probabilities of 10-2 result in a negligible degradation in throughput. So, we can choose a target bit error probability that will result in result in packet error probabilities below 102. The probability of bit error for an information bit can be estimated as the minimum of the aposteriori probabilities, which is given by Pb min{P(uk=+1y),P(uk = -1y)} = + e y) (3.17) The required probability of bit error, Pb to achieve a specified packet error probability will depend, in general, on a number of different parameters like E,/No, the jammer param- eters and the number of retransmissions allowed. For the work presented in this paper, simulations are used to find the value of Pb which achieves the desired P,. We compare these RB-HARQ approaches to conventional approaches in which the set of retransmitted symbols is not adapted based on reliability information. We consider Type-I HARQ schemes in which the entire packet is retransmitted in response to error detection. We consider both the original Type-I HARQ (in which the new packet replaces the previous packet) and Type-I HARQ with packet combining. These schemes retransmit significantly more bits than the RB-HARQ schemes that we propose, so we also consider a HARQ scheme that does not use reliability information and that retransmits the same number of bits as our RB-HARQ scheme. The schemes that we consider transmit either a random set of bits or a set of bits that is uniformly spaced throughout the packet so as to achieve the same overhead as our reliability-based schemes. This approach is analogous to incremental redundancy hybrid ARQ schemes that are used with punctured codes, in which the symbols to be transmitted are selected uniformly from the set of code symbols that were not previously transmitted. 3.3.1 Analysis of Probability of Packet Error for HARQ We provide a brief analysis of several of the HARQ schemes discussed above. In this section, we derive an upper bound on the probability of packet error after a single retrans- mission for each scheme, but the bounds are easily extended to multiple retransmissions. We make several assumptions that differ from our simulations in order to make the analysis feasible. Our upper bounds are calculated based on codeword maximum-likelihood (ML) decoding. However, for the simulation results, we employ bitwise MAP decoding. For suf- ficiently high signal-to-noise ratio, these will match very closely, as the BCJR algorithm becomes more closely approximated by its max-log-MAP form. The max-log-MAP form has been shown to be equivalent to the soft-output Viterbi algorithm, a codeword ML al- gorithm [35]. The bounds also assume perfect knowledge of the jammer state. In addition, we calculate the bound under the assumption of ideal interleaving, although for most of our simulation results we use finite, rectangular interleaving. We first consider conventional approaches to HARQ. For Type-I HARQ without packet combining, the packet error probability after one retransmission is given by (Pe)2, where Pe is given in (3.14). For Type-I HARQ with packet combining, each symbol is received twice, and the packet error probability can be determined from (3.15) with PEP given by 2d1 2d- ))(2d)l(lp)- (3.18) We now consider HARQ schemes that do not retransmit the entire packet. The analy- sis at the beginning of this section indicates that the asymptotic performance will be dom- inated by the set of jammed symbols. Let Nc = (n/k)T denote the total number of trans- mitted bits. Then before retransmission, the expected number of symbols that are jammed is pNc, so we constrain the average number of symbols to be retransmitted to also equal pNc. We consider a conventional approach to incremental redundancy HARQ (IR-HARQ) in which the pNc bits are uniformly spaced throughout the entire packet. For the purposes of analysis, we model this as a system in which a random set of symbols is retransmitted such that the average number of symbols retransmitted is pNc. Any given symbol is inde- pendently selected to be retransmitted with probability p. The pairwise error probability after retransmission for this HARQ scheme is given by P = d d+di E (I d + 2 Pd E E_ _lQ_+_2 _(d+ di)pj(1- P) +- l P) d-d, (3.19) where dl of the d symbols in the error event are randomly selected for retransmission. Then of the total d + di symbols that are transmitted in either the original transmission or the retransmission, j denotes the number of symbols that are jammed. In the RB-HARQ(J) approach, the the set of symbols to be retransmitted depends on the set of symbols that is estimated to be jammed. Assuming perfect knowledge of the jamming state, the pairwise error probability after one retransmission is d d( +d2 d d2 Pd Z Q E 2 + 2 di=0d2 =01 (dP P)d2( l p)dl-2(d) -p)- (3.20) where di is the number of symbols out of d that are jammed before the retransmission. All the di jammed symbols are retransmitted, and d2 of them are jammed during the retrans- mission. With the RB-HARQ(J) scheme, there is a question of what to do if we allow further re- transmissions. If we request that only the jammed symbols from the previous transmission are resent, then after k transmissions, only pk symbols will be requested for retransmission. This number may be very small (for example the third retransmission with p = 0.4 will contain only 6.4% of the symbols in the packet). So, we consider an alternative approach that can provide a higher throughput at low Es/No. For RB-HARQ(J) with multiple re- transmissions, the source alternates between retransmitting the symbols that are estimated to be jammed and retransmitting the entire packet (as in Type-I HARQ). In each case, soft combining is employed. For example with three retransmissions, the first retransmission will consist of those bits that are estimated to be jammed in the original transmission. If the packet can still not be decoded successfully, the entire packet is retransmitted. In the third retransmission, only those bits that were jammed during the previous transmission will be retransmitted. The PEP for this scheme is given by (3.21). d di d d3 E d2 d + d3d4 + 2d-d2- d4 dd = oLr2 + r 2o di =0d2=0d3 =0 d4=0 \ \dd= d=O dd2= d4=3 d4 (1- p)2d-d2-d4. (3.21) As in (3.20), dl denotes the number of symbols that are jammed in the first retransmission. All of these di symbols are retransmitted, and d2 denotes the number of those symbols that are jammed. Similarly, the entire packet is retransmitted in the second retransmis- sion, and d3 denotes the number of symbols that are jammed. All of these d3 symbols are retransmitted in the third iteration, and d4 denotes the number of those symbols that are jammed. 3.3.2 Size of retransmission-request packet In conventional HARQ, it is theoretically possible for a single feedback bit to be sent from the receiver to the transmitter to indicate an ACK or NACK. In practice, unless this bit is piggybacked on a data packet, the ACK or NACK typically uses much more resources including a synchronization preamble and MAC address information for the sender and receiver. In our results, we consider the best-case scenario of single feedback bit for the conventional HARQ schemes so that our results are not tied to a particular system. In the RB-HARQ schemes considered in this paper, the feedback packet is larger, as it contains information about the set of unreliable bits. In order to evaluate the throughput, we first evaluate the size of the retransmission-request packet. We calculate the expected value of the size of the retransmission-request packet for RB-HARQ schemes under different approaches to compress the retransmission-request packet. Size of retransmission-request packet i ith transmission of uncompressed bit indices: Recall that for the RB-HARQ schemes with fixed retransmission size, the number of bits to be retransmitted is equal to the expected number of jammed code symbols per packet, which is given by p L T. The simplest (and one of the least efficient) ways to design the retransmission-request packet is to provide the source S with a list of the bits to be retransmitted. The number of bits required to represent the position of a code symbol is equal to [log2( T)], where [-] denotes the ceiling operator. As an alternative, the retransmission-request packet can be equal to the size of the transmitted packet, N = (n/k)T, with a 1 in the position of each symbol to be retransmitted and 0 in the other positions. Then the average size of the retransmission-request packet, denoted by Nf, is given by N =min (p T)- log2 .T T (3.22) This is because if (pjT) [log2 ( T)] > .- T, then the retransmission-request packet can be constructed as a bit-stream of length -T in which a 1 is used to indicate the positions of symbols to be retransmitted and a 0 is used for symbols that do not need to be retransmitted. Size of retransmission-request packet ii ith run-length arithmetic coding: Both the bit reliabilities and jamming states are correlated over time and thus are amenable to compression. The jamming states are Markovian and thus can be optimally compressed using arithmetic run-length coding [36, 37] for a Markov source. Bit reliabilities can also be treated as approximately Markovian, and thus can also be compressed in a similar way. However, modeling and compression of bit reliabilities is beyond the scope of this paper. Consider the RB-HARQ(J) scheme. Once the receiver has identified the jammed sym- bols, it can use the estimates of the jamming parameters in the arithmetic runlength source coding process. The compression rate achievable using the arithmetic runlength coding is equal to the entropy rate of the Markov source, which is given by H(S) = Po H(So) + Pi H(S1), (3.23) where H(So) and H(S1) are the entropy of state 0 and 1, respectively, of the jammer. The entropy, H(Si), of state i is given by the standard entropy of a binary source with output probabilities pii and 1 pi, corresponding to the transition probabilities from state i in Figure 3.3. The expected size of the retransmission-request packet is then given by Nf= -. T H(S) (3.24) Size of retransmission-request packet ii ilh simple compression Because of the complexity of arithmetic coding and decoding, as well as the need to ac- curately estimate the transition probabilities of the hidden Markov model for the jammer in order to achieve optimal compression, we propose the following suboptimal scheme for use with RB-HARQ(J). In this simple compression scheme, the retransmission-request packet consists of the start and end positions of all the bursts of jammed symbols. Here a burst of jammed symbols is a consecutive sequence of jammed symbols such that the symbols immediately before and after the burst are unjammed. To calculate the size of the retransmission-request packet with simple compression, we first calculate the average number of bursts of jammed symbols in the received packet. Let B be the number of bursts in the received packet and ji E {0, 1} represent the state of the jammer at time i. Let Bi be the number of bursts starting at time i, where a burst is defined to start at time i if either i = 0 and jo = 1 or ifji = 0 and ji,+ = 1. Then N-2 E[B] = E [ B i.=0 N-2 = E [Bo] + E [Bi] i=l = 1 Pi + Popol + (N 2) Popol (N- )p = + p, (3.25) E{Tj} where Po and Pi are the steady-state probabilities of the jammer being in state 0 and 1, respectively. Thus, the average size of the retransmission-request packet is the expected number of bursts multiplied by the number of bits required to represent the start and end positions of the bursts, which is given by Nf= E[B] -2 log2 ( T) (3.26) 3.4 Performance of Estimation Algorithm We assume that D knows the statistics of the thermal noise, but in general does not have any channel side information (CSI) about the jamming state, the transition probabil- ities, and the PSD in the jamming state. This information about the jamming needs to be accurately estimated for best performance in decoding the packet. In this section we show the performance of the iterative MAP algorithm for jamming estimation and decoding. For all of the results presented in this paper, the code used for transmission from S to D is a rate 1/2, constraint length K = 7 convolutional code with generator polynomials 554 and 744 (in octal). In all of the results, the total block size is 1000 information bits, including the tail bits. Except where noted, the coded bits are interleaved using a rectangular interleaver of size 45 x 45. The retransmission process effectively reduces the code rate and hence increases the received energy per bit, Eb, at the receiver. We present results in terms of the channel symbol energy-to-noise density ratio, E/,No, and the average symbol-energy to jammer-noise density ratio, E,/Nj. These ratios remain constant during the ARQ process. The parameters of the Markov chain for the jammer are p = 0.4 and E{Tj} = 40. For the case of no CSI, all of the jamming parameters are estimated using the Baum- Welch/BCJR algorithm. The Baum-Welch algorithm requires some initial estimate to dis- tinguish the densities emitted by the two states. We use the initial estimate that the variance in the jamming state is twice the variance in the unjammed state. We can measure the performance of the estimation and detection algorithm directly in terms of the probability of miss and probability of false alarm. The probability of miss is calculated as the ratio of the number of symbols that are jammed and not detected to be jammed to the number of symbols that are jammed. The probability of false alarm is calculated as the ratio of the number of symbols that are unjammed and detected to be jammed to the total number of unjammed symbols. These performance metrics are illustrated in Figure 3.4 for the estimation algorithm after 10 iterations at E,/Nj = -3 dB. The performance of the ML estimation algorithm is compared with the performance of jamming detection with perfect knowledge of all the jammer parameters including the transition probabilities, the average jammer PSD Nj/2, and p. The performance of the decoding algorithm has been shown to be most sensitive to misses in jamming detection, in which a jammed symbol is identified as unjammed [30]. The results in Figure 3.4 show that for E,/Nj = -3 dB, the iterative MAP algorithm with ML estimation achieves probability of miss less than 0.05 for all values of E,/No greater than 0 dB. Detection with estimation of all parameters performs as well as detection when all parameters are known except at very low values of E,/No. This is because at low values of E,/No, the variance of the thermal noise, No/2 is comparable to the variance, Nj/2p of the jammer signal. Thus it is difficult to detect whether a symbol is jammed. However, at such low Eg/No, the packet error probability will be very high with even perfect knowledge of the jammer state. The results in Figure 3.4 show that the ML estimation algorithm achieves a probability of false alarm of less than one percent for all values of E,/No greater 0.4 I 0.016 0.35 Prob. of false alarm -0.014 \ with ML estimation 0.3 \ -0.012 Prob. of false alarm o \ with parameters known 0 - S 0.25 -0.01 4-- 4-- 0.2:- 0.008 O 0 Prob. of miss > co with ML estimation \ S015 0.006 S0.15 " a iProb. of miss - 0.1 \- \ with parameters known 0 0.002 0.05- 4' 0 -4 -2 0 2 4 6 8 10 Es / N (dB) Figure 3.4: Probability of miss and false alarm of jammed symbols when all jamming parameters must be estimated in comparison to when all jamming parameters are known at E,/Nj = -3 dB. than 1 dB. The performance of ML estimation, in terms of false alarm probability, is close to the performance when the jammer parameters are known. The results in Figure 3.5 show the probability of packet error at E,/Nj = -3 dB for RB-HARQ(J), which requests retransmission for all symbols that are identified as jammed. The performance of RB-HARQ(J) scheme with estimation of all parameters is compared with the case when the decoder has perfect channel-side information (CSI). Perfect CSI means that the decoder knows all the jammer parameters and which symbols are jammed. The results show that the performance of the estimation algorithm is within 0.25 to 0.5 dB of the CSI case. The results in this section show that iterative parameter estimation achieves very good performance and that having to estimate the jamming parameters does not significantly 4 -e- No A 10-4 No AR CS + No ARQ ML Estimation Es / N (dB) Figure 3.5: Probability of packet error for RB-HARQ(J) with estimation of jamming pa- rameters or perfect CSI, p = 0.4 and E,/Nj = -3 dB. degrade the performance of RB-HARQ. In the next section, we compare the performance of the different proposed RB-HARQ schemes with conventional HARQ schemes. We show the results in terms of probability of packet-error and assume perfect CSI for these results. 3.5 Performance Results In this section we compare the performance of the proposed RB-HARQ schemes to conventional HARQ schemes. The convolutional code is the same as in the previous sec- tion. Except where noted, the parameters of the jammer are given by E,/Nj = -3 dB, p = 0.4 and E{Tj} = 40. We evaluate the performance in terms of packet error probabili- ties and throughput. 3.5.1 Packet error probabilities We first compare analytical and simulation results for the probability of packet error, Pe, after one retransmission for the HARQ schemes analyzed in Section 3.3. In the RB- HARQ(J) scheme, all jammed symbols are retransmitted. We compare the performance of this approach with three conventional HARQ schemes. We consider Type-I HARQ with and without packet combining. These scheme retransmit significantly more bits than RB-HARQ(J), so we also consider an IR-HARQ scheme that retransmits a random set of bits such that the average overhead is the same as for RB-HARQ(J). The results of this comparison are illustrated in Figure 3.6. The analytical upper bounds are shown using solid lines, and the simulation results are shown using dashed lines. 0 10- >a, 4-Q 0 o 10 10-4 -2 -1 0 E1 / N (dB) 3 4 5 6 S 0 Figure 3.6: Probability of packet error for RB-HARQ(J), Type-I HARQ and retransmission of a random set of symbols, p = 0.4 and E,/Nj = -3 dB. The results show that to achieve P, = 10-1, Type-I HARQ without packet combining provides approximately 1.5 dB gain over no ARQ. If Type-I HARQ is used with packet combining, the gain is approximately 6 dB. For the other HARQ results, the overhead is only 40% of that of the Type-I HARQ schemes. The IR-HARQ scheme can achieve P, = 10-1 with 1.5 dB lower E,/No than Type-I HARQ without packet combining. RB- HARQ(J) requires 1.25 dB lower Es/No than incremental redundancy with random re- transmissions at P, = 10-1 and the performance difference increases drastically for lower target values of P. Although RB-HARQ(J) requires approximately 1.2 dB to 1.6 dB higher E,/No than Type-I HARQ with packet combining, it only retransmits 40% of the bits of Type-I HARQ. The results also show that the upper bounds computed using (3.14) and (3.18)-(3.20) provide very tight bounds on the packet error probabilities. The results in Figure 3.7 show the performance of RB-HARQ(J) when three retrans- missions are allowed. The results show that combining RB-HARQ(J) with Type-I HARQ provides very good performance, particularly at low values of E,/No. The results also show that the upper bound computed using (3.21) provides a very good approximation for probability of packet error after three retransmissions For the remainder of the results, the channel symbols are interleaved using a 45 x 45 rectangular bit interleaver. For these results, the conventional IR-HARQ scheme transmits a uniformly spaced set of bits. The results in Figure 3.8 illustrate the packet error rate for different RB-HARQ and conventional HARQ schemes. For these results E,/Nj = 0 dB. The average number of symbols retransmitted in response to NACK is equal to p(n/k)T = 800 (the expected number of jammed symbols) for all of the HARQ schemes except for Type-I HARQ in which the entire packet is retransmitted. The results in Figure 3.8 show that all three RB-HARQ schemes achieve better per- formance than the conventional HARQ approaches that do not employ reliability, except for Type-I HARQ with packet combining, which retransmits significantly more symbols. To achieve a packet error rate of less than 10-2, the required E,/No for RB-HARQ is at 10 \ \\\ O \ 0.. 2 \ 4 10-2 0 -3 10 -3 3 (2+1) retransmissions of 3 retransmission of RB-HARQ(J) + Type- d HARQ RB-HARQ(J) with packet combining 10-4 -4 -3 -2 -1 0 1 2 Es /N, (dB) least 3 dB less than for IR-HARQ, which retransmits the same number of symbols but does not use reliability information. RB-HARQ(R+J) achieves the best performance because it uses both the log-APPs to decide which symbols are to be retransmitted. This scheme performs about 0.25 dB better than RB-HARQ(J) in which all jammed symbols are re- transmitted. Among all the proposed RB-HARQ schemes, RB-HARQ(R) that selects the bits to be retransmitted based only on 3L(uk)\ performs the worst. This because at high values of E,/No, the performance is limited by the jamming, as shown in the analysis in Section 3.3. Since RB-HARQ(R) retransmits both code symbols for information bits that have low values of tL(uk)| and one or both of these code symbols are unjammed, some jammed symbols will not be retransmitted because the the total number of retransmitted 100 o No ARQ IR-HARQ 10-1 -2 \ RB-HARQ(R) ,, 10 4-- 0 Type-I HARQ with Type-1 HARQ S10-3 packet combining -U 10 -\ l RB-HARQ(R+J) . 10-4 RB-HARQ(J) -2 -1 0 1 2 3 4 5 Es / N (dB) Figure 3.8: Probability of packet error for different RB-HARQ schemes compared with Type-I HARQ and conventional HARQ, p = 0.4 and E,/Nj = 0 dB. symbols is equal to the average number of jammed symbols. The residual set of jammed symbols results in an error floor for high EI/No. The results in Figure 3.9 show the performance if the number of symbols to be re- transmitted is reduced to 0.5p(n/k)T. The symbols to be retransmitted are selected in two ways. In the RB-HARQ(J) scheme, the decoder uses L(jk) to identify all the jammed sym- bols and then requests the retransmission of every alternate jammed symbol. In the figure, this scheme is denoted by "50% uniform RB-HARQ(J)". In the RB-HARQ(R+J) scheme, the decoder first uses L(jk) to identify all the jammed symbols. Then, it uses L(uk) to identify half of all the jammed symbols which correspond to information bits having the least values of log-APP. This scheme is denoted by "50% LRB jam symbols ARQ" in 100 10- ~ 10-2 -e- NoARQ !!! l!!!^ !!! !!! !;! !!!!!!!! !:! !!! ll^^ -s^ ^. l :--- 50 % uniform RB-HARQ(J) S10 50 % RB-HARQ(R+J) -A R B -HA R Q (J) . . . . . . . . . . . No jamming -s 3 10-4113 Es / N (dB) Figure 3.9: Probability of packet error for different RB-HARQ schemes, p = 0.4 and E,/Nj = -3 dB. Figure 3.9. For these results, E,/Nj = -3 dB. The results in Figure 3.9 show that to achieve a probability of packet error of 10-2, the RB-HARQ(R+J) scheme that uses both the soft-outputs requires 1 dB less ES/No than the RB-HARQ(J) scheme. The performance disparity increases for lower target error probabilities. Thus these results clearly indicate that the RB-HARQ scheme that uses both the soft-outputs, L(jk) and L(uk), achieves a significant gain over the one that only uses one of the soft-outputs. In Figure 3.10, we consider the RB-HARQ(R-A) scheme, in which the number of bits to be retransmitted is adaptive selected based on a specified target packet error probability, P.. For these results only one retransmission is considered. As discussed in Section 3.3, offline simulations were used to determine that a target bit error probability Pb = 10-5 achieves Pe 102. Using (3.17), this translates to requiring retransmission for all bits 100 10 -E EB3 10- -3 -2 -1 0 1 2 3 4 o 10-2 4-/ -3dB. 0 -4 104 -A- RB-HARQ(J) -e- RB-HARQ(R-A) a E Type-I HARQ -- Type-I HARQ with packet combining -3 -2 -1 0 1 2 3 4 Es / N (dB) Figure 3.10: Probability of packet error for adaptive and fixed RB-HARQ, p = 0.4 and E,/Nj = -3 dB. with L(uk)| < 11.5. The results in Figure 3.10 illustrate the packet error probability achieved at E,/Nj = -3 dB for RB-HARQ(R-A), RB-HARQ(J), and Type-I HARQ with and without packet combining. The results show that for E,/No < 0 dB, none of the schemes are able to achieve the target packet error probability of 10-2. For E,/No > 0 dB, the adaptive retransmission scheme does achieve packet error probabilities below 10-2. The real effect of adaptive RB-HARQ is that the average number of symbols to be retransmitted decreases as the E,/No increases. We study this in terms of its effect on throughput in the next subsection. 3.5.2 Throughput Results We now compare the throughput performance of RB-HARQ and conventional HARQ schemes. We first consider the performance of RB-HARQ(J) that retransmits all thej ammed code symbols. Throughput is defined as the ratio of the number of bits per packet to the expected number of coded bits that must be transmitted to achieve correct decoding of the packet. Thus, the throughput S is given by T S = TPs, where T is the number of information bits in a packet, X is the expected number of coded symbols that are transmitted in both directions during the HARQ process, and Ps is the probability of packet success by the end of the HARQ process. For these results, we consider up to three retransmissions. If the packet is still in error after three retransmissions, then the whole packet is retransmitted and the HARQ process starts over. The results in Figure 3.11 show the throughput of RB-HARQ(J) and the conventional HARQ schemes for E,/Nj = -3 dB. As previously discussed, RB-HARQ(J) alternates between retransmitting the set of symbols that are estimated to be jammed and complete packet retransmission (as in Type-I HARQ). The size of the retransmission-request packet for the conventional HARQ scheme is taken to be 1 bit. The size of the retransmission- request packet for RB-HARQ is calculated using the formulas in Section 3.3.2. The size of the retransmission-request packet composed of bit indices (no compression) is 2000 bits. The average size of the retransmission-request packet compressed using arithmetic run- length coding, calculated using (3.24), is 282 bits. Thus, using arithmetic coding helps in reducing the size of retransmission-request packet by almost 85 percent. For RB-HARQ(J) with the simple compression scheme, the average size of the retransmission-request packet is 462 bits. The results in Figure 3.11 show that despite larger retransmission-request pack- ets, RB-HARQ(J) technique that uses compression achieves better throughput than all the other HARQ techniques for all values of E,/No > -0.5 dB. At very low values of E,/No (< -1 dB) Type-I HARQ with packet combining performs around 0.5 dB better than RB- HARQ(J) because in this regime, the performance gain from retransmitting more symbols outweighs the additional overhead of retransmitting the entire packet. The results also show 0.5 0.45 RB-HARQ(J) with 0.4 arithmetic coding 0.35- 35 Type-I HARQ with packet combining RB-HARQ(J) with S0.3- i simple compression 5 0.25- 0.2 - Uniform HARQ 0.15- 0.1 Type-I HARQ 0.05- 0&^--A---" -A-A'"i----------------- -3 -2 -1 0 1 2 3 4 5 E / N (dB) Figure 3.11: Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ, after 3 retransmissions at p = 0.4 and Es/Nj = -3 dB. that using the simple compression scheme for the retransmission-request packet achieves throughput close to that achieved by using optimal arithmetic runlength coding. The results in Figure 3.12 show the throughput for RB-HARQ(R-A) in comparison with RB-HARQ(J) and the conventional schemes. Recall that in RB-HARQ(R-A), the number of retransmitted bits is adaptively selected to achieve some target error probability. For these results, up to three retransmissions are allowed, and simulations were carried out to find the target Pb that achieves the maximum throughput. It was observed that a target bit error probability of 5 x 10-3 offered the best throughput for the range of Es/No and jammer parameters considered in our work. We show two curves for RB-HARQ(R-A), one in which the overhead is determined based on the retransmission-request packet consisting of the bit indices of all symbols to be retransmitted (no compression) one in which that overhead is ignored. Our reason for including the results without the overhead is twofold. First, in many cases, it might not be desired to treat the overhead on the retransmission- request packet the same as the forward transmission because that link is assumed to not be jammed. Secondly, although outside of the scope of this paper, compression can be applied to this retransmission-request packet, and the results we present represent upper and lower bounds on the performance with compression. The results show that if the over- head in the retransmission-request packet can be ignored or significantly reduced through compression, then RB-HARQ(R-A) achieves the best throughput at all values of E/,No. This is because adaptive RB-HARQ(R) adapts the size of retransmission to the reliability of the received bits. It retransmits more bits at low E,/No to achieve correct decoding of the packet and retransmits fewer bits at high E,/No while still achieving a sufficiently low P,. Even when we account for the size of uncompressed retransmission-request packet in throughput calculations, adaptive RB-HARQ(R) performs better than conventional HARQ and Type-I HARQ that does not use packet combining for the entire range of E,/No. Finally, we investigate the effect of different values of p on the performance of the various HARQ techniques. The results in Figure 3.13 compare the throughput of RB- HARQ(J) and RB-HARQ(R-A) with the conventional HARQ schemes as a function of p. For these results E /No = 0 dB, E,/Nj = -3 dB, and E{Tj} = 40. The results show that if we neglect the overhead in the retransmission-request packet, RB-HARQ(R-A) achieves the best performance over all p. Thus the RB-HARQ(R-A) scheme can effectively adapt the set of retransmitted bits to different values of p. The RB-HARQ(J) scheme achieves the same performance as RB-HARQ(R-A) for p < 0.5 For higher values of p, the overhead in the retransmission-request packet reduces the performance of RB-HARQ(J). Above p = 0.58, Type-I HARQ with packet combining outperforms RB-HARQ(J). This suggests that if p is estimated to be very high, then the RB-HARQ(J) scheme can be simply modified to request retransmission of the whole packet. Note that neither Type-I HARQ without packet ._ .. RB-HAF 0) arithmeti D0.25 -E>-e 0.1 IR-HARQ RB-HARQ(R-A) with IR-ARQ 0.1- feedback overhead SType-I HARQ 0.05 - -3 -2 -1 0 1 2 3 E / N (dB) Figure 3.12: Throughput of adaptive RB-HARQ(R), RB-HARQ(J), conventional (uniform) HARQ, p = 0.4 and E,/Nj = -3 dB. Type-I HARQ and combining nor IR-HARQ are competitive techniques for dealing with jamming except at very low values of p. ' U. \ lII IIIIL ^uu IIy 0) 0.25- --. -- 0- 0-A - 0.2 - \ X \ '^ -^0-^ --0 0.15 RB-HARQ(R-A) with 0.1 feedback overhead 0.05 IR-HARQ Type-I HARQ 0 ---------i ~~~Q -- 6 -- 6 -- = p (Probability a symbol is jammed) Figure 3.13: Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ as a function ofp at E,/No = 0 dB, E,/Nj = -3 dB. CHAPTER 4 RELIABILITY-BASED HYBRID-ARQ FOR CSMA-CA-BASED WIRELESS NETWORKS In this chapter we explore the application of reliability-based hybrid-ARQ (RB-HARQ) in wireless networks. Wireless networks are strongly affected by errors caused by fading and collisions. Carrier-sense multiple access with collision avoidance (CSMA-CA) is a commonly used medium access control (MAC) protocol in wireless local area networks (WLAN) and wireless ad hoc networks [38]. In most research on the performance of the CSMA-CA protocol, it is commonly assumed that collisions are the only source of trans- mission failure and that collisions result in the complete corruption of the packet. However, packet failure may also occur because of errors due to channel fading or Gaussian noise. To enhance throughput in wireless networks, channel coding at the physical layer [39, 40] and automatic repeat request (ARQ) protocol at the data link layer [2,41] have been stud- ied separately. Recently, cross-layer design that combines these two layers judiciously to improve the performance has been studied [42, 43]. All of these works either consider the packet failure due to channel fading or packet failure due to collisions. However, a truly cross-layer design methodology for wireless networks must consider both: i.e. the packet errors due to channel fading and noise and the packet errors due to collisions with the other simultaneously transmitted packets in the network. In order to consider packet failure due to collisions, it is essential to model the interference caused by simultaneous transmission by other nodes in the network. The next section describes this work in detail. 4.1 Interference Modelling The MAC protocol commonly used in research studies on wireless ad-hoc networks [44] is based on IEEE 802.11 [45]. The IEEE 802.11 specifies two modes of MAC protocol: distributed co-ordination function (DCF) mode for ad hoc networks and point co-ordination function (PCF) mode for infrastructure-based networks. The DCF in IEEE 802.11 is based on CSMA-CA and uses the RTS-CTS-DATA-ACK sequence between the sender and the receiver. While IEEE 802.11 DCF works well in LAN environments, studies show that it is not particularly suitable for multi-hop ad-hoc networks with mobile nodes [46,47]. This is because issues like hidden-node problems cause collisions [38]. Collisions may result in parts of a packet being corrupted while other parts are received without corruption. For example, part of a DATA packet may be corrupted by collision with a shorter RTS packet. To evaluate the effect of collisions on a DATA packet we simulate an ad-hoc network using network simulator ns2 [48], which is a very commonly used tool in research studies involving the MAC layer. The objectives of this simulation are: To determine what percentage of DATA packets suffer from interference. In other words what percentage of DATA packets collide with other packets which may be RTS, CTS, DATA or ACK packets. Given that a particular DATA packet suffers from interference, to determine the prob- ability of it suffering from interference due to multiple interfering packets. To determine the probability density function of the power of the interfering packet. To determine the distribution of the type (RTS/CTS/DATA/ACK) of the interfering packet. To determine the difference between the starting times of the DATA the packet and the interfering packet. Table 4.1 shows the parameters used in our simulation. The routing protocol was chosen to be DumbAgent in order to minimize the routing overhead. The following parameters about the interference that affects the DATA packets were calculated from the simulation output. PI : Probability that a DATA packet suffers from interference. Pir : Probability that a DATA packet suffers from interference due to n (n > 1) or more interfering packets conditioned on the event that it suffers from interference. * PRTS : Probability that the interfering packet is a RTS packet. Table 4.1: Simulation parameters in ns2 Number of nodes 60 Topology random placement in 1000 x 1000 m Traffic type constant bit-rate UDP Number of traffic flows 60 Packet size 512 bytes Packet rate 10 packets/s MAC protocol 802.11 Data rate 1 Mbps Routing protocol DumbAgent Mobility model random way-point Maximum node speed 2 m/s Simulation time 10 s PCTS : Probability that the interfering packet is a CTS packet. PDATA : Probability that the interfering packet is a DATA packet. PACK : Probability that the interfering packet is a ACK packet. In addition to the parameters defined above, we also calculate the probability density function (PDF) of the power of the interfering packet and the PDF of the start time of the interfering packet with respect to the start time of the DATA packet. For the simulation pa- Table 4.2: Interference parameters obtained using simulation Parameter Value PI 0.36 PI2 0.53 PI, 0.25 PRTS 0.55 PCTS 0.16 PDATA 0.16 PACK 0.13 rameters shown in Table 4.1, the values of the interference parameters obtained are shown in Table 4.2. These values have been obtained after averaging across all those nodes in the network that experience collisions. It should be noted from Table 4.2 that only 36 percent of the total transmitted DATA packets are affected by interference. The fact that this value C C 0 0 L 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Normalized Interference Power Figure 4.1: Probability density function of the normalized power of the interfering packet. of P, has been obtained after averaging across all the nodes that experience collisions im- plies that it is very likely that for some node in the network, P, may be more than 0.36. Later in this chapter, we evaluate performance, in terms of throughput, for one such node. The probability density function (PDF) of the ratio of the power of interfering packet to that of the data packet is shown in Figure 4.1. The normalized interference power of 0.1 is used as the threshold in ns2 to distinguish between 'capture' and 'collision'. It was ob- served from the simulation output that the start time of the interfering packet is uniformly distributed across the entire DATA packet. 4.2 Non-Fading Channel Model As mentioned previously, any cross-layer design approach that considers the channel coding at the physical layer and ARQ at the data link layer should consider packet errors due to channel fading and noise as well as those due to interference from other nodes. As a first step in that direction, we propose a channel model that considers additive white Gaussian noise (AWGN) and interference due to simultaneous transmission by other nodes in the network. The basic system model remains the same as that shown in Figure 2.2. The data packet is convolutionally encoded and then transmitted over the AWGN channel using BPSK modulation. Interference, determined according to the parameters calculated in the previous section, is added to the transmitted packet. It should be noted that not every transmitted packet suffers from interference because P, is less than one. For a packet that suffers from interference, only those symbols are affected whose transmission overlaps the transmission of the interfering packet. Therefore the received symbol, not affected by interference, can be modeled as yk = CkEs+ nk (4.1) where ck is the transmitted code symbol, which takes values from 1 and nk represents the contribution from zero-mean white Gaussian noise with variance ao = No/2. If the symbol is affected by interference, then it is modeled as follows. Yk = Ck E + nk + bk /X E (4.2) The third term on the right hand side represents the interference. Here bk is 1 and X is a random variable representing the interference power. It should be noted that X is generated according to the PDF shown in Figure 4.1. It is possible that some symbols experience in- terference due to multiple interfering packets. In that case, the received symbol is modeled by having multiple interference terms. We evaluate the probability of packet error under the new channel model and compare it with the channel model that does not consider interference. For the results presented in this section the DATA packet is encoded using rate 1/2 convolutional code with constraint length K = 7 and generator polynomials 554 and 744 (in octal). The packet lengths of different types of packets were chosen to be the same as that in ns2 simulation. Therefore, the DATA packet consists of 4512 message bits which includes 512 bytes of payload, 28 bytes of MAC layer header and 24 bytes of physical layer header [45] The size of RTS packet is 352 bits and the size of CTS and ACK packet is 304 bits. These values were obtained from the 1 megabits per second (Mbps) version of the IEEE 802.11 standard [45]. Figure 4.2 shows the packet error probability when we consider the interference compared with the packet error probability in the presence of Gaussian noise only. The results in 100 .. .. .. . . . . . .. . . , -- AWGN o- AWGN + interference 1-- :0"1 iiiii ;:iii iiii ;:ii iiiii i;: ::: : :::: ::::: : :::: : :::: : i : iii iiii ^ 10 ::: ::::: ::.:. :: ::.:. :: :::: ::::: ::::: :: :: :Q : ^ \ : ^ a : : : : S .. : : : : : : . . . . O N o .. . . . . . . . . . . . . . . . . . . . . . . -1 -0.5 0 0.5 1 1.5 2 2.5 3 Es / N (dB) Figure 4.2: Effect of interference on probability of packet error for AWGN channel. Figure 4.2 show that under the new channel model, the probability of packet error is worse by 0.25 0.75 dB for E,/No greater than 1 dB. It is observed that in order to achieve a packet error probability of 10-2 under the new channel model, an additional E1/No of around 0.25 dB is required. It should be noted that for the results shown in Figure 4.2 approximately 36 percent of the DATA packets suffer from interference. Next, we investigate the throughput performance under the new channel model and compare it with the throughput performance under the AWGN channel model that does not consider interference. Throughput is calculated as the number of bits per second delivered correctly to the destination. In our calculation for throughput, we take into account the overhead due to RTS, CTS, ACK, the inter-frame spacing (IFS) and the random backoff during the contention period [38, 45]. To determine the worst case performance under the new channel model, we consider P, = 1. In other words every DATA packet collides with one or more packets and suffers from interference. We consider up to two retransmissions and assume Type-I ARQ in which the complete packet is retransmitted. The retransmis- sions also under go collisions. For every new DATA packet the size of contention window is initially CWmin. Every time the packet is in error, the size of the contention window increases exponentially [38, 45]. For the throughput results shown in Figure 4.3, the size of DATA, RTS, CTS and ACK packets is the same as that for the results in Figure 4.2. The value of CWmin is 31 and the duration of one slot in the contention window is 20 microsec- onds [45]. The value of SIFS (short IFS) is 10 microseconds and that of DIFS (DCF IFS) is 50 microseconds. These values correspond to the 1 Mbps version of the IEEE 802.11 standard [45]. Therefore, the maximum throughput that can be achieved is 1 Mbps. The results in Figure 4.3 show that the maximum achievable throughput is approximately 0.7 Mbps. This is because in addition to the time taken for transmitting the payload, we also take into account the time for transmitting the MAC header, physical layer header, RTS, CTS and the ACK and also the overhead due to the DIFS, back-off period and the SIFS. We observe that for all values of E,/No shown in Figure 4.3, the throughput achieved un- der the new channel model, even when P, = 1, is nearly the same as that achieved when we do not consider the interference. This observation leads to the conclusion that either the interference power is too weak to cause any significant degradation in performance or the error-correcting convolutional code used in our simulations is strong enough to correct most packet errors due to interference. 0.7 I I I I I I ---- 0.65 0.6 0.55 -Q 0.5 0.45 c- 0) o 0.4 .- 0.35 0.3 0.25 0.2 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 E / N (dB) Figure 4.3: Throughput for Type-I HARQ with up to 2 retransmissions and P1 = 1 4.3 Performance of Reliability-Based Hybrid-ARQ in CSMA-CA-Based Networks In this section we propose a RB-HARQ technique for CSMA-CA-based networks and compare its performance with Type-I HARQ. First we describe the RB-HARQ tech- nique. We propose to introduce a negative acknowledgement (NACK) in the MAC pro- tocol. Therefore, the receiver always sends either an ACK or a NACK after the DATA packet is received. The ACK or the NACK is sent after SIFS time after the DATA packet is received. When the receiver detects an error in the DATA packet, it sends a NACK. The NACK contains information about the least reliable sections of the DATA packet. The receiver uses the log-APP to determine what parts of the payload are less reliable. The transmitter, after receiving the NACK, retransmits those least reliable sections of the DATA packet. The retransmissions occur the same way as in the IEEE 802.11 standard [45]. It should be noted that the NACK is larger than the ACK because the NACK contains infor- mation indicating what parts of the DATA packet should be retransmitted. 0.8 0.7 RB-HARQ (50%, CWmin) 0.6 SType-I HARQ O_ 0.5 0.4 0 RB-HARQ (50%) 0.3 H -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Es / N (dB) Figure 4.4: Throughput for RB-HARQ and Type-I HARQ with up to 2 retransmissions and AWGN channel The results in Figure 4.4 show the throughput achieved by the proposed RB-HARQ scheme and the Type-I HARQ. For these results we assume an AWGN channel model without any interference. The results in Figure 4.3 show that even when we consider the interference the degradation in throughput is negligible. For the results in this section, we assume that the RTS-CTS mechanism is turned off. However, we still take into account the overhead due to the MAC layer header, the physical layer header, the DIFS, random back-off, the SIFS, the ACK and the NACK. The values of these parameters is the same as those in the previous section. When the receiver detects an error, it divides the payload (512 x 8 bits) into 128 sections and determines the minimum log-APP for each section. These log-APPs are then sorted to find the least reliable sections of the payload. The NACK includes a field of length 128 bits with ones indicating those sections that need to be retransmitted. Therefore, the NACK is larger than the ACK by 128 bits. The curve labelled "RB-HARQ(50%)" denotes the throughput of the RB-HARQ technique when only half of the payload is transmitted in response to the NACK. The results show that RB-HARQ achieves better throughput than the Type-I HARQ for all E,/No in the range -3 to 2 dB. This is because for each error packet RB-HARQ adaptively determines the least reliable sections of the packet and then only those least reliable sections are retransmitted where as the complete packet is retransmitted in Type-I HARQ. With the Rb-HARQ scheme, the NACK can also be used to inform the transmitter whether the size of contention window should be increased. We investigate the throughput when the size of contention window is fixed at CWin. The curve labelled "RB-HARQ (50%, CWmin)" shows that there is a marginal improvement in throughput by keeping the contention window size fixed. The curve labelled "RB-HARQ (25%, CWmi)" shows the throughput of RB-HARQ technique in which the 25 percent least reliable sections of the payload are retransmitted and the size of contention window is always fixed at CWmn. The results show that at very low values of Es/No, the throughput achieved is significantly less than that achieved by Type-I HARQ. This is because retransmitting just 25 percent of the payload is not enough to achieve correct decoding of the packet for E,/No < -2 dB. However, for E,/No > -1.5 dB, RB-HARQ that retransmits 25 percent least reliable sections of the payload achieves the highest throughput. CHAPTER 5 CONCLUSIONS AND DIRECTIONS FOR FUTURE WORK In this chapter I present the conclusions of my work and also give directions for future work. 5.1 Conclusion In this work, we propose and evaluate the performance of reliability-based hybrid ARQ schemes for nonfading AWGN channels. First we investigate the performance of reliability-based hybrid ARQ schemes in the absence of any type of interference. We be- gin by evaluating the performance of RB-HARQ scheme that uses fixed-rate convolutional codes and exploits the time-correlation properties of these codes. The proposed scheme achieves a gain of more than 2 dB over a system with no ARQ. We then further develop these schemes to use rate-compatible punctured convolutional codes in the forward chan- nel and source encoding in the feedback channel. The proposed schemes achieve a perfor- mance gain of over 3 dB over a system with no ARQ. We also compare the performance of the proposed scheme with the hybrid ARQ scheme that is proposed by Hagenauer [7] in which rate-compatible punctured convolutional codes are used. Results, in terms of bit and packet error probability show that the proposed scheme achieves a performance gain of up to 2.5 dB over the latter when the initial code rate is 4/7. Throughput results show that the proposed scheme achieves a performance gain of up to 1 dB. The size of the feedback packet is accounted for in the throughput results. Although the proposed scheme has larger retransmission-request packets, it achieves higher throughput at all signal-to-noise ratios than the hybrid-ARQ scheme proposed by Hagenauer [7]. Next, we investigate the performance of RB-HARQ schemes in the presence of a hos- tile partial-time jammer. The proposed schemes use the MAP algorithm to estimate the a posteriori probabilities for the information bits and the j ammer state [49]. Results show that the performance of the estimation algorithm is within 0.25 to 0.5 dB of the perfect chan- nel side-information case. In terms of packet error rate, all of the proposed RB-HARQ schemes are shown to offer significantly better performance than an incremental redun- dancy HARQ (IR-HARQ) scheme that has the same overhead but does not utilize reliabil- ity information. We also presented throughput results that take into account the overhead of the retransmission-request packet. An optimal arithmetic run-length coding technique and a suboptimal but much simpler run-length coding technique are proposed to compress the retransmission-request packet for the RB-HARQ(J) scheme, which retransmits the sym- bols that are estimated to be jammed. The results show that RB-HARQ(J) offers a higher throughput than Type-I HARQ with packet combining except at very low E,/No or very high p. We also presented performance results for a scheme that adapts the size of the retransmission-request packet based on the bit reliabilities. This RB-HARQ(R-A) scheme offers the highest throughput if the overhead of the retransmission-request packet can be neglected. Thus, adaptation in the HARQ scheme based on reliability is shown to be an effective means for dealing with hostile jamming. In chapter 4, we propose a new channel model that considers the packet errors due to channel noise as well as those due to interference from simultaneous transmission by other nodes. To evaluate the effect of collisions that occur due to simultaneous transmissions, we simulate a CSMA-CA based wireless ad hoc network. Different parameters about the interference that affects the data packets were calculated from the simulation output. These parameters take into account the fact that collisions may result in parts of a packet being corrupted while other parts are received without corruption. Therefore, the proposed chan- nel model is more realistic than a AWGN channel model and can be used in a cross-layer design approach which considers to combine ARQ at the data link layer and channel cod- ing at the physical layer. We investigate the performance in terms of packet error rate and throughput for the new channel model. The results show that the degradation in throughput when we consider the interference is negligible. We also propose a RB-HARQ technique for CSMA-CA-based networks that achieves better performance than Type-I HARQ under several scenarios. 5.2 Directions for Future Work The work presented in this dissertation can be extended in different directions. It would be interesting to evaluate the channel capacity of the Markov channel considered in chapter 3. The performance of different RB-HARQ schemes can then be compared with the channel capacity. The work presented in this dissertation considered a non fading channel model which is not very realistic. An interesting study will be to evaluate the performance of RB-HARQ for fading channels and compare it with the performance of conventional HARQ techniques. The work presented in chapter 4 can be extended by considering fading as well as interference. Another interesting study would be to examine the effect of node density on the interference power and overall system performance. REFERENCES [1] S. Lin and D. 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BIOGRAPHICAL SKETCH Abhinav Roongta received the B.Tech. in electrical engineering from the Indian In- stitute of Technology, Delhi (IITD), India, in 2001 and the M.S. in electrical engineering from the University of Florida in 2003. Since August 2001, he has been working towards a Ph.D. degree in electrical and computer engineering at University of Florida, Gainesville. His research interests include error control coding, signal processing and system design for wireless communications. |

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PAGE 1 RELIABILITY -B ASED HYBRID-ARQ USING CONV OLUTION AL CODES By ABHIN A V R OONGT A A DISSER T A TION PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF DOCT OR OF PHILOSOPHY UNIVERSITY OF FLORID A 2005 PAGE 2 Cop yright 2005 by Abhina v Roongta PAGE 3 T o my parents and my sister PAGE 4 A CKNO WLEDGMENTS First I w ould lik e to thank and e xpress my sincere gratitude to my advisor Dr John M. Shea. This w ork w ould not ha v e been possible without his e xpertise, hard w ork and patience. He guided me at each and e v ery stage of my Ph.D. program and w as al w ays easily accessible. He read and re vised all our conference papers and presentations and w ork ed unlimited nights and week ends for our journal article. Besides being a great research advisor I also wish to thank him for his e xcellent teaching in EELand EEL The ef forts that he put in his teaching, in his lectures and creating questions for the e xam, really amazed me right from day one of 5544 when he ga v e the Monte-Hall problem. I w ould also lik e to thank Dr T an W ong, Dr Y uguang F ang and Dr Richard Ne wman for pro viding v aluable input at the time of my Ph.D. proposal defense. Dr Richard Ne wman read this dissertation from co v er to co v er and pro vided detailed feedback for impro ving it. I w ould also lik e to thank all the students in our lab, NEB-. Thanks to Arun for helping me deb ug my code on se v eral occasions and strengthening my belief that reliability-based hybrid ARQ is a practical solution; Jang-W ook for patiently answering my questions on jamming model and estimation; Deniz for gi ving me his LaT e x templates and or ganizing the WING picnic; Sarv a and Jianfeng for or ganizing the WING seminar I w ould also lik e to thank Hongqiang Zhai for bringing me up to speed with netw ork simulator (ns2). I also thank my friends Adrian and Brock for b urning the midnight oil with me while coding adapti v e signal processing algorithms in MA TLAB. T ogether we managed to sail across the troubled w aters of EELn I wish to thank certain Â“behind-the-sceneÂ” people who directly or indirectly contrib uted to w ards this dissertation. I thank Linda Kahila and Shannon Chillingw orth in i v PAGE 5 the ECE Graduate Student Services Of ce for advising on de gree requirements, taking care of paper w ork and sending re gular reminders re garding re gistration and fee payment deadlines. Thanks to them I ne v er had to read the Graduate Student Handbook. Thanks to Janet Holman, our administrati v e secretary for k eeping the lab well stock ed and doing the paper w ork for tra v el to conferences. I also thank all my Â“non-ECEÂ” friends and my current and past apartment-mates for making life fun. Thanks to Abhudaya and Nitin, my current apartment-mates, for gi ving me ride to the lab on week ends. T ogether we survi v ed the hurricanes in the Gatorland. Finally I w ould lik e to thank my parents, Santosh and Madhu Roongta, and my sister Aastha to whom I o we e v erything. I ha v e become what I am because of their sacrices, blessings and unconditional lo v e and support. Thank you! v PAGE 6 T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . . . i v LIST OF T ABLES . . . . . . . . . . . . . . . . . viii LIST OF FIGURES . . . . . . . . . . . . . . . . . ix ABSTRA CT . . . . . . . . . . . . . . . . . . . xi CHAPTER 1 INTR ODUCTION . . . . . . . . . . . . . . . 1 1.1 Pre vious W ork on Hybrid ARQ . . . . . . . . . . 2 1.2 Objecti v e . . . . . . . . . . . . . . . . 4 1.3 Main Contrib utions . . . . . . . . . . . . . 4 1.4 Outline of This Dissertation . . . . . . . . . . . 6 2 RELIABILITY -B ASED HYBRID ARQ FOR NON-F ADING CHANNELS WITHOUT INTERFERENCE . . . . . . . . . 7 2.1 System Model . . . . . . . . . . . . . . 8 2.2 RB-HARQ using Con v olutional Codes without Puncturing . . 9 2.3 RB-HARQ with V ariable Redundanc y and Smaller Request P ack et 12 2.4 RB-HARQ with RCPC Codes and Arithmetic Coding . . . . 15 2.4.1 Error Probability Comparison of RB-HARQ with HARQ with RCPC codes . . . . . . . . . . . 19 2.4.2 Throughput Comparison of RB-HARQ with HARQ with RCPC codes . . . . . . . . . . . . 20 3 RELIABILITY -B ASED HYBRID ARQ FOR P AR TIAL-TIME J AMMING CHANNELS . . . . . . . . . . . . . . 25 3.1 MAP Estimation Algorithms . . . . . . . . . . 27 3.2 Maximum-Lik elihood Estimation of Jammer P arameters . . . 30 3.3 Reliability-Based Hybrid ARQ Schemes . . . . . . . 31 3.3.1 Analysis of Probability of P ack et Error for HARQ . . . 34 3.3.2 Size of retransmission-request pack et . . . . . . 36 3.4 Performance of Estimation Algorithm . . . . . . . . 39 3.5 Performance Results . . . . . . . . . . . . . 42 3.5.1 P ack et error probabilities . . . . . . . . . 43 vi PAGE 7 3.5.2 Throughput Results . . . . . . . . . . . 48 4 RELIABILITY -B ASED HYBRID-ARQ FOR CSMA-CA-B ASED WIRELESS NETW ORKS . . . . . . . . . . . . . . 54 4.1 Interference Modelling . . . . . . . . . . . . 54 4.2 Non-F ading Channel Model . . . . . . . . . . . 57 4.3 Performance of Reliability-Based Hybrid-ARQ in CSMA-CABased Netw orks . . . . . . . . . . . . . 61 5 CONCLUSIONS AND DIRECTIONS FOR FUTURE W ORK . . . 64 5.1 Conclusion . . . . . . . . . . . . . . . 64 5.2 Directions for Future W ork . . . . . . . . . . . 66 REFERENCES . . . . . . . . . . . . . . . . . . 67 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 71 vii PAGE 8 LIST OF T ABLES T able page 4.1 Simulation parameters in ns2 . . . . . . . . . . . . 56 4.2 Interference parameters obtained using simulation . . . . . . . 56 viii PAGE 9 LIST OF FIGURES Figure page 2.1 Probability of bit error by reliability rank for rate 1/2, (5,7) con v olutional code. . . . . . . . . . . . . . . . . . . 8 2.2 System model for hybrid ARQ with con v olutional codes. . . . . . 9 2.3 Probability of bit error vs. Ef fecti v efor three retransmissions ofn incremental redundanc y each. . . . . . . . . . . 11 2.4 Reliability v alues for e xample pack et ofn information bits. . . . 13 2.5 Reliability v alues, after elimination and smoothing for e xample pack et ofn information bits. . . . . . . . . . . . . . 15 2.6 A v erage number of bit indices fedback (r) and a v erage number of information bits requested for retransmission () vs.for RBHARQ scheme. . . . . . . . . . . . . . . . 16 2.7 Probability of bit error vs. Ef fecti v efor RB-HARQ scheme with v ariable redundanc y and reduced retransmission-request pack et . . . 17 2.8 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/7. . . . . . . . 20 2.9 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/7. . . . . . . . 21 2.10 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/3. . . . . . . . 22 2.11 Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/3. . . . . . . . 23 2.12 Throughput comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate . . . . . . . 24 3.1 Communication scenario. . . . . . . . . . . . . . 25 3.2 System model. . . . . . . . . . . . . . . . . 26 3.3 T w o-state Mark o v model for jammer . . . . . . . . . . . 27 ix PAGE 10 3.4 Probability of miss and f alse alarm of jammed symbols when all jamming parameters must be estimated in comparison to when all jamming parameters are kno wn at dB. . . . . . . . . 41 3.5 Probability of pack et error for RB-HARQ(J) with estimation of jamming parameters or perfect CSI, and = -3 dB. . . . . . 42 3.6 Probability of pack et error for RB-HARQ(J), T ype-I HARQ and retransmission of a random set of symbols, n and dB. . . 43 3.7 Probability of pack et error for three retransmissions of RB-HARQ(J), and dB. . . . . . . . . . . . 45 3.8 Probability of pack et error for dif ferent RB-HARQ schemes compared with T ype-I HARQ and con v entional HARQ, and = 0 dB. 46 3.9 Probability of pack et error for dif ferent RB-HARQ schemes, and dB. . . . . . . . . . . . . . . . 47 3.10 Probability of pack et error for adapti v e and x ed RB-HARQ, and = -3 dB. . . . . . . . . . . . . . . . 48 3.11 Throughput for RB-HARQ, T ype-I HARQ and con v entional (uniform) HARQ, after 3 retransmissions at and dB. . . 50 3.12 Throughput of adapti v e RB-HARQ(R), RB-HARQ(J), T ype-I HARQ and con v entional (uniform) HARQ, and = dB. . . . 52 3.13 Throughput for RB-HARQ, T ype-I HARQ and con v entional (uniform) HARQ as a function ofat dB, dB. . . . 53 4.1 Probability density function of the normalized po wer of the interfering pack et. . . . . . . . . . . . . . . . . . . 57 4.2 Ef fect of interference on probability of pack et error for A WGN channel. . 59 4.3 Throughput for T ype-I HARQ with up to 2 retransmissions andn n . 61 4.4 Throughput for RB-HARQ and T ype-I HARQ with up to 2 retransmissions and A WGN channel . . . . . . . . . . . . . . 62 x PAGE 11 Abstract of Dissertation Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Doctor of Philosophy RELIABILITY -B ASED HYBRID-ARQ USING CONV OLUTION AL CODES By Abhina v Roongta August 2005 Chair: John M. Shea Major Department: Electrical and Computer Engineering In this w ork we de v elop selecti v e-retransmission hybrid-ARQ protocols for communication systems that use soft-input soft-output (SISO) decoders. The schemes that we propose are based on reliability-based hybrid-ARQ that use the estimated a posteriori probabilities at the output of the SISO decoder to adapti v ely determine the set of bits to be retransmitted in response to error detection. First we sho w the performance of the proposed scheme for nonf ading additi v e white Gaussian noise channels without an y interference. W e be gin by e v aluating the performance of a simple reliability-based hybrid ARQ scheme that uses x ed rate con v olutional codes in the forw ard channel and e xploits their time-correlation properties to achie v e smaller retransmission requests. Then we e xtend our w ork where rate-compatible punctured con v olutional (RCPC) codes are used in the forw ard channel and arithmetic coding is used in the feedback channel. W e compare the performance of the proposed scheme with the common approach to hybrid-ARQ that uses punctured con v olutional codes. The results sho w that the proposed RB-HARQ scheme achie v es better performance than a hybrid-ARQ scheme that uses only RCPC codes. xi PAGE 12 Ne xt we e xtend our w ork to impro v e communication performance on partial-time jamming channels. F or channels with partial-time jamming, we can e xtend our measure of reliability to incorporate not only a posteriori probability information b ut also estimates of the probability that a bit w as jammed. W e compare the performance of the proposed scheme with that of a con v entional approach in which a predetermined set of bits is retransmitted in response to a pack et f ailure. The results sho w that RB-HARQ schemes can achie v e better performance than the con v entional approach. Ne xt we e xtend our w ork to wireless netw orks that use carrier sense multiple access with collision a v oidance (CSMA-CA). W e rst propose a ne w channel model that considers the pack et errors due to channel noise as well as those due to interference from simultaneous transmission by other nodes. The proposed channel model tak es into account the f act that collisions may result in parts of a pack et being corrupted while other parts are recei v ed without corruption. Therefore, the proposed channel model is more realistic than an A WGN channel model and can be used in a cross-layer design approach which considers combining ARQ at the data link layer and channel coding at the physical layer W e also in v estigate the performance of a RB-HARQ technique for CSMA-CA-based wireless netw orks. xii PAGE 13 CHAPTER 1 INTR ODUCTION Automatic-repeat-request (ARQ) and forw ard-error -correction (FEC) are tw o basic techniques for controlling transmission errors in data communication systems [ 1 2 ]. Automaticrepeat-request schemes typically use a high-rate error -detecting code. The y are simple and pro vide high system reliability Ho we v er one se v ere dra wback of ARQ systems is that their throughput ef cienc y f alls rapidly with increasing channel-error rate. An FEC communication system uses a po werful error -correcting code to combat transmission errors. The throughput ef cienc y of such systems is maintained at a constant le v el (equal to the code rate) re gardless of the channel error rate. The dra wback of an FEC system is that it is dif cult to achie v e high system reliability and decoding is hard to implement. Thus, ARQ is often preferred o v er FEC for error control in data communication systems, such as pack et-switching data netw orks and computer communication netw orks. F orw ard-error correction is preferred o v er ARQ in communication systems where return channels are not a v ailable or retransmission is not possible for some reason. Hybrid-ARQ (HARQ) schemes that use a proper combination of ARQ and FEC can o v ercome the dra wbacks of both ARQ and FEC schemes. Systems that use HARQ consist of an FEC subsystem contained within an ARQ system. The FEC subsystem reduces the frequenc y of retransmissions by correcting man y common error patterns without retransmission, thus increasing the throughput of the system. When an uncorrectable error is detected, the ARQ system requests retransmission instead of passing the unreliably decoded message to the user Thus HARQ systems pro vide higher reliability than an FEC system alone and higher throughput than the system with ARQ only Hybrid-ARQ schemes are broadly classied into T ype-I and T ype-II hybrid-ARQ schemes. T ype-I HARQ schemes 1 PAGE 14 2 use a code designed for simultaneous error correction and error detection. Therefore, the codes used in such schemes require more parity bits than a code used only for error detection. This increases the o v erhead for each transmission. As a result, when the channel error rate is lo w the type-I hybrid ARQ scheme has a lo wer throughput than its corresponding ARQ scheme. Ho we v er type-I HARQ schemes pro vide higher throughput than the cor responding ARQ scheme when channel error rate is high because HARQ scheme' s error correction capability reduces the frequenc y of retransmissions. T ype-II HARQ schemes are based on the concept that the parity check bits for error correction are sent to the recei v er only when the y are needed. 1.1 Pre vious W ork on Hybrid ARQ The concept of type-II HARQ or the incremental-redundanc y HARQ schemes w as rst introduced by Mandelbaum [ 3 ] and then e xtended by Metzner [ 4 ], Ancheta [ 5 ] and Lin and Y u [ 6 ]. In these schemes, a message is encoded using a code for error -detection only If the recei v er detects the presence of errors in a recei v ed code w ord, it sa v es the erroneous message in a b uf fer and sends a N A CK to the transmitter The transmitter then transmits a block of parity-check bits formed based on the original message and an error correcting and error -detecting code. When this parity block is recei v ed, it is used to correct the erroneous message stored in the b uf fer In case the error correction is successful, the corrected message is deli v ered to the data sink. If the error correction is unsuccessful, the recei v er requests a second retransmission, from the transmitter which may be either the original code w ord or again a parity block. T ype-II HARQ scheme pro vides better perfor mance than the type-I HARQ scheme if the code used for error correction and the retransmission strate gy is properly chosen. Incremental-redundanc y hybrid-ARQ schemes that use punctured con v olutional codes and code combining were proposed by Hagenauer [ 7 ]. In these and other hybrid-ARQ schemes [ 1 2 ], the set of bits to be transmitted in response to error detection is a predetermined part of the ARQ algorithm. F or e xample, consider the PAGE 15 3 HARQ scheme proposed by Hagenauer [ 7 ] in which rate-compatible punctured con v olutional (RCPC) codes are used. In this scheme if the higher rate codes are not suf ciently po werful to decode channel errors, a predetermined subset of the bits that were pre viously punctured is transmitted in order to decrease the code rate. Automatic-repeat-request has also been considered to impro v e the performance of wireless communications in the presence of interference. Hostile jamming can se v erely disrupt wireless communications. The typical responses to such disruptions are retransmissions through ARQ, ARQ with adaptation of the signaling parameters [ 8 12 ], and adaptation in the netw ork layer [ 13 17 ]. The performance of T ype-I hybrid-ARQ protocols in a slotted direct-sequence code-di vision multiple-access netw ork operating in a hostile jamming en vironment w as studied by Hanratty and Stuber [ 18 ]. The ef fect of jamming on throughput of HARQ protocol w as also studied by Feldman and Le v annier et al. [ 19 20 ]. W ilkins and Pursle y [ 11 ] e v aluated the performance of an adapti v e rate coding system for channels with Rayleigh f ading, partial-band interference, and thermal noise. It w as sho wn that adapti v e-rate coding systems pro vide signicantly higher throughput than systems that use x ed-rate coding. This is because adapti v e-rate coding systems use a highrate code, which gi v es high throughput rate, when channel conditions are good, and use a lo w-rate code only when necessary to combat a lar ge amount of interference. Pursle y and W ilkins [ 10 ] sho wed that it is benecial to be able to change both the transmission po wer and the code rate in a slo w-frequenc y hopping communication system. It w as suggested that the code rate should be adapted based on the jammer parameters while the po wer le v el should be adapted based on signal-to-noise ratio. Most of the pre vious w ork identies that adaptation is the k e y to responding to jamming. Ho we v er in each of these w orks, traditional ARQ is assumed. Although traditional ARQ is adapti v e in the sense that retransmissions only occur when a pack et is in error it is non-adapti v e in the sense that the response to a pack et error is x ed: the entire pack et should be retransmitted. Ev en if hybrid-ARQ is used, the response neither adapts to the PAGE 16 4 reliability of the recei v ed pack et nor to the set of symbols that w as jammed. A reliabilitybased hybrid ARQ (RB-HARQ) algorithm that is truly adapti v e w as proposed by Shea [ 21 ]. In RB-HARQ, soft-input soft-output decoders are used to identify which bits in a recei v ed pack et are unreliable, and retransmissions are requested for only those unreliable bits. By requesting information for the unreliable bits, the performance of the decoder can impro v e more quickly than if a x ed HARQ scheme is used. The performance of RB-HARQ using turbo codes and con v olutional codes o v er A WGN channel w as sho wn by Kim and Shea [ 22 ] and Roongta and Shea [ 23 ], respecti v ely Another RB-HARQ scheme that uses recei v ed pack et reliability to optimize throughput o v er static and time-v arying channels w as independently proposed by T ripathi et al. [ 24 ]. All of the pre vious w ork on RB-HARQ [ 21 25 ] uses the magnitude of the log a posteriori probability (-APP) ratio computed by the maximum a posteriori (MAP) [ 26 ] algorithm to identify the unreliable bits. 1.2 Objecti v e The objecti v e of this w ork is to de v elop selecti v e-retransmission hybrid-ARQ protocols that will ef ciently use the soft-output a v ailable at the decoder and achie v e better performance than the con v entional HARQ schemes considered in dif ferent research studies [ 3 20 ]. These protocols are aimed at impro ving the performance of wireless communication systems that suf fer from hostile interference. Ho we v er the protocols that we de v elop are general enough that the y can be used for an y communication system that uses soft-input soft-output (SISO) decoders. 1.3 Main Contrib utions In this w ork we propose and e v aluate the performance of selecti v e-retransmission hybrid-ARQ protocols that signicantly impro v e the performance of communication systems that use soft-input soft-output decoders In all of the pre vious w ork that uses ARQ [ 3 20 ], the set of bits to be retransmitted is not adapted to the set of bits that are lik ely to be in error The w ork presented here is unique in this sense. The proposed w ork uses a MAP PAGE 17 5 decoding algorithm to identify bits that are lik ely to be in error F or communication systems that suf fer from hostile jamming, the proposed w ork uses iterati v e MAP algorithms to estimate the probabilities that a bit is jammed and in error The retransmissions in the proposed hybrid-ARQ schemes are adapted to the the set of bits that are lik ely to be in error or jammed. The main contrib utions of this w ork are:W e propose reliability-based hybrid-ARQ (RB-HARQ) for nonf ading A WGN channels without an y interference. The proposed scheme Â– adapts the retransmission to the set of unreliable bits identied using the APP for each information bit, Â– uses rate-compatible punctured con v olutional (RCPC) codes, with or without puncturing, in the forw ard channel, Â– achie v es small retransmission request pack ets byusing simple arithmetic coding on the feedback channel, orusing the time correlation properties of con v olutional codes. This also adapts the size of retransmission to the channel conditions.W e de v elop RB-HARQ to impro v e communication performance in a hostile jamming en vironment. The proposed scheme Â– uses the -APP of the information bits and the-APP ratio of jammer state to identify the unreliable bits, Â– uses iterati v e MAP algorithms to estimate the probability that each bit is jammed as well as the reliability of each bit, Â– adapts the retransmission based on the output of these MAP algorithms, and Â– uses optimal run-length arithmetic coding or a suboptimal b ut less comple x source coding to compress the retransmission request pack et.W e pro vide a performance comparison of the proposed RB-HARQ schemes with the con v entional HARQ in which a predetermined set of bits is retransmitted.W e propose a ne w channel model for ad-hoc wireless netw orks that not only considers errors due to channel noise b ut also considers errors due to interference caused by simultaneous transmission by other nodes. PAGE 18 6W e propose a RB-HARQ technique for wireless netw orks that use carrier -sense multiple access with collision a v oidance (CSMA-CA) and in v estigate the performance of the proposed technique. 1.4 Outline of This Dissertation This dissertation is or ganized as follo ws. Chapter 1 gi v es the introduction to the w ork presented in this report. Chapter 2 presents the proposed w ork and e v aluates its perfor mance for nonf ading additi v e white Gaussian noise channels without an y interference. Chapter 3 presents the w ork for partial-time jamming channels. Chapter 4 presents a ne w channel model for ad-hoc wireless netw orks which can be used to design ef cient HARQ protocols. In Chapter 5 we present conclusions and directions for future w ork. PAGE 19 CHAPTER 2 RELIABILITY -B ASED HYBRID ARQ FOR NON-F ADING CHANNELS WITHOUT INTERFERENCE In this chapter we propose and e v aluate the performance of RB-HARQ techniques for nonf ading A WGN channels without an y interference. W e also compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [ 7 ], which uses punctured con v olutional codes. The RB-HARQ technique that we propose is moti v ated by an understanding of the decoding process and analysis of the error pack ets. W e use the MAP algorithm [ 26 ] for the decoding of con v olutional codes. F or each information bit, the decoder computes the a posteriori probability (-APP) ratio [ 27 ] as follo ws n nr nr (2.1) whereis the recei v ed code w ord in noise. When the decoder f ails to decode a pack et correctly it is because the decoder has f ailed to nd soft-decision-APP v alues with the correct signs for some of the information bits in the pack et. The bits that ha v e soft-decision-APP v alues with incorrect signs result in errors at the decoder output. Analysis of error pack ets re v eals that the decoder can use the -APP v alues to accurately identify the bits that pre v ent the pack et from decoding correctly [ 21 ]. W e refer to such bits as weak bits T o see this, consider a block of 1000 information bits encoded by a raten con v olutional code with generator polynomialsn andn nfor transmission o v er an additi v e white Gaussian noise (A WGN) channel. F or each error pack et, rank the bits at the output of the con v olutional decoder by the magnitude of their soft-decision -APP v alues. The bit with the smallest soft-output is considered the least reliable (0), and the bit with the lar gest soft-output is considered most reliable (999). The probability of error for each bit by rank is sho wn in Figure 2.1 These results indicate that 7 PAGE 20 8 0 200 400 600 800 1000 0 0.1 0.2 0.3 0.4 0.5 Bit reliability (0=least reliable) Probability bit is in error E b / N o = 0 dB E b / N o = 1 dB Figure 2.1: Probability of bit error by reliability rank for rate 1/2, (5,7) con v olutional code. the least reliable bits correspond to errors aboutof the time, while v ery reliable bits are rarely in error Thus the bits that ha v e small-APPs are lik ely to be the weak bits. The performance of the decoder is lik ely to impro v e if additional information about the weak bits can be used to impro v e their soft-decision estimates. 2.1 System Model The system model for the w ork presented in this chapter is sho wn in Figure 2.2 The communication system consists of the source radioand the destination radiolink ed by a data channel through which a pack et of information is to be deli v ered fromto. Con v olutional codes are used for encoding the data bits in. The encoded pack et is then appropriately punctured to get the desired initial code rate. The resulting code bits are modulated using BPSK and then transmitted o v er an A WGN channel. The destination radio PAGE 21 9 u k Source Radio Destination Radio D S Source Encoder Feedback Channel Conv. Encoder BPSK Modulator Data Channel Puncture Conv. Decoder u k Error Detector Source Decoder Figure 2.2: System model for hybrid ARQ with con v olutional codes.attempts to decode the pack et and sends a retransmission request through the feedback channel if an error is detected.uses the magnitudes of the-APPs to identify the leastreliable bits and constructs the retransmission-request pack et, which contains a list of such bits. The source encoder in the destination radiois used to compress the retransmissionrequest pack et. The source radiodecodes the encoded retransmission-request pack et and then retransmits the code bits corresponding to those requested information bits. T o further clarify for an y requested information bittransmits all the corresponding code bits irrespecti v e of whether the y were punctured in the initial transmission. Noisy v ersions of the retransmitted code bits are recei v ed atand are added to an y pre viously recei v ed v alues of the same code bits. In our study we assume perfect error detection and the presence of a highly reliable feedback channel fromto. Note that the source encoder inand source decoder inare only used for retransmission-request pack ets transmitted o v er the feedback channel. 2.2 RB-HARQ using Con v olutional Codes without Puncturing W e rst in v estigate the performance of the RB-HARQ scheme without puncturing and without an y source coding. W e will use the results to determine the relati v e de gradation of the approach to compressing the request pack et, as discussed in the ne xt section. F or all the results in this section, the code used for transmission fromtois a rate 1/2, constraint length con v olutional code with generator polynomials (in octal) 554 and 744. These results also apply if the feedback channel has a high capacity so that a lar ge PAGE 22 10 retransmission-request pack et can be sent fromto. The sourceinitially transmits the pack et using a rate 1/2 con v olutional code. Iff ails to decode the pack et correctly it sends a retransmission-request pack et containing a list of the positions of the leastreliable information bits. In the w ork by Kim and Shea [ 22 ],responds to the request pack et by retransmitting the information bits. Ho we v er the code in their w ork [ 22 ] is a systematic turbo code, whereas the code we consider in this section is a nonsystematic con v olutional code. Thus, for these results,retransmits the tw o code bits corresponding to each of the positions identied by. T o further clarify ,is using the reliability of the information bits to identify weak sections in the code trellis and then requests ne w code information for those trellis sections. The recei v ed code symbols are combined with all pre viously recei v ed copies of those symbols. F or BPSK transmission o v er an A WGN channel, the soft-outputs for the symbols can be added together F or the results presented in this section, each pack et consists of 1000 information bits. Each retransmission request consists of a list of 50 bit positions, andtransmits 100 code bits in response to each request. This corresponds toincremental redundanc y per retransmission. W e consider the performance when the request and retransmission process can occur up to three times. Each retransmission ef fecti v ely reduces the code rate and hence increases the at the recei v er W e account for this additional recei v ed ener gy by dening the ef fective as the a v erage at the recei v er taking into account the a v erage number of incremental redundanc y transmissions per pack et. The results in Figure 2.3 sho w the probability of bit error for reliability-based hybrid-ARQ with the rate 1/2, constraint-length se v en con v olutional code. In Figure 2.3 we observ e that to achie v e a probability of bit error of less thann a system using RB-HARQ technique with three retransmissions ofn incremental redundanc y each requiresn dB lo wer than a system with no ARQ. Most of the performance has been gained after only tw o incremental transmissions, and the third transmission only impro v es performance by approximately PAGE 23 11 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Effective E b / N o (dB)Probability of bit error No ARQ After 1st retransmission After 2nd retransmission After 3rd retransmission Figure 2.3: Probability of bit error vs. Ef fecti v e for three retransmissions ofn incremental redundanc y each. 0.1 dB. Further impro v ement in performance may be achie v ed by optimizing the number of bits retransmitted in each iteration. W e note that for the technique presented in this section, the retransmission-request pack et can be v ery lar ge. Consider the follo wing e xample. F or a pack et ofn information bits, each bit inde x can be represented by a ten-bit binary number So, without an y compression, the retransmission-request pack et consisting ofleast-reliable bit indices, will consist of bits. Such a lar ge retransmission-request pack et will generally decrease the o v erall system throughput. In the ne xt section, we present results for a v ariable redundanc y RB-HARQ scheme which has a much smaller retransmission-request pack et. PAGE 24 12 2.3 RB-HARQ with V ariable Redundanc y and Smaller Request P ack et The RB-HARQ scheme that we present in this section has v ariable redundanc y As channel conditions impro v e, fe wer bits are retransmitted. The scheme that we propose in here is based on tw o important observ ations during our simulations. The rst observ ation, as sho wn in Figure 2.1 is that in an y pack et with errors, the bits that are in error ha v e lo w reliability (magnitude of-APP) v alues. The second observ ation is that in an y pack et with errors, the error e v ents (the bits that are in error) are correlated in time. The results in Figure 2.4 illustrate the reliability v alues for each bit in an e xample pack et that w as decoded in error as a function of the bit inde x (position in the pack et). The pack et size isn information bits, and it w as transmitted o v er an A WGN channel using the raten con v olutional code with constraint length The results in Figure 2.4 also indicate the bits that were in error W e observ e from the gure that bits that are in error ha v e lo w reliability v alues and occur in groups (time-correlated). There is one group of error bits around bit inde x and another group of error bits around bit inde x Based on the tw o observ ations made abo v e, we modify the RB-HARQ technique proposed earlier The system model remains the same as in Figure 2.2 Whene v er the destination radiof ails to decode a pack et correctly it calculates a thresholdbased on the reliability v alues of the bits in that pack et. Then it performs annrnoperation in which all the reliabilities greater thanare made zero. F ollo wing thenrnoperation,performs arnoperation as follo ws: #" (2.2) In our study the thresholdis calculated as follo ws: %$ n'&( (2.3) PAGE 25 13 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 Bit indexMagnitude of log-APP Reliability value Bits in error Figure 2.4: Reliability v alues for e xample pack et ofn information bits. where$is the minimum reliability v alue and the(is the a v erage reliability v alue of the pack et in consideration. W e were guided by the follo wing considerations while selecting the threshold in ( 2.3 ): (i) The threshold calculation should be computationally simple. (ii) The threshold should be lar ge enough so that it is greater than the least reliability v alue because the bits with lo w reliabilities are the ones that are lik ely to be in error (iii) The threshold should be small enough that the size of retransmission request pack et is small and the number of bits retransmitted is not v ery lar ge. Thernoperation w as performed using a rectangular windo w of lengthas described by ( 2.2 ). Figure 2.5 sho ws the reliability v alues, after thenrnandrnoperations were performed, for the pack et with errors sho wn in Figure 2.4 W e observ e in Figure 2.5 that there arewindo ws (groups) of non-zero reliabilities in the entire pack et. PAGE 26 14 The destination radio,, sends the rst bit inde x and the last bit inde x, of each windo w to. The sourcethen retransmits the code bits, corresponding to all the information bits, in each of the windo w Thus, the number of bit indices sent back fromtois fe wer than the number of information bits that are actually requested for retransmission. W e denerto be the a v erage number of bit indices per retransmission-request pack et sent fromto. W e also deneto be the a v erage number of information bits requested for retransmission for e v ery pack et in error The results in Figure 2.6 sho w the abo v e tw o quantities ( rand ) at v arious v alues of the channel symbol ener gy-to-noise density ratio (). W e observ e that a lar ge reduction in the size of retransmissionrequest pack et has been obtained. F or e xample, at dB the a v erage number of bit indices per retransmission-request pack et (r) isn nwhereas the a v erage number of information bits requested per pack et with errors () isn AtdB,ris and isnn W e note that in the RB-HARQ technique presented in the pre vious section, all the bit indices had to be fed back ( r ) to the source radio. Thus we ha v e obtained more than percent reduction in the size of the retransmission-request pack et. The scheme presented in this section has v ariable redundanc y compared to x ed redundanc y in the pre vious section. By doing this we are able to tak e adv antage of better channel conditions. As impro v es, we request fe wer information bits and hence, fe wer code bits are retransmitted. Hence, the redundanc y decreases with increasing SNR, which leads to higher throughput. The results in Figure 2.7 sho w the probability of bit error for a system that uses RBHARQ technique with v ariable redundanc y and small retransmission-request pack ets. Figure 2.7 sho ws that to achie v e a probability of bit error of less thann a system using the abo v e ARQ technique requiresn dB lo wer than a system with no ARQ. W e note that this impro v ement in the system performance has been obtained by using a simple heuristic for calculation of threshold. System performance can be further impro v ed by optimizing the threshold, pack et size and the lenth and shape of the windo w used for the rnoperation. The RB-HARQ scheme in this section performs about dB w orse PAGE 27 15 0 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 Bit index Magnitude of log-APP Reliability value Bits in error Figure 2.5: Reliability v alues, after elimination and smoothing for e xample pack et ofn information bits. than the scheme in the pre vious section, b ut reduces the size of the retransmission-request pack et by at least percent at all signal to noise ratio (SNR) v alues. 2.4 RB-HARQ with RCPC Codes and Arithmetic Coding In this section we e v aluate the performance of a RB-HARQ scheme that uses ratecompatible punctured con v olutional (RCPC) codes in the forw ard channel and arithmetic coding in the feedback link. First we compare the performance of the proposed technique with a system without ARQ. Then in section 2.4.1 we compare the performance of the proposed technique with that of the HARQ technique that uses only RCPC codes. The performance is e v aluated in terms of probability of bit error and probability of pack et error The results presented in this section illustrate the potential of RB-HARQ combined with PAGE 28 16 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 20 40 60 80 100 120 140 E s / N o (dB) Average number of bit indices fed back and Average number of information bits requested N R N F Figure 2.6: A v erage number of bit indices fedback (r) and a v erage number of information bits requested for retransmission () vs.for RB-HARQ scheme. RCPC codes. F or all of the results presented in this chapter the information pack et transmitted fromtois encoded using a con v olutional code of raten constraint length with generator polynomials (in octal)and. In this chapter we present the results for a block size ofn information bits, including the tail bits. The rst transmission for e v ery pack et is at rate higher thann This is achie v ed by puncturing the raten code using the puncturing pattern specied in the w ork by Hagenauer [ 7 ]. If pack et is recei v ed in error at, it sends a retransmission request to. In this w ork we consider the use of lossless arithmetic coding [ 28 ] to compress the retransmission-request pack et. The sourceinitially transmits the pack et using either a rate or con v olutional code. Iff ails to decode the pack et correctly it sends a retransmission-request pack et containing a list of the positions of eitheror of the least-reliable information bits. The numbers and PAGE 29 17 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Effective E b / N o (dB) Probability of bit error No ARQ After 1st retransmission After 2nd retransmission After 3rd retransmission Figure 2.7: Probability of bit error vs. Ef fecti v efor RB-HARQ scheme with v ariable redundanc y and reduced retransmission-request pack etare chosen so that in the ne xt section we can mak e a f air comparison between the proposed scheme and the HARQ scheme proposed by Hagenauer [ 7 ]. In studies that consider RB-HARQ based on turbo codes [ 21 22 ],responds to the request pack et by retransmitting the information bits. Ho we v er the code in these studies [ 21 22 ] is a systematic turbo code, whereas the code we consider in this w ork is a nonsystematic con v olutional code. Thus, for these results,retransmits the tw o code bits corresponding to each of the positions identied by. T o further clarify ,is using the reliability of the information bits to identify unreliable sections in the code trellis and then requests ne w code information for those trellis sections. The recei v ed code symbols are combined with all pre viously recei v ed PAGE 30 18 copies of those symbols. F or BPSK transmission o v er an A WGN channel, the soft-outputs for the symbols can be added together F or the results presented in this section, each pack et consists ofn information bits, including the tail bits. F or initial transmission rate a total ofn (n & ) coded bits per pack et are transmitted in the rst transmission. Each retransmission request consists of a list of bit positions, andtransmitscode bits in response to each request. This corresponds to incremental redundanc y per retransmission. W e consider the performance when the request and retransmission process can occur up to v e times. Each retransmission ef fecti v ely reduces the code rate. After v e retransmissions, a total of (n & ) coded bits are recei v ed at. Thus the code rate after v e retransmissions isn F or initial transmission rate a total ofn (n & ) coded bits per pack et are transmitted in the rst transmission. Each retransmission request consists of a list ofbit positions andtransmitsn code bits in response to each request. After v e retransmissions, a total of (n n & ) coded bits are recei v ed at, thus lo wering the code rate ton Note that in this section, the size of the retransmission-request pack et is not tak en into account; the additional o v erhead from the request pack et is considered in Section 2.4.2 where we e v aluate the throughput. The results in Figure 2.8 and Figure 2.9 sho w the probability of bit error and probability of pack et error respecti v ely as a function of the channel symbol ener gy-to-noise density ratio ( ). The initial code rate for these results is In Figure 2.8 we observ e that to achie v e a probability of bit error ofn a system using the proposed RBHARQ technique with v e retransmissions of incremental redundanc y each requires dB lo werthan a system that uses rate code with no ARQ. This is a significant performance gain, and most of it has been achie v ed after only tw o retransmissions. It should be noted that the error curv es indicate ooring at higher v alues of The results in Figure 2.9 sho w that to achie v e a probability of pack et error ofn a system PAGE 31 19 using the proposed RB-HARQ technique with v e retransmissions of incremental redundanc y each requires dB lo wer than a system that uses rate code with no ARQ. The results in Figure 2.10 and 2.11 sho w the probability of bit error and probability of pack et error respecti v ely for the initial code rate In Figure 2.10 we observ e that to achie v e a probability of bit error ofn a system using the proposed RB-HARQ technique with v e retransmissions ofn incremental redundanc y each requires dB lo wer than a system that uses rate code with no ARQ. In Figure 2.11 we observ e that to achie v e a probability of pack et error ofn a system using the proposed RB-HARQ technique with v e retransmissions ofn incremental redundanc y each requires dB lo wer than a system that uses rate code with no ARQ. These results sho w that the proposed technique can signicantly impro v e the performance of communication systems where con v olutional codes are used, pro vided there is a reliable feedback channel for retransmission-request pack ets. 2.4.1 Error Probability Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [ 7 ] (RCPC-HARQ). W e compare the tw o schemes in terms of probability of bit error and probability of pack et error Results in Figures 2.10 and 2.11 sho w the performance comparison of the tw o schemes when the initial code rate is Ev ery pack et is rst transmitted using a rate con v olutional code. The RCPC-HARQ scheme, in response to a N A CK, mo v es to a lo wer code rate by retransmitting bits in each retransmission thus achie ving raten after tw o retransmissions. The performance of the RCPC-HARQ scheme is sho wn in Figures 2.10 and 2.11 using solid lines. In the RB-HARQ scheme, that we propose,n bits are transmitted in a series of v e retransmissions thus achie ving a raten after v e retransmissions. The performance of the RB-HARQ scheme is sho wn in Figures 2.10 and 2.11 using dashed lines. In Figure 2.10 we observ e that to achie v e a probability of bit error ofn the proposed RB-HARQ scheme requiresdB lo wer than the RCPC-HARQ scheme. In PAGE 32 20 -3 -2 -1 0 1 2 3 4 5 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of bit error first transmission rate 4/7 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 1/2 4/7 1/2 1/2 Figure 2.8: Performance comparison of the proposed RB-HARQ scheme with the RCPCHARQ scheme with initial code rate 4/7. Figure 2.11 we observ e that to achie v e a probability of pack et error ofn the proposed RB-HARQ scheme requiresdB lo wer than the RCPC-HARQ scheme. Thus we conclude that the proposed scheme achie v es signicant performance impro v ement o v er the RCPC-HARQ scheme. Note that this gain is achie v ed at the cost of lar ge retransmissionrequest pack ets and more retransmissions than in the RCPC-HARQ scheme. 2.4.2 Throughput Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the tw o schemes in terms of throughput. W e do the performance comparison for the case when the initial code rate is First let us consider the size of retransmission-request pack et in the proposed scheme. As pre viously mentioned, the retransmission-request pack et consists of the least reliable bit positions. PAGE 33 21 -3 -2 -1 0 1 2 3 4 5 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error first transmission rate 4/7 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 1/2 4/7 1/2 1/2 Figure 2.9: Performance comparison of the proposed RB-HARQ scheme with the RCPCHARQ scheme with initial code rate 4/7. F or a pack et ofn information bits, each bit position can be represented by an -bit inde x. Thus each retransmission-request pack et consists of bits if no source coding is used. Ho we v er we can apply arithmetic coding to compress the retransmission-request pack et. The w ay the compressed retransmission-request pack et is generated is as follo ws. The destination radioconstructs an all-zero bit pack et of size equal to the number of information bits in the transmitted pack et. Thus for the results presented in this paper ,constructs a pack et ofn bits. Then it places a one in the bit positions corresponding to the least reliable bit positions. Thus the pack et consists of zeros and ones. The arithmetic coding is then applied on thisn bit pack et that consists of zeros and ones. Our results sho w that arithmetic coding produces compressed retransmission-request PAGE 34 22 -3 -2 -1 0 1 2 3 4 5 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of bit error rate 2/3 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 4/7 rate 1/2 1/2 1/2 2/3 4/7 Figure 2.10: Performance comparison of the proposed RB-HARQ scheme with the RCPCHARQ scheme with initial code rate 2/3. pack ets that ha v e an a v erage size ofn bits thus achie ving a compression ratio ofn (n n ). Thus by using arithmetic coding we are able to sa v e ( minusn ) bits e v ery time a retransmission-request pack et is sent fromto. Figure 2.12 illustrates the throughput of the RCPC-HARQ scheme proposed by Hagenauer [ 7 ] and the RB-HARQ scheme proposed in this paper W e assume that when the limits of retransmission are reached for either HARQ scheme, the pack et is retransmitted at the original rate and the HARQ process be gins again. Then the throughput is dened as the ratio of the number of bits per pack et to the e xpected number of coded bits that must be transmitted to achie v e correct decoding of the pack et. Thus, the throughputis gi v en by PAGE 35 23 -3 -2 -1 0 1 2 3 4 5 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error rate 2/3 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 4/7 rate 1/2 1/2 1/2 2/3 4/7 Figure 2.11: Performance comparison of the proposed RB-HARQ scheme with the RCPCHARQ scheme with initial code rate 2/3. whereis the pack et size in bits,is the e xpected number of coded bits that are transmitted in both the directions by the HARQ process, and is the probability of pack et success by the end of the HARQ process. In our simulations, throughput is calculated as the ratio of number of information bits in pack ets that are decoded correctly to the total number of bits transmitted in both the directions. The throughput of the RCPCHARQ scheme is illustrated by the curv e labeled by RCPC-HARQ. The curv es labeled RB-HARQ,andillustrate the performance of the proposed RB-HARQ schemes. F or RB-HARQ2, the retransmission-request pack et is sent without source coding. F or RBHARQ3, retransmission-request pack et is sent with source encoding at. RB-HARQ4 denotes the throughput of the proposed RB-HARQ scheme without taking into account retransmission-request pack et. Thus, RB-HARQ4 can be interpreted as the throughput PAGE 36 24 when the o v erhead on the retransmission request is not considered important, or RBHARQ4 can be interpreted as a simple, loose upper bound on the throughput that can be achie v ed with an y source coding algorithm. Results in Figure 2.12 sho w that the proposed scheme achie v es signicantly higher throughput at most signal to noise ratios. F or e xample, at dB the throughput (RCPC-HARQ) of the RCPC-HARQ scheme is approximately nnwhile the throughput of the proposed scheme with compressed retransmissionrequest pack et (RB-HARQ3) is approximatelyn The results sho w that e v en if we send the retransmission-request pack et without an y source coding, we still achie v e a higher throughput (RB-HARQ2) than the RCPC-HARQ scheme. -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0 0.1 0.2 0.3 0.4 0.5 E s / N 0 (dB) Throughput RCPC-HARQ RB-HARQ2 RB-HARQ3 RB-HARQ4 Figure 2.12: Throughput comparison of the proposed RB-HARQ scheme with the RCPCHARQ scheme with initial code rate PAGE 37 CHAPTER 3 RELIABILITY -B ASED HYBRID ARQ FOR P AR TIAL-TIME J AMMING CHANNELS In this chapter we e xtend the RB-HARQ technique to impro v e performance in a hostile jamming en vironment. Consider the communication scenario sho wn in Figure 3.1 in which the transmitteris communicating with the recei v erin the presence of a partialtime jammer. W e consider an asymmetric situation in which the recei v er () and the transmitter () e xperience dif ferent le v els of jamming. In particular we focus on the scenario in which the recei v er is e xperiencing high jamming le v els compared to the transmitter n r n r Figure 3.1: Communication scenario. The system model for the abo v e communication scenario is sho wn in Figure 3.2 W e consider pack etized communication in which pack ets atare encoded using a con v olutional code for transmission to. Code symbols are modulated using BPSK and recei v ed in the presence of white Gaussian thermal noise and time-v arying jamming. The jammer is modeled using a discrete-time tw o-state Mark o v model as sho wn in Figure 3.3 If at timethe jammer is in state, then the code symbol transmitted at timeis not jammed. Statenindicates that the jammer is on and the code symbol is jammed. The proportion of time for which the jammer is acti v e is specied as, and represents the e xpected v alue of the time (in terms of number of code symbols) spent in the jamming state before returning 25 PAGE 38 26 to the unjammed state. The four transition probabilities where n sho wn in Figure 3.3 can be calculated fromand using the follo wing tw o equations. (3.1) n (3.2) n n r n n n n r n n n r n n n n n # $ r ku'ku Figure 3.2: System model. The po wer spectral density of the thermal noise is The jamming po wer spectral density (PSD) is Ho we v er as the jammer is only acti v e for proportionof all time, PAGE 39 27 Figure 3.3: T w o-state Mark o v model for jammer the ef fecti v e jamming PSD when the jammer is acti v e is Thus, the total PSD of the noise (thermal noise and jammer noise) in statenis Let denote the ener gy per modulation symbol. Matched-lter reception is assumed. Then if the jammer is in statenat time, the recei v ed symbol can be modeled by (3.3) where is the transmitted code symbol, which tak es v alues fromn1. Here, represents the contrib ution from thermal noise and is a zero-mean Gaussian random v ariable with v ariance The jamming is modeled as a Gaussian random v ariable that has zero mean and v ariance Thus the total v ariance of the noise plus jamming is gi v en by 3.1 MAP Estimation Algorithms The destination radiouses MAP algorithms to estimate the jammer state for each recei v ed symbol and to decode the recei v ed pack et. The use of the channel interlea v er pre v ents the application of a single MAP algorithm to a hyper -trellis containing the states of the con v olutional code and the jammer Therefore we consider tw o MAP algorithms connected in a feedback loop, as sho wn in Figure 3.2 The estimation of the jammer state and impact on MAP decoding is considered briey in Section 3.4 and in detail by Kang PAGE 40 28 et al. and Moon et al. [ 29 30 ]. W e pro vide a brief re vie w of these algorithms and their interaction, and then describe ho w the y are impacted by the ARQ transmissions. Consider rst the MAP algorithm for estimating the jammer state. In the absence of an y channel side-information, the parameters of the jamming signal (, and ) can also be estimated using the Baum-W elch algorithm (cf. [ 29 30 ]). W e briey consider the case where the parameters of the jamming signal are kno wn, as it of fers some insight into the processing used in this paper At each time, the destinationcomputes the-APP ratio for the jammer state gi v en the recei v ed code w ord, which is gi v en by nr r (3.4) whereis the recei v ed code w ord in noise and n denotes the jammer state at time instant. This calculation is performed using the BCJR algorithm [ 26 ] operating on the recei v ed symbols in the order in which the y are transmitted. The branch metric connecting jammer stateto jammer stateat timeis gi v en by r r & r r & r n nr r n n r (3.5) where and represent the recei v ed and transmitted code symbols, respecti v ely at time. Note that r corresponds to one of the four transition probabilities sho wn in Figure 3.3 The forw ardand backw ard-looking state probabilities are determined in the usual w ay from the branch metrics. The probabilities nr and nr are set ton in the rst iteration, and are updated in later iterations according to the a posteriori estimates produced by the MAP algorithm for decoding the message. The BCJR algorithm for the message computes the -APP ratio F or each information bit gi v en, n nr nr (3.6) PAGE 41 29 Note that this BCJR algorithm operates in the order of the original code symbols before interlea ving (i.e., in the order of the deinterlea v ed recei v ed symbols). W e assume the use of a raten con v olutional code. Then the metric for the branch connecting state to stateis r & r & r (3.7) where and are the matched-lter outputs for the tw o code symbols corresponding to theth message bit, Here r is the a priori probability of information bit, which is tak en to be Note that r and r depend on whether the symbol is jammed. Let and be the states of the jammer for the recei v ed code symbols and respecti v ely where nif the symbol is jammed and otherwise. Then r r r r n nr (3.8) where we are approximating the probability of jamming as independent from symbol to symbol, although this will not be true for a nite interlea v er As e xplained pre viously r and n r are estimated using the MAP algorithm for the jammer state. If the recei v ed pack et is in error after decoding,sends a retransmission-request pack et tothrough the feedback channel. In this paper we assume perfect pack et error detection and an error -free feedback channel. The retransmission-request pack et contains information about the set of bits that are estimated to be unreliable. The set of unreliable bits is identied using the -APPs for the jammer states and information bits, which are computed using ( 3.4 ) and ( 3.6 ), respecti v ely The source encoder atis used to compress the retransmission request pack et.decodes the retransmission-request pack et and then retransmits the requested set of code symbols. Noisy (and possibly jammed) v ersions of the PAGE 42 30 retransmitted code symbols are recei v ed at the recei v er and combined in an optimal manner with the pre viously recei v ed copies as follo ws. Let and be the tw o recei v ed copies of the symbol after the rst and second transmission, respecti v ely The recei v ed lik elihood ratio (LLR) for symbol is gi v en by (3.9) if the jamming state is kno wn e xactly Here is the v ariance of the noise plus jamming for theth recei v ed cop y of If the jamming state is not kno wn e xactly then r n r n r n r n (3.10) where each of the four terms is a v eraged o v er the tw o possible jamming states as follo ws r r r n n (3.11) where is approximated by r 3.2 Maximum-Lik elihood Estimation of Jammer P arameters The MAP algorithms described pre viously need the estimates of the transition probabilities of the jammer model and the estimate of the jammer v ariance. Maximum-lik elihood (ML) estimation of these parameters is briey described in this section. The ML estimator for the transition probability from state to state, gi v en in the paper by Liporace [ 31 ], is as follo ws nr nr (3.12) whereis the number of message bits in the pack et andis code rate. Here is the forw ard-looking state probability is the backw ard-looking state probability and [ 26 ] is the branch metric, The ML estimator for the v ariance of the noise when PAGE 43 31 the jammer is in state 1 is gi v en by [ 31 ] nr n n r r nr n n (3.13) 3.3 Reliability-Based Hybrid ARQ Schemes Consider the pack et error rate for coded communication in the presence of a partialtime jammer Letbe the total number of information bits plus tail bits encoded with a rate con v olutional code. Then for soft-decision, maximum-lik elihood (ML) decoding, an upper bound on the pack et error probability is gi v en by the follo wing e xpression [ 32 33 ] n r n (3.14) where is the number of error e v ents of weight#and is the pairwise error probability (PEP) for tw o code w ords separated by Hamming distance#. Consider the performance of a system that does not emplo y ARQ. Assume that an ideal interlea v er is used in which the jamming symbols at the input to the decoder e xperience independent jamming. Then the PEP is gi v en by %$ '&)( # # # +* & # # %$ n %$ (3.15) Here# is the number of symbols that are jammed out of the total#symbols that mak e up the error e v ent. As mentioned pre viously , and An upper bound and good approximation for ( 3.15 ) is as follo ws [ 34 ]: & ( ,# -$ /.10'2 # n n & # # %$ n %$ &3(54 # %$ & # # 76 98-: %$ n %$ (3.16) where; PAGE 44 32 Then it is simple to sho w that the maximum term in the summation in ( 3.16 ) is for# # where# # n 8 n n n 8n F or x ed and, asincreases# r #, and the performance will be dominated by the e v ent that all#code symbols are jammed. Thus to ensure maximum asymptotic gain from a HARQ scheme, all jammed symbols should be retransmitted. At high retransmitting unjammed symbols will pro vide a small performance gain, and thus the number of symbols to be retransmitted can be reduced by not retransmitting symbols that are unjammed. W e use the MAP algorithm for the jammer state to estimate which symbols are jammed and the MAP algorithm for the message to estimate which bit decisions are reliable. W e rst consider RB-HARQ strate gies that use this information to retransmit a x ed number of bits in response to a decoding error By combining the tw o reliability measures, we propose se v eral HARQ strate gies that request retransmission for some set of bits that is determined to be unreliable. 1. In RB-HARQ(J), the destination only uses the jamming information to decide which code symbols are jammed. In the absence of perfect jammer state information, a symbol is estimated to be jammed if r and is estimated to be unjammed otherwise. The information about the set of code symbols is con v e yed to the source, which retransmits the code symbols that are estimated to be jammed by the destination. 2. In RB-HARQ(R), the destination only uses the reliabilityr rto decide which information bits are unreliable. The information about the set of such unreliable information bits is con v e yed to the source. The source then retransmits the code symbols corresponding to those information bits. 3. In RB-HARQ(R+J), the destination uses bothr rand to determine those information bits which ha v e the least v alue ofr rand also ha v e one or both code symbols jammed. Information about the set of such information bits is con v e yed to the source, which then retransmits the code symbols corresponding to such bits. PAGE 45 33 W e also consider an RB-HARQ scheme that adapts the number of bits to be retransmitted based on reliability information. In the RB-HARQ(R-A) scheme, the size of the retransmission is adapted based on the bit reliabilitiesr rof the bits in the pack et. W e use determine whether a bit should be retransmitted by comparing an estimate of the probability of error for the bit to a tar get bit error probability F or e xample, pack et error probabilities ofn result in a ne gligible de gradation in throughput. So, we can choose a tar get bit error probability that will result in result in pack et error probabilities belo wn The probability of bit error for an information bit can be estimated as the minimum of the a posteriori probabilities, which is gi v en by n nr nr n n (3.17) The required probability of bit error to achie v e a specied pack et error probability will depend, in general, on a number of dif ferent parameters lik e the jammer parameters and the number of retransmissions allo wed. F or the w ork presented in this paper simulations are used to nd the v alue of which achie v es the desired W e compare these RB-HARQ approaches to con v entional approaches in which the set of retransmitted symbols is not adapted based on reliability information. W e consider T ype-I HARQ schemes in which the entire pack et is retransmitted in response to error detection. W e consider both the original T ype-I HARQ (in which the ne w pack et replaces the pre vious pack et) and T ype-I HARQ with pack et combining. These schemes retransmit signicantly more bits than the RB-HARQ schemes that we propose, so we also consider a HARQ scheme that does not use reliability information and that retransmits the same number of bits as our RB-HARQ scheme. The schemes that we consider transmit either a random set of bits or a set of bits that is uniformly spaced throughout the pack et so as to achie v e the same o v erhead as our reliability-based schemes. This approach is analogous to incremental redundanc y hybrid ARQ schemes that are used with punctured codes, in PAGE 46 34 which the symbols to be transmitted are selected uniformly from the set of code symbols that were not pre viously transmitted. 3.3.1 Analysis of Probability of P ack et Error for HARQ W e pro vide a brief analysis of se v eral of the HARQ schemes discussed abo v e. In this section, we deri v e an upper bound on the probability of pack et error after a single retransmission for each scheme, b ut the bounds are easily e xtended to multiple retransmissions. W e mak e se v eral assumptions that dif fer from our simulations in order to mak e the analysis feasible. Our upper bounds are calculated based on code w ord maximum-lik elihood (ML) decoding. Ho we v er for the simulation results, we emplo y bitwise MAP decoding. F or sufciently high signal-to-noise ratio, these will match v ery closely as the BCJR algorithm becomes more closely approximated by its max-log-MAP form. The max-log-MAP form has been sho wn to be equi v alent to the soft-output V iterbi algorithm, a code w ord ML algorithm [ 35 ]. The bounds also assume perfect kno wledge of the jammer state. In addition, we calculate the bound under the assumption of ideal interlea ving, although for most of our simulation results we use nite, rectangular interlea ving. W e rst consider con v entional approaches to HARQ. F or T ype-I HARQ without pack et combining, the pack et error probability after one retransmission is gi v en by where is gi v en in ( 3.14 ). F or T ype-I HARQ with pack et combining, each symbol is recei v ed twice, and the pack et error probability can be determined from ( 3.15 ) with PEP gi v en by $ & ( # # # +* & # # %$ n %$ (3.18) W e no w consider HARQ schemes that do not retransmit the entire pack et. The analysis at the be ginning of this section indicates that the asymptotic performance will be dominated by the set of jammed symbols. Let denote the total number of transmitted bits. Then before retransmission, the e xpected number of symbols that are jammed is so we constrain the a v erage number of symbols to be retransmitted to also equal PAGE 47 35 W e consider a con v entional approach to incremental redundanc y HARQ (IR-HARQ) in which the bits are uniformly spaced throughout the entire pack et. F or the purposes of analysis, we model this as a system in which a random set of symbols is retransmitted such that the a v erage number of symbols retransmitted is An y gi v en symbol is independently selected to be retransmitted with probability. The pairwise error probability after retransmission for this HARQ scheme is gi v en by %$ $ &3( # # & # # n $ # # $ n $ (3.19) where# of the#symbols in the error e v ent are randomly selected for retransmission. Then of the total# # symbols that are transmitted in either the original transmission or the retransmission,denotes the number of symbols that are jammed. In the RB-HARQ(J) approach, the the set of symbols to be retransmitted depends on the set of symbols that is estimated to be jammed. Assuming perfect kno wledge of the jamming state, the pairwise error probability after one retransmission is -$ %$ &3( # # # # & # # n %$ # # %$ n %$ (3.20) where# is the number of symbols out of#that are jammed before the retransmission. All the# jammed symbols are retransmitted, and# of them are jammed during the retransmission. W ith the RB-HARQ(J) scheme, there is a question of what to do if we allo w further retransmissions. If we request that only the jammed symbols from the pre vious transmission are resent, then aftertransmissions, only symbols will be requested for retransmission. This number may be v ery small (for e xample the third retransmission with will contain only of the symbols in the pack et). So, we consider an alternati v e approach PAGE 48 36 that can pro vide a higher throughput at lo w F or RB-HARQ(J) with multiple retransmissions, the source alternates between retransmitting the symbols that are estimated to be jammed and retransmitting the entire pack et (as in T ype-I HARQ). In each case, soft combining is emplo yed. F or e xample with three retransmissions, the rst retransmission will consist of those bits that are estimated to be jammed in the original transmission. If the pack et can still not be decoded successfully the entire pack et is retransmitted. In the third retransmission, only those bits that were jammed during the pre vious transmission will be retransmitted. The PEP for this scheme is gi v en by ( 3.21 ). %$ %$ /&3( # # # # # # # +* & # # # # # # # # %$ " & n (3.21) As in ( 3.20 ),# denotes the number of symbols that are jammed in the rst retransmission. All of these# symbols are retransmitted, and# denotes the number of those symbols that are jammed. Similarly the entire pack et is retransmitted in the second retransmission, and# denotes the number of symbols that are jammed. All of these# symbols are retransmitted in the third iteration, and#denotes the number of those symbols that are jammed. 3.3.2 Size of retransmission-request pack et In con v entional HARQ, it is theoretically possible for a single feedback bit to be sent from the recei v er to the transmitter to indicate an A CK or N A CK. In practice, unless this bit is piggyback ed on a data pack et, the A CK or N A CK typically uses much more resources including a synchronization preamble and MA C address information for the sender and recei v er In our results, we consider the best-case scenario of single feedback bit for the con v entional HARQ schemes so that our results are not tied to a particular system. PAGE 49 37 In the RB-HARQ schemes considered in this paper the feedback pack et is lar ger as it contains information about the set of unreliable bits. In order to e v aluate the throughput, we rst e v aluate the size of the retransmission-request pack et. W e calculate the e xpected v alue of the size of the retransmission-request pack et for RB-HARQ schemes under dif ferent approaches to compress the retransmission-request pack et. Size of r etr ansmission-r equest pac k et with tr ansmission of uncompr essed bit indices : Recall that for the RB-HARQ schemes with x ed retransmission size, the number of bits to be retransmitted is equal to the e xpected number of jammed code symbols per pack et, which is gi v en by & & The simplest (and one of the least ef cient) w ays to design the retransmission-request pack et is to pro vide the sourcewith a list of the bits to be retransmitted. The number of bits required to represent the position of a code symbol is equal to & where & denotes the ceiling operator As an alternati v e, the retransmission-request pack et can be equal to the size of the transmitted pack et, with anin the position of each symbol to be retransmitted andin the other positions. Then the a v erage size of the retransmission-request pack et, denoted by, is gi v en by n & & n & (3.22) This is because if & & n & then the retransmission-request pack et can be constructed as a bit-stream of length & in which anis used to indicate the positions of symbols to be retransmitted and ais used for symbols that do not need to be retransmitted. Size of r etr ansmission-r equest pac k et with run-length arithmetic coding : Both the bit reliabilities and jamming states are correlated o v er time and thus are amenable to compression. The jamming states are Mark o vian and thus can be optimally compressed using arithmetic run-length coding [ 36 37 ] for a Mark o v source. Bit reliabilities can also be treated as approximately Mark o vian, and thus can also be compressed in a similar w ay Ho we v er modeling and compression of bit reliabilities is be yond the scope of this paper PAGE 50 38 Consider the RB-HARQ(J) scheme. Once the recei v er has identied the jammed symbols, it can use the estimates of the jamming parameters in the arithmetic runlength source coding process. The compression rate achie v able using the arithmetic runlength coding is equal to the entrop y rate of the Mark o v source, which is gi v en by & & (3.23) where and are the entrop y of stateandn, respecti v ely of the jammer The entrop y , of stateis gi v en by the standard entrop y of a binary source with output probabilities andn corresponding to the transition probabilities from statein Figure 3.3 The e xpected size of the retransmission-request pack et is then gi v en by & (3.24) Size of r etr ansmission-r equest pac k et with simple compr ession Because of the comple xity of arithmetic coding and decoding, as well as the need to accurately estimate the transition probabilities of the hidden Mark o v model for the jammer in order to achie v e optimal compression, we propose the follo wing suboptimal scheme for use with RB-HARQ(J). In this simple compression scheme, the retransmission-request pack et consists of the start and end positions of all the b ursts of jammed symbols. Here a b ur st of jammed symbols is a consecuti v e sequence of jammed symbols such that the symbols immediately before and after the b urst are unjammed. T o calculate the size of the retransmission-request pack et with simple compression, we rst calculate the a v erage number of b ursts of jammed symbols in the recei v ed pack et. Letbe the number of b ursts in the recei v ed pack et and n represent the state of the jammer at time. Let be the number of b ursts starting at time, where a PAGE 51 39 b urst is dened to start at timeif either and nor if and n. Then n n n'& n (3.25) where and are the steady-state probabilities of the jammer being in stateandn, respecti v ely Thus, the a v erage size of the retransmission-request pack et is the e xpected number of b ursts multiplied by the number of bits required to represent the start and end positions of the b ursts, which is gi v en by & & n (3.26) 3.4 Performance of Estimation Algorithm W e assume thatkno ws the statistics of the thermal noise, b ut in general does not ha v e an y channel side information (CSI) about the jamming state, the transition probabilities, and the PSD in the jamming state. This information about the jamming needs to be accurately estimated for best performance in decoding the pack et. In this section we sho w the performance of the iterati v e MAP algorithm for jamming estimation and decoding. F or all of the results presented in this paper the code used for transmission fromtois a rate 1/2, constraint length con v olutional code with generator polynomials and (in octal). In all of the results, the total block size is 1000 information bits, including the tail bits. Except where noted, the coded bits are interlea v ed using a rectangular interlea v er of size The retransmission process ef fecti v ely reduces the code rate and hence increases the recei v ed ener gy per bit,, at the recei v er W e present results in terms of the channel symbol ener gy-to-noise density ratio, and the a v erage symbol-ener gy to jammer -noise density ratio, These ratios remain constant during the ARQ process. PAGE 52 40 The parameters of the Mark o v chain for the jammer are and F or the case of no CSI, all of the jamming parameters are estimated using the BaumW elch/BCJR algorithm. The Baum-W elch algorithm requires some initial estimate to distinguish the densities emitted by the tw o states. W e use the initial estimate that the v ariance in the jamming state is twice the v ariance in the unjammed state. W e can measure the performance of the estimation and detection algorithm directly in terms of the probability of miss and probability of f alse alarm. The probability of miss is calculated as the ratio of the number of symbols that are jammed and not detected to be jammed to the number of symbols that are jammed. The probability of f alse alarm is calculated as the ratio of the number of symbols that are unjammed and detected to be jammed to the total number of unjammed symbols. These performance metrics are illustrated in Figure 3.4 for the estimation algorithm aftern iterations at dB. The performance of the ML estimation algorithm is compared with the performance of jamming detection with perfect kno wledge of all the jammer parameters including the transition probabilities, the a v erage jammer PSD and. The performance of the decoding algorithm has been sho wn to be most sensiti v e to misses in jamming detection, in which a jammed symbol is identied as unjammed [ 30 ]. The results in Figure 3.4 sho w that for dB, the iterati v e MAP algorithm with ML estimation achie v es probability of miss less than for all v alues of greater thandB. Detection with estimation of all parameters performs as well as detection when all parameters are kno wn e xcept at v ery lo w v alues of This is because at lo w v alues of, the v ariance of the thermal noise, is comparable to the v ariance, of the jammer signal. Thus it is dif cult to detect whether a symbol is jammed. Ho we v er at such lo w the pack et error probability will be v ery high with e v en perfect kno wledge of the jammer state. The results in Figure 3.4 sho w that the ML estimation algorithm achie v es a probability of f alse alarm of less than one percent for all v alues of greater PAGE 53 41 -4 -2 0 2 4 6 8 10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Probability of miss -4 -2 0 2 4 6 8 10 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 E s / N 0 (dB) Probability of false alarm Prob. of false alarm with ML estimation Prob. of false alarm with parameters known Prob. of miss with ML estimation Prob. of miss with parameters known Figure 3.4: Probability of miss and f alse alarm of jammed symbols when all jamming parameters must be estimated in comparison to when all jamming parameters are kno wn at dB. thanndB. The performance of ML estimation, in terms of f alse alarm probability is close to the performance when the jammer parameters are kno wn. The results in Figure 3.5 sho w the probability of pack et error at dB for RB-HARQ(J), which requests retransmission for all symbols that are identied as jammed. The performance of RB-HARQ(J) scheme with estimation of all parameters is compared with the case when the decoder has perfect channel-side information (CSI). Perfect CSI means that the decoder kno ws all the jammer parameters and which symbols are jammed. The results sho w that the performance of the estimation algorithm is within ton dB of the CSI case. The results in this section sho w that iterati v e parameter estimation achie v es v ery good performance and that ha ving to estimate the jamming parameters does not signicantly PAGE 54 42 -2 -1 0 1 2 3 4 5 6 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error No ARQ CSI No ARQ ML Estimation ARQ CSI ARQ ML Estimation No Jamming Figure 3.5: Probability of pack et error for RB-HARQ(J) with estimation of jamming parameters or perfect CSI, and = -3 dB. de grade the performance of RB-HARQ. In the ne xt section, we compare the performance of the dif ferent proposed RB-HARQ schemes with con v entional HARQ schemes. W e sho w the results in terms of probability of pack et-error and assume perfect CSI for these results. 3.5 Performance Results In this section we compare the performance of the proposed RB-HARQ schemes to con v entional HARQ schemes. The con v olutional code is the same as in the pre vious section. Except where noted, the parameters of the jammer are gi v en by dB, and W e e v aluate the performance in terms of pack et error probabilities and throughput. PAGE 55 43 3.5.1 P ack et error probabilities W e rst compare analytical and simulation results for the probability of pack et error , after one retransmission for the HARQ schemes analyzed in Section 3.3 In the RBHARQ(J) scheme, all jammed symbols are retransmitted. W e compare the performance of this approach with three con v entional HARQ schemes. W e consider T ype-I HARQ with and without pack et combining. These scheme retransmit signicantly more bits than RB-HARQ(J), so we also consider an IR-HARQ scheme that retransmits a random set of bits such that the a v erage o v erhead is the same as for RB-HARQ(J). The results of this comparison are illustrated in Figure 3.6 The analytical upper bounds are sho wn using solid lines, and the simulation results are sho wn using dashed lines. -2 -1 0 1 2 3 4 5 6 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB)Probability of packet error Upper Bound Simulation Random Retransmission No ARQ Type-I HARQ RB-HARQ(J) Type-I HARQ with packet combining Figure 3.6: Probability of pack et error for RB-HARQ(J), T ype-I HARQ and retransmission of a random set of symbols, and dB. PAGE 56 44 The results sho w that to achie v e n T ype-I HARQ without pack et combining pro vides approximatelyn dB gain o v er no ARQ. If T ype-I HARQ is used with pack et combining, the gain is approximatelydB. F or the other HARQ results, the o v erhead is onlyof that of the T ype-I HARQ schemes. The IR-HARQ scheme can achie v e n withn dB lo werthan T ype-I HARQ without pack et combining. RBHARQ(J) requiresn dB lo wer than incremental redundanc y with random retransmissions at n and the performance dif ference increases drastically for lo wer tar get v alues of. Although RB-HARQ(J) requires approximatelyn dB ton dB higher than T ype-I HARQ with pack et combining, it only retransmitsof the bits of T ype-I HARQ. The results also sho w that the upper bounds computed using ( 3.14 ) and ( 3.18 )Â–( 3.20 ) pro vide v ery tight bounds on the pack et error probabilities. The results in Figure 3.7 sho w the performance of RB-HARQ(J) when three retransmissions are allo wed. The results sho w that combining RB-HARQ(J) with T ype-I HARQ pro vides v ery good performance, particularly at lo w v alues of The results also sho w that the upper bound computed using ( 3.21 ) pro vides a v ery good approximation for probability of pack et error after three retransmissions F or the remainder of the results, the channel symbols are interlea v ed using a rectangular bit interlea v er F or these results, the con v entional IR-HARQ scheme transmits a uniformly spaced set of bits. The results in Figure 3.8 illustrate the pack et error rate for dif ferent RB-HARQ and con v entional HARQ schemes. F or these results dB. The a v erage number of symbols retransmitted in response to N A CK is equal to (the e xpected number of jammed symbols) for all of the HARQ schemes e xcept for T ype-I HARQ in which the entire pack et is retransmitted. The results in Figure 3.8 sho w that all three RB-HARQ schemes achie v e better per formance than the con v entional HARQ approaches that do not emplo y reliability e xcept for T ype-I HARQ with pack et combining, which retransmits signicantly more symbols. T o achie v e a pack et error rate of less thann the requiredfor RB-HARQ is at PAGE 57 45 -4 -3 -2 -1 0 1 2 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB)Probability of packet error Simulation Analytical 3 retransmissions of RB-HARQ(J) 3 (2+1) retransmissions of RB-HARQ(J) + Type-I HARQ with packet combining Figure 3.7: Probability of pack et error for three retransmissions of RB-HARQ(J), and dB. leastdB less than for IR-HARQ, which retransmits the same number of symbols b ut does not use reliability information. RB-HARQ(R+J) achie v es the best performance because it uses both the -APPs to decide which symbols are to be retransmitted. This scheme performs about dB better than RB-HARQ(J) in which all jammed symbols are retransmitted. Among all the proposed RB-HARQ schemes, RB-HARQ(R) that selects the bits to be retransmitted based only onr rperforms the w orst. This because at high v alues of the performance is limited by the jamming, as sho wn in the analysis in Section 3.3 Since RB-HARQ(R) retransmits both code symbols for information bits that ha v e lo w v alues ofr rand one or both of these code symbols are unjammed, some jammed symbols will not be retransmitted because the the total number of retransmitted PAGE 58 46 -2 -1 0 1 2 3 4 5 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error No ARQ IR-HARQ Type-I HARQ RB-HARQ(R) RB-HARQ(R+J) RB-HARQ(J) Type-I HARQ with packet combining Figure 3.8: Probability of pack et error for dif ferent RB-HARQ schemes compared with T ype-I HARQ and con v entional HARQ, and = 0 dB. symbols is equal to the a v erage number of jammed symbols. The residual set of jammed symbols results in an error oor for high The results in Figure 3.9 sho w the performance if the number of symbols to be retransmitted is reduced ton The symbols to be retransmitted are selected in tw o w ays. In the RB-HARQ(J) scheme, the decoder uses to identify all the jammed symbols and then requests the retransmission of e v ery alternate jammed symbol. In the gure, this scheme is denoted by Â“uniform RB-HARQ(J)Â”. In the RB-HARQ(R+J) scheme, the decoder rst uses to identify all the jammed symbols. Then, it uses to identify half of all the jammed symbols which correspond to information bits ha ving the least v alues of -APP This scheme is denoted by Â“LRB jam symbols ARQÂ” in PAGE 59 47 -2 -1 0 1 2 3 4 5 6 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error No ARQ 50 % uniform RB-HARQ(J) 50 % RB-HARQ(R+J) RB-HARQ(J) No jamming Figure 3.9: Probability of pack et error for dif ferent RB-HARQ schemes, and dB. Figure 3.9 F or these results, dB. The results in Figure 3.9 sho w that to achie v e a probability of pack et error ofn the RB-HARQ(R+J) scheme that uses both the soft-outputs requiresndB less than the RB-HARQ(J) scheme. The performance disparity increases for lo wer tar get error probabilities. Thus these results clearly indicate that the RB-HARQ scheme that uses both the soft-outputs, and achie v es a signicant gain o v er the one that only uses one of the soft-outputs. In Figure 3.10 we consider the RB-HARQ(R-A) scheme, in which the number of bits to be retransmitted is adapti v e selected based on a specied tar get pack et error probability F or these results only one retransmission is considered. As discussed in Section 3.3 of ine simulations were used to determine that a tar get bit error probability n achie v es n Using ( 3.17 ), this translates to requiring retransmission for all bits PAGE 60 48 -3 -2 -1 0 1 2 3 4 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error RB-HARQ(J) RB-HARQ(R-A) Type-I HARQ Type-I HARQ with packet combining Figure 3.10: Probability of pack et error for adapti v e and x ed RB-HARQ, and = -3 dB. withr r nn The results in Figure 3.10 illustrate the pack et error probability achie v ed at dB for RB-HARQ(R-A), RB-HARQ(J), and T ype-I HARQ with and without pack et combining. The results sho w that for dB, none of the schemes are able to achie v e the tar get pack et error probability ofn F or dB, the adapti v e retransmission scheme does achie v e pack et error probabilities belo wn The real ef fect of adapti v e RB-HARQ is that the a v erage number of symbols to be retransmitted decreases as the increases. W e study this in terms of its ef fect on throughput in the ne xt subsection. 3.5.2 Throughput Results W e no w compare the throughput performance of RB-HARQ and con v entional HARQ schemes. W e rst consider the performance of RB-HARQ(J) that retransmits all the jammed PAGE 61 49 code symbols. Throughput is dened as the ratio of the number of bits per pack et to the e xpected number of coded bits that must be transmitted to achie v e correct decoding of the pack et. Thus, the throughputis gi v en by whereis the number of information bits in a pack et,is the e xpected number of coded symbols that are transmitted in both directions during the HARQ process, and is the probability of pack et success by the end of the HARQ process. F or these results, we consider up to three retransmissions. If the pack et is still in error after three retransmissions, then the whole pack et is retransmitted and the HARQ process starts o v er The results in Figure 3.11 sho w the throughput of RB-HARQ(J) and the con v entional HARQ schemes for dB. As pre viously discussed, RB-HARQ(J) alternates between retransmitting the set of symbols that are estimated to be jammed and complete pack et retransmission (as in T ype-I HARQ). The size of the retransmission-request pack et for the con v entional HARQ scheme is tak en to be 1 bit. The size of the retransmissionrequest pack et for RB-HARQ is calculated using the formulas in Section 3.3.2 The size of the retransmission-request pack et composed of bit indices (no compression) is bits. The a v erage size of the retransmission-request pack et compressed using arithmetic runlength coding, calculated using ( 3.24 ), is bits. Thus, using arithmetic coding helps in reducing the size of retransmission-request pack et by almost percent. F or RB-HARQ(J) with the simple compression scheme, the a v erage size of the retransmission-request pack et is bits. The results in Figure 3.11 sho w that despite lar ger retransmission-request packets, RB-HARQ(J) technique that uses compression achie v es better throughput than all the other HARQ techniques for all v alues of dB. At v ery lo w v alues of ( ndB) T ype-I HARQ with pack et combining performs around dB better than RBHARQ(J) because in this re gime, the performance gain from retransmitting more symbols outweighs the additional o v erhead of retransmitting the entire pack et. The results also sho w PAGE 62 50 -3 -2 -1 0 1 2 3 4 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 E s / N 0 (dB) Throughput Type-I HARQ Uniform HARQ Type-I HARQ with packet combining RB-HARQ(J) with arithmetic coding RB-HARQ(J) with simple compression Figure 3.11: Throughput for RB-HARQ, T ype-I HARQ and con v entional (uniform) HARQ, after 3 retransmissions at and dB. that using the simple compression scheme for the retransmission-request pack et achie v es throughput close to that achie v ed by using optimal arithmetic runlength coding. The results in Figure 3.12 sho w the throughput for RB-HARQ(R-A) in comparison with RB-HARQ(J) and the con v entional schemes. Recall that in RB-HARQ(R-A), the number of retransmitted bits is adapti v ely selected to achie v e some tar get error probability F or these results, up to three retransmissions are allo wed, and simulations were carried out to nd the tar get that achie v es the maximum throughput. It w as observ ed that a tar get bit error probability of n of fered the best throughput for the range of and jammer parameters considered in our w ork. W e sho w tw o curv es for RB-HARQ(R-A), one in which the o v erhead is determined based on the retransmission-request pack et consisting of the bit indices of all symbols to be retransmitted (no compression) one in which that PAGE 63 51 o v erhead is ignored. Our reason for including the results without the o v erhead is tw ofold. First, in man y cases, it might not be desired to treat the o v erhead on the retransmissionrequest pack et the same as the forw ard transmission because that link is assumed to not be jammed. Secondly although outside of the scope of this paper compression can be applied to this retransmission-request pack et, and the results we present represent upper and lo wer bounds on the performance with compression. The results sho w that if the o v er head in the retransmission-request pack et can be ignored or signicantly reduced through compression, then RB-HARQ(R-A) achie v es the best throughput at all v alues of This is because adapti v e RB-HARQ(R) adapts the size of retransmission to the reliability of the recei v ed bits. It retransmits more bits at lo w to achie v e correct decoding of the pack et and retransmits fe wer bits at high while still achie ving a suf ciently lo w Ev en when we account for the size of uncompressed retransmission-request pack et in throughput calculations, adapti v e RB-HARQ(R) performs better than con v entional HARQ and T ype-I HARQ that does not use pack et combining for the entire range of Finally we in v estigate the ef fect of dif ferent v alues ofon the performance of the v arious HARQ techniques. The results in Figure 3.13 compare the throughput of RBHARQ(J) and RB-HARQ(R-A) with the con v entional HARQ schemes as a function of. F or these results dB, dB, and The results sho w that if we ne glect the o v erhead in the retransmission-request pack et, RB-HARQ(R-A) achie v es the best performance o v er all. Thus the RB-HARQ(R-A) scheme can ef fecti v ely adapt the set of retransmitted bits to dif ferent v alues of. The RB-HARQ(J) scheme achie v es the same performance as RB-HARQ(R-A) for F or higher v alues of, the o v erhead in the retransmission-request pack et reduces the performance of RB-HARQ(J). Abo v e T ype-I HARQ with pack et combining outperforms RB-HARQ(J). This suggests that ifis estimated to be v ery high, then the RB-HARQ(J) scheme can be simply modied to request retransmission of the whole pack et. Note that neither T ype-I HARQ without pack et PAGE 64 52 -3 -2 -1 0 1 2 3 4 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 E s / N 0 (dB) Throughput Type-I HARQ IR-HARQ RB-HARQ(R-A) with feedback overhead Type-I HARQ with packet combining RB-HARQ(R-A) without feedback overhead RB-HARQ(J) with arithmetic coding Figure 3.12: Throughput of adapti v e RB-HARQ(R), RB-HARQ(J), T ype-I HARQ and con v entional (uniform) HARQ, and = dB. combining nor IR-HARQ are competiti v e techniques for dealing with jamming e xcept at v ery lo w v alues of. PAGE 65 53 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 r (Probability a symbol is jammed) Throughput Type-I HARQ IR-HARQ RB-HARQ(R-A) with feedback overhead Type-I HARQ with packet combining RB-HARQ(J) with arithmetic coding RB-HARQ(R-A) without feedback overhead Figure 3.13: Throughput for RB-HARQ, T ype-I HARQ and con v entional (uniform) HARQ as a function ofat dB, dB. PAGE 66 CHAPTER 4 RELIABILITY -B ASED HYBRID-ARQ FOR CSMA-CA-B ASED WIRELESS NETW ORKS In this chapter we e xplore the application of reliability-based hybrid-ARQ (RB-HARQ) in wireless netw orks. W ireless netw orks are strongly af fected by errors caused by f ading and collisions. Carrier -sense multiple access with collision a v oidance (CSMA-CA) is a commonly used medium access control (MA C) protocol in wireless local area netw orks (WLAN) and wireless ad hoc netw orks [ 38 ]. In most research on the performance of the CSMA-CA protocol, it is commonly assumed that collisions are the only source of transmission f ailure and that collisions result in the complete corruption of the pack et. Ho we v er pack et f ailure may also occur because of errors due to channel f ading or Gaussian noise. T o enhance throughput in wireless netw orks, channel coding at the physical layer [ 39 40 ] and automatic repeat request (ARQ) protocol at the data link layer [ 2 41 ] ha v e been studied separately Recently cross-layer design that combines these tw o layers judiciously to impro v e the performance has been studied [ 42 43 ]. All of these w orks either consider the pack et f ailure due to channel f ading or pack et f ailure due to collisions. Ho we v er a truly cross-layer design methodology for wireless netw orks must consider both: i.e. the pack et errors due to channel f ading and noise and the pack et errors due to collisions with the other simultaneously transmitted pack ets in the netw ork. In order to consider pack et f ailure due to collisions, it is essential to model the interference caused by simultaneous transmission by other nodes in the netw ork. The ne xt section describes this w ork in detail. 4.1 Interference Modelling The MA C protocol commonly used in research studies on wireless ad-hoc netw orks [ 44 ] is based on IEEE nn[ 45 ]. The IEEE nnspecies tw o modes of MA C protocol: distrib uted co-ordination function (DCF) mode for ad hoc netw orks and point co-ordination 54 PAGE 67 55 function (PCF) mode for infrastructure-based netw orks. The DCF in IEEE nnis based on CSMA-CA and uses the R TS-CTS-D A T A-A CK sequence between the sender and the recei v er While IEEE nnDCF w orks well in LAN en vironments, studies sho w that it is not particularly suitable for multi-hop ad-hoc netw orks with mobile nodes [ 46 47 ]. This is because issues lik e hidden-node problems cause collisions [ 38 ]. Collisions may result in parts of a pack et being corrupted while other parts are recei v ed without corruption. F or e xample, part of a D A T A pack et may be corrupted by collision with a shorter R TS pack et. T o e v aluate the ef fect of collisions on a D A T A pack et we simulate an ad-hoc netw ork using netw ork simulator ns2 [ 48 ], which is a v ery commonly used tool in research studies in v olving the MA C layer The objecti v es of this simulation are:T o determine what percentage of D A T A pack ets suf fer from interference. In other w ords what percentage of D A T A pack ets collide with other pack ets which may be R TS, CTS, D A T A or A CK pack ets.Gi v en that a particular D A T A pack et suf fers from interference, to determine the probability of it suf fering from interference due to multiple interfering pack ets.T o determine the probability density function of the po wer of the interfering pack et.T o determine the distrib ution of the type (R TS/CTS/D A T A/A CK) of the interfering pack et.T o determine the dif ference between the starting times of the D A T A the pack et and the interfering pack et. T able 4.1 sho ws the parameters used in our simulation. The routing protocol w as chosen to be DumbAgent in order to minimize the routing o v erhead. The follo wing parameters about the interference that af fects the D A T A pack ets were calculated from the simulation output. n: Probability that a D A T A pack et suf fers from interference. n : Probability that a D A T A pack et suf fers from interference due to( n) or more interfering pack ets conditioned on the e v ent that it suf fers from interference. : Probability that the interfering pack et is a R TS pack et. PAGE 68 56 T able 4.1: Simulation parameters in ns2 Number of nodes 60 T opology random placement inn n m T raf c type constant bit-rate UDP Number of traf c o ws 60 P ack et size n bytes P ack et rate n pack ets/s MA C protocol nn Data rate nMbps Routing protocol DumbAgent Mobility model random w ay-point Maximum node speed m/s Simulation time n s : Probability that the interfering pack et is a CTS pack et. : Probability that the interfering pack et is a D A T A pack et. : Probability that the interfering pack et is a A CK pack et. In addition to the parameters dened abo v e, we also calculate the probability density function (PDF) of the po wer of the interfering pack et and the PDF of the start time of the interfering pack et with respect to the start time of the D A T A pack et. F or the simulation paT able 4.2: Interference parameters obtained using simulation P arameter V alue n 0.36 n 0.53 n 0.25 0.55 0.16 0.16 0.13 rameters sho wn in T able 4.1 the v alues of the interference parameters obtained are sho wn in T able 4.2 These v alues ha v e been obtained after a v eraging across all those nodes in the netw ork that e xperience collisions. It should be noted from T able 4.2 that only percent of the total transmitted D A T A pack ets are af fected by interference. The f act that this v alue PAGE 69 57 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 5 10 15 20 25 30 Normalized Interference PowerProbability density function Figure 4.1: Probability density function of the normalized po wer of the interfering pack et. of nhas been obtained after a v eraging across all the nodes that e xperience collisions implies that it is v ery lik ely that for some node in the netw ork,nmay be more than Later in this chapter we e v aluate performance, in terms of throughput, for one such node. The probability density function (PDF) of the ratio of the po wer of interfering pack et to that of the data pack et is sho wn in Figure 4.1 The normalized interference po wer ofn nis used as the threshold in ns2 to distinguish between 'capture' and 'collision'. It w as observ ed from the simulation output that the start time of the interfering pack et is uniformly distrib uted across the entire D A T A pack et. 4.2 Non-F ading Channel Model As mentioned pre viously an y cross-layer design approach that considers the channel coding at the physical layer and ARQ at the data link layer should consider pack et errors PAGE 70 58 due to channel f ading and noise as well as those due to interference from other nodes. As a rst step in that direction, we propose a channel model that considers additi v e white Gaussian noise (A WGN) and interference due to simultaneous transmission by other nodes in the netw ork. The basic system model remains the same as that sho wn in Figure 2.2 The data pack et is con v olutionally encoded and then transmitted o v er the A WGN channel using BPSK modulation. Interference, determined according to the parameters calculated in the pre vious section, is added to the transmitted pack et. It should be noted that not e v ery transmitted pack et suf fers from interference becausenis less than one. F or a pack et that suf fers from interference, only those symbols are af fected whose transmission o v erlaps the transmission of the interfering pack et. Therefore the recei v ed symbol, not af fected by interference, can be modeled as (4.1) where is the transmitted code symbol, which tak es v alues fromn1 and represents the contrib ution from zero-mean white Gaussian noise with v ariance If the symbol is af fected by interference, then it is modeled as follo ws. & (4.2) The third term on the right hand side represents the interference. Here isn1 andis a random v ariable representing the interference po wer It should be noted thatis generated according to the PDF sho wn in Figure 4.1 It is possible that some symbols e xperience interference due to multiple interfering pack ets. In that case, the recei v ed symbol is modeled by ha ving multiple interference terms. W e e v aluate the probability of pack et error under the ne w channel model and compare it with the channel model that does not consider interference. F or the results presented in this section the D A T A pack et is encoded using raten con v olutional code with constraint length and generator polynomials and (in octal). The pack et lengths of PAGE 71 59 dif ferent types of pack ets were chosen to be the same as that in ns2 simulation. Therefore, the D A T A pack et consists of n message bits which includes n bytes of payload, bytes of MA C layer header and bytes of physical layer header [ 45 ] The size of R TS pack et is bits and the size of CTS and A CK pack et isbits. These v alues were obtained from thenme gabits per second (Mbps) v ersion of the IEEE nnstandard [ 45 ]. Figure 4.2 sho ws the pack et error probability when we consider the interference compared with the pack et error probability in the presence of Gaussian noise only The results in -1 -0.5 0 0.5 1 1.5 2 2.5 3 10 -4 10 -3 10 -2 10 -1 10 0 E s / N 0 (dB) Probability of packet error AWGN AWGN + interference Figure 4.2: Ef fect of interference on probability of pack et error for A WGN channel. Figure 4.2 sho w that under the ne w channel model, the probability of pack et error is w orse by dB forgreater thanndB. It is observ ed that in order to achie v e a pack et error probability ofn under the ne w channel model, an additional of PAGE 72 60 aroundn dB is required. It should be noted that for the results sho wn in Figure 4.2 approximately percent of the D A T A pack ets suf fer from interference. Ne xt, we in v estigate the throughput performance under the ne w channel model and compare it with the throughput performance under the A WGN channel model that does not consider interference. Throughput is calculated as the number of bits per second deli v ered correctly to the destination. In our calculation for throughput, we tak e into account the o v erhead due to R TS, CTS, A CK, the inter -frame spacing (IFS) and the random back of f during the contention period [ 38 45 ]. T o determine the w orst case performance under the ne w channel model, we consider n n. In other w ords e v ery D A T A pack et collides with one or more pack ets and suf fers from interference. W e consider up to tw o retransmissions and assume T ype-I ARQ in which the complete pack et is retransmitted. The retransmissions also under go collisions. F or e v ery ne w D A T A pack et the size of contention windo w is initially Ev ery time the pack et is in error the size of the contention windo w increases e xponentially [ 38 45 ]. F or the throughput results sho wn in Figure 4.3 the size of D A T A, R TS, CTS and A CK pack ets is the same as that for the results in Figure 4.2 The v alue of is nand the duration of one slot in the contention windo w is microseconds [ 45 ]. The v alue of SIFS (short IFS) isn microseconds and that of (DCF IFS) ismicroseconds. These v alues correspond to thenMbps v ersion of the IEEE nnstandard [ 45 ]. Therefore, the maximum throughput that can be achie v ed isnMbps. The results in Figure 4.3 sho w that the maximum achie v able throughput is approximately Mbps. This is because in addition to the time tak en for transmitting the payload, we also tak e into account the time for transmitting the MA C header physical layer header R TS, CTS and the A CK and also the o v erhead due to the DIFS, back-of f period and the SIFS. W e observ e that for all v alues of sho wn in Figure 4.3 the throughput achie v ed under the ne w channel model, e v en when n n, is nearly the same as that achie v ed when we do not consider the interference. This observ ation leads to the conclusion that either the interference po wer is too weak to cause an y signicant de gradation in performance or PAGE 73 61 the error -correcting con v olutional code used in our simulations is strong enough to correct most pack et errors due to interference. -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 E s / N 0 (dB)Throughput (Mbps) AWGN AWGN + Interference Figure 4.3: Throughput for T ype-I HARQ with up to 2 retransmissions andn n 4.3 Performance of Reliability-Based Hybrid-ARQ in CSMA-CA-Based Netw orks In this section we propose a RB-HARQ technique for CSMA-CA-based netw orks and compare its performance with T ype-I HARQ. First we describe the RB-HARQ technique. W e propose to introduce a ne gati v e ackno wledgement (N A CK) in the MA C protocol. Therefore, the recei v er al w ays sends either an A CK or a N A CK after the D A T A pack et is recei v ed. The A CK or the N A CK is sent after SIFS time after the D A T A pack et is recei v ed. When the recei v er detects an error in the D A T A pack et, it sends a N A CK. The N A CK contains information about the least reliable sections of the D A T A pack et. The recei v er uses the -APP to determine what parts of the payload are less reliable. The PAGE 74 62 transmitter after recei ving the N A CK, retransmits those least reliable sections of the D A T A pack et. The retransmissions occur the same w ay as in the IEEE nnstandard [ 45 ]. It should be noted that the N A CK is lar ger than the A CK because the N A CK contains infor mation indicating what parts of the D A T A pack et should be retransmitted. -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Throughput (Mbps)E s / N 0 (dB) Type-I HARQ RB-HARQ (25%, CWmin) RB-HARQ (50%) RB-HARQ (50%, CWmin) Figure 4.4: Throughput for RB-HARQ and T ype-I HARQ with up to 2 retransmissions and A WGN channel The results in Figure 4.4 sho w the throughput achie v ed by the proposed RB-HARQ scheme and the T ype-I HARQ. F or these results we assume an A WGN channel model without an y interference. The results in Figure 4.3 sho w that e v en when we consider the interference the de gradation in throughput is ne gligible. F or the results in this section, we assume that the R TS-CTS mechanism is turned of f. Ho we v er we still tak e into account the o v erhead due to the MA C layer header the physical layer header the DIFS, random back-of f, the SIFS, the A CK and the N A CK. The v alues of these parameters is the same PAGE 75 63 as those in the pre vious section. When the recei v er detects an error it di vides the payload ( n bits) inton sections and determines the minimum-APP for each section. These-APPs are then sorted to nd the least reliable sections of the payload. The N A CK includes a eld of lengthn bits with ones indicating those sections that need to be retransmitted. Therefore, the N A CK is lar ger than the A CK byn bits. The curv e labelled Â“RB-HARQ(50%)Â” denotes the throughput of the RB-HARQ technique when only half of the payload is transmitted in response to the N A CK. The results sho w that RB-HARQ achie v es better throughput than the T ype-I HARQ for all in the range todB. This is because for each error pack et RB-HARQ adapti v ely determines the least reliable sections of the pack et and then only those least reliable sections are retransmitted where as the complete pack et is retransmitted in T ype-I HARQ. W ith the Rb-HARQ scheme, the N A CK can also be used to inform the transmitter whether the size of contention windo w should be increased. W e in v estigate the throughput when the size of contention windo w is x ed at The curv e labelled Â“RB-HARQ (50%, )Â” sho ws that there is a mar ginal impro v ement in throughput by k eeping the contention windo w size x ed. The curv e labelled Â“RB-HARQ (25%, )Â” sho ws the throughput of RB-HARQ technique in which the percent least reliable sections of the payload are retransmitted and the size of contention windo w is al w ays x ed at The results sho w that at v ery lo w v alues of the throughput achie v ed is signicantly less than that achie v ed by T ype-I HARQ. This is because retransmitting just percent of the payload is not enough to achie v e correct decoding of the pack et for dB. Ho we v er for n dB, RB-HARQ that retransmits percent least reliable sections of the payload achie v es the highest throughput. PAGE 76 CHAPTER 5 CONCLUSIONS AND DIRECTIONS FOR FUTURE W ORK In this chapter I present the conclusions of my w ork and also gi v e directions for future w ork. 5.1 Conclusion In this w ork, we propose and e v aluate the performance of reliability-based hybrid ARQ schemes for nonf ading A WGN channels. First we in v estigate the performance of reliability-based hybrid ARQ schemes in the absence of an y type of interference. W e begin by e v aluating the performance of RB-HARQ scheme that uses x ed-rate con v olutional codes and e xploits the time-correlation properties of these codes. The proposed scheme achie v es a gain of more thandB o v er a system with no ARQ. W e then further de v elop these schemes to use rate-compatible punctured con v olutional codes in the forw ard channel and source encoding in the feedback channel. The proposed schemes achie v e a perfor mance gain of o v erdB o v er a system with no ARQ. W e also compare the performance of the proposed scheme with the hybrid ARQ scheme that is proposed by Hagenauer [ 7 ] in which rate-compatible punctured con v olutional codes are used. Results, in terms of bit and pack et error probability sho w that the proposed scheme achie v es a performance gain of up to dB o v er the latter when the initial code rate is Throughput results sho w that the proposed scheme achie v es a performance gain of up tondB. The size of the feedback pack et is accounted for in the throughput results. Although the proposed scheme has lar ger retransmission-request pack ets, it achie v es higher throughput at all signal-to-noise ratios than the hybrid-ARQ scheme proposed by Hagenauer [ 7 ]. Ne xt, we in v estigate the performance of RB-HARQ schemes in the presence of a hostile partial-time jammer The proposed schemes use the MAP algorithm to estimate the a 64 PAGE 77 65 posteriori probabilities for the information bits and the jammer state [ 49 ]. Results sho w that the performance of the estimation algorithm is within to dB of the perfect channel side-information case. In terms of pack et error rate, all of the proposed RB-HARQ schemes are sho wn to of fer signicantly better performance than an incremental redundanc y HARQ (IR-HARQ) scheme that has the same o v erhead b ut does not utilize reliability information. W e also presented throughput results that tak e into account the o v erhead of the retransmission-request pack et. An optimal arithmetic run-length coding technique and a suboptimal b ut much simpler run-length coding technique are proposed to compress the retransmission-request pack et for the RB-HARQ(J) scheme, which retransmits the symbols that are estimated to be jammed. The results sho w that RB-HARQ(J) of fers a higher throughput than T ype-I HARQ with pack et combining e xcept at v ery lo w or v ery high. W e also presented performance results for a scheme that adapts the size of the retransmission-request pack et based on the bit reliabilities. This RB-HARQ(R-A) scheme of fers the highest throughput if the o v erhead of the retransmission-request pack et can be ne glected. Thus, adaptation in the HARQ scheme based on reliability is sho wn to be an ef fecti v e means for dealing with hostile jamming. In chapter 4 we propose a ne w channel model that considers the pack et errors due to channel noise as well as those due to interference from simultaneous transmission by other nodes. T o e v aluate the ef fect of collisions that occur due to simultaneous transmissions, we simulate a CSMA-CA based wireless ad hoc netw ork. Dif ferent parameters about the interference that af fects the data pack ets were calculated from the simulation output. These parameters tak e into account the f act that collisions may result in parts of a pack et being corrupted while other parts are recei v ed without corruption. Therefore, the proposed channel model is more realistic than a A WGN channel model and can be used in a cross-layer design approach which considers to combine ARQ at the data link layer and channel coding at the physical layer W e in v estigate the performance in terms of pack et error rate and throughput for the ne w channel model. The results sho w that the de gradation in throughput PAGE 78 66 when we consider the interference is ne gligible. W e also propose a RB-HARQ technique for CSMA-CA-based netw orks that achie v es better performance than T ype-I HARQ under se v eral scenarios. 5.2 Directions for Future W ork The w ork presented in this dissertation can be e xtended in dif ferent directions. It w ould be interesting to e v aluate the channel capacity of the Mark o v channel considered in chapter 3 The performance of dif ferent RB-HARQ schemes can then be compared with the channel capacity The w ork presented in this dissertation considered a non f ading channel model which is not v ery realistic. An interesting study will be to e v aluate the performance of RB-HARQ for f ading channels and compare it with the performance of con v entional HARQ techniques. The w ork presented in chapter 4 can be e xtended by considering f ading as well as interference. Another interesting study w ould be to e xamine the ef fect of node density on the interference po wer and o v erall system performance. PAGE 79 REFERENCES [1] S. 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Xu and T Saada wi, Â“Does the IEEE nnMA C protocol w ork well in multihop wireless ad hoc netw orks?, Â” IEEE Comm. Ma g .. pp. 130Â–137, June 2001. [48] S. McCanne and S. Flo yd, Â“The LBNL netw ork simulator Â” La wrence Berk ele y Laboratory 1997. Softw are on-line: http://www .isi.edu/nsnam/ns, Accessed in June 2005. [49] A. Roongta, J.-W Moon, and J. M. Shea, Â“Reliability-based hybrid arq as an adapti v e response to jamming, Â” IEEE J Select. Ar eas Commun. v ol. 23, pp. 1045Â–1055, May 2005. PAGE 83 BIOGRAPHICAL SKETCH Abhina v Roongta recei v ed the B.T ech. in electrical engineering from the Indian Institute of T echnology Delhi (IITD), India, in 2001 and the M.S. in electrical engineering from the Uni v ersity of Florida in 2003. Since August 2001, he has been w orking to w ards a Ph.D. de gree in electrical and computer engineering at Uni v ersity of Florida, Gainesville. His research interests include error control coding, signal processing and system design for wireless communications. 71 |