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RELIABILITYBASED HYBRIDARQ 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 MonteHall 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 403405. Thanks to Arun for helping me debug my code on several occasions and strengthening my belief that reliabilitybased hybrid ARQ is a practical solution; JangWook 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 "behindthescene" 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 "nonECE" friends and my current and past apartmentmates for making life fun. Thanks to Abhudaya and Nitin, my current apartmentmates, 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 RELIABILITYBASED HYBRID ARQ FOR NONFADING CHAN NELS WITHOUT INTERFERENCE .......... . .. 7 2.1 System M odel ........ ..... .. .. ........... 8 2.2 RBHARQ using Convolutional Codes without Puncturing . 9 2.3 RBHARQ with Variable Redundancy and Smaller Request Packet .12 2.4 RBHARQ with RCPC Codes and Arithmetic Coding . ... 15 2.4.1 Error Probability Comparison of RBHARQ with HARQ with RCPC codes .......... ...... ...... 19 2.4.2 Throughput Comparison of RBHARQ with HARQ with RCPC codes . ......... ... .. ... 20 3 RELIABILITYBASED HYBRID ARQ FOR PARTIALTIME JAM MING CHANNELS ............................ 25 3.1 MAP Estimation Algorithms ... ............ 27 3.2 MaximumLikelihood Estimation of Jammer Parameters . ... 30 3.3 ReliabilityBased Hybrid ARQ Schemes ..... . ..... 31 3.3.1 Analysis of Probability of Packet Error for HARQ . .. 34 3.3.2 Size of retransmissionrequest 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 RELIABILITYBASED HYBRIDARQ FOR CSMACABASED WIRE LESS NETW ORKS ............................ .. 54 4.1 Interference Modelling .. ............ .... 54 4.2 NonFading Channel Model . . . . 57 4.3 Performance of ReliabilityBased HybridARQ in CSMACA 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 RBHARQ scheme with variable redundancy and reduced retransmissionrequest packet .. . 17 2.8 Performance comparison of the proposed RBHARQ scheme with the RCPCHARQ scheme with initial code rate 4/7. . . . 20 2.9 Performance comparison of the proposed RBHARQ scheme with the RCPCHARQ scheme with initial code rate 4/7. . . . 21 2.10 Performance comparison of the proposed RBHARQ scheme with the RCPCHARQ scheme with initial code rate 2/3. . . . 22 2.11 Performance comparison of the proposed RBHARQ scheme with the RCPCHARQ scheme with initial code rate 2/3. . . . 23 2.12 Throughput comparison of the proposed RBHARQ scheme with the RCPCHARQ scheme with initial code rate 4/7. . . . 24 3.1 Communication scenario. . . . . . . 25 3.2 System m odel . . . . . . . . 26 3.3 Twostate 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 RBHARQ(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 RBHARQ(J), TypeI 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 RBHARQ(J), p = 0.4 and E,/Nj = 3 dB . . . .. . . 45 3.8 Probability of packet error for different RBHARQ schemes compared with TypeI HARQ and conventional HARQ, p = 0.4 and E,/Nj = 0 dB. 46 3.9 Probability of packet error for different RBHARQ schemes, p = 0.4 and E,/Nj = 3 dB . . . . . . . 47 3.10 Probability of packet error for adaptive and fixed RBHARQ, p = 0.4 and E /N j = 3 dB . . . . . . . 48 3.11 Throughput for RBHARQ, TypeI HARQ and conventional (uniform) HARQ, after 3 retransmissions at p = 0.4 and E,/Nj = 3 dB. .. 50 3.12 Throughput of adaptive RBHARQ(R), RBHARQ(J), TypeI HARQ and conventional (uniform) HARQ, p = 0.4 and Es/Nj = 3 dB. .. . 52 3.13 Throughput for RBHARQ, TypeI 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 TypeI HARQ with up to 2 retransmissions and PI = 1 .61 4.4 Throughput for RBHARQ and TypeI 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 RELIABILITYBASED HYBRIDARQ USING CONVOLUTIONAL CODES By Abhinav Roongta August 2005 Chair: John M. Shea Major Department: Electrical and Computer Engineering In this work we develop selectiveretransmission hybridARQ protocols for commu nication systems that use softinput softoutput (SISO) decoders. The schemes that we propose are based on reliabilitybased hybridARQ 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 reliabilitybased hybrid ARQ scheme that uses fixed rate convolutional codes in the forward channel and exploits their timecorrelation properties to achieve smaller re transmission requests. Then we extend our work where ratecompatible 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 hybridARQ that uses punctured convolutional codes. The results show that the proposed RBHARQ scheme achieves better performance than a hybridARQ scheme that uses only RCPC codes. Next we extend our work to improve communication performance on partialtime jamming channels. For channels with partialtime 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 RBHARQ 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 (CSMACA). 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 crosslayer 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 RBHARQ technique for CSMACAbased wireless networks. CHAPTER 1 INTRODUCTION Automaticrepeatrequest (ARQ) and forwarderrorcorrection (FEC) are two basic techniques for controlling transmission errors in data communication systems [1,2]. Automatic repeatrequest schemes typically use a highrate errordetecting 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 channelerror rate. An FEC com munication system uses a powerful errorcorrecting 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 packetswitching data networks and computer communication networks. Forwarderror correction is preferred over ARQ in communication systems where return channels are not available or retransmission is not possible for some reason. HybridARQ (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. HybridARQ schemes are broadly classified into TypeI and TypeII hybridARQ schemes. TypeI 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 typeI hybrid ARQ scheme has a lower throughput than its corresponding ARQ scheme. However, typeI 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. TypeII 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 typeII HARQ or the incrementalredundancy 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 errordetection 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 paritycheck bits formed based on the original message and an error correcting and errordetecting 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. TypeII HARQ scheme provides better perfor mance than the typeI HARQ scheme if the code used for error correction and the retrans mission strategy is properly chosen. Incrementalredundancy hybridARQ schemes that use punctured convolutional codes and code combining were proposed by Hagenauer [7]. In these and other hybridARQ 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 ratecompatible 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. Automaticrepeatrequest 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 [812], and adapta tion in the network layer [1317]. The performance of TypeI hybridARQ protocols in a slotted directsequence codedivision multipleaccess 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, partialband interference, and thermal noise. It was shown that adaptiverate coding systems provide significantly higher throughput than sys tems that use fixedrate coding. This is because adaptiverate coding systems use a high rate code, which gives high throughput rate, when channel conditions are good, and use a lowrate 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 slowfrequency 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 signaltonoise 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 nonadaptive in the sense that the response to a packet error is fixed: the entire packet should be retransmitted. Even if hybridARQ 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 (RBHARQ) algorithm that is truly adaptive was proposed by Shea [21]. In RBHARQ, softinput softoutput 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 RBHARQ using turbo codes and convolutional codes over AWGN channel was shown by Kim and Shea [22] and Roongta and Shea [23], respectively. Another RBHARQ scheme that uses received packet reliability to optimize throughput over static and timevarying channels was inde pendently proposed by Tripathi et al. [24]. All of the previous work on RBHARQ [2125] uses the magnitude of the log a posteriori probability (logAPP) 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 selectiveretransmission hybridARQ pro tocols that will efficiently use the softoutput available at the decoder and achieve better performance than the conventional HARQ schemes considered in different research stud ies [320]. 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 softinput softoutput (SISO) decoders. 1.3 Main Contributions In this work we propose and evaluate the performance of selectiveretransmission hybridARQ protocols that significantly improve the performance of communication sys tems that use softinput softoutput 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 hybridARQ 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 reliabilitybased hybridARQ (RBHARQ) 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 ratecompatible 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 RBHARQ to improve communication performance in a hostile amming environment. The proposed scheme uses the logAPP of the information bits and the logAPP 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 runlength arithmetic coding or a suboptimal but less complex source coding to compress the retransmission request packet. We provide a performance comparison of the proposed RBHARQ schemes with the conventional HARQ in which a predetermined set of bits is retransmitted. We propose a new channel model for adhoc 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 RBHARQ technique for wireless networks that use carriersense mul tiple access with collision avoidance (CSMACA) 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 partialtime jamming channels. Chapter 4 presents a new channel model for adhoc wireless networks which can be used to design efficient HARQ protocols. In Chapter 5 we present conclusions and directions for future work. CHAPTER 2 RELIABILITYBASED HYBRID ARQ FOR NONFADING CHANNELS WITHOUT INTERFERENCE In this chapter, we propose and evaluate the performance of RBHARQ 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 RBHARQ 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 (logAPP) 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 softdecision logAPP values with the correct signs for some of the information bits in the packet. The bits that have softdecision logAPP values with incorrect signs result in errors at the decoder output. Analysis of error packets reveals that the decoder can use the logAPP 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 softdecision logAPP values. The bit with the smallest softoutput is considered the least reliable (0), and the bit with the largest softoutput 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 logAPPs 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 softdecision 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 logAPPs to identify the least reliable bits and constructs the retransmissionrequest 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 retransmissionrequest 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 retransmissionrequest packets transmitted over the feedback channel. 2.2 RBHARQ using Convolutional Codes without Puncturing We first investigate the performance of the RBHARQ 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 retransmissionrequest 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 retransmissionrequest 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 softoutputs 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 reliabilitybased hybridARQ with the rate 1/2, constraintlength seven convolutional code. In Figure 2.3 we observe that to achieve a probability of bit error of less than 106, a system using RBHARQ 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 retransmissionrequest 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 tenbit binary number. So, without any compression, the retransmissionrequest packet consisting of 50 leastreliable bit indices, 0 \ 106IIIII"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 retransmissionrequest packet will generally decrease the overall system throughput. In the next section, we present results for a variable redun dancy RBHARQ scheme which has a much smaller retransmissionrequest packet. 2.3 RBHARQ with Variable Redundancy and Smaller Request Packet The RBHARQ 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 logAPP) 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 (timecorrelated). 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 RBHARQ 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 nonzero 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 retransmissionrequest 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 energytonoise 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 retransmissionrequest 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 RBHARQ 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 retransmissionrequest 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 retransmissionrequest packets. Fig ure 2.7 shows that to achieve a probability of bit error of less than 106, 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 RBHARQ 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 retransmissionrequest packet by at least 80 percent at all signal to noise ratio (SNR) values. 2.4 RBHARQ with RCPC Codes and Arithmetic Coding In this section we evaluate the performance of a RBHARQ 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 RBHARQ 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 RBHARQ 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 retransmissionrequest 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 retransmissionrequest packet containing a list of the positions of either 50 or 25 of the leastreliable information bits. The numbers 25 and the positions of either 50 or 25 of the leastreliable information bits. The numbers 25 and 100 No ARQ After 1st retransmission .... After 2nd retransmission After 3rd retransmission 101 102 0 4 105 "\ 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 RBHARQ scheme with vari able redundancy and reduced retransmissionrequest 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 RBHARQ 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 \> \ \ \ 106r \ 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 RBHARQ scheme with vari able redundancy and reduced retransmissionrequest 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 RBHARQ 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 softoutputs 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 retransmissionrequest 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 energytonoise 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 106, 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 103, a system using the proposed RBHARQ 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 105, a system using the proposed RBHARQ 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 102, a system using the proposed RBHARQ 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 retransmissionrequest packets. 2.4.1 Error Probability Comparison of RBHARQ with HARQ with RCPC codes In this section we compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [7] (RCPCHARQ). 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 RCPCHARQ 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 RCPCHARQ scheme is shown in Figures 2.10 and 2.11 using solid lines. In the RBHARQ 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 RBHARQ 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 106, the pro posed RBHARQ scheme requires 2 dB lower E1/No than the RCPCHARQ scheme. In 100 first transmission rate 4/7 0 first retransmission 10  second retransmission 10  third retransmission S fourth retransmission S2 fifth retransmission 103 10 rate 1/2 10 \ n 10 40 \\ \ 0 Z 104 0 :\\\ \ \ \ \ \ 2 \1 0 2 / 1/2 10 S\ \\ \ \ \ \ x 107 \\ \ 18 \1 0. 108 109 3 2 1 0 1 2 3 4 5 E /N (dB) Figure 2.8: Performance comparison of the proposed RBHARQ 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 103, the proposed RBHARQ scheme requires 2 dB lower E,/No than the RCPCHARQ scheme. Thus we conclude that the proposed scheme achieves significant performance improvement over the RCPCHARQ scheme. Note that this gain is achieved at the cost of large retransmission request packets and more retransmissions than in the RCPCHARQ scheme. 2.4.2 Throughput Comparison of RBHARQ 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 retransmissionrequest packet in the proposed scheme. As previously mentioned, the retransmissionrequest packet consists of the 25 least reliable bit positions. 100 101 \ S\ \ \ \ a \ \ \ \ o 1/2\re\ 104 \\ first transmission rate 4/7 \ \ 0 first retransmission \ 105 u second retransmission \ b S  third retransmission  fourth retransmission  fifth retransmission 6 rate 1/2 106  3 2 1 0 1 2 3 4 5 Es /N (dB) Figure 2.9: Performance comparison of the proposed RBHARQ 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 10bit index. Thus each retransmissionrequest packet consists of 250 bits if no source coding is used. However we can apply arithmetic coding to compress the retransmissionrequest packet. The way the compressed retransmissionrequest packet is generated is as follows. The destination radio D constructs an allzero 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 retransmissionrequest 100 10 102 10 0 103 4/7 S:\ n 11/2 106 rate 2/3 \ \ O 10  first retransmission ' 0 second retransmission \ 1 third retransmission \ 1/2 SA fourth retransmission 10  fifth retransmission \ rate 4/7 e rate 1/2 109 3 2 1 0 1 2 3 4 5 Es /N (dB) Figure 2.10: Performance comparison of the proposed RBHARQ 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 retransmissionrequest packet is sent from D to S. Figure 2.12 illustrates the throughput of the RCPCHARQ scheme proposed by Ha genauer [7] and the RBHARQ 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 10 102 \ \ \ .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 RBHARQ 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 RCPCHARQ. The curves labeled RBHARQ 2, 3 and 4 illustrate the performance of the proposed RBHARQ schemes. For RBHARQ2, th retransmissionrequest packet is sent without source coding. For RB ARQ3 retransmissionrequest packet is sent with source encoding at D. RBHARQ4 e rate 1/2 106 3 2 1 0 1 2 3 4 5 Es/NO (dB) Figure 2.notes1: Performance comparisonughput of the proposed RBHARQ scheme without taking into account retransmissionrequest packet. Thus, RBHARQ4 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 RCPCHARQ. The curves labeled RBHARQ 2, 3 and 4 illustrate the performance of the proposed RBHARQ schemes. For RBHARQ2, the retransmissionrequest packet is sent without source coding. For RB HARQ3, retransmissionrequest packet is sent with source encoding at D. RBHARQ4 denotes the throughput of the proposed RBHARQ scheme without taking into account retransmissionrequest packet. Thus, RBHARQ4 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 (RCPCHARQ) of the RCPCHARQ scheme is approxi mately 0.11 while the throughput of the proposed scheme with compressed retransmission request packet (RBHARQ3) is approximately 0.39. The results show that even if we send the retransmissionrequest packet without any source coding, we still achieve a higher throughput (RBHARQ2) than the RCPCHARQ 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 RBHARQ scheme with the RCPC HARQ scheme with initial code rate 4/7. CHAPTER 3 RELIABILITYBASED HYBRID ARQ FOR PARTIALTIME JAMMING CHANNELS In this chapter we extend the RBHARQ 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 timevarying jamming. The jammer is modeled using a discretetime twostate 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: Twostate 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. Matchedfilter 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 zeromean 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 hypertrellis 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 sideinformation, the parameters of the jamming signal (p, E{Tj} and N,/2) can also be estimated using the BaumWelch 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 logAPP 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 backwardlooking state probabilities are determined in the usual way from the branch metrics. The probabilities P(ck = +1ly) and P(ck = ly) 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 logAPP 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 matchedfilter 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 retransmissionrequest packet to S through the feedback channel. In this paper, we assume perfect packet error detection and an errorfree feedback channel. The retransmissionrequest packet contains information about the set of bits that are estimated to be unreliable. The set of unreliable bits is identified using the logAPPs 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 retransmissionrequest 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 Yk, + 2Yk,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 MaximumLikelihood 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. Maximumlikelihood (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 AkI(Z1 AkI(Z1) where N is the number of message bits in the packet and R is code rate. Here Ak(z') is the forwardlooking state probability, Ak (z) is the backwardlooking 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 ReliabilityBased 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 softdecision, maximumlikelihood (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 211 d) (d\pd (lp)add 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 + pIN/ 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 RBHARQ 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 RBHARQ(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 RBHARQ(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 RBHARQ(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 RBHARQ scheme that adapts the number of bits to be retrans mitted based on reliability information. In the RBHARQ(RA) 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 102 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 RBHARQ approaches to conventional approaches in which the set of retransmitted symbols is not adapted based on reliability information. We consider TypeI HARQ schemes in which the entire packet is retransmitted in response to error detection. We consider both the original TypeI HARQ (in which the new packet replaces the previous packet) and TypeI HARQ with packet combining. These schemes retransmit significantly more bits than the RBHARQ 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 RBHARQ 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 reliabilitybased 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 maximumlikelihood (ML) decoding. However, for the simulation results, we employ bitwise MAP decoding. For suf ficiently high signaltonoise ratio, these will match very closely, as the BCJR algorithm becomes more closely approximated by its maxlogMAP form. The maxlogMAP form has been shown to be equivalent to the softoutput 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 TypeI HARQ without packet combining, the packet error probability after one retransmission is given by (Pe)2, where Pe is given in (3.14). For TypeI 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 (IRHARQ) 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) dd, (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 RBHARQ(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)dl2(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 RBHARQ(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 RBHARQ(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 TypeI 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 + 2dd2 d4 dd = oLr2 + r 2o di =0d2=0d3 =0 d4=0 \ \dd= d=O dd2= d4=3 d4 (1 p)2dd2d4. (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 retransmissionrequest 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 bestcase scenario of single feedback bit for the conventional HARQ schemes so that our results are not tied to a particular system. In the RBHARQ 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 retransmissionrequest packet. We calculate the expected value of the size of the retransmissionrequest packet for RBHARQ schemes under different approaches to compress the retransmissionrequest packet. Size of retransmissionrequest packet i ith transmission of uncompressed bit indices: Recall that for the RBHARQ 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 retransmissionrequest 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 retransmissionrequest 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 retransmissionrequest 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 retransmissionrequest packet can be constructed as a bitstream 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 retransmissionrequest packet ii ith runlength 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 runlength 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 RBHARQ(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 retransmissionrequest packet is then given by Nf= . T H(S) (3.24) Size of retransmissionrequest 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 RBHARQ(J). In this simple compression scheme, the retransmissionrequest 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 retransmissionrequest 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 N2 E[B] = E [ B i.=0 N2 = 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 steadystate probabilities of the jammer being in state 0 and 1, respectively. Thus, the average size of the retransmissionrequest 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 energytonoise density ratio, E/,No, and the average symbolenergy to jammernoise 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 BaumWelch 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 RBHARQ(J), which requests retransmission for all symbols that are identified as jammed. The performance of RBHARQ(J) scheme with estimation of all parameters is compared with the case when the decoder has perfect channelside 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 104 No AR CS + No ARQ ML Estimation Es / N (dB) Figure 3.5: Probability of packet error for RBHARQ(J) with estimation of jamming pa rameters or perfect CSI, p = 0.4 and E,/Nj = 3 dB. degrade the performance of RBHARQ. In the next section, we compare the performance of the different proposed RBHARQ schemes with conventional HARQ schemes. We show the results in terms of probability of packeterror and assume perfect CSI for these results. 3.5 Performance Results In this section we compare the performance of the proposed RBHARQ 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 TypeI HARQ with and without packet combining. These scheme retransmit significantly more bits than RBHARQ(J), so we also consider an IRHARQ scheme that retransmits a random set of bits such that the average overhead is the same as for RBHARQ(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, 4Q 0 o 10 104 2 1 0 E1 / N (dB) 3 4 5 6 S 0 Figure 3.6: Probability of packet error for RBHARQ(J), TypeI HARQ and retransmission of a random set of symbols, p = 0.4 and E,/Nj = 3 dB. The results show that to achieve P, = 101, TypeI HARQ without packet combining provides approximately 1.5 dB gain over no ARQ. If TypeI 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 TypeI HARQ schemes. The IRHARQ scheme can achieve P, = 101 with 1.5 dB lower E,/No than TypeI HARQ without packet combining. RB HARQ(J) requires 1.25 dB lower Es/No than incremental redundancy with random re transmissions at P, = 101 and the performance difference increases drastically for lower target values of P. Although RBHARQ(J) requires approximately 1.2 dB to 1.6 dB higher E,/No than TypeI HARQ with packet combining, it only retransmits 40% of the bits of TypeI 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 RBHARQ(J) when three retrans missions are allowed. The results show that combining RBHARQ(J) with TypeI 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 IRHARQ scheme transmits a uniformly spaced set of bits. The results in Figure 3.8 illustrate the packet error rate for different RBHARQ 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 TypeI HARQ in which the entire packet is retransmitted. The results in Figure 3.8 show that all three RBHARQ schemes achieve better per formance than the conventional HARQ approaches that do not employ reliability, except for TypeI HARQ with packet combining, which retransmits significantly more symbols. To achieve a packet error rate of less than 102, the required E,/No for RBHARQ is at 10 \ \\\ O \ 0.. 2 \ 4 102 0 3 10 3 3 (2+1) retransmissions of 3 retransmission of RBHARQ(J) + Type d HARQ RBHARQ(J) with packet combining 104 4 3 2 1 0 1 2 Es /N, (dB) least 3 dB less than for IRHARQ, which retransmits the same number of symbols but does not use reliability information. RBHARQ(R+J) achieves the best performance because it uses both the logAPPs to decide which symbols are to be retransmitted. This scheme performs about 0.25 dB better than RBHARQ(J) in which all jammed symbols are re transmitted. Among all the proposed RBHARQ schemes, RBHARQ(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 RBHARQ(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 IRHARQ 101 2 \ RBHARQ(R) ,, 10 4 0 TypeI HARQ with Type1 HARQ S103 packet combining U 10 \ l RBHARQ(R+J) . 104 RBHARQ(J) 2 1 0 1 2 3 4 5 Es / N (dB) Figure 3.8: Probability of packet error for different RBHARQ schemes compared with TypeI 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 RBHARQ(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 RBHARQ(J)". In the RBHARQ(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 logAPP. This scheme is denoted by "50% LRB jam symbols ARQ" in 100 10 ~ 102 e NoARQ !!! l!!!^ !!! !!! !;! !!!!!!!! !:! !!! ll^^ s^ ^. l : 50 % uniform RBHARQ(J) S10 50 % RBHARQ(R+J) A R B HA R Q (J) . . . . . . . . . . . No jamming s 3 104113 Es / N (dB) Figure 3.9: Probability of packet error for different RBHARQ 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 102, the RBHARQ(R+J) scheme that uses both the softoutputs requires 1 dB less ES/No than the RBHARQ(J) scheme. The performance disparity increases for lower target error probabilities. Thus these results clearly indicate that the RBHARQ scheme that uses both the softoutputs, L(jk) and L(uk), achieves a significant gain over the one that only uses one of the softoutputs. In Figure 3.10, we consider the RBHARQ(RA) 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 = 105 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 102 4/ 3dB. 0 4 104 A RBHARQ(J) e RBHARQ(RA) a E TypeI HARQ  TypeI 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 RBHARQ, 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 RBHARQ(RA), RBHARQ(J), and TypeI 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 102. For E,/No > 0 dB, the adaptive retransmission scheme does achieve packet error probabilities below 102. The real effect of adaptive RBHARQ 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 RBHARQ and conventional HARQ schemes. We first consider the performance of RBHARQ(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 RBHARQ(J) and the conventional HARQ schemes for E,/Nj = 3 dB. As previously discussed, RBHARQ(J) alternates between retransmitting the set of symbols that are estimated to be jammed and complete packet retransmission (as in TypeI HARQ). The size of the retransmissionrequest packet for the conventional HARQ scheme is taken to be 1 bit. The size of the retransmission request packet for RBHARQ is calculated using the formulas in Section 3.3.2. The size of the retransmissionrequest packet composed of bit indices (no compression) is 2000 bits. The average size of the retransmissionrequest packet compressed using arithmetic run length coding, calculated using (3.24), is 282 bits. Thus, using arithmetic coding helps in reducing the size of retransmissionrequest packet by almost 85 percent. For RBHARQ(J) with the simple compression scheme, the average size of the retransmissionrequest packet is 462 bits. The results in Figure 3.11 show that despite larger retransmissionrequest pack ets, RBHARQ(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) TypeI 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 RBHARQ(J) with 0.4 arithmetic coding 0.35 35 TypeI HARQ with packet combining RBHARQ(J) with S0.3 i simple compression 5 0.25 0.2  Uniform HARQ 0.15 0.1 TypeI HARQ 0.05 0&^A" AA'"i 3 2 1 0 1 2 3 4 5 E / N (dB) Figure 3.11: Throughput for RBHARQ, TypeI 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 retransmissionrequest packet achieves throughput close to that achieved by using optimal arithmetic runlength coding. The results in Figure 3.12 show the throughput for RBHARQ(RA) in comparison with RBHARQ(J) and the conventional schemes. Recall that in RBHARQ(RA), 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 103 offered the best throughput for the range of Es/No and jammer parameters considered in our work. We show two curves for RBHARQ(RA), one in which the overhead is determined based on the retransmissionrequest 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 retransmissionrequest 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 retransmissionrequest packet can be ignored or significantly reduced through compression, then RBHARQ(RA) achieves the best throughput at all values of E/,No. This is because adaptive RBHARQ(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 retransmissionrequest packet in throughput calculations, adaptive RBHARQ(R) performs better than conventional HARQ and TypeI 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 RBHARQ(RA) 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 retransmissionrequest packet, RBHARQ(RA) achieves the best performance over all p. Thus the RBHARQ(RA) scheme can effectively adapt the set of retransmitted bits to different values of p. The RBHARQ(J) scheme achieves the same performance as RBHARQ(RA) for p < 0.5 For higher values of p, the overhead in the retransmissionrequest packet reduces the performance of RBHARQ(J). Above p = 0.58, TypeI HARQ with packet combining outperforms RBHARQ(J). This suggests that if p is estimated to be very high, then the RBHARQ(J) scheme can be simply modified to request retransmission of the whole packet. Note that neither TypeI HARQ without packet ._ .. RBHAF 0) arithmeti D0.25 E>e 0.1 IRHARQ RBHARQ(RA) with IRARQ 0.1 feedback overhead STypeI HARQ 0.05  3 2 1 0 1 2 3 E / N (dB) Figure 3.12: Throughput of adaptive RBHARQ(R), RBHARQ(J), conventional (uniform) HARQ, p = 0.4 and E,/Nj = 3 dB. TypeI HARQ and combining nor IRHARQ are competitive techniques for dealing with jamming except at very low values of p. ' U. \ lII IIIIL ^uu IIy 0) 0.25 .  0 0A  0.2  \ X \ '^ ^0^ 0 0.15 RBHARQ(RA) with 0.1 feedback overhead 0.05 IRHARQ TypeI HARQ 0 i ~~~Q  6  6  = p (Probability a symbol is jammed) Figure 3.13: Throughput for RBHARQ, TypeI HARQ and conventional (uniform) HARQ as a function ofp at E,/No = 0 dB, E,/Nj = 3 dB. CHAPTER 4 RELIABILITYBASED HYBRIDARQ FOR CSMACABASED WIRELESS NETWORKS In this chapter we explore the application of reliabilitybased hybridARQ (RBHARQ) in wireless networks. Wireless networks are strongly affected by errors caused by fading and collisions. Carriersense multiple access with collision avoidance (CSMACA) 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 CSMACA 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, crosslayer 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 crosslayer 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 adhoc networks [44] is based on IEEE 802.11 [45]. The IEEE 802.11 specifies two modes of MAC protocol: distributed coordination function (DCF) mode for ad hoc networks and point coordination function (PCF) mode for infrastructurebased networks. The DCF in IEEE 802.11 is based on CSMACA and uses the RTSCTSDATAACK 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 multihop adhoc networks with mobile nodes [46,47]. This is because issues like hiddennode 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 adhoc 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 bitrate 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 waypoint 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 NonFading Channel Model As mentioned previously, any crosslayer 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 zeromean 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 102 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 interframe 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 TypeI 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, backoff 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 errorcorrecting 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 TypeI HARQ with up to 2 retransmissions and P1 = 1 4.3 Performance of ReliabilityBased HybridARQ in CSMACABased Networks In this section we propose a RBHARQ technique for CSMACAbased networks and compare its performance with TypeI HARQ. First we describe the RBHARQ 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 logAPP 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 RBHARQ (50%, CWmin) 0.6 STypeI HARQ O_ 0.5 0.4 0 RBHARQ (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 RBHARQ and TypeI HARQ with up to 2 retransmissions and AWGN channel The results in Figure 4.4 show the throughput achieved by the proposed RBHARQ scheme and the TypeI 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 RTSCTS 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 backoff, 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 logAPP for each section. These logAPPs 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 "RBHARQ(50%)" denotes the throughput of the RBHARQ technique when only half of the payload is transmitted in response to the NACK. The results show that RBHARQ achieves better throughput than the TypeI HARQ for all E,/No in the range 3 to 2 dB. This is because for each error packet RBHARQ 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 TypeI HARQ. With the RbHARQ 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 "RBHARQ (50%, CWmin)" shows that there is a marginal improvement in throughput by keeping the contention window size fixed. The curve labelled "RBHARQ (25%, CWmi)" shows the throughput of RBHARQ 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 TypeI 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, RBHARQ 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 reliabilitybased hybrid ARQ schemes for nonfading AWGN channels. First we investigate the performance of reliabilitybased hybrid ARQ schemes in the absence of any type of interference. We be gin by evaluating the performance of RBHARQ scheme that uses fixedrate convolutional codes and exploits the timecorrelation 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 ratecompatible 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 ratecompatible 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 retransmissionrequest packets, it achieves higher throughput at all signaltonoise ratios than the hybridARQ scheme proposed by Hagenauer [7]. Next, we investigate the performance of RBHARQ schemes in the presence of a hos tile partialtime 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 sideinformation case. In terms of packet error rate, all of the proposed RBHARQ schemes are shown to offer significantly better performance than an incremental redun dancy HARQ (IRHARQ) 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 retransmissionrequest packet. An optimal arithmetic runlength coding technique and a suboptimal but much simpler runlength coding technique are proposed to compress the retransmissionrequest packet for the RBHARQ(J) scheme, which retransmits the sym bols that are estimated to be jammed. The results show that RBHARQ(J) offers a higher throughput than TypeI 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 retransmissionrequest packet based on the bit reliabilities. This RBHARQ(RA) scheme offers the highest throughput if the overhead of the retransmissionrequest 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 CSMACA 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 crosslayer 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. 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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. 