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PAGE 1 1 MULTI USER INTERFERENCE REDUCTION AND THROUGHPUT ENHANCEMENT IN OFDM BASED MULTICAR RIER COMMUNICATION SYSTEMS By KYOUNGNAM SEO 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 FLO RIDA 2009 PAGE 2 2 2009 Kyoungnam Seo PAGE 3 3 To my Parents and Family PAGE 4 4 ACKNOWLEDGMENTS First of all I would like to thank my parents who ha ve kept encouraging and inspiring me to pursue my dream in many ways with unconditional love. I also have to thank my lovely wife, Juhee Kang, who willingly dedicated her drea m and life to me for my dream and brought two precious lives, Youjee and Minhy o ung. For all of this I will always be grateful and in awe of her. I also t hank my parents in law for their ceaseless support and belief on me. I also thank my sister and all the family members for their endless love for me. I thank my academic advisor, Dr. Haniph A. Latchman for his patient guidance, encouragement and plentiful advice until I can successfully finish my Doctoral research I would also like to thank the members of my PhD. committee, (Prof. Fred J. Taylor, Prof. Janise McNair, and Prof. Norman Fitz Coy ). I am grateful for their willingness to serve on my committee a nd their helpful advice I also thank my colleagues at Laboratory for Information Systems and Tele communications (LIST ) in ECE department F or their many helpful and friendly discussion that a lways gave me a new realization I w ill never forget. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 TABLE OF CONTENTS ................................ ................................ ................................ ................. 5 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRACT ................................ ................................ ................................ ................................ ... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 12 Historical Background and OFDM B ased Standards ................................ ............................. 12 MC CDMA Systems ................................ ................................ ................................ .............. 13 Power Line Communication Systems ................................ ................................ ..................... 15 Imp ulsive Noise Mitigation in PLC S ystems ................................ ................................ .. 16 Spread Spectrum Scheme in PLC Networks ................................ ................................ ... 17 Contribution and Organization ................................ ................................ ............................... 18 2 THE PRINCIPLES OF OFDM ................................ ................................ ............................... 20 Conceptual Description of OFDM ................................ ................................ .......................... 20 Mathematical Description of OFDM ................................ ................................ ...................... 21 3 JOINT TRANSCEIVER OPTIMIZATION IN OFDM BASED MC CDMA SYSTEMS ... 28 Introduction ................................ ................................ ................................ ............................. 28 System Model ................................ ................................ ................................ ......................... 28 Spatially Dependent Fading ................................ ................................ ............................ 31 Spatially Independent Fading ................................ ................................ .......................... 32 Joint Optimization of Transmitter and Receiver ................................ ................................ .... 34 Receiver Optimization ................................ ................................ ................................ ..... 34 Transmitter Optimization ................................ ................................ ................................ 39 Simulations and Comparisons ................................ ................................ ................................ 41 Conclusions ................................ ................................ ................................ ............................. 46 4 POWER LINE COMMUNICATIONS ................................ ................................ .................. 47 PLC History and Competitions ................................ ................................ ............................... 47 PLC Medium ................................ ................................ ................................ .......................... 49 HomePlug AV PHY ................................ ................................ ................................ ............... 50 PAGE 6 6 5 IMPROVED IMPULSIVE NOISE DETECTION IN POWER LINE COMMUNICATION SYSTEMS ................................ ................................ .......................... 54 Introduction ................................ ................................ ................................ ............................. 54 I mpulsive Noise Mitigation in P ower Line N etworks ................................ ............................ 54 T ighter T hreshold S etting ................................ ................................ ................................ ....... 58 S imulations ................................ ................................ ................................ ............................. 60 Scenarios and Impulsive N oise Data ................................ ................................ ............... 60 Primary Simulations: Parameter Setting ................................ ................................ ......... 65 Performance Comparison ................................ ................................ ................................ 67 Performance Tests in the Real Power Line Networks ................................ ..................... 69 Lab Test Results ................................ ................................ ................................ .............. 71 C onclusions ................................ ................................ ................................ ............................. 75 6 UNIVERSAL ALGORITHM OF IMPULSIVE NOISE DETECTION IN PLC SYSTE MS ................................ ................................ ................................ .............................. 76 Introduction ................................ ................................ ................................ ............................. 76 Threshold Setting and Impulsive Noise Detection ................................ ................................ 77 Simulations ................................ ................................ ................................ ............................. 80 Conclusions ................................ ................................ ................................ ............................. 81 7 ADAPTIVE SUB CARRIER ALLOCATION ALGORITHM IN SS MC MA BASED PLC SYSTEMS ................................ ................................ ................................ ...................... 82 Introduction ................................ ................................ ................................ ............................. 82 System Model ................................ ................................ ................................ ......................... 83 Power L ine C hannel and B it L oading ................................ ................................ .................... 86 Subchannel A llocation A lgorithm ................................ ................................ .......................... 89 Simulations ................................ ................................ ................................ ............................. 91 Conclusions ................................ ................................ ................................ ............................. 95 8 CONCLUSIONS AND FUTURE RESEARCH DIRECTION ................................ .............. 96 LIST OF REFERENCES ................................ ................................ ................................ ............... 99 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 105 PAGE 7 7 LIST OF TABLES Table page 1 1 OFDM based standards and products ................................ ................................ ................ 13 5 1 Average SNR i n the case of CP length 1052 ................................ ................................ ..... 67 5 2 Average SNR in the case of CP length 5028 ................................ ................................ ..... 69 6 1 False Impulse Detection Threshold Rate (%) ................................ ................................ .... 81 7 1 Proposed Subchannel Allocation Algorithm ................................ ................................ ..... 90 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Compari son of the bandwidth utilization for FDM and OFDM ................................ ........ 20 2 2 Block diagram of the transmitter for the k th transmitter ................................ .................... 21 3 1 Block diagr am of OFDM based MC CDMA system ................................ ........................ 29 3 2 Performance comparison between MC CDMA schemes and DS CDMA schemes when K=10, N=10, M=2, L=0 ................................ ................................ ........................... 42 3 3 Average transmit power updates with K=16, N=16, M=2, L=5 ................................ ........ 43 3 4 Performance comparison among a number of MC CDMA system models when K=16, N=16, L=5 ................................ ................................ ................................ ............... 44 3 5 Performance comparison among the joint algorithm and existing algorithms in MC CDMA systems when K=16, N=16, M=2, L=5 ................................ ................................ 45 4 1 HomePlug AV Transceiver ................................ ................................ ................................ 51 5 1 Impulsive noise Detection Flow Chart ................................ ................................ .............. 55 5 2 Windowing and averaging for 1052 CP size ................................ ................................ ..... 57 5 3 Averaging for 5028 CP size ................................ ................................ ............................... 57 5 4 SmImp noise ................................ ................................ ................................ ...................... 61 5 5 Hair Dryer noise ................................ ................................ ................................ ................. 61 5 5 Hair Dryer noise ................................ ................................ ................................ ................. 63 5 6 Dimmer noise ................................ ................................ ................................ ..................... 63 5 7 Electrical drill noise ................................ ................................ ................................ ........... 64 5 8 Receive signal with typical impulsive noise in power line communication ...................... 64 5 9 P erformance comparison using various detection parameters ................................ ........... 65 5 10 Threshold s caling f actor ................................ ................................ ................................ ..... 66 5 11 PHY data rates for the short CP ................................ ................................ ......................... 70 5 12 Lab Test results with a Hair dryer in use ................................ ................................ ........... 72 PAGE 9 9 5 13 Lab Test results with a n Electrical Drill in use ................................ ................................ .. 72 5 14 Lab Test results with a Dimmer in use ................................ ................................ .............. 73 5 15 Lab Test results with a Lamp in use ................................ ................................ .................. 73 5 16 Lab Test results with a Yard Lamp in use ................................ ................................ ......... 75 6 1 Performance comparison: single impulse and a burst of impulses ................................ .... 80 7 1 Block diagram of the adaptive SS MC MA system ................................ .......................... 84 7 2 Independent channel responses of four user scenario ................................ ........................ 89 7 3 Correlated channel responses of five users regarding distance attenuation ....................... 92 7 4 Throughput performance comparison ................................ ................................ ................ 93 7 5 Throughput performance comparison along with channel attenuation .............................. 94 PAGE 10 10 Abstract of Dissertation Pre sented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MULTI USER INTERFERENCE R EDUCTION AND THROUGHPUT ENHANCEMENT IN OFDM BASED MULTICARRIER COMMUNICAT ION SYSTEMS By Kyoungnam Seo August 2009 Chair: Haniph A. Latchman Major: Electrical and Computer Engineering Orthogonal frequency division multiplexing (OFDM) uses a number of closely spaced orthogonal sub carriers to transmit data. OFDM based multi ca rrier modulation schemes have a vast variety of applications in current wireless and wired communication systems, which require high speed data rate s Th e popularity of these OFDM based schemes comes from their primary advantage over single carrier schemes : the ability to convert a frequency selective channel into parallel distinctive frequency flat sub channels orthogonal to each other. T his results in a simplified equalization and the elimination of inter symbol interference (ISI) without loss of bandwid th efficiency. T his dissertation considers three OFDM based system models Multi Carrier Code Division Multiple Access (MC CDMA), Discrete Multi Tone (DMT) in power line communication (PLC) systems and Spread spectrum Multi carrier Multiple Access (SS MC MA ) in PLC networks. MC CDMA is the combination of OFDM and a CDMA spread spectrum technique, which enables multi user channel access. In MC CDMA systems, multi user interference (MUI) comes from t he destruction of code orthogonality by the channel convers ion process of OFDM. W e study MUI suppression techniques and propose a joint algorithm of minimum mean square error PAGE 11 11 ( MMSE ) multi user detector and transmit power control, which results in an enhanced signal to noise ratio (SNR) and reduced transmit power c onsumption. In PLC systems, OFDM is combined with a bit loading algorithm to increase throughput. S ince the number of bits to carry at each sub carrier is assigned by the SNR level, the throughput of the system is directly affected by impulsive noise. O u r study focuses on the detection and mitigation of impulsive noise in PLC networks. W e propose a time domain impulsive noise mitigation algorithm. T his two step iterative algorithm improves the data rate by up to 15 percent with a small addition of one OFD M block size memory. Finally, we consider SS MC MA systems that take advantage of DMT s adaptive bit loading technique and CDMA s multi user channel access. T o further increase the throughput, we propose a dynamic sub carrier allocation algorithm in SS MC MA based PLC systems. S ystems with the proposed algorithm show the average throughput increase up to 2 0 percent comparing to the conventional DMT systems and 1 0 percent comparing to the existing SS MC MA based PLC systems PAGE 12 12 CHAPTER 1 INTRODUCTION Histor ical B ackground and OFDM B ased S tandards OFDM based multi carrier modulation systems are well su ited for high data rate multimedia services due to their ability to convert frequency selective fading channels to distinct flat fading channels With this conv ersion, the equalization process can be much simplified Inter symbol Interference (ISI) can also be easily removed by adding the guard interval. The first OFDM scheme was proposed in 1966 [1 ] for dispersive fading channels. T he idea was to use parallel d ata streams and FDM with overlapping subchannels to avoid the use of high speed equalization and to combat impulsive noise and multipath distortion The concept would also all the full use of the available bandwidth. Since then, tremendous research effort s have taken place in the evolution of OFDM. One of the major contributions was made by Weinstein and Ebert [2 ]. In their work, the discrete Fourier transform (DFT) was employed to replace the banks of sinusoidal generators and the demodulators, which sign ificantly reduces the implementation complexity of OFDM modems. This is even more simplified by using low cost /low complexity fast Fourier transform (FFT) devices which is one of the major advantages of OFDM systems Although the concept of OFDM was pr o posed in 1966 [2 ], it did not reach sufficient maturity for employment in standard systems until the 1990s [3 ] The European digital audio broadcast (DAB) wa s the first OFDM based standard for digital broadcasting system s Currently, this digital multi ca rrier modulation scheme i s be ing applied in a wide variety of practical wireless and wired communication systems and extended with multiple accesses in a 4 th generation mobile communication standard. Table 1 1 shows a summary of existing OFDM based standar ds and products. PAGE 13 13 Table 1 1 OFDM based standards and products Wired systems Wireless systems 4G mobile Comm. standards ADSL and VDSL Powerline Communication Multimedia over Coax Alliance Wireless LAN Wireless PAN and UWB DAB, DVB 3GPP LTE WiMAX WiBRO W e consider three OFDM based system models in this work. One is the OFDM based MC CDMA system where we propose a joint MUI reduction algorithm which enhance s SINR and reduce s transmit power. Another is DMT in PLC systems where we propose impulsive noise det ection and a mitigation algorithm to enhance system SNR. T he last is SS MC MA in PLC systems where we propose a dynamic sub carrier allocation algorithm which significantly increases system throughput. MC CDMA Systems As a promising candidate for high dat a rate wireless multimedia services, MC CDMA relies on FFT based OFDM technology to convert frequency selective fading channels into parallel frequency flat fading channels, thereby reducing receiver complexity [ 4 5 ] The converted frequency flat fading c hannels may be independent or dependent depending on the order of the frequency selectivity. However, even if orthogonal spreading codes are employed, the different fading effect s on each sub carrier will eliminate the mutual orthogonality and induce multi user interference, especially in the uplink scenario. When users are at different distances from the base station, the so t ermed near far effect also emerges. Hence, MC CDMA systems are essentially interference limited. T o suppress interference, multiuser detectors are often employed at the receiver [ 6]. Multiuser detectors are temporal filters which exploit the structure of MUI Among multiuser detectors, the linear minimum mean square error (MMSE) multiuser detector is gaining popularity by providing a go od balance between complexity and performance [ 6]. It has also PAGE 14 14 been noticed that employing an antenna array at the base station help s suppress multiuser interference by exploiting spatial diversity. A widely used method in array processing is to build a fi lter which is matched to the array response of the user combine the array observation through the filter, and then make bit decisions for the user. A performance analysis of MC CDMA systems using an antenna array at the base station was presented [7, 8 ]. The c ombined application of multiuser detection and array processing in MC CDMA sy stems was also investigated [9 ], where the combined approach was shown to outperform the individual ones. In addition to these receiver processing techniques, transmitter opt imization such as power control has been shown to mitigate the near far effect by balancing the received power of all users so that no user creates excessive interference for others while maintaining a certain SINR requirement which is the deciding factor of the system's quality of service (QoS). In single carrier direct sequence (DS ) CDMA systems, there has been a significant amount of research on transmitter power control [10]. However, only a few investigations have been carried out for multi carrier s ystems. Several papers [11, 12, 13, 14 ] propose an optimum power allocation across multiple sub carrier s while requiring a high feedback overhead of 80 %. Others (see e.g. [15, 16 ]) suggest power allocation across bands of sub carrier s while still others [1 7, 18, 19 ] implement power allocation across multiple users where power control algorithms are combined with successive interference cancelation multiuser detectors. In this work we investigate the joint optimization of power control, multiuser detection and array processing in MC CDMA systems, where power control is affected as transmitter optimization and multiuser detection and array processing are implemented as receiver optimization. In contrast with the algorithms [20] for DS CDMA systems in an addi tive white Gaussian noise (AWGN) channel, here we consider MC CDMA systems in frequency selective PAGE 15 15 channels. The objective of the joint algorithm is to minimize the transmit power while achieving the target SINR without modifying the power allocation across multiple sub carrier s. Depending on the antenna spacing, the channels between the transmitter and each element of the receive antenna array can be either dependent or independent. Hence, our system models are specified for both cases. It is important to n ote that while frequency selectivity induces multiuser interference in MC CDMA systems, it also introduces multipath diversity which can in fact enhance system performance. We consider a decentralized linear MMSE multiuser detector as [21 ] by treating oth er users' signals as interference and using the SINR of individual users as the optimization criterion. Power Line Communication Systems Power lines, being ubiquitously deployed as a wire line network for car rying electrical power, are the obvious choice as the medium for communication amongst the superabundance of home based and personal devices. They offer the convenience of already being in place and having outlets in almost all locations in a household for easy access. Further, devices can easily obtai n electric power if they are deployed on PLC systems, while wireless mobile devices rely on batteries and thus have difficulty maintaining continuous power. PLC systems, however, are not free of problems. The PLC channel is notorious for electric noise an d interference, as well as channel variability depending on the appliances that are in use at various time s T o make communication more reliable through PLC channel s our study focuse s on an impuls ive noise detection algorithm. W e also consider PLC systems combined with a spread spectrum scheme, which takes advantage of multiple access and adaptive bit loading for high data rate s PAGE 16 16 Imp ulsive Noise Mitigation in PLC S ystems Impulsive noise is a short burst of energy consisting of either a single impulse or a series of impulses which are non Gaussian. Impulsive noise is present in power line networks is highly unpredictable, and is highly damaging to the performance of multi carrier systems [ 22 2 3 ]. Most impulsive noise mitigation algorithms operate in the time domain and require impulse detection identifying which time domain samples are affected by impulsive noise and impulse processing operating on those time domain samples to improve overall SNR [ 24 25 ]. Time domain impulse detection is based on the assumption that the amplitudes of impulsive noise samples are larger than the amplitudes of the desired signal samples. When the amplitude of an impulsive noise sample is much larger than the amplitude of a signal sample, its detection is relatively simp le and the algorithm works well. A lgorithms that are based in the frequency domain detect impulsive noise samples with a significant magnitude over a relatively large number of time domain samples that are concentrated in a narrow frequency band [ 25 ]. This type of algorithm requires additional FFT and IFFT steps. Some algorithms are based on decision directed noise estimation, which show the ability to detect impulse noise sample s that are smaller than the amplitude of a signal sample [ 26, 27 ]. T hese types of algorithm s also require additional FFT and IFFT, as well as an estimation of impulses based on the primary signal detection result. Thus, b ecause of their computational simplicity, time domain impulse mitigation algorithms are more widely employed in cu rrent power line communication system s and will be the focus of this chapter T o zero in on impulsive noise locations, it is important to set a detection threshold that works well to separate signal samples from noise samples. A simple way of setting a de tection threshold is to base it relative to the upper and lower limits of the ADC inputs (ADC rails). Alternatively, the threshold can be chosen to be proportional to the average received power of PAGE 17 17 the signal. This second method typically requires more comp utations and memory, but can result in sup erior performance. In this work we propose two iteratively computed threshold setting algorithm s One wa s developed through an exhaustive number of simulations and the other wa s obtained by the analytical study o f the characteristics of impulsive noise. Both algorithm s compute a threshold that performs well in all test cases with the added benefit of also reduc ing the memory requirement compared to conventional signal envelope based threshold setting. T he propose d simple two step iterative algorithm s require only limited additional memory of OFDM symbol size Spread Spectrum Scheme in PLC Networks Since the spread spectrum technique has been considered to be robust against interference and able to operate multiple access systems the combination of OFDM multi carrier modulation and the spread spectrum technique ha ve been applied in PLC systems. The p erformance of power line communication systems using multi carrier code division multiple access (MC CDMA) and OFDM a re compared [ 28 ] with equal number s of bits assignment for all subchannels. MC CDMA PLC systems are proposed as high speed data rate communication systems with the aid of an advanced signal processing technique [ 29 ]. The p erformance of MC CDMA systems is c onsidered with impulsive noise [ 30 31 ]. I n contrast with prescribed systems that consider only down link scenarios [ 32 33 ] considered uplink scenarios with multi user detection techniques to counteract the multiple access interference. H owever, none of the MC CDMA systems consider a bit loading scheme like that used in OFDM based PLC systems. A s an interesting alternative to MC CDMA, spread spectrum multi carrier multiple access (SS MC MA) has been proposed [ 34 35 ]. A lthough SS MC MA is a multiple acces s scheme based o n OFDM as MC CDMA, it does not require a multiuser detector and take s advantage of the spread spectrum technique. Moreover, this scheme can employ a bit loading technique that PAGE 18 18 serves as the major factor in increas ing systems data rate s PL C systems based on SS MC MA schemes are proposed [ 36 37 ], where bit loading with the proposed multi user dynamic subchannel allocation algorithm is employed. I ts performance in terms of data rate is compared with the PLC systems based on the OFDM scheme. Although the proposed subchannel allocation algorithm performs well in some circumstances, its performance in terms of data rate will be degraded when any user h as poor channel condition s T his performance degradation is caused by the strict fairness consi deration in which the algorithm always tr ies to allocate the subchannels with priority going to the user with the poorest channel condition. In this work we propose a dynamic channel allocation algorithm that maximizes the systems data rate s while sligh tly relaxing the fairness consideration Contribution and Organization T he systems considered in this work are based on OFDM based multi carrier modulation There are two main focuses in this work : to mitigate Multi user Interference ( MUI ) in multi user mu ltiple access environments and to achieve a very high data rate in PLC systems. In our proposed MC CDMA systems, we improve the SNR by reducing MUI. To do this we present a joint algorithm that combines a power control algorithm at the transmitter and M MSE multiuser detection at the receiver with antenna array processing Interestingly, the frequency selectivity that causes MUI also provides multipath diversity which can help suppress MUI I n addition to mitigat ing MUI, the transmitter power control als o helps reduc e the total transmit power. In PLC systems, a high data rate is achieved by bit loading which assigns the number of bits by SNR on each sub carrier. The SNR of a system can be lowered in the entire frequency band by impulsive noise since the impulsive noise in the time domain is transformed as constant like noise in the frequency domain. T o enhance SNR, we propose time domain impulsive noise PAGE 19 19 detection algorithms based on an excessive number of simulation s and the characteristics of the impuls ive noises in the PLC channel. T o increase the data rate, we apply the SS MC MA scheme. This is a good alternative for MC CDMA since it does not suffer from MUI but can be combined with bit loading. W e propose an adaptive subcarrier allocation algorithm to further increase the data rate of the PLC systems. The remainder of this manuscript has the following organiz ation. C hapter 2 presents a brief overview and the mathematical derivation of the OFDM scheme. C hapter 3 describes the proposed joint transceiver optimization algorithm of the transmitter power control and MMSE MUD with array processing in MC CDMA systems. In chapter 4, PLC channel characteristics and a current physical layer specification are presented. I n chapter 5, impulsive noise mitigation alg orithm s in power line networks are proposed, where the detection threshold parameters are selected empirically after a massive number of simulation work. C hapter 6 proposes an impulsive noise detection algorithm using the statistical characteristics of imp ulsive noise in PLC systems. In chapter 7, SS MC MA based PLC systems are described C onclusions and a future research direction follow. Notation : We use lower case letters to denote scalars, lower bold case letters to denote vectors, and bold upper case letters to denote matrices. represents an identity matrix, represents an null matrix, and diag{ } represents a diagonal matrix whose di agonal entries are elements from the vector We use and to denote the conjugation, Hermitian, and transposition operations, for an N point FFT matrix, for expectation, fo r a convolution operator, and := for ``is defined as''. PAGE 20 20 CHAPTER 2 THE PRINCIPLES OF OF DM Conceptual D escription of OFDM OFDM is a digital modulation scheme using a parallel data transmission in w hich a wideband signal is split into a number of narrowband signals. I n a conventional serial data system, the symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth. I n a para llel data transmission system, multiple symbols are transmitted at the same time, where the data is divided among large number of closely spaced carriers. Therefore, only a small amount of the data is carried on each carrier and by this lowering of the bit rate per carrier, the influence of inter symbol interference is significantly reduced. Fig ure 2 1 Comparison of the bandwidth utilization for FDM and OFDM W hen an efficient use of band width is not required, the most effecti ve parallel system uses FDM where the total signal frequency band is divided into multiple non overlapping frequency subchannels. Each subchannel is modulated with a sepa rate symbol and the subchannels are frequency multiplexed. I n such a system, there is sufficient guard space between adjacent subchannels to isolate them at the receiver using conventional filters. In OFDM, the total frequency band is divided into overlapping frequency subchannels that are mutually orthogonal. Orthogonality can be achieved by carefully selecting carrier spacing, such as letting the carrier spacing be equal to the reciprocal of the useful symbol period. T he DFT transform is used at the PAGE 21 21 OFDM transmitter to map an input signal onto a set of orthogonal sub carrier s. T he sinusoid s of the DFT form an orthogonal basis set and a signal in the vector space of the DFT can be represented as a linear combination of the orthogonal sinusoids. T he DFT is used at the receiver again. S ince the orthogonal basis func tions of the DFT are uncorre lated, the correlation performed in the DFT for a given sub carrier only sees energy for that corresponding sub carrier T his separation of signal energy is the reason that the OFDM subchannels can overlap without causing interference. Using this method, b oth transmitter and receiver can be implemented using efficient FFT techniques that reduce the number of operations form in DFT, down to Mathematical Description of OFDM W e present the mathematical de scription of OFDM in this subsection in order to see how the signal is generated and how receiver must operate. This also makes us a clear understanding of the effects of imperfections in the transmission channel. Consider an OFDM system with N sub carrier s where the number of transmitters and receivers are K and M, respectively. Figure 2 2 Block diagram of the transmitter for the k th transmitter The continuous time signal at the output of the k th transmitter's digital to anal og convertor (DAC) can be expressed as PAGE 22 22 (2 1) where represents the transmit power of the th transmitter, is the discrete time signal resulting from the transmitter processing, and is the transmitter filter with duration The signal then propagates through a frequency selective channel before arriving at the Figure 2 3 Block diagram of the receiver th element of the receive antenna array. Denoting the receiver filter as we can represent the overall channel impulse response between the th transmitter and the th receiver as As in [38 ] the overall channel will be regarded as quasi static. In other words, the channel response remains invariant within the channel coher ence time, but can change independently after that. The corresponding antenna response of the signal over the overall channel is denoted as Hence, the received signal at the output of the th receiver filter can be expressed as (2 2) PAGE 23 23 where the antenna response corresponds to the T c delayed channel h k,m (t lT c ) and rep resents the AWGN. The sampled output of the DAC operating at the chip rate is given by (2 3) where the summation is limited from to with being the channel order determined by the maximum multipath delay and the sampling period in which is the index of the discrete time equivalent channel taps is the corresponding antenna response to be specified in the next chapter according to the different system models, and is the sampled AWGN. When adjacent symbols interfere with each other and the inter symbol interference (ISI) emerges. Partitioning and converting the sampled output into blocks of size where is an arbitrary integer greater than the input output (I/O) relationship with ISI can be reformulated in terms inter block interference (IBI). Specifically, the I/O relationship of the th block can be expressed as (2 4) where is a AWGN vector, is a lower triangular Toeplitz matrix and is a upper triangular Toeplit z matrix which can be expressed as PAGE 24 24 In OFDM systems, the orthogonality of subchannels created by inverse FFT can be maintained and individual subchannel s can be separated by FFT at the receiver if the delay spread is not longer than the symbol duration. T he longer delay spread than the symbol duration will cause two problems, which are ISI and inter carrier interference (ICI). In order to solve these problems, a guard time is introduced. It is clear that the IBI can be removed either by padding zero s (ZP) at the end of each block However, ZP still does not treat ICI. To reduce ICI, OFDM symbols are cyclically extended into the guard tim e in such a way that cyclic prefixing the last symbols to the head of each block. Both the ZP and the CP options can be adopted and compared by a multi carrier transmission system [38 ] W ith its ability of reducing ICI here we w ill focus on the CP option. The insertion of CP can be represented with the CP inserting matrix where By pre multiplying the th information symbol b lock with we obtain the th CP inserted signal vector as depicted in Fig 2 2 Since PAGE 25 25 now contains the redundancy, the CP ca n be removed at the receiver by the CP removing matrix The CP insertion and removal processes can be regarded as left and right multiplying the channel matrices and by and respectively. Since all the non zero elements of are contained in its first rows, the product turns out to be an all zero matrix, which removes the IBI. In addition, the product is a circulant Toeplitz matrix, which we will henceforth denote as As a result, the th received signal block after CP removal can be expressed as (2 5) where is an AWGN vector. As we can see from Eq. ( 2 5), the CP insertion and removal proce ss converts an ISI channel into an IBI free channel with a circulant channel matrix [38 ]. T he circulant channel matrix ensures removal of ICI. For notational convenience, we will drop the block index hereafter. OFDM systems are implemented using a combination of FFT and IFFT blocks in practice. A t the transmitter of OFDM systems, the source symbols are treated as if they are in the frequency domain. Thus, IFFT takes in input source symbols at a time and convert s them into time domain data where is the number of sub carrier s T he output of IFFT is the summation of PAGE 26 26 all sinusoids which the orthogonal basis functions of IFFT. T he block of output samples from the IFFT make up a single OFDM symbol. A t the receiver, this time domain OFDM symbol possibly corrupt ed by the channel will be processed by FFT, which brings it back to the frequency domain. One of the desirable properties of the circulant matrix is that it can be diagonalized by pre and post multiplying IFFT and FFT matrices, respectively. That is, where In order to exploit this property, an poi nt IFFT operator is employed at the transmitter to generate the information symbol vector and, correspondingly, an point FFT operator is also used at the receiver. The th elemen t of the vector is essentially the response of the channel on the th sub carrier It is obvious that the multipath channel of order affects each sub carrier ; the channel provid es each sub carrier with multipath diversity in the order of Multiplying by an point FFT, we obtain the signal vector at the th receive antenna as (2 6) where is the AWGN vector. Finally we have arrived at an orthogonal frequency division multiplexing (OFDM) system model, where the signal riding on the th sub carrier essentially undergoes a frequency flat fading with channel gain W ith all the processing in this basic OFDM scheme, we PAGE 27 27 see that OFDM convert the frequency selective channel in to parallel frequency flat chan nels and ISI and ICI problem can be solved by employing CP processing.. PAGE 28 28 CHAPTER 3 JOINT TRANSCEIVER OP TIMIZATION IN OFDM BASED MC CDMA SYSTEMS Introduction Multi carrier code division multiple access (MC CDMA) systems are well suited for high data rate wireless multimedia services, due to their ability to convert frequency selective fading channels to distinct flat fading channels with low complexity fast Fourier transform (FFT) devices. However, when multiple users are present, the performance of MC CDM A systems is degraded by the multiuser interference (MUI) when the channel is frequency selective. In order to mitigate MUI, we present a joint algorithm that combines transmit power control, antenna array processing and multiuser detection at the receiver Interestingly, the frequency selectivity that entails the MUI also provides multipath diversity which can help suppress the MUI. Performance of the algorithm in a number of MC CDMA system models is evaluated in terms of the average transmit power to achi eve the target signal to interference plus noise ratio (SINR). Simulations confirm the outstanding performance of this algorithm compared with the existing ones in MC CDMA systems. The reminder of the chapter is organized as follows. I n th e next subsection the system models are established. Then, we describe the receiver optimization of the joint array processing and linear MMSE multiuser detection, assuming fixed transmit powers at all users. A fter that, we present the transmitter optimization using the n otion of a standard interference function with the assumption that the receiver structure is fixed. F inally, Simulations and comp arisons are provided at the end. System Model Consider a multiuser system where each mobile terminal employs a single antenna d ue to its size and complexity limitation, while the base station is equipped with an antenna array PAGE 29 29 consisting of elements. In a user MC CDMA system, the transmitter spreads the original data stream from each user using a user specific signature sequence onto a total of digital sub carrier s. In this section, we will establish the system model accounting for the multi access spreading, the frequency selective channel propagation and the antenna array response. We will also specify the system model for the cases of spatially dependent and spatially independent fading. Figure 3 1 Block diagram of OFDM based MC CDMA system In order to accommodate multipl e users, user specific spreading is needed. Specifically, the th user's symbol block b k is generated by spreading the symbol d k w ith the spreading sequence c k := [ c k,1 c k,2 c k, N ] T as b k = d k c k where c k,n represents the th chip from the signature sequence of the th user. Substituting back into Eq. (2 6), we obtain the following I/O relationship ( 3 1) In the special case of frequency flat fading we have so that the diagonal channel matrix is simply a scaled identity matrix PAGE 30 30 The I/O relationship in Eq. ( 3 1) can be re written as ( 3 2) whe re the mutual orthogonality of the spreading codes can be preserved. This makes the MC CDMA system free from multiuser interference (MUI). However, in general for frequency selective fading channels, the elements of are typically different from each other. Then, so Eq. ( 3 1) can be expressed as ( 3 3) where denotes the matrix formed by the first columns of the channel vector and the antenna gain vector Notice that the distinct fading coefficient on each sub carrier destroys the mutual orthogonality among users, whi ch gives rise to MUI. In addition, each user may experience a distinct channel fading effect. This, together with the near far problem induced by differing user locations, may further aggravate the MUI. Collecting the signals at the array consisting of receive antenna elements, the overall system model can be expressed as follows ( 3 4) W here the channel matrix and the noise matrix, contains the temp oral and spatial AWGN samples. Depending on the relative spacing among the elements of the receive antenna array, the channel fading coefficients can be spatially dependent PAGE 31 31 or independent across different elements of the antenna array. Next, we will specif y the MC CDMA system model for these two cases. Spatially Dependent Fading In this subsection, we derive the complete system model employing the array of receive antenna elements with a spatially dependent fading channel. A spati ally dependent fading channel is assumed when the spacing among the elements of an antenna array is small such that the channel fading coefficient corresponding to each antenna array element is identical, When we consider a freq uency selective fading channel, the antenna response vector can be expressed as Chap. 6 of [39 ] ( 3 5) where is the carrier frequency, is the distance between the elements of t he receive antenna array, is the direction of arrival of the th user signal over the delay path and is the speed of light. Thus, Accordingly, we can express the I/O relationship as (3 6) w here In this case of frequency selective fading channel, we can observe that the channel coefficients, vary across the sub carrier s and the maximum PAGE 32 32 channel delay order of the multipath channel effects allow the MC CDMA system to exploit multipath diversity. When we consider a frequency flat fading channel, the channel fading coe fficient h k,m ( l ) = h k a nd the antenna response vector can be reformulated as ( 3 7) Thus, The I/O relationship can be expressed as ( 3 8) where The channel fading effect across all the sub carrier s is identical. It can be stated that the system undergoes single frequency flat fading channel across all the sub carrier s and all the elements of an antenna array. Unlike the case of the frequency sele ctive channel, the system cannot exploit the multipath diversity. Spatially Independent Fading In this subsection, we also derive the complete system model employing the array of receive antenna elements with the spatially indepe ndent fading channel such that the path from each user to each element of an antenna array is essentially an independent fading channel, In order to guarantee the independence of each channel, it is common to deploy the elements of the antenna array at a minimum distance of half the wavelength. Due to the spatial independence of the channel coefficients, the elements of the antenna response vector, which shows phase differences, can be set to be 1. PAGE 33 33 When we consider a frequency se lective fading channel, the channel coefficient Accordingly, the channel coefficient vector can be expressed as The I/O relationship can then be expressed as ( 3 9) where In this case of frequency selective fading channel, we have temporally and spatially independent fading channels which enable the MC CDMA system to exploit multipath diversity of order and spatial divers ity of order In contrast with the inherent characteristic of MC CDMA system to exploit the multipath diversity in frequency selective fading channels, DS CDMA systems may need additional processing such as a Rake receiver to ach ieve the diversity. Therefore, we can achieve diversity gain more efficiently for MC CDMA in a frequency selective fading channel than with DS CDMA scheme in the same channel. When we consider a frequency flat fading channel, th e channel coefficient The I/O relationship can be expressed as ( 3 10) PAGE 34 34 where We can observe that the channel coefficients across all the sub carrier are identical, and spat ial independence provides the diversity of order We will describe the joint optimization of the transmitter and the receiver in the next section. Joint Optimization of Transmitter and Receiver With the goal of minimizing the tot al power consumption while satisfying specified SINR objectives, we will develop a joint optimization algorithm which combines antenna array processing, multiuser detection (MUD), and power control. Notice that the first two operations are carried out at t he receiver, whereas the power level adjustment is made at the transmitter. Receiver Optimization For arbitrary transmission power levels our goal in the receiver optimization is to maximize the SINR of each user. Specifically with a given observation matrix as in Eq. ( 3 6) user specific filters will be constructed to maximize each user's SINR. Multiuser detectors perform temporal filtering of the received signals by exploiting the structures in mu ltiuser environments. Among many multiuser detectors, we employ the MMSE multiuser detector which is the linear filter maximizing the output SINR. Given the observation matrix the elements of th column can be considered as a temporally received signal at the th element of the antenna array, and each column can be considered as the spatially separated received signal. In order to apply the MMSE multiuser detector for the observat ion matrix we convert the matrix form of the observation into a long vector form by stacking its columns such that ( 3 11) where is constructed by stacking the columns of in Eq. ( 3 6) and consists of the combined temporal spatial received signal of the th user which contains the channel PAGE 35 35 propagation effects. Likewise, the noise vector, is also constructed in the same manner, and has zero mean and covariance matrix Let denote the MUD filter coefficients vector corresponding to the th user. The n, the decision statistic for the th user's symbols can be obtained as follows ( 3 12) Our objective of maximizing the SINR then amounts to minimizing the mean square error (MSE) of the estimate [ 6] ; th at is, the optimum filter coefficients vector can be obtained by solving the following equation ( 3 13) assuming that the symbols are uncorrelated. Substituting Eq. ( 3 12) int o Eq. ( 3 13), we have the following MSE expression ( 3 14) It then follows that the th user's optimum filter coefficients vector and the corresponding MMSE are [21 ] : ( 3 15) ( 3 16) Since the matrix i s positive definite for all its inverse always exists. This guarantees the existence of the MMSE filter coefficients vector The frequency selectivity in MC CDMA systems enables multipath diversity and the array of multiple receive PAGE 36 36 antenna provides the spatial diversity. Given multipath diversity and the receiver diversity in the MC CDMA systems, the MMSE MUD may be expected t o benefit from those diversities, and the expectation is confirmed later in this section and by a number of simulations described at the end of this chapter From the decision statistic given in Eq. ( 3 12), we obtain the SINR expression of the th user as ( 3 17) Substituting Eq. ( 3 15) into Eq. ( 3 17) we get the maximum SINR for the th user: ( 3 18) which is inversely proportional to the in Eq. ( 3 16). In order to see if the MMSE MUD is benefited from multipath diversity in the proposed system, we apply the th user's filter coefficients vector for the received signal. For m athematical simplicity, we only use the received signal from the th user The th user's receive signal output from MMSE MUD can be expressed as ( 3 19 ) Consider the system with single receive antenna. The number of users and sub carrier s are two, and the channel is frequency selective. Then, is a vector which can be expressed as ( 3 20) PAGE 37 37 Without loss of generality, the received signal from user 1 can be chosen for mathematical analysis. The filter coefficient vector for user 1 can be expressed as w here Then, the output from the filter can be expressed as ( 3 21) Substituting Eq. (3 21) for Eq. (3 18), we get the maximum SINR for user 1 as (3 22) In case of frequency flat fading channel ( L = 0), the vector the vector can be expressed as (3 23) The terms in Eq. (3 22) can be turned into (3 2 4 ) (3 25) (3 2 6 ) When w e consider the frequency selective fading channel where the multipath delay order of the vector can be expressed as PAGE 38 38 ( 3 2 7 ) The first two terms and the last two in the denominator in Eq. ( 3 2 2 ) can be turned into ( 3 2 8 ) (3 29) ( 3 30 ) From Eq. ( 3 2 2 ) through Eq. (3 30) we see that the difference in SINRs between frequency flat and frequency selective fading channel in the system is mostly affected by the terms shown in Eq. (3 26) and Eq. (3 30). Therefore, we can state that SINR in frequency selective case is likely higher unless Since we can assume that the channel tap coefficients are independent or have small correlation with each other, it is most likely that Consequently, we can conclude that MMSE MUD is benefit ed from multipath diversity in the above case. We consider more general case where the multipath delay order is and the number of sub carrier s is equal to Then, Eq. ( 3 21) can be turned into ( 3 31 ) Eq. ( 3 31 ) is linear addition from Eq. ( 3 21) due to the increment of multipath delay order The last term in Eq. (3 31) affects the SINR of the system PAGE 39 39 in such a way that SINR increases as L gets larger corresponding to the previous case. T his general case also confirms the system with MMSE MUD is benefit from multipath diversity. If we substitute the multipath delay order index or from Eq. ( 3 31 ) for the number of elements in receive antenna array, we can deduce that MMSE MUD also can be benefited from spatial diversity. Transmitter Optimization Our goal in the transmitter optimization is to find an adaptive power control a lgorithm which minimizes the average total transmit power with rapid convergence, while satisfying a certain minimum required target SINR. Consider the following SINR based power updating algorithm ( 3 32 ) where and represent the current and updated power levels, respectively, and and respectively denot e the current SINR and the target SINR. Intuitively speaking, the algorithm works as follows: when the current SINR is less (or more) than the target SINR, the updated power will be increased (or decreased). However, Eq. ( 3 32 ) only works on the basis of a n individual user without the total power considerations and the minimum target SINR constraint. Taking all these into account, we formulate the joint optimization problem such that ( 3 33 ) ( 3 34 ) ( 3 3 5 ) PAGE 40 40 where is the target SINR for the th user, and the right hand side part of Eq. (3 34) is obtained from multiplying the inverse of shown in Eq. (3 17) by Including the iteration index we can treat the SINR obtained by the MMSE MUD as a function of the iteration index For the th user, the MMSE weighting vector now depends on the instantaneous power levels of (see Eq. ( 3 15) ). Consequently, the maximum instantaneous SINR for the th user at the iteration can be expressed as ( 3 31) where is the MMSE weighting vector at Let us denote the right hand side of Eq ( 3 34 ) as an interference function where the vector namely contains the instantaneous power levels at all transmitters. It turns out that is a standard interference function by satisfying the following three properties [40 ] : Positivity: Monotonicity: Scalability: As a result, the pow er control iteration in Eq. ( 3 34 ) is guaranteed to converge to the optimum solution for the power vector. The resulting joint power control approach is a two step iterative algorithm. The receiver is optimized by Eq. ( 3 15) with fixed transmit power in th e first step, and the transmitter is PAGE 41 41 optimized by Eq. ( 3 34 ) in the second step with fixed receiver filter. At each iteration step of the algorithm, the maximum interference suppression is achieved by choosing the MMSE filter coefficients and applying the filter to the receiver. The suppression of interference then allows us to reduce the total transmit power of the users while satisfying the minimum SINR requirements. Compactly written, the two step receiver and transmitter optimization is given by: ( 3 32) In the next section, we will evaluate the performance of the joint transceiver optimization by simulations and comparisons with existing alternatives. Simulations and Comparisons In our simulations, we consider two cases of cha nnel fading: frequency selective and frequency flat fading channels. In both cases, the channel gains are Rayleigh distributed with expected total power normalized to 1: where for frequency selective a nd for frequency flat. We consider quasi static channels, where the channel gains remain invariant within the channel coherence time, but can change independently afterwards. Users' signature sequences are length pseudo random codes. The target SINR is set to be 5 (7dB) for all users. The number of antenna array elements at the receiver is denoted by For all simulations presented in this chapter we compare the performance of the systems in terms of the convergence rates to the target SINR or the average transmit power consumption. The number of trials is 1000. The average SINR and the average transmit power are obtained by averaging across all the users. PAGE 42 42 (a) Convergence rate to the target SINR (b) Average transmit power update Figure 3 2. Performance comparison between MC CDMA schemes and DS CDMA schemes when K=10, N=10, M=2, L=0 Test Case 1 : We compare the performance of the joint power control algorithm in DS CDMA systems proposed in [20] and in MC CDMA systems proposed in this chapter We set the number of users K = 10 and the length of the signature sequences N = 10 Since the algorithm in [20] only applies to DS CDMA syste ms in frequency flat fading channels while our algorithm here is tailored for MC CDMA systems experiencing frequency selective fading channels, we carry out the comparison between them in frequency flat fading channels. In both systems, we consider two cas es: i) the spatially dependent fading (dp) and ii) the spatially independent fading (idp), thus we have four setups: DS CDMA systems with spatially dependent fading channels (DS dp), DS CDMA systems with spatially independent fading channels (DS idp), MC C DMA systems with spatially dependent fading channels (MC dp), and MC CDMA systems with spatially independent fading channels (MC idp). Fig. 3 2(a) shows the convergence rates. The MC idp and DS idp both take three iterations to reach the target SINR, while MC dp and DS dp PAGE 43 43 (a) Spatially dependent case with L=0,1,2,3 (b) Spatially independent case with L=0,1,2,3 Figure 3 3. Average t r ansmit power updates with K=16, N=16, M=2, L=5 both take four iterations. Fig. 3 2(b) depicts the average transmit power required for all users to achieve the target SINRs. Not surprisingly, the MC CDMA and DS CDMA systems show the identical performance in both the SINR convergence rate and the power consumption, regardless of the spa tially dependent or independent fading. However, the systems with spatially independent fading result in a lower total transmit powers than ones with spatially dependent fading. This is due to the spatial diversity gain provided by the independent fading. Test Case 2 : When the channel is frequency selective, it provides an additional multipath diversity gain. In contrast with the power control algorithm in [20] the algorithm proposed in this chapter can exploit multipath diversity. To see this, we test th e performance of our algorithm for MC CDMA systems in frequency flat ( L = 0) and frequency selective ( L > 0) channels. Fig. 3 3 shows the average transmit power updates required for all users to achieve the target SINR 5. From this simulation, it is confir med that the joint algorithm effectively exploits the multipath PAGE 44 44 diversity. Furthermore, we observe that the system performance is better in the spatially independent case than the spatially dependent case. (a) Convergence rate to the target SINR (b) Average transmit power update Figure 3 4. Performance comparison among a number of MC CDMA system models when K=16, N=16, L=5 Test Case 3 : In this simulation, we compare the system performance in a number of M C CDMA system models. We use the following abbreviations for simplicity: the spatially independent (idp), spatially dependent (dp), single antenna (sngl), frequency flat (flat) and frequency selective (sel). Specifically, the six setups considered here are Sel idp, Sel dp, Sel sngl, Flat idp, Flat dp and Flat sngl. We set and for multiple receive antennas. In case of the frequency selective fading channel, we set the channel order From Fig. 3 4(a) we observe that the spatial diversity helps the convergence rate of the algorithm. However, we can see that the frequency selectivity does not play an important role to the convergence rate. Fig. 3 4(b) shows the average transmit power updates required for all users to PAGE 45 45 achieve the target SINR 5. In this plot, we observe that both spatially diversity and the multipath diversity help reduce the transmit power. (a) Convergence r ate to the target SINR (b) Average transmit power update Figure 3 5 Performance comparison among the joint algorithm and existing algorithms in MC CDMA systems when K=16, N=16, M=2, L=5 Test Case 4 : In this simulation, we compare the p erformance of the proposed algorithm (MC jnt) with the performance of three existing algorithms for MC CDMA systems. The first algorithm, which we term MC mrc, utilizes the conventional matched filter detector matched to the temporal spatial signature [7 ] The second one, which we term MC sngl, utilizes a single receive antenna and a linear MMSE multiuser detector. The third algorithm, which we term MC tf, utilizes the Time Frequency power adaptation scheme in [16 ] For all algorithms, we set (except for MC sngl), and Fig. 3 5(a) shows the convergence rates corresponding to the four algorithms. Clearly, our proposed joint algorithm (MC jnt) outperfor ms the others. In addition, the MC mrc and MC tf algorithms do not even converge to the target SINR. Moreover, we observe in Fig. 3 5(b) that the MC jnt case consumes the lowest transmit power to achieve the target SINR; while the MC tf and MC mrc algorith ms keep PAGE 46 46 increasing the average transmit power at each iteration, but can never reach the target SINR. Although the proposed system requires an additional complexity mainly due to MMSE MUD, its performance enhancement makes it promising solution for MUI and transmit power reduction. Conclusions In this chapter we presented a joint transceiver optimization algorithm for MC CDMA systems. Our analysis and simulations show that this joint algorithm for MC CDMA systems is well suited for frequency selective fadi ng channels, and that both spatial diversity and multipath diversity are exploited to enhance the MUI suppression performance. These result in an increase of the MC CDMA system capacity. PAGE 47 47 CHAPTER 4 POWER LINE COMMUNICA TIONS PLC History and Competitions P ower Line Communications (PLC) basically means any technology that enables data transfer at narrow or broad band speeds through power lines by using advanced modulation technology. PLC has been around for quite some time ; the first remote electricity supp ly metering in 1838 and the first patent on power line signaling were proposed in the United Kingdom in 1873 [ 41 42 ]. It has only been used for narrow band tele remote relay applications, public lighting and home automation. T he growth of the internet acc elerates the demand for the high data rate communication services to almost every premise. If such services can be carried over power line networks, it can provide interconnectio n to every home, factory and office without any additional cost of deploying t he communication medium. HomePlug 1.0, which is the first high speed solution for Local Area Networking in Small Office/Home Office (SOHO), was standardized in 2001 and widely available in both North America and Europe [ 43 44 ]. HomePlug AV [ 45 46 ], stand ardized in 2005, is one of the most popular power line communication technologies, and it supports up to 200Mbps transmission rate using power lines. There are several technology choices for home networking. W hen existing wires are used, two more options a re available in addition to the PLC. The Home Phone line Networking Alliance ( HomePNA ) 3.0 standard [ 4 7 ], using telephone lines, released in 2003 specifies data rates up to 128 Mbps with optional extensions to 240Mbps. I t also has deterministic Quality of Service (QoS), but suffers from a limited number of available outlets in the house. R eleased in 2005, the Multimedia over Coax Alliance ( MoCa ) standard [ 4 8 ], using coax cables, uses 50 MHz of bandwidth in the 850MHz to 1500MHz band. S imilar to using existi ng telephone wiring, PAGE 48 48 cable outlets are typically limited to 3 or 4 in the average home and are certainly not present in all rooms. T here are two main wireless contenders for home multimedia distribution: Ultra Wide Band (UWB) [ 4 9 5 0 ] and 802.11 a/g/ n [ 5 1 ] UWB is capable of providing up to 480Mbps at short range (3meters) and 110Mbps at 10 meters. B eyond th ese distances, UWB signals suff er high attenuation; hence it is primarily useful for in room Personal Area Networks. The 802.11 family includes over the air m odulation techniques that use the same basic protocol. 802.11b was the first widely accepted one, followed by 802.11g and 802.11n. 802.11n is a new multi streaming modulation technique that is still under draft development It uses multiple input mu ltiple output (MIMO) and space time coding schemes. The wireless option, with the advantage of flexibility, is certainly viable except for the fact that a dedicated wired infrastructure connecting multiple access points is required to cover the entire home I n addition, wireless mobile devices rely on batteries and have difficulty in maintaining continuous electric power. The recent study shows that the present version of the HomePlug 1.0 and AV have been shown to out perform the traditional IEEE 802.11 a/g /n in many field tests of connectivity, throughput and link stability [ 5 2 5 3 ]. Power lines, being ubiquitously deployed as a wire line network for carrying electrical power, are then the obvious choice as the medium for communication amongst the plethora of home based and personal devices. They offer the convenience of already being there, and having outlets in almost all locations in a household for easy access. Further, devices can easily obtain electric power if t hey are deployed on PLC systems. The PLC systems, however, are not free of problems. The PLC channel is notorious for electric noise and interference, as well as channel variability depending on the appliances that are PAGE 49 49 in use from time to time. I n the following subsections, we present the power line channel condition and the advanced techniques used for reliable communication through power line networks. PLC Medium While many have attempted to use the power line as a communication medium in the past, it has not lived up to expectations, earning a reputation for questionable reliability. The fact is tha t the power line is a difficult and noisy communications medium, characterized by several unpredictable and strong forms of interference. The major sources of noise on the power line are from electr ical appliances, which generate noise components that extend well into the high frequency spectrum. T he appliance s connected to an outlet contribute line interference, which can be approximated as Additive White Gaussian Noise (AWGN). In addition, the radi o frequency signals also impair certain frequency bands. Dimmer switches, motorized electrical appliances and computers, also introduce impulsive noise F requency selective fading also corrupts PLC channels, which have non flat frequency responses T here i s an another channel impairment that the signal can be highly attenuated in PLC channel, an average attenuation of approximately 40 dB. Because of both physical attenuation and delay spread, the frequency response of the power line channel is variable over frequency band. PLC channels are typically non symmetric since the noise experienced at each node may be highly localized due to the attenuation. PLC systems also follow the regulatory constraints, which may be different between countries. T his unstable i nternational regulatory environment requires that PLC systems be flexible to adapt with changing regulations. PAGE 50 50 A ll the prescribed facts contribute PLC channels to be unstable. Therefore, it is critical that PLC systems continually adapt to the changing chan nel conditions. E specially, the bit loading OFDM is used in PLC systems which means that the systems determine the highest order constellation that each carrier can support, in order to maximize the data rate. HomePlug AV PHY The HomePlug AV, the current PLC standard, physical layer is designed to ensure that m ultiple multimedia streams can be supported simultaneously and delivered to the whole house [ 5 4 ]. I n order to do so, the AV PHY incorporates a number of features, which can deal with the harsh PLC c hannel condition and the regulatory constraints. T he AV PHY is based on OFDM modulation, which is combined with adaptive bit loading to provide great flexibility with which to adapt the PLC channel, allowing optimized and stable channel throughput. T he bit loaded OFDM works in such a way that each sub carrier with a high enough SNR to support data can be coherently modulated up to 10 coded bits per carrier [ 5 5] This is the major effect of the higher maximum data rate in HomePlug AV over HomePlug 1.0. Impul sive noise is well handled in HomePlug AV by this combination of channel adaptation and efficient retransmission scheme. I n order to satisfy different regulatory constraints throughout the world, time domain pulse shaping of the OFDM symbols is employed to provide flexible spectral notching [ 56 ] I n addition, the AV PHY considers the compatibility with the previous versions of PLC standards. PHY Protocol Data Unit (PPDU) consists of the preamble, the Frame Control (FC) and PHY payload blocks. T hese HomePlu g AV PHY frames uses 1155 sub carrier s in the frequency range from 1.8 MHz to 30 MHz where 917 sub carrier s are active and 238 sub carrier s are turned off in the US for FCC regulation. The sub carrier s can be modulated with Phase Shift Keying (PSK) and Qu adrature Amplitude Modulation (QAM) schemes up to 10 bits per sub carrier depending on the SNR on each sub carrier T he preamble block is essentially employed PAGE 51 51 for synchronization, and it also provides a training sequence for channel estimation and equaliza tion, as the preamble is an a priori known signal. The FC contains such information as Tone Map Identifier (TMI) and length of PHY body. The TMI is an index of Tone Map, which contains the modulation types of the OFDM symbols of the PHY body. TMI is chosen by the receiver during channel adaptation and is sent along with the Tone Map to the transmitter. PHY demodulate the symbols by the informed PHY body length. Figure 4 1. HomePlug AV Transceiver PAGE 52 52 A block diagram of a HomePlug A V transceiver is shown below in Figure 4 1 S ince the purpose of this section is to briefly introduce the HomePlug AV, we only include HomePlug AV data blocks in detail. On the transmitter side, the PHY layer receives its inputs from the Medium Access Cont rol (MAC) layer. Two separate processing chains are shown because of the different error correction coding for Control Information, and HomePlug AV data. T he HomePlug AV data stream passes through a Scrambler, a Turbo FEC Encoder and a Channel Interleaver A Scrambler is employed for the security purpose. Turbo FEC coding is widely known to provide performance close to theoretical channel throughput limits with manageable complexity. T he larger the block size is, the higher the coding gain can achieve H ow ever, the large block size on Turbo FEC cause s decoding latency and computational overhead. Interleaving is used in digital data transmission technology to protect the transmission against burst errors such as impulse burst in PLC systems. The outputs of both types of FEC Encoders lead into a c ommon OFDM Modulation structure The coded symbols blocks are passed through the Mapper resulting in baseband constellation symbols. Then, Inverse Fast Fo urier Transform (IFFT) Preamble and Cyclic Prefix insertion a re processed. A fter that, windowed overlapping which eventually feeds the Analog Front End (AFE) module that couples the signal to the Powerline medium. F or windowing process, a specifically designed pulse shape is applied to each time domain OFDM symbol, causing reduced bandwidth occupancy of the sidelobes of each sub carrier At the receiver, an AFE operates with an Automatic Gain Controller (AGC) and a time synchronization module to feed separate control and dat a information recovery circuits The sample d data stream (which contains only HomePlug AV formatted symbols) is processed PAGE 53 53 through a 3072 point FFT, a demodulator with SNR estimation, a De i nterleaver followed b y a Turbo FEC decoder, and a De scrambler to recover the data stream. HomePlug AV represent s a significant advance in PLC technology even there is no revolutionary technical advance. In order to enhance SNR performance Turbo convolutional coding and coherent modulation are employed T ransmission is synchronized with respect to the AC line cycle, and flexible frequency notching is achieved using OFDM symbol shaping. Adaptive bit loading corresponds to the significant improvement of data rate. These results confirm that HomePlug AV is capable of supporting multiple high data rate multimedia stream. PAGE 54 54 CHAPTER 5 IMPROVED IMPULSIVE N OISE DETECTION IN PO WER LINE COMMUNICATI ON SYSTEMS Introduction Impulsive noise is generated by many house hold appliances that are attached to the electrical network. Its presence is often detrimental to the performance of a power line communication system, causing PHY throughput degradation in the order of 30 50%. The goal of impulsive noise mitigation is to improve the SNR of the received signal by means of signal processing tools. In this work we focus on optimizing the d etection of impulsive noises. A new method is developed for the setting of the detection threshold, that is both efficiently computed (in an iterative manner), and performs well in various impulsive noise conditions. Once impulses are detected they are rem oved from the received waveform by applying simple windowing mechanisms. To evaluate different impulse detection algorithms we test them against real life (impulsive) noise waveforms that have been captured on the power line. The selected algorithm is fur ther validated on the power line against real time captures of impulsive noise impeded signals. The remainder of the chapter is o rganized as follows. I n the beginning we review some conventional impulse detection and mitigation techniques and introduce s ome of the common concepts in more detail. The next subsection contains the description of our new threshold setting algorithm for impulse detection. Then, si mulation r esults are discussed where we also describe the effects of some of the impulsive noise s ources considered, and finally conclusions will be following. I mpulsive Noise M itigation in P ower L ine N etworks In this section, we discuss existing detection and processing methods. We also mention the processing method we will use in this study. The algo rithm for declaring the start and stop PAGE 55 55 sample of an impulsive noise hit is shown in Figure 5 1. In order to find the impulsive noise starting point, a length M shift register R is employed. At first, the detection algorithm tries to find the starting point s of the impulsive noise samples. Figure 5 1 Impulsive noise Detection Flow Chart PAGE 56 56 At time instance t, the first element of the shift register is set to be 1 if the amplitude of the received signal is larger than or equal to a detection threshold then the register shifts. If the sum of all the elements of the shift register are larger than N which is the impulse starting point threshold, then the element of the impulse map I map ( t ) at that time instan ce is set to be 1 which is the impulse starting point. From the impulse starting point up to fifteen samples C if the signal is larger than or equal to the t hreshold, then, the element of the impulse map at that time instance is set to be 1 After fiftee n samples from the last detected impulsive noise sample, the algorithm tries to find the next impulse starting point. Once the locations of impulsive noise samples are identified by the detection step, one of several impulsive noise processing algorithms c an be employed, choices include Clipping : reduce the voltages of affected samples to a hard limit. Blanking Windowing : similar to blanking, but use a window shape to ramp down and ramp up samples around impulses to better preserve orthogonality and not turn narrowband jammers into broadband jammers. The overall performance of this technique is better than but more dependent on the type of impulsive noise than Blanking. Choosing a w indow and window length is another problem to solve. Overwriting/Averaging : replace affected samples in IFFT interval with copies from the cyclic prefix (CP). LLR Reduction : reduce log likelihood ratios ( LLR ) from OFDM symbols in proportion to the number of samples affected by impulsive noise Can celing : attempt to reproduce time domain waveform of impulse and subtract it from receive waveform before demodulation. PAGE 57 57 In this chapter we consider two different sizes of CP for inter symbol interference reduction. The first CP size is 1052, which contain s the last part of the payload information. The second CP size is 5028, which contains all the information of the payload. For 1052 CP size, our system performs Hanning windowing and averaging with copies from the CP for jammer mitigation, which also helps for impulsive noise mitigation. Since the length of CP is short, the portion of the receive signal to be processed is very restricted. Therefore, we perform Hanning windowing to mitigate the effect of the impulsive noise using the detected impulse informa tion. Figure 5 2 Windowing and averaging for 1052 CP size Figure 5 3 Averaging for 5028 CP size For 5028 CP size, the algorithm also uses Hanning windowing, and it performs overwriting and averag ing. Since the long CP contains all the payload symbol information, the performance improvement using the algorithm is significant. However, employing long CP basically reduces the effective PHY data rate by more than 50%. PAGE 58 58 T ighter T hreshold S etting In this section, we propose a detection threshold setting algorithm. The receive signal in the time domain can be expressed as ( 5 1) where represent channel response, tra nsmit signal and noise, respectively. and represent the total number of samples and the convolution operation, respectively. In order to set a threshold, the Envelope Threshold setting method uses a peak to ave rage power ratio (PAPR) and a receive waveform average power (RWAP) information defined as ( 5 2) where represent an arbitrary time domain signal. At the first step, a rough threshold, is first set by multiplying known transmit waveform (TW) PAPR by computed RWAP namely ( 5 3) This value should be located between the maximum signal envelope without noise and the maximum receive waveform ( RW ) envelope defined respectively as ( 5 4) ( 5 5) When the threshold is smaller than the detection algorithm identifies the signal samples as impulsive noise samples When the threshold is larger than the algorithm does not work at all. After a rough threshold being set, we should adjust the value using a threshold scaling factor such as PAGE 59 59 ( 5 6) where represents the threshold scaling factor. By setting the threshold scaling factor to 1.1, we achieve an impulse detection threshold that is 10 % higher than approximate threshold. Since RWAP contains signal power and noise power, the threshold will be loosened (increased) when impu lsive noise power is large. In order to make the threshold tight with respect to the envelope of the desired signal without impulsive noise we manipulate the Envelope Threshold method in a two step algorithm. In the first step, we set a threshold as a rough threshold and a threshold scaling factor as 1.10 as follows ( 5 7) Then, we detect the impulsive noise samples with the rough threshold value such as ( 5 8) We cancel the rece ive waveform samples at the impulsive noise detected location to zero as ( 5 9) We can then calculate a roughly impulsive noise cancelled RWAP as When the average power of impulsive noise is large, we can observe two things. One is that the difference between a rough threshold and the which can be viewed as the optimum impulsive noise detection threshold, gets large. We want the difference to be as small as possible for better de tection. In order to do so, we have to manipulate RWAP value. The other observation is that the difference between the original RWAP and the approximately impulsive noise cancelled RWAP gets large where we define the difference as PAGE 60 60 ( 5 10) Then, we can have a RWAP expression, which results in a tighter threshold. ( 5 11) ( 5 12) where is a constant. A proper adjustment of allows the up dated RWAP value to be as close to as possible. In the simulation section, we find that the threshold setting is good when equals to 3. This threshold setting algorithm results in a very good performance of impu lsive noise detection as shown in simulation results presented in the next section S imulations Scenarios and Impulsive N oise Data The performance analysis of the impulsive noise mitigation in power line networks is evaluated using the threshol d setting al gorithm proposed in this chapter To perform a comparatively assess of the impact of the impulse mitigation, we evaluate system performance using the following three scenarios: NoImpulseNoise : This represents the performance limit of the impulsive noise mi tigation algorithm. Instead of inserting noise, we only insert impulse free Gaussian noise to the system. ImpulseDetection : This represents the performance of the system in which we detect impulsive noise up to a certain threshold and mitigate it through W indowed Blanking or Blanking. When setting the first step of the threshold, a 10% higher rough threshold is chosen to obtain a tighter threshold. For Windowed Blanking, we use a Hanning window with a length of thirteen; the window starting points are set a t zero. PAGE 61 61 NoImpulseDetection : This represents the performance of the system without the impulse detection step. Figure 5 4 SmImp noise Figure 5 5 Hair Dryer noise PAGE 62 62 The simulations use measured power line impulse responses and noise, in particular, we u se the impulsive noise captures described below and HomePlug AV style data packets as the signal. In order to achieve as practical an analysis as possible, sets of actual impulsive noise data in power line networks are captured and used in the simulations. For comprehensive testing, four typical and distinctive noise sources, SmImp Hairdryer Dimmer and Drill are employed, which represent most of the power line impulsive noise patterns. The noise we are considering can be expressed mathematically as where and represents Gaussian and impulsive noise respectively. From Figure 5 4 to Figure 5 7 the four noise sources are plotted in the time domain. SmImp contains a large number of small am plitude impulsive noise samples. This type of impulsive noise is present in most power line communication environments. Similar to the additional three impulsive noise cases described in this chapter this type of impulsive noise is present all the other n oise scenarios However, for analytical simplicity, we assume that small impulsive noise samples in the three other impulsive noise cases are background Gaussian noises. Hairdryer contains a small number of large amplitude short duration (about 100 samples ) impulse samples shown in Figure 5 5 Dimmer contains a few impulsive noise samples that have a large amplitude long duration (over 1000 samples) shown in Figure 5 6 Drill contains a large number of large amplitude short duration impulse samples shown in Figure 5 7 Using these four noise sources, we first separate Gaussian noise samples from impulsive noise samples. In order to do so, we set the threshold by carefully observing the original noise data. Any noise samples exceeding this threshold are assum ed to be impulsive noise sa m ples. Impulsive noise samples are extracted from original noise samples. The extracted part of original noise samples cancelled to be zeros is then filled with previous samples of the original noise. We PAGE 63 63 Figure 5 5 Hair Dryer noise now have pure impulsive noise data and impulse free Gaussian noise. By adding these two, we have noise data for which we know the exact impulsive noise information. Figure 5 6 Dimmer noise PAGE 64 64 Figure 5 7 Electrical drill noise By completing this step in noise manipulation, we can now analyze the performance of the impulsive noise mitigation algorithm in realistic impulsive noise environments. Figure 5 8 Receive signal with typical impulsive noise in power line communication PAGE 65 65 Primary Simulations: Parameter Setting The performance analysis of the impulsive noise mitigation in HomePlug systems with the proposed threshold setting algorithm is performed in these simulations. We have signal, pre measured channel, and noise data described in the previou s section. The received signals with four noise sources are shown in Figure 5 8 Figure 5 9 P erformance comparison using various detection parameters Throughout the simulation, we have observed that detection performance is relatively good when an impul se starting point threshold N is chosen to be one the shift register length 8 and C in figure to be 15 as shown in figure 5 9 Mitigation using Windowed Blanking was found to perform better than other processing methods. Therefore, we set N =1 and use Wind owed Blanking for the impulse mitigation algorithm. Since we want the impulse mitigation algorithm to be tested using a wide variety of noise conditions, we use a scaling factor for the noise part of PAGE 66 66 the received signal so that we can see some differences in performance of the algorithm. The received signal can then be expressed as where represents a noise scaling factor. In order to enhance the performance of the impulse mitigation algorithm in a power line com munication system, it is crucial to properly set the impulse detection threshold. Figure 5 10 shows the independence of an average SNR on the detection threshold. As can be seen from this plot, a particular threshold scaling factor that produces good perfo rmances in different case of impulsive noise scenarios as shown in Eq. ( 5 7), cannot be selected. However, our proposed tighter threshold setting algorithm selects a very good threshold point for each impulsive noise The corresponding threshold scaling f actors with tighter thresholds are 0.6 for Drill 0.88 for Hairdryer and 0.98 for Dimmer switch. These thresholds are located near the highest performance point, shown in Figure 5 10 Figure 5 10 Threshold s caling f actor PAGE 67 67 Althoug h the performance comparisons of the proposed algorithm with exist threshold setting methods are not included, our proposed algorithm consistently outperforms the existing methods Hereafter, only results using the proposed algorithm will be included. Perf ormance Comparison In this performance testing, the performance of the proposed algorithm is compared with NoImpulseNoise and NoImpulseDetection using the four prescribed impulsive noise sources. Table 5 1 shows the performance results in the case of 1052 CP. For a simple comparison, SNR is used as the performance criterion. In order to obtain this expression, 68 OFDM symbols are simulated and SNR vectors are averaged for each setting. All elements of the averaged SNR vector are again averaged to obtain a single value, which we define to be the average SNR. Table 5 1 Average SNR in the case of CP length 1052 Hairdryer Dimmer Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2 NoImpulseDetection 19.3 13.3 9.76 15.4 9.33 5.8 ImpulseDetection 19.5 13.5 10.1 15.3 9.3 5.79 NoImpulseNoise 20.2 14.1 10.6 15.4 9.37 5.85 Drill SmImp Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2 NoImpulseDetection 12.5 6.47 2.95 22.1 16.1 12.6 ImpulseDetection 13 7.69 4.55 22.1 16.1 12.6 NoImpulseNoise 18.4 12.3 8.81 27.8 21.8 18.3 As shown in Table 5 1 we observe that the higher the amplitude of impulsive noise the greater the b enefit when using the algorithm. Moreover, we observe that, in most cases, the algorithm contributes to the enhancement of system performance. A detailed analysis follows. Hairdryer shows performance results for the impulsive noise mitigation algorithm whi le a hairdryer is in use. As can be seen from the noise plot, impulsive noise from Hairdryer shows a large distinctive amplitude and a short duration. This indicates easy detection and the processing of impulsive noise As expected, results clearly show a performance gain using the algorithms. PAGE 68 68 When impulsive noise is not present, the best performance is observed. Although the locations of impulsive noise samples are not perfectly detected, ImpulseDetection still shows good levels of performance. As noise po wer increases, the algorithm shows greater gains in performance. Drill shows performance results when an electrical drill is in use. The noise plot indicates that impulsive noise samples of Drill are densely located and large in amplitude. Therefore, the average SNR is very low, compared to other noise cases and NoImpulseNoise However, the observed improvement in performance when using the algorithm is quite large, compared to NoImpulseDetection, where the performance difference becomes larger than the am plitude and the density of impulsive noise samples increases. The noise plot for Dimmer indicates that only a few impulsive noise samples have a large amplitude and long pulse duration. Since a dimmer switch creates a small number of impulsive noise sampl es, the performance degradation is small. Even the perfect detection of impulsive noise underperforms the detection of no impulsive noise We believe that Hanning windowing is not well suited for this type of impulsive noise detection. In addition, the cho ice of window length also affects performance. However, the performance degradation in Dimmer is so small that there is little difference between its performance results and no performance degradation using the algorithm. SmImp shows the performance of th e algorithm when a large number of small amplitude impulsive noise samples are present. As shown in the table, this type of impulsive noise severely degrades system performance. Gaussian type impulsive noise s prevent detection through the use of a detectio n algorithm. Even though these types of small impulses will most likely be detected by chance, impulse mitigation results in performance that is almost equal to NoImpulseDetection Impulse mitigation is not suitable for this type of noise. Since our detect ion does not detect any PAGE 69 69 impulse samples smaller than the signal sample, impulse mitigation does not degrade the system performance. Table 5 2. Average SNR in the case of CP length 5028 Table 5 2 shows performance results for CP length 5028. The simulation settings are the same as those previously listed, except for the CP length and the mitigation technique d escribed previously where averaging is used. Consistent with the short CP case, the bigger the noise scaling factor is, the clearer the benefit of using the algorithm. Unlike the short CP case, performance results using the algorithm are better than those obtained using the NoImpulse Detection algorithm. Even in the case of SmImp ImpulseDetection outperforms NoImpulse Detection, since the long CP contains all information for the payload of the symbol. Performance Tests in the R e al Power L ine Networ k s In this subsection, the system performance with real power line channels in an office building is tested. HomePlug AV style data packets are used as a signal, while Hairdryer, Dimmer and Drill are used as impulsive noise s. Performance results are expressed a s an effective PHY data rate (Mbps) in a steady state, showing an error free PHY data rate. There are two main goals for this real time performance testing. One is to see if the proposed algorithm helps improve the PHY data rate in real power line network s when impulsive noise is present. The other is to check if the algorithm degrades the system performance when Hairdryer Dimmer Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2 NoImpu lseDetection 21.6 15.6 12.1 18.4 12.4 8.84 ImpulseDetection 22.2 16.6 13.1 18.4 12.4 8.87 NoImpulseNoise 23 17 13.5 18.4 12.4 8.9 Drill SmImp Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2 NoImpulseDetection 13.6 7.55 4.03 24.8 18.8 15.3 ImpulseDetect ion 15 10.3 7.16 24.8 18.8 15.3 NoImpulseNoise 20.9 14.8 11.3 30.8 24.8 21.3 PAGE 70 70 there is no impulsive noise in the network. We use the three impulsive noise sources used in previous simulations. Using the simulation results f rom this subsection, we can also check whether the simulation results shown in the previous subsections are valid. Figure 5 11 PHY data rates for the short CP The performance results in the case of CP length 1052 are shown in Figure 5 11 Corresponding with the results shown in Table 5 2, the algorithm helps improve the system performance of Hairdryer and does not degrade the system performance of Dimmer In the case of Drill system performance is severely degraded. With the help of the proposed algori thm, performance enhancement is fairly large, with a reading of 20% data rate enhancement. When there is no impulsive noise present in the network, the presence of the algorithm does not degrade system performance. Although there is a gap between system pe rformance, NoImpulseNoise and Impulse Detection in these cases, a fairly large performance enhancement is PAGE 71 71 achieved using this algorithm. Moreover, the presence of the algorithm in the system does not degrade system performance. The performance results of C P 5028 are shown in Figure 5 11 In all cases of impulsive noise sources used during testing, performance enhancement is observed. In spite of the enhancement, this long CP case still underperforms the short CP case in terms of data, due to large CP overhe ad. Lab Test Results In this lab testing, we have isolated powerline channels, which are not affected by the unpredictable and uncontrollable channel impairments. With these channel settings, we test the exact effects of impulsive noise impairments and th e performance gain using the impulse mitigation algorithm. Another reason for this test is to see the performance enhancements in different levels of the channel impairments. The test is done with both cases of the long CP and the short CP. In case of the short CP, data rate is averaged by 10 received signal captures. During one signal capture, we have four packets of the signal. Therefore, the average data rate is obtained over forty packets of the signal. In case of the long CP, data rate is averaged by 1 5 received signal captures. In one signal capture, there are two signal packets, so we have average data rate over thirty signal packets. Figure 5 12 shows the lab testing results when a hair dryer is in use. We observe that the performance gain using the impulse mitigation algorithm is obvious in this case. Throughout all the attenuation level we test, the algorithm consistently improves the system performance in the both cases of the long CP and the short CP. The performance improvement we obtain using t he algorithm is about 10 percents higher data rate on average. The lab test results using an electri cal drill are shown in F igure 5 13 Since impulsive noise from a drill is not so consistent during the testing, we expect more variation for the performanc e results. Although we observe that the results are not stable and consistent as in the case of PAGE 72 72 Hairdryer we obtain good performance gains using the algorithm. At some points of the attenuation level, we get 20 percents higher data rate and we still get about 10 percent higher data rate at the other points using the algorithm, which are overall a better improvement than in case of Hairdryer Figure 5 12 Lab Test results with a Hair dryer in use Figure 5 13 Lab Test results with a n Electrical Drill i n use PAGE 73 73 Figure 5 14 Lab Test results with a Dimmer in use Figure 5 15 Lab Test results with a Lamp in use The performance results of the lab testing in case of Dimmer are shown in F igure 5 14 For the short CP case, the system performance difference be tween with algorithm and without algorithm is very small, which we can conclude that there is not gain or losing using the impulse mitigation algorithm with the short CP Dimmer case. However, for the long CP, we have a large improvement using the algorithm We observe about 30 to 40 percent of the performance PAGE 74 74 improvement in terms of data rate, which is obtained by the windowing and averaging the impulsive noise impaired signal part with the CP part of the symbol. In every case using the algorithm, we also o bserve that the data rate using the short CP is much higher than one using the long CP despite the fact that the performance improvement using the algorithm in the long CP cases are higher. Figure 5 15 shows the performance results when the Lamp is in use. The impulsive noise pattern produced by the Lamp is very similar to the one of SmImp which is characterized as small amplitude and very high density. Therefore, we expect that the performance result of this case is similar to SmImp When impulsive noise from the Lamp presents, the performance degradation is significant because the impulsive noise samples are so densely located. Since the amplitude of impulse is smaller than the amplitude of the signal, the impulse mitigation algorithm does not help improv e the system performance in both cases of the short CP and the long CP. Figure 5 16 shows the performance results for the case when a Yard Lamp is turned on. Impulsive noise from the Yard Lamp is characterized as large amplitude and large density, which i s less than Drill and more than Hairdryer We observe that the amplitude of some impulsive noise samples is about the same in amplitude as the signal samples at the attenuation level 15, where the system performance with the impulse mitigation algorithm ge ts better than one without the algorithm. The performance enhancement using the algorithm is about 5 to 10 percent. Although the performance improvement using the long CP is higher than the short CP, the system with the short CP outperforms the one with th e long CP in terms of data rate. PAGE 75 75 Figure 5 16 Lab Test results with a Yard Lamp in use C onclusions The proposed impulse mitigation algorithm in power line networks works well in most cases, with performance gains of 10 to 20 percent. The additional compu tational burden of the algorithm in the system is very low when used to update OFDM symbol based thresholds. Moreover, the algorithm does not degrade system performance when there is no impulsive noise present in the system. This is very important, since i mpulsive noise may not be present for long periods of time in power line networks. R eal time power line network testing confirms the anticipated advantages for the proposed algorithm. PAGE 76 76 CHAPTER 6 UNIVERSAL ALGORITHM OF IMPULSIVE NOISE D ETECTION IN PLC SY STEMS Introduction Impulsive noise presented in the Power L ine C ommunication (PLC) networks is one of the main reasons for the degrad ation of the throughput performance. The goal in this work is to optimize the detection performance of impulsive noise. In order to do so, we propose a new impulsive noise detection threshold setting algorithm that works well in a wide vari ety of cases of impulsive noise in PLC networks. A simple way of setting a detection threshold is to base it relative to the upper and lowe threshold can be chosen to be proportional to the average received power of the signal. This second method typically requir es more computations and memory but can result in superior performance. In our previous work [ 57 ], we proposed an iterative impulsive noise detection threshold setting algorithm which outperforms the existing impulse detection alternatives Since the parameters are chosen by an excessive number of simulations in some particula r impulsive noise sources, the algorithm may not work well on some other impulsive noise sources. In order to ma ke the detection algorithm work in general, we want to derive the threshold mathematically using the characteristics of impulsive noise in PLC s ystems. The characteristics of impulsive noise in PLC systems are well studied [ 5 8, 5 9]. Based on these impulsive noise models, we present the detection threshold setting algorithm. The remainder of the c hapter is organized as follows. Section 6 1 contain s the description of our new threshold setting algorithm for impulsive noise detection. In section 6 2 we present the detection rule to declare the location of impulsive noise samples. Simulation results are discussed in Section 6 3 where we also describe the characteristics of the impulsive noise presented in PLC networks Section 6 4 contains some conclusions. PAGE 77 77 Threshold Setting and Impulsive Noise Detection In this section, we propose a detection threshold setting algorithm. At the receiver, the time dom ain input output relationship can be expressed as (6 1) where h ( t ), x ( t ), g ( t ), and i ( t ) represent channel response, transmit signal, Gaussian noise and impulsive noise respectively. represents the convolution operation. A single impulsive noise or each elementary pulse inside a burst behaves as a damped sinusoid and the exponential decrease versus time can be put in the form as Then, the magnitude of the impulsive noise pulse can be expressed as (6 2) where k represents a damping factor and represent s the peak value of the impulsive noise. At the certain time instance T the magnitude of the impulsive noise pulse can be expressed as (6 3) So, the time instance T can be expressed as (6 4) The integration of the magnitude of impulsive noise from 0 to T can be expressed as (6 5) Substituting T in Eq. ( 6 5) f or Eq. ( 6 4), we get (6 6) PAGE 78 78 In this work, we want to find impulsive noise samples which are larger than the peak of the desired signal. Therefore, it is crucial to set a good detect ion threshold which separate signal sam ples from noise samples. For good detection performance, the threshold value should be as close to the peak of the desired signal as possible since the peak of the desired signal is the ideal detection threshold. Now, we assume that we know the ideal threshold as From Eq. ( 6 6), the damping factor k can be obtained as (6 7) where P I is the integration of impulsiv e waveform envelope that is larger than the ideal threshold. Substituting k in Eq. ( 6 6) for Eq. ( 6 7), P can be re expressed as (6 8) The ideal threshold can be obtained using Eq. ( 6 2) as (6 9) where represents the time instance corresponding to the ideal threshold. Using Eq. ( 6 5), P I can be expressed as (6 10) Then, the time instance can be expressed as (6 11) Substit uting Eq. ( 6 11) for Eq. ( 6 2), the ideal threshold can be expressed as ( 6 12) PAGE 79 79 Since the purpose of this work is to identify the impulsive noise impaired samples from the receive d signal, we consider that the received signal consists of the impulsive noise impaired samples and the other sample s A is defined as the mean of the absolute value of a waveform envelope. A y A i and A x correspond to the received signal, impulsive noise i mpaired samples and the other sample s that are related as A y = A x + A i R is defined as the pick to average ratio of the absolute value of the transmit signal waveform envelope. Therefore, the ideal threshold can be expressed as When m anipulating Eq. ( 6 8), P I can be expressed as (6 13) where A i = P I / L and L is the block size of the impulsive noise detection process. P I now can be expressed as (6 14) The exact value of the damping factor is not known unless the ideal threshold is available as in Eq. ( 6 7). Instead, substitut ing in Eq. ( 6 7) for as the alternative value we get the estimate of the damping factor (6 15) Finally, the new impulsive noise detection threshold can be expressed as (6 16) Once the t hreshold is set, the locations of the impulsive noise samples are identified by the detection step. The algorithm for declaring the start and stop sample of an impulsive noise hit is described in the previous chapter with Figure 5 1 PAGE 80 80 Fig ure 6 1 Performance comparison: single impulse and a burst of impulses Simulations In these simulations, we compare four threshold values : and and represent the ideal threshold which is the maximum magnitude of the signal without impulsive noise and the rough threshold which is obt ained by Envelope threshold method, respectively. is a previously proposed threshold [ 57 ] and is a newly proposed threshold We generate 1000 impulsive noises using the statistical model presented in [ 5 9] in order to lead our test the most general manner as possible. In the simulations, we use a c ombination of both classes of impulsive noises : single impulses and bursts of impulses. The main parameters of a n impulsive noise model include the pseudo frequ ency, inter arrival time, the duration of each pulse, the amplitude distribution and the damping factor k Except for the amplitude distribution, which is well fitted by a normal distribution, the others are well fitted by PAGE 81 81 Weibull distribution. The parame ters of the distributions used in the simulations are referred from [ 5 9] Fig ure 6 1 shows the performance when there is a combination of single impulses and a burst of impulsive noise. Comparing to the ideal threshold, the rough threshold shows the huge g ap with the ideal threshold. Two threshold setting methods, and seem to show similar performances such that and are very close ly value d at Moreover, is sometimes more close ly value at than However, is much more desirable than since it is v ery rare to have smaller value than When the obtained threshold is smaller than the system falsely detect s the desired signal samples as impulsive noise ones. Table 6 1 summarizes the false detection threshold setting performance comparison betwe en the previous ly suggested algorithm and the newly proposed algorithm where the newly proposed algorithm outperforms the previously proposed one. Table 6 1 False Impulse Detection Threshold Rate (%) Impulsive noise Type Single 2.2 30.1 Burst 2.1 73 Single + Burst 1.8 51.2 Conclusions In this paper, we propose an impulse detection threshold setting algorithm which universally performs well in PLC system s. The algorithm not only find s a tight threshold that is very close to the ideal threshold but it also rarely obtain s a threshold value lower than the ideal threshold. Since this simple two step iterative algorithm requires only a limited additional memor y of OFDM symbol size, it could easily be fitted in the current PLC systems PAGE 82 82 CHAPTER 7 ADAPTIVE SUB CARRIER ALLOCATION ALGORITHM IN SS MC MA BASED PLC SYSTEMS Introduction The idea of using power lines as a communication medium was realized in the 1980 s f or low bit rate applications such as ut ility control and measurement [6 0]. Since then, the power line communication (PLC) technology has not been extensively used due to low data rates. T he growth of the internet accelerates the demand for high data rate c ommunications services on almost every premise D ue to the significant advances in signal processing and the ubiquity of power supply grid infrastructure, PLC technology is foreseen as one of the possible candidates for the future high data rate communicat ion systems. Since the power line networks are not specifically built for communication purpose s there exist some notable barriers to use of the networks as a communication medium such as frequency selectivity, impulsive noise and narrow band interferen ce [ 6 1 6 2 ]. T hese barriers make communication through PLC channels extremely challenging. In order to cope with such a hostile channel and achieve a high data rate, orthogonal frequency division multiplexing (OFDM) based multi carrier transmission schemes which are robust and frequency efficient, are employed in PLC communication systems. OFDM is considered to be the preferred carrier modulation scheme for broadband power line communication systems by most researchers. HomePlug AV, which is the most widel y known broadband power line communication standard, is also based on OFDM technique. O ne of the main reasons to employ OFDM is the efficient way it deals with multipath delay spread in broadband transmission systems. T he total bandwidth is divided into pa rallel subchannels and bits are assigned to subchannels in proportion to each subchannel s SNR [ 6 3 6 4 ]. I t has some additional notable merits such as simplified channel equalization, and high bandwidth efficiency and flexibility in high bit rates. PAGE 83 83 In thi s chapter adaptive spread spectrum multi carrier multiple access (SS MC MA) is considered, which is a combination of DMT modulation and spread spectrum technique and frequency division multiple access W e propose an adaptive sub carrier allocation algorit hm that attempts to maximize the total throughput of the system under power spectral density (PSD) and finite order modulation constraints. I n the simulations, it is shown that the proposed systems outperform DMT systems and the systems with the existing c hannel allocation algorithm. T he performance difference is more significant when the power attenuation due to distance is taken into account. The remainder of the chapter is organized as follows. In th e next section, the system models are established by pr esenting the relationship among spread spectrum technique, OFDM, adaptive bit loading and frequency division multiple access (FDMA). Then, we describe the PLC channel characteristics and capacities, and the data rate using an adaptive bit loading scheme A fter that, we present the sub carrier allocation algorithm which attempts to maximize the total throughput of the system Finally, simulations and comparisons are provided at the end. System Model SS MC MA is an OFDM based multi carrier multiple access sch eme combined with spread spectrum techniques. T he adaptive SS MC MA system investigated in this paper combines SS MC MA with an adaptive sub carrier distribution and bit loading technique. T he adaptive sub carrier distribution enables an effective share of the bandwidth of the system among the users and bit loading brings a significant increase in the data rate by assigning the number of bits to transmit for each sub carrier depend ing on the channel condition. I t is assumed that the channel state informatio n is known at the transmitter because of the quasi static characteristic of PLC channels. PAGE 84 84 Figure 7 1 Block diagram of the adaptive SS MC MA system T he block diagram of the adaptive SS MC MA system is shown in Figure 7 1. W e employ a conventional OFDM scheme inserted cyclic prefix as the guard interval with perfect synchronization assumption. T he output of OFDM block can be expressed as (7. 1 ) where is the diagonal OFDM converted channel matrix and is the a dditive white Gaussian noise vector such that The n th diagonal element of the channel matrix, represent the frequency flat fading channel gain corresponding to n th element of the transmit symbol vec tor T he input of OFDM block can be written as (7. 2 ) PAGE 85 85 T he out put vector of M QAM symbol Mapper is obtained by stacking K cluster vectors as where K is the number of clusters per OFDM block. The k th cluster vector of can be expressed a s where P is the number of symbols per cluster. T he l th symbol in the k th cluster is M QAM modulated complex valued data where P complex valued data symbols of the k th cluster are spread by multiplication with orthogonal Walsh Hadamard codes of size L in such a way that where Then, the spread symbols are superimposed with each other on L sub carrier s Using orthogonal Walsh Hadamard codes for spreading the data symbols, the maximum number of symbols we can separate for each cluster is L where T he resulting k th cluster spread symbol vector can be expressed as (7. 3 ) where the spreading matrix and the l th element of can be expressed as Combining and stacking the spread symbol vectors from all the clusters, we obtain the vector (7. 4 ) where and The sub carrier mapping process assigns each element of the vector to the corresponding sub carrier which intends to maximize the syst em performance. In order to represent this process, a permutation matrix is multiplied by the vector in Eq. ( 7. 2). I n this mapping process, a cluster of data is assigned to a group of subcarriers which have the same level of SNR T he group of sub carriers assigned for the same cluster is not restricted to be adjacent with each other. A ny cluster is assigned to only one user and multiple clusters can be assigned to each user. PAGE 86 86 T he spreading process is done at the cluster level, so spreading is not for the user separation but for symbol separation in each cluster. Consider the following blocks of OFDM block in the figure 7 1 as the receiver part of the system. T he OFDM block can be viewed as a simplified cha nnel matrix In order to compensate for the channel effects, a simple zero forcing (ZF) equalizer is employed. The ZF equalizer, Sub carrier Demapper and Despreader are simply inverse matrix operations of OFDM, Sub carrier Mapper and Spreader, respectively. D ue to the inverse operation of ZF equalizer, the receiver blocks works as an orthogonal restoring combiner and the final output can be expressed as (7. 5 ) T he k th output cluster vector can be expressed as T he p th element of the k th output cluster vector can be expressed as (7. 6 ) where represent the frequency flat fading channel gain and the white Gaussian noise corresp onding to the l th chip in the k th cluster, respectively. I n the following section, we present the channel characteristics and the capacity of the system. Power L ine C hannel and B it L oading A power line channel is a harsh and challenging communication med ium since it is not designed for communication. T he frequency response of the PLC channels is not close to the ideal such as an AWGN channel. T he channel is frequency selective and slowly time varying as electric devices are turned on and off in the PLC ne tworks. In a PLC channel, the Signal propagates along non line of sight reflected paths between transmitter and receiver as well as a PAGE 87 87 direct path. This results in a multipath scenario with frequency selective fading. T he attenuation of the signal propagate d on each path increases as increasing the path length and the frequency range to use. An intensive channel measurement and modeling study is carried out in [ 65 ] where authors show the statistical characteristics of widths, heights and numbers of the peak and notch of the channel transfer function. O ur study is based on the PLC channel models proposed in [ 65 ]. B ased on the input output relationship shown in Eq. ( 7. 6), the capacity of k th cluster in system can be derived as (7. 7 ) W here represents power assigned to the p th spreading code of k th cluster. Let us con sider block transmission by combining K clusters. T he k th subset of the k th cluster belongs to which is the set of indices k such that subsets belong to user u the capacit y of system can be expressed as (7. 8 ) T he capacity of the system can be obtained as fol lowing. S ubchannels are grouped into clusters, and each cluster is assigned to a specific user, where a multiple number of clusters can be assigned to one user. T he capacity of the system is the sum of the capacities of all the user specified clusters. Bas ed on the capacity expression, the throughput can be simply expressed using a convenient quantity called the signal to noise ratio (SNR) gap which is a measure of loss with respect to PAGE 88 88 theoretically optimum capacity. Since power spectral density (PSD) of PLC systems should not exceed a certain level by regulation, the throughput is maximal for .The optimum throughput at the k th cluster can be expressed as in [ 36 ] (7. 9 ) I n order to obtain the maximum throughput using a bit loading scheme, we have to consider discrete modulations which constrain the throughput to be a n integer number. Under PSD constraint, and assuming the Finite Granularity (FG) of rates, the optimal loading solution to achieve the maximal throughput is proposed in [ 36 ], where the maximal achieved throughput of the k th cluster is expressed as (7. 10 ) C orresponding to the capacity formulation of the system shown in Eq. ( 7. 8), the throughput of the system is the su m of the maximal throughput of all the clusters where each cluster is assigned to a specific user. Since the channel gain of each subchannel of each user can be different, the throughput of the system is significantly dependent on the subchannel allocatio n to the users. T he maximization of the throughput can be formulated as following (7. 11 ) I n the following chapter, we present the subchannel allocation algorithm achieving the balance between the throughput and the fairness. PAGE 89 89 Figure 7 2 Independent channel responses of four user scenario S ubchannel A llocation A lgorithm In this chapter, we present the subchannel all ocation algorithm to maximize the throughput of the system. T he goal of the throughput maximization algorithm is to maximize each user s throughput while balancing the total throughput and the fairness of the system. In order to see the advantage of this a lgorithm, consider the multi user case where the signal from one user is severely attenuated due to distance. T he level of channel gain from that user will be well below from the others. When we just try to maximize the total throughput of the system, we c hoose the best subchannels which are not likely associated with the poor channel user. Therefore, the poor channel user may not be allocated any subchannels, which prevents communication from the poor channel user. When we just consider the fairness, we se lect the best subchannels from the poor channel user with priority. This may cause dominant subchannel allocation from the poor channel over the good channels, which cause severe degradation of the total throughput of the system. PAGE 90 90 Table 7 1 Proposed Subch annel Allocation Algorithm Subchannel Allocation Algorithm Initialization PAGE 91 91 The proposed subchannel allocation algorithm is presented in Table 1. T he algorithm consist s in finding and assigning subchannels to each user in the following method. Since the number of bits to transmit is dependent on SNR of each subchannel, we first set the multiple SNR ranges using the SNR range setting threshold vector A t the highest SNR range, the best subchannels of the user with the smallest sum of the instantaneous SNR are selected and assigned first, then the second lowest, and so on. T he sums of SNRs assigned to each user are calcu lated to be used for sub carrier allocation at the next stage. O nce a sub carrier is assigned to a user, other users are prevented from us ing that sub carrier by eliminating the sub carrier from the set From the second highest SN R ranges, the best subchannels of the user that has the smallest element of at the higher SNR ranges and the lowest instantaneous SNR at the current range are selected and assigned as described previously T he algorithm assigns the equal number of sub carrier s to each user. I f the number of sub carrier s assigned to one user reaches that limit an algorithm does not assign any sub carrier to that user any more. T he algorithm ends when there is no more sub carrier to be assigned. After all the sub carrier s are assigned to the users, the assigned sub carrier s are sorted in descending order and grouped as clusters. In each cluster, bits are loaded in such a way that the maximum throughput can be achieved by Eq. ( 7. 10). T he loss of th e system throughput can be minimized, since each subchannel is competing within the same SNR range, and the user with poor channel conditions can still communicate in the system since the poorest channel has the priority to be selected within the same SNR range. Simulations In this section simulation results are presented for the proposed adaptive sub carrier allocation algorithm in SS MC MA PLC systems. Assuming perfect synchronization at the PAGE 92 92 receiver and the channel state information (CSI) at the transm itter, the throughput performance of the PLC system employing the proposed algorithm is compared with that of the adaptive LP DMT system as in [ 37 ] and the DMT system. W e consider that the system uses the frequency band from 0 through 37.5 MHz The total n umber of sub carrier s is 1536, which makes the even sub carrier spacing of 24.414 KHz, and we set the length of each cluster at 16 ( P = 16). W e simulate PLC channels using the channel models proposed in [ 65 ]. W e assume that the signal with 40 dBm/Hz flat PSD is transmitted through the simulated PLC channel with the white Gaussian noise with 110 dBm/Hz noise PSD. F or the bit loading process, we allocate m bits on each sub carrier according to Eq. ( 7. 10), where F or the target sy mbol error probability of the SNR gap of the uncoded QAM system can be approximated as as in [ 66 ]. Figure 7 3 Correlated channel responses of five users regarding distance attenuation PAGE 93 93 Figure 7 2 s hows the PLC channel r esponse that is generated by class 5 of the PLC channel model proposed in [ 6]. We set the number of channels is 4, where each user has an exclusively dedicated channel and each channel is independent of each other. W ith these given ch annels, we compare the throughput performances. C ase 1 in figure 7 4 shows the result where DMT corresponds to the conventional DMT system and New Algo. represents our proposed algorithm Since the conventional DMT system is designated for a single user co mmunication system, we use the average value of the throughput s from the four user s channel s. A s we can see from case 1 in figure 7 4, the proposed algorithm outperforms the conventional DMT system and the SS MC MA based LD DMT system. Figure 7 4 Thr oughput performance comparison F igure 7 3 shows the class 5 channel responses where the channel responses are correlated with each other. A t first, we consider the case in which four users in the network are closely located. Therefore all the channel respo nses show the s imilar magnitudes, which can be grouped PAGE 94 94 by Ch1, Ch2, Ch3 and Ch4. T he throughput performance comparison is shown in figure 7 4 as case 2. F or this scenario we also see that the performance of the system with the proposed algorithm is still better than the others. Figure 7 5 Throughput performance comparison along with channel attenuation From figure 7 3, we can find one more scenario where there is a notable attenuation due to the distance difference. We also consider four user scenario T he channels are grouped together with Ch1, Ch2, Ch3 and Ch5. Ch5 is attenuated by 15 dB compar ed with the other channel responses. F or the conventional DMT system, we just obtain the average throughput over the four channel responses as before. I nterest ingly, we see from case 3 in figure 7 4 that the throughput of the LP DMT system is lower than the conventional DMT system even t hough the intention in pr opos ing the LP DMT system is basically to increase the throughput of PLC systems. Due to the sub carri er allocation rule, where the user with the smallest computed rate is given unrestricted priority to occupy the sub carrier the LP DMT achieves an even lower PAGE 95 95 throughput than the conventional DMT system. Since our proposed algorithm dictates that the user with the smallest computed rate occupies the sub carrier with priority only in the same SNR range, the proposed algorithm does not choose the poorer su bchannels from Ch. 5 without consideration of performance degradation as in the DP DMT system. F igure 7 5 shows the comparison results of the throughput performances which take into account the attenuation due to the increase of distance and noise W e assume that the distance between the receiver and each transmitter is different, which differentiates the a verage channel gains. I n order to do simulate this, we randomly assign n (dB) attenuation on each channel where W ith the randomly attenuated channel, we test the throughput performance by equally varying the average attenuation l evels of the channels in o rder to see the general performance over various attenuation levels. A s we can see from the resulting plots, the proposed algorithm performs better in terms of the total throughput over all the attenuation levels. Conclusions In t his paper we presented an SS MC MA based PLC system that maximizes the throughput of the system. In order to increase the throughput, we propose an adaptive sub carrier allocation algorithm, which assigns sub carrier s to each user based on SNR information of the channel. The algorithm groups the subchannels of all the users based on those SNR levels, then assigns sub carrier s to the user with the lowest bit rate at each SNR range. Throughout the simulation, we confirm that the algorithm achieves a notable increase of PLC system throughput. PAGE 96 96 CHAPTER 8 CONCLUSIONS AND FUTU RE RESEARCH DIRECTIO N Due to its robustness against channel frequency selectivity and low complexity implementation using FFT circuits, OFDM based multi carrier modulated systems are well su ited for high data rate multimedia services. In this dissertation, we consider three OFDM based multi carrier systems: MC CDMA, DMT, and SS MC MA. MC CDMA takes advantage of user separation by using the spread spectrum. However, MUI emerges when the mutua l orthogonality among the spreading codes is violated by the frequency selective channel propagation, and in the presence of the so called near far effect. T o mitigate MUI, we present a joint algorithm that combines transmitter power control, receiver arra y processing and multiuser detection. The joint algorithm exploits both the multipath diversity and the spatial diversity, where the former is provided by frequency selectivity and the latter is provided by appropriate spacing among the receiver antenna ar ray elements. These diversity collections are realized by using a decentralized linear MMSE multiuser detector at the receiver. The mathematical analysis of the diversity collections is described in chapter 3. In addition to the aforementioned receiver pro cessing technique, power control at the transmitter has been shown to mitigate the near far effect by balancing the received power of all users ( so that no user creates excessive interference for others ) while maintaining a certain SIR requirement. Simulat ions confirm the outstanding performance of the joint algorithm in MUI suppression. In addition, we observe that the algorithm provides the best performance when the propagation channel is frequency selective and channel fading is independent across differ ent receiver antenna array elements. The DMT scheme used in current PLC systems makes it possible to achieve data rate s of up to 200Mbps depending on the SNR level of each subcarrier. Due to its spreading in the PAGE 97 97 frequency domain, impulsive noise in PLC sys tems results in a significant decrease of the overall data rate. T o mitigate the effect of impulsive noise, we propose an impulsive noise detection algorithm, which mainly focuses on the impulsive noise detection threshold setting. In chapter 5, we propose a two step iterative threshold setting algorithm, which compute s the threshold based on the overall signal envelope. After impulsive noise processing, systems gain up to a 15 percent performance improvement in terms of data rate. However, the threshold se tting proposed in chapter 5 is based on an excessive number of simulations on particular sources of impulsive noise. T o make a threshold setting as globally applicable as possible, we develop a threshold setting algorithm based on the characteristics of im pulsive noise in PLC systems. We compare impulsive noise detection performance using both threshold setting methods. As expected, the threshold setting developed for universal use outperforms the previously proposed setting in terms of false detection rate as shown in chapter 6. If we are allowed to access real PLC systems, the next step of our research is to test the newly developed threshold setting against real impulsive noise sources in real PLC networks. We consider SS MC MA as a possible alternative to DMT in PLC systems due to its ability of multiple access, which can increase total system throughput by reducing MAC processing. T o further increase throughput, we propose an adaptive subcarrier allocation algorithm in chapter 7. The proposed algorithm selects the best subcarriers of each user and assigns the subcarriers to the user with the lowest SNR sum first ( for fairness consideration ) Simulations show a notable increase in throughput with the proposed algorithm over the existing alternatives. Whe n we consider the various attenuation levels for each user due to varying locations and propagation losses, the performance gap becomes even more significant. 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PAGE 105 BIOGRAPHICAL SKETCH Kyoungnam Seo received hi s Bachelor of Science degree Tele communication e ngineering at Cheju N ational University, Korea in 2001 and his M aster of Science in e lectrical and c omputer e ngineering at the University of Florida in 200 4 He is currently working toward his Ph.D. degree in e lectrical and c omputer e ngineering at the University of Florida. H is research interests are in the area of signal processing, w ireless and p ower l ine c ommunications. Specifically, h e is working on impulsive noise mitigation and multiuser interference suppression in multicarrier communication systems. 