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Divakaran, Dinesh.
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OWSS and MIMOSTCOFDM :
b signaling systems for the next generation of high speed wireless LANs
h [electronic resource] /
by Dinesh Divakaran.
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[Tampa, Fla] :
University of South Florida,
2008.
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Title from PDF of title page.
Document formatted into pages; contains 131 pages.
Includes vita.
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Dissertation (Ph.D.)University of South Florida, 2008.
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Includes bibliographical references.
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Text (Electronic dissertation) in PDF format.
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ABSTRACT: The current popularity of WLANs is a testament primarily to their convenience, cost efficiency and ease of integration. Even now the demand for high data rate wireless communications has increased fourfold as consumers demand better multimedia communications over the wireless medium. The next generation of high speed WLANs is expected to meet this increased demand for capacity coupled with high performance and spectral efficiency. The current generation of WLANs utilizes Orthogonal Frequency Division Multiplexing (OFDM) modulation. The next generation of WLAN standards can be made possible either by developing a different modulation technique or combining legacy OFDM with Multiple Input Multiple Output (MIMO) systems to create MIMOOFDM systems. This dissertation presents two different basis technologies for the next generation of high speed WLANs: OWSS and MIMOSTCOFDM.OWSS, or Orthogonal Wavelet Division Multiplexed Spread Spectrum is a new class of wavelet pulses and a corresponding signaling system which has significant advantages over current signaling schemes like OFDM. In this dissertation, CSMA/CA is proposed as the protocol for full data rate multiplexing at the MAC layer for OWSS. The excellent spectral characteristics of the OWSS signal is also studied and simulations show that passband spectrum enjoys a 3040% bandwidth advantage over OFDM. A novel predistortion scheme was developed to compensate for the passband PA nonlinearity. Finally for OWSS, the fundamental limits of its system performance were also explored using a multilevel matrix formulation. Simulation results on a 108 Mbps OWSS WLAN system demonstrate the excellent effectiveness of this theory and prove that OWSS is capable of excellent performance and high spectral efficiency in multipath channels.This dissertation also presents a novel MIMOSTCOFDM system which targets data rates in excess of 100 Mbps and at the same time achieve both high spectral efficiency and high performance. Simulation results validate the superior performance of the new system over multipath channels. Finally as channel equalization is critical in MIMO systems, a highly efficient time domain channel estimation formulation for this new system is also presented. In summary, both OWSS and MIMOSTCOFDM appear to be excellent candidate technologies for next generation of high speed WLANs.
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Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
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Coadvisor: Wilfrido A. Moreno, Ph.D.
Coadvisor: Paris H. Wiley, Ph.D.
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Wireless systems
Wlans
Wavelets
Space time coding
Multiplexing
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Dissertations, Academic
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x Electrical Engineering
Doctoral.
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t USF Electronic Theses and Dissertations.
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u http://digital.lib.usf.edu/?e14.2755
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DEDICATION
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ACKNOWLEDGEMENTS
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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FI GURES iv ABSTRACT vii CHAPTER 1 INTRODUCTION 1 CHAPTER 2 BACKGROUND 8 2.1 Background on OWSS Systems 8 2.1.1. Orthogonal Wavelet Division Multiplexing (OWDM) 8 2.1.2 OWDM Pulses from Full Tree Wavelet Filters 10 2.1.3 OWSS Pulses 13 2.1.4 OWSS Signaling System 19 2.1.5 Equalization in the OWSS Receiver 21 2.1.6 Bandwidth Estimate and Multiple Access Capability of OWSS 23 2.2 Background on MIMOSTCOFDM 25 2.2.1 Background on OFDM 25 2.2.2 Background on MIMO and STC 28 2.3 Conclusion 39 CHAPTER 3 MEDIUM ACCESS CONTROL IN OWSS WLANS 40 3.1 Introduction 40 3.2 CSMA/CA: The Basic Access Method 41 3.3 Performance Analysis of the DistributedCoordi nation Function 45 3.3.1. Markov Model 46 3.3.2 Throughput Analysis 48 3.3.3 Delay Analysis 50 3.4 Performance Analysis of CSMA /CA MAC Layers in OWSS WLANs 51 3.5 Conclusion 54 CHAPTER 4 SPECTRAL CHARACTERIS TICS OF THE OWSS SIGNAL 55 4.1 Baseband Spectrum of the OWSS Signal 56 4.2 Passband Spectrum of the OWSS Signal 57 4.2.1 Passband Spectrum of 108 Mbps OWSS 59 4.2.2 Bandwidth Efficiency of OWSS visvis OFDM 61 4.3 Compensation of PA NonLinearity in OWSS 63
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ii 4.3 Conclusion 66 CHAPTER 5 PERFORMANCE LIMITS OF THE OWSS WLAN SYSTEM 67 5.1 Multilevel Matrix Formulation of OWSS Receiver 68 5.1.1 TMSE in the OWSS Receiver 69 5.1.2 Optimum FEDFE Receiver 72 5.2 Simulation Results on the Performance Limits 76 5.2.1 Experiment 1 (100 ns DelaySpread Channel) 76 5.2.2 Experiment 2 (50 ns DelaySpread Channel) 77 5.3 Conclusion 80 CHAPTER 6 A NOVEL MIMOSTCOFDM SYSTEM 81 6.1 Introduction 81 6.2 Group Coded Antennas and Array Pro cessing in Flat Fading Channels 83 6.3 Grouped Antennas and Array Processing in MIMOOFDM. 86 6.3.1 Frequency Selective Channels in MIMOOFDM 86 6.2.2 Array Processing for Frequency Selective Channels 88 6.4 The New MIMOSTCOFDM System 91 6.5 Performance of the New MIMOSTCOFDM System 95 6.5.1 Simulation Results 95 6.5.2 Comparison with Othe r MIMOOFDM Techniques 96 6.5.3 Benefits of Channe l Coding and Interleaving 97 6.5 Conclusion 99 CHAPTER 7 CHANNEL ESTIMATION FOR THE MIMOSTCOFDM SYSTEM 100 7.1 Introduction 100 7.2 Channel Estimation for Grouped Antennas and Array Processed MIMO System in Flat Fading Channels 101 7.3 Frequency Domain Estimation for the New MIMOSTCOFDM System in Multipath Fading Channels. 105 7.4 Time Domain Estimation for the New MIMOSTCOFDM System in Multipath Fading Channels. 107 7.5 Simulations Based on the Time Domain Channel Estimation 112 7.6 Conclusion 114 CHAPTER 8 CONCLUSIONS AND FUTURE WORK 115 REFERENCES 121 APPENDICES 127 Appendix A An Example Based on the Multi Level Matrix Formulation 128 ABOUT THE AUTHOR End Page
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iii LIST OF TABLES Table 2.1 OWDM Pulses Derived from 2stage Tree with 4tap Daubechies Filter 16 Table 2.2 OWDM Pulses Derived from 2stage Tree with 4tap Daubechies Filter 16 Table 3.1 MAC Attributes of OWSS 52 Table 4.1 Spectrum and Emission Mask BW of 108 Mbps OWSS Signal 60 Table 4.2 Comparison of 54 Mbps OWSS and 802.11a OFDM Spectrums 62 Table 4.3 Comparison of OWSS and 802.11a OFDM Emission Masks 63 Table 5.1 Simulation Results with Adaptive Loading for 100 ns DelaySpread Channels 79 Table 5.2 Simulation Results with Adaptive Loading for 50 ns DelaySpread Channels 79 Table 6.1 Comparison of the New MIMOSTCOFDM with Other MIMOOFDM Systems 97 Table 6.2 Coding and Interleaving Ga ins for MIMOSTCOFDM System 98
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iv LIST OF FIGURES Figure 2.1 OWDM Synthesis Tree 11 Figure 2.2 Block Diagram of OWSS Transmitter (For kth User) 14 Figure 2.3 Block Diagram of Correlator Bank and Summer at OWSS Receiver (For kth User) 14 Figure 2.4 A Typical OWSS Pulse and its Magnitude Spectrum 17 Figure 2.5 Autocorrelation of OWSS Pulse 0 18 Figure 2.6 Cross Correlation Map of 4 OWSS pulses 18 Figure 2.7 OWSS Pulses M=16 fr om 4 stage OWSS Filter Tree 19 Figure 2.8 OWSS Signaling System 20 Figure 2.9 Simplified ROM Based OWSS Signaling System 22 Figure 2.10 Details of the Baseba nd portion of the OWSS Receiver 23 Figure 2.11 Simple Baseba nd OFDM Transreceiver 26 Figure 2.12 802.11a OFDM Passband Spectrum and Spectrum Mask 29 Figure 2.13 Basic MIMO System 28 Figure 3.1 CSMA/CA 41 Figure 3.2 Four Way Handshake RTSCTS Scheme 42 Figure 3.3 Basic Access Mechanism 44 Figure 3.4 RTS/CTS Mechanism 45
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v Figure 3.5 Markov Chain M odel for the Backo ff Window Size 47 Figure 3.6 OWSS Frame Format 52 Figure 3.7 System Throughput for 108 Mbps OWSS WLAN 53 Figure 3.8 Average Delay for 108 Mbps OWSS WLAN 53 Figure 4.1 Baseband Spectrum of OWSS 57 Figure 4.2 Simple Passband OWSS Transm ission System for Spectral Analysis 58 Figure 4.3 Simulated Baseband and Pa ssband Spectrum of OWSS Signal 59 Figure 4.4 Spectrum and Emission Mask for 108 Mbps OWSS Signal 60 Figure 4.5 Comparison of OWSS and 802.11a OFDM Spectrums 62 Figure 4.6 Passband 108 Mbps OWSS Spectrum with PA Nonlinearity using Rapp Model 64 Figure 4.7 Novel Pr edistortion Scheme for PA NonLinearity Compensation 65 Figure 4.8 Compensated 108 Mbps Passband Spectrum using PreDistortion 66 Figure 5.1 OWSS Transreceiver System 69 Figure 5.2 BER for 108 Mbps 64QAM with 2:1 Se lection Diversity (over 100 ns DelaySpread channels) 77 Figure 6.1 The Overall Approach 81 Figure 6.2. Frequency Diversity in New System 82 Figure 6.3 Grouped Antennas and Array Processing for 4 4 system 83 Figure 6.4 Array Processing in Frequency Selective MIMOOFDM Channels 89 Figure 6.5 Novel MIMOSTCOFDM System 91 Figure 6.6 Eigen Value Analysis of Frequency Diversity for Novel MIMOSTCOFDM System 94
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vi Figure 6.7 MIMOSTCOFD M Simulation Results 95 Figure 7.1 Channel Estimation for Flat Fading Channels 103 Figure 7.2 SNR of Estimated Flat Channels and Associated BER for Varying Values of D in a 4 4 MIMOS TCOFDM System (Eb/No = 19dB) 105 Figure 7.3 Frequency Domain Channe l Estimation for the New MIMOSTCOFDM System 106 Figure 7.4 SNR of Estimated Flat Channels for Va rying Values of D in a 4 4 MIMOSTCOFDM system (Eb/No = 19dB) 107 Figure 7.5 Time Domain Channel Estimation for the New MIMOSTCOFDM System 108 Figure 7.6 SNR of Time Domain Estimated Channel Parameters at 19 dB Signal SNR 113 Figure 7.7 System Performance with Known Channels and Time Domain Channel Estimation 114
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vii OWSS AND MIMOSTCOFDM: SIGNALING SYSTEMS FOR THE NEXT GENERATION OF HIGH SPEED WLANS DINESH DIVAKARAN ABSTRACT The current popularity of WLANs is a test ament primarily to their convenience, cost efficiency and ease of integration. Even now the demand for high data rate wireless communications has increased fourfold as consumers demand better multimedia communications over the wireless medium. The next generation of high speed WLANs is expected to meet this increased demand fo r capacity coupled with high performance and spectral efficiency. The current generation of WLANs utilizes Orthogonal Frequency Division Multiplexing (OFDM) modulation. Th e next generation of WLAN standards can be made possible either by developing a different modulation technique or combining legacy OFDM with Multiple Input Multiple Output (MIMO) systems to create MIMOOFDM systems. This dissertation presents tw o different basis technologies for the next generation of high speed WLANs: OWSS and MIMOSTCOFDM. OWSS, or O rthogonal W avelet Division Multiplexed S pread S pectrum is a new class of wavelet pulses a nd a corresponding signaling sy stem which has significant advantages over current signaling schemes lik e OFDM. In this dissertation, CSMA/CA is proposed as the protocol for full data rate multiplexing at the MAC layer for OWSS. The excellent spectral characteristics of the OWSS signal is also studied and simulations show
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viii that passband spectrum enjoys a 3040% ba ndwidth advantage over OFDM. A novel predistortion scheme was developed to comp ensate for the passband PA nonlinearity. Finally for OWSS, the fundamental limits of its system performance were also explored using a multilevel matrix formulation. Simulation results on a 108 Mbps OWSS WLAN system demonstrate the excellent effectivene ss of this theory and prove that OWSS is capable of excellent performance and high spectral efficiency in multipath channels. This dissertation also presents a nove l MIMOSTCOFDM system which targets data rates in excess of 100 Mbps and at the same time achieve both high spectral efficiency and high performance. Simulation re sults validate the superior performance of the new system over multipath channels. Finally as channel equalization is critical in MIMO systems, a highly efficient time domain channel estimation formulation for this new system is also presented. In summary, both OWSS and MIMOS TCOFDM appear to be excellent candidate technologies for next generation of high speed WLANs.
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CHAPTER 1 INTRODUCTION In recent years the demand for high data rate wireless communications [1] has increased steadily as consumers demand better multimedia communications over the wireless medium. A wireless LAN or WLAN [2], [3] is a wireless local area network which connects two or more computers or devi ces without using wire s. Current state of the art WLAN systems like 802.11a/g [4],[5 ] utilize Orthogonal Frequency Division Multiplexing (OFDM) [6][8] modulation technology based on radio waves in the 5 and 2.4 GHz public spectrum bands, to enable co mmunication between devices in a limited area, also known as the basic service set. This gives users the mobility to move around within a broad coverage area and still be connected to the network. The popularity of wireless LANs is a testament primarily to th eir convenience, cost e fficiency, and ease of integration with other networks and network components. The majority of computers sold to consumers today come preequipp ed with all necessary WLAN technology. The current WLAN systems are capable of a maximum data rate of 54 Mbps [2][5]. The next generation of WLAN standards is expected to touch bit rates of 108 Mbps and possible even 240 Mbps [2]. This can be made possible either by developing new standards based on a different modulation t echnique than OFDM or combining OFDM with state of the art Multiple Input Multiple Output (MIMO) [9][12] systems (systems
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employing multiple transmit and receive antenn as) to create MIMO OFDM systems [12][16]. Current R&D efforts including the eagerly awaited 802.11n standard [17][18] are directed at MIMOOFDM, however there is an urgent need to look at other signaling schemes which can overcome the inherent di sadvantages of OFDM without the use of MIMO. OWSS, or O rthogonal W avelet Division Multiplexed S pread S pectrum [19][22] is a new class of wavelet [23] pulses and a corres ponding signaling system which can be a candidate technology for the next generation high speed WLANs. These pulses are generated through a combination of Orthogonal Wavelet Division Multiplexing (OWDM) [24] and Spread Spectrum (SS) [25] concepts. The OWSS system has significant advantages over current signaling schemes like OFDM, TDMA [1] and even OWDM. Some of these unique advantages ar e: wide time and frequency support [19], multiple user capability [28], [32] [19], ef fective multipath channel equalization [27], [29],[31], continuously pipe lined operation (in contrast to OFDM), high bandwidth efficiency [26], [31] and robustness agains t deep fading frequency selective channels unlike OFDM [19],[21]. OWSS is a new modulation scheme for high speed WLANs, however as mentioned earlier current research trends based on combining the current modulation scheme OFDM with MIMO. Towards this end, a new MIMOSTCO FDM system [33][35] was developed which target s next generation data rates (108 Mbps), and at the same time achieve both high spectral efficiency and hi gh performance (high data rate with low BER) over frequency selective channels. This new system is accomplished by a combination, or layering [36] of MIMO OFDM [12][16], group transmit signals and
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antennas [37], space time coding [38], [39], arra y processing [37] at the receiver and a new Least Squares (LS) decoding scheme [33] The current system is a 4 system (4 transmit and 4 receive antennas) but can easily be extended to larger MIMO systems that achieve data rates in excess of 108 Mbps. In this dissertation, two different basis technologies for the next generation of high speed WLANs are presented: OW SS and the new MIMOSTCOFDM. The dissertation is organized as follows. Following the introduction the outline of this dissertation consists of five parts (1) Background on OWSS system, OFDM, MI MO Systems and STC (Chapter 2) (2) Medium Access Control in OWSS WLANs and Spectral Charact eristics of OWSS. (Chapter 3 and 4) (3) Performance limits of OWSS based on a th eoretical multilevel matrix formulation. (Chapter 5) (4) The new MIMOSTCOFDM system w ith high spectral efficiency and high performance (Chapter 6). (5) Multipath Channel Mode ling and Estimation for the new MIMOSTCOFDM system. (Chapter 7). The first part given above provides detail ed information about OWSS system and a background on OFDM, MIMO systems and STC. The last four parts contain the main contribution of the dissertation and in clude original research results.
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Specific novel contributions of this dissertation in different chapters are listed below: (1) OWSS and MIMOSTCOFDM are both presented as viable candidates for the next generation of high speed WLANs. OWSS is a new modulation technique capable of high data rates without using multiple antennas at the transmitter and receiver. MIMOSTCOFDM on the other hand, achieves next gene ration data rates by combining transmit and receive diversity techniques w ith legacy OFDM systems. (2) A CSMA/CA based MAC protocol is propos ed for OWSS to access the medium [28]. The frame format for OWSS data packets and MAC attributes of OWSS are also proposed. Performance of OWSS at the MAC la yer in terms of saturation throughput and average delay is analyzed using a simple theoretical model. (3) The spectrum efficiency of OWSS is an alyzed visavis OFDM. The OWSS passband spectrum is found to have 3040% bandwid th advantage over OFDM for 54 Mbps operation [26]. OWSS also readily extends to hi gher bit rates, such as 108 Mbps, in a bandwidth efficient manner. (4) A novel predistortion scheme [70] was developed to compensate for the passband spectral regrowth due to PA nonlinearity. At 6 dB backoff in 108 Mbps OWSS, this scheme yields an improvement of 10 dB in spectral regrowth distortion levels. (5) A Forward Equalizer Decision Fee dback Equalizer (FEDFE) structure was originally proposed for the OWSS receiver. To wards this end, a novel multilevel matrix formulation [27] has been conceptualized to model the entire OW SS transreceiver and establish its fundamental theoretical performance (BER) in random multipath fading channels. This formulation can also be used for channel estimation, i.e. to estimate the optimum channel equalizer (weights of th e FE and DFE) for these channels.
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(6) A new MIMOSTCOFDM system [33] ha s been developed that achieves both high spectral efficiency and high performance ove r frequency selective channels. This new system was achieved combini ng MIMOOFDM, group coding antennas using STC, array processing at the receiver (for interference suppression) and new LS decoding technique. (7) A highly effective channel equalization technique [34] in the time domain has also been developed for the new MIMOSTCO FDM system. The multipath channel model for the system is also conceptualized. The dissertation is organized in detail as follows. It starts by providing a detailed background for both OWSS and MIMOSTCO FDM in Chapter 2. OWDM and its combination with Spread Spectrum (SS) concepts to synthesize OWSS pulses is studied. The inherent advantages and special natu re of the OWSS pulses is discussed. The corresponding OWSS signaling system is pres ented and a powerful adaptive equalizer structure in the OWSS receiver [27], [29] which combats multipath fading is described. In the second part of the chapter 2, a review of OFDM, MIMO systems and STC, key concepts that serve as a basis for the new MIMOSTCOFDM system is provided. Chapter 3 looks at the Medium A ccess Control (MAC) layer in OWSS WLAN system. OWSS will use a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) [40] based MAC protocol similar to the IEEE 802.11a [4] standard to access the medium. A frame format for OWSS da ta packets in the MAC layer and MAC attributes of OWSS in terms of DCF parame ters are proposed. Using a simple theoretical model called Bianchis Model [ 41], [42], an analysis of th e performance of OWSS in the
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MAC layer in terms of two key parameters, system throughput and average packet delay is carried out. Chapter 4 analyzes the excellent spectral characteristics of the OWSS signal and studies its bandwidth efficiency as compared to OFDM. It is shown that the theoretical baseband spectrum of OWSS is perfectly flat, and the passband spectrum offers a 3040% bandwidth advantage [26], [31] over 802.11a OFDM for 54 Mbps operation. OWSS also readily extends to higher bit rates, such as 108 Mbps, in a bandwidth efficient manner. The effect of spectral regrow th in the OWSS passband spectrum was analyzed using the Rapp Model. This spectral regrowth can be co mpensated to a large extent using a novel predistortion scheme. At 6 dB backoff in 108 Mbps OWSS, this scheme yields an improvement of 10 dB in the spec tral regrowth di stortion levels. Chapter 5 explores the fundamental lim its to OWSS performance. Towards this purpose, a multilevel matrix formulation [27] is employed to model the signal processing system. The total minimum meansquare error (TMSE) for the Forward Equalizer Decision Feedback Equalizer (FEDFE) structure [27], [29], [30] is derived in a closed form, and thereupon minimized rigorously to provide the optimum equalizer weights and corresponding theoretical BER performance of the OWSS system. Simulation results on a 108 Mbps system demonstrate the effectiveness of this theory and prove that OWSS is capable of excellent pe rformance and high spectral efficiency in multipath fading channels.
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Chapter 6 introduces the new MIMOSTCO FDM system [33][35] that achieves both high spectral efficiency and high perf ormance over frequency selective channels. This is accomplished by a combination, or layering [36] of MIMO OFDM [12][16], group transmit signals and antennas [37], space time coding [38], [39], array processing [37] at the receiver and a ne w Least Squares (LS) decoding scheme [33]. The new system is compared with other MIMO OFDM syst ems and simulation results validate the superior performance of the new system. Chapter 7 presents an efficient new ti me domain channel estimation [34], [35] formulation for the new high performance MIMO STCOFDM system, which uses high power QPSK symbols. Four matrixvector multi plications and a single data frame enables high accuracy estimation of all sixteen MIMO channels in the 4 4 system. Chapter 8 provides a list of novel contributions of this dissertation, concluding remarks and suggestions for future re search in OWSS and MIMOSTCOFDM.
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CHAPTER 2 BACKGROUND 2.1 Background on OWSS Systems OWSS, or O rthogonal W avelet Division Multiplexed S pread S pectrum [19][22] is a new class of pulses and a corresponding signaling system for next generation high speed WLANs and targets bit rates upward s of 108 Mbps. These pulses are generated through a combination of Orthogonal Wavelet Division Multiplexing (OWDM) [24] and Spread Spectrum (SS) concepts [25]. The OW SS system has signifi cant advantages over current signaling schemes like OFDM [6][8 ], TDMA [1] and even OWDM. Some of these unique advantages are : (1) single or multiple user capability at the PHY or MAC layer (2) effective multipath channel equalization due to wide time and frequency support (3) continuously pipelined operation (in contrast to OFDM) (4) high bandwidth efficiency, which is about twice for DSCDM A [43] (assuming rectangular chips for DSCDMA). As mentioned earlier, OWSS pulse s are derived from OWDM pulses by spreading them in the wavele t domain [23], using a suitable family of PN codes [25]. Therefore, let us begin with a discussion on OWDM pulses. 2.1.1. Orthogonal Wavelet Division Multiplexing (OWDM) OWDM is based on the concepts of orthogonal multipulse signaling [44]. Consider that the pulses m(t) m = 0 1, . M 1, form an orthonormal set over a
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certain period of time and that each puls e is orthogonal to itself shifted by nonzero integer multiples of a certain interval T [44]. Each basis pulse m(t) can then serve to create a virtual channel over which the symbol am is carried. The vector of symbols A = [ a0, a1, . aM 1]T is called a supersymbol, and the interval T = MTs as the supersymbol/block interval, where Ts is the basic symbol interval Then the base band transmitted signal becomes )iTt(A)iTt(a )t(si T i i 1M 0m mm,i (2.1) At the receiver, symbol and block tim ing extraction is performed, and the received signal is correlated with (t iT) to detect the n th supersymbol at time iT (actually at time iT + where denotes the optimum timing phase [44]). Since CMOS VLSI implementation of signal processing techniques is often less complicated and economical in the discrete time domai n, discrete time formulation of orthogonal multipulse signaling will be used from now on. The discrete time orthogonal multipulses are m(n) m = 0 1, . M 1, and the corresponding transmitted orthogonal multipulse signal becomes )iMn(A)iMn(a )n(si T i i 1M 0m mm,i (2.2) However for convenience and simplicity, the variable t will be used to denote both the continuous time variable as well as th e discrete time sample index. Also, M and T will be used interchangeably to denote the block length.
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Orthogonal multipulse signaling has the fo llowing distinct advantages: (1) potentially less sensitive to multipath fading (2 ) potential to reach channel capacity and countering selective fading (3) potential for mu ltiplexing at the physical layer. For a more detailed review of OWDM pulses, refer to [24]. The OWDM system uses wavelet pulses as the basis pulses in orthogonal multipulse signaling. 2.1.2 OWDM Pulses from Full Tree Wavelet Filters The use of basis functions in the analysis of signals modulated by transforms is a time proven concept. For example, in the Disc rete Fourier transform (DFT) [45] the basis set consists of all complex sinusoids of the form ejn where can take on any real value. In recent years attention has been focused on basis sets generated from wavelets [23]. The OWDM basis sets are generated through the process of scaling or shifts from a single parent function, called the mother wavelet (t) Appropriately, then, the basis pulses are indexed by two indices x and y signifying scale and shift respectively. Thus, the basis pulses are of the form yt22x 2/x y,x (2.3) A three stage ( M= 23= 8 input nodes) synthesis tree for generating the wavelet pulses)( ti which serve as the basis pulses, is shown in Figure 2.1. More generally, for an s stage tree there would be M = 2s input nodes. The impulse response from the i th input node to the output node is denoted as1.,..,1,0 where),( M iti The prototype type filter G0 can be a Haar wavelet [23], a Daubech ies filter [23], or other [45] [48].
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As an example, consider the wellknown Haar wavelet 211 and its scaling function 211 Either of them or both can be used to create the OWDM basis set. In terms of implementation this is frequently done through th e tree structure [8]. To illustrate, let us define the high pass and low pass filters as g0 = [1 1] and g1 = [1 ]. Both are identical to the mother wavelet and its scaling functi on, except they are not normalized. In the Figure 2.1, several differe nt sampling frequencies are observed. The input sampling frequency Fs will be doubled in each stage to become an output sampling frequency of 8 Fs. The z transforms G0( z ) and G1( z ) are shown as the filter transfer functions. Figure 2.1 OWDM Synthesis Tree 2 2 2 2 2 2 2 2 2 2 2 2 2 2 High Pass Filter a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 G1(z) G 1 (z) G 1 (z) G 1 (z) G 1 (z) G1(z) G 1 (z) G 0 (z) G 0 (z) G0(z) G0(z) G 0 (z) G 0 (z) G 0 (z) s(t)Low Pass Filter 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 High Pass Filter G 0 (z) G 0 (z) G 1 (z) G 1 (z) G 1 (z) G 1 (z) G1(z) G 0 (z) G0(z) G0(z) G 0 (z) G 0 (z) Low Pass Filter G 1 (z) G1(z) a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0
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In the figure, a member of the OWDM basis set can be generated by applying a unit pulse at only one input node while all other nodes receive a zero input. Thus, for example if input node 5 is driven by a unit pu lse, and all other input nodes are held at zero, the output turns out to be 5 = [1 1 1 1]. Here is a general formula: consider an arbitrar y leaf node, say node n = [ i j k ] (binary address). Then the transfer function from this node to the output node is Pi,j,k = Pi( z ) Pj( z2) Pk( z4), where for node 5, Pi( z ) = G1( z ), Pj( z ) = G0( z ), and Pk( z ) = G1( z ). The tree of Figure 2.1 can be represented by a equivalent tree as shown in Figure 2.2. It can be shown that the pulses generated in this set are orthogonal, and in f act if the normalization factor 1/ 2 was not ignored, these pulses would be orthonormal. Hereafter the norma lization factor is included so that the set of wavelet pulses { 0, 1, .... M} will be doubly orthonormal, i.e. the pulses satisfy the generalized Nyqui st criterion [23]. nki ki)nTt(),t( for i, k=0,1,.., M1 and all n. (2.4) Also, it can be shown that these pulses are power complementary, i.e., 1)f( M 1M 1m 2 m (2.5) The structure shown in Figure 2.1 and 2.2., can be used for other wavelets as well. Thus, the synthesis tree can generate eight Daubechies wavelet pulses i(t), i = 0, 7 if the Daubechies scaling function [23] and the corr esponding mother wavelet [23] are used as the filters g0 and g1. In this dissertation, the OWDM pulses generated by through a Daubechies filter as the prototype G0(z) are used. An example family, generated from a 4tap Daubechies
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filter G0(z) = [0.3415, 0.5915, 0.1585, 0.0915] and a 2stage tree, is given in Table 2.1. Note that each pulse is normalized to unit en ergy. Actually as shown originally in Figure 2.1 the tree structure shown can be used to synthesize the transmitted OWDM signal s(t) of (2.2) and (2.3). By applying the ith supersymbol Ai = [a0,i, a1,i, . aM 1,i]Tat instant iM, and of course repeating this process for all i, it is easily seen using superposition that the output signal from the synthesis tree is (2.1). The synthesis tree is a multirate multiple input single output (MIS O) [38] linear filter. The co rresponding analysis trees at the receiver will also be multi rate linear filter, but of the single input multiple output (SIMO) type [38]. 2.1.3 OWSS Pulses While the OWDM pulses do satisfy the gene ralized Nyquist criterion, they are not broadband and are just as susceptible to deep fades, as are the OFDM pulses. Overcoming this deficiency, the OWSS pulses are derived from OWDM pulses m(t) by spreading them in the wavelet domain through a suitable family of PN codes. The OWSS transmit signal synthesizer and receiver si gnal analyzer is illustrated in Figure 2.2 and 2.3. The new broadband OWSS pulse is given by )t(c)t(c)t(T)i( 1M 0m m )i( m )i( (2.6) Here c(i), i = 0, . M 1, are the code vectors which pe rform the spreading in wavelet domain. The superscript connotes the ith pulse, which is assigned to the ith user. In this dissertation, Hadamard codes [25] will be use d. Using Hadamard codes, it can readily be shown that the OWSS pulses, (i)(t ), i = 0, . M 1, are also doublyorthogonal.
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co (k)cM1 (k)o(t) M1(t) an (k)s(k)(t) co (k)cM1 (k)o(t) M1(t) an (k)s(k)(t) Figure 2.2 Block Diagram of OWSS Transmitter (For kth User) qo (k)qM1 (k)o *(t) M1 *(t) r(t) LPF LPF (k) qo (k)qM1 (k)o *(t) M1 *(t) r(t) LPF LPF (k) Figure 2.3 Block Diagram of Correlator Ba nk and Summer at OWSS Receiver (For kth User) That is, they (like OWDM pulses) satisfy the generalized Nyquist criterion. nki ki)nTt(),t( for i, k=0,1,.., M1 and all n. (2.7) Thus, these pulses provide a means for creating M virtual channels. Also, it can be shown
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that these pulses are pow er complementary, i.e., 1)f( M 1M 1m 2 m (2.8) Most importantly, they are broadband. Th at is, each pulse in the family of M pulses broadband [1]. For M = 4 and M = 8, the corresponding Hadamard code matrices are given by 11111111 11111111 11111111 11111111 1 1111111 11111111 11111111 11111111 8 1 H 1111 1111 1111 1111 2 1 H8 4 (2.9) For the OWDM pulses of Table 2.1 and code H4 of (2.9) the OWSS pulses are listed in Table 2.2. It is importa nt to remark that these pulse s need not be generated online; they can be computed offline and conveniently stored in a ROM.
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Table 2.1 OWDM Pulses Derived from 2st age Tree with 4tap Daubechies Filter Table 2.2 OWSS Pulses Derived from 2stage Tree with 4tap Daubechies Filter Tap Weights Tap 0 1 2 3 4 5 6 7 8 9 Pulse 0 0.1845 0.3248 0.5123 0.4542 0.1373 0.5123 0.0792 0.2958 0.1083 0.0625 Pulse 1 0.1083 0.1875 0.2958 0.2623 0.5123 0.4542 0.1373 0.5123 0.1875 0.1083 Pulse 2 0.1083 0.1875 0.1373 0.5123 0.6708 0.1373 0.3873 0.0792 0.1875 0.1083 Pulse 3 0.0625 0.1083 0.0792 0.2958 0.1373 0.5123 0.6708 0.1373 0.3248 0.1875 Tap Weights 9 Tap 0 1 2 3 4 5 6 7 8 Pulse 0 0.2333 0.4040 0.2958 0.7623 0.0792 0.2958 0.1127 0.0792 0.0290 0.0167 Pulse 1 0.0625 0.0183 0.0792 0.2042 0.4542 0.6708 0.4208 0.2958 0.1083 0.0625 Pulse 2 0.0625 0.1083 0.5123 0.0458 0.7288 0.3538 0.1708 0.1373 0.1083 0.0625 Pulse 3 0.0167 0.0290 0.1373 0.0123 0.0792 0.2958 0.6373 0.5123 0.4040 0.2333
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Pulse 0 and its magnitude spectrum is shown in Figure 2.4. In the interest of e other three pulses are not displaye d, but they generally have similar time and lation for Pulse 0 is shown in Figure 2.5 using pletransmit pulse. The cro sscorrelation map of all 4 member pulses is ic scale. The actual matrix of crosscorrelations is a 4 atrix. To summarize, OWSS ha s the following properties : (1) the pulses their spectrum, (2) the pulses are broadtime, since their timehas an excellent autocorrel ation behavior, and (4) the ogonal, so as to support multiuser operation. This excellent channel fades. For a detailed discussion icial properties of OWSS pulses, refer to [19][22]. The set of 16 pulses SS synt hesizer is illustrated in Figure 2.7. space, th spectral behavior. The blockwise autocorre a rectangular sam shown in Figure 2.6 on a logarithm x 4 identity m are broadband as seen from support is long, (3) each pulse pulses are mutually orth behavior holds up even in the presence of deep on the benef synthesized by a four stage OW Figure 2.4 A Typical OWSS Pulse and its Magnitude Spectrum 0 5 10 15 20 25 30 35 0.4 0.2 0 0.2 0.4 OWSS; Stages=2 pulse#0 from an 8tap Daubechies w avelet filter 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 40 20 0 20 Mag Spectrum of pulse#0dB
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10 5 0 5 10 15 0.2 0 0.2 0.4 0.6 0.8 1 1.2 Autocorrelation of a Broadband OWSS pulse Block Based Shifts Figure 2.5 Autocorrela tion of OWSS Pulse 0 Crosscorrelation map of Broadband OWSS pulses ij 1 2 3 4 1 2 3 4 Figure 2.6 Cross Correlation Map of 4 OWSS Pulses
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Figure 2.7 OWSS Pulses M=16 from a 4 stage OWSS Filter Tree 2.1.4 OWSS Signaling System An overview of OWDM SpreadSpectrum (OWSS) transreceiver is illustrated in Figure 2.8 and a simplified ROM based system is shown in Figure 2.9. The training phase is not shown, during which a set of known samples s(t), previously stored at the receiver and produced by a set of known transmitted sym bols, is used for training the channel equalizer [44]. The details of the transmitter block and the 'correlator and summer' block at the receiver were give n in Figure 2.2 and 2.3. Here (t) is the set of the OWSS pulses, assembled in the form of a vector.
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r(t) Channel Equalizer T S T ST Detect & DFB Error Adaptation s(t) p(t) Symbols Out ^ a n Z n c (t) c (t) a n TX Corr bank, sum Figure 2.8 OWSS Signaling System Referring to Figure 2.3 and Figure 2.8, the tr ansmitted signal for the ith user is )nTt(a)nTt(ca)t(s)i( n )i( n n 1M 0m m )i( n )i( n )i( (2.10) where is the new OWSS broadband pulse for the ith user. The received signal equals the sum of the signals received from all transmitters. For this discussion, assume ideal channel conditions without channel attenuation and multip ath effects [1],[50]. Thus, at kth receiver the r eceived signal is )()(ti (2.11) U 1i i )i( n )i( n U 1i )i()nTt(a)t(r)t(r Assuming perfect timing, the output of the kth correlator in the OWSS receiver is )k( )k( n )k( n )k( n AWGN )k( ICI ki k )i( i )i( l )k( l ISI nl k )i( k )i()k( n k )i( k )i()k( n k )i( )k( nNICIISIa N nTt,lTta nTt,lTta nTt,nTta nTt),t(rz (2.12)
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The inter symbol interference term (ISI) [1] is zero due to the impulsive nature of the autocorrelation of the OWSS pulses. Also for the downlink case, all i, are equal, so that the inter channel interference term (ICI) [1] is also zero. Thus the output of the kth OWSS receiver correlator is (2.13) )k()k( n )k( nNaz This means that except for the addition of Adaptive White Gaussian Noise (AWGN) [1], [44], the input to the decision device is the nth symbol of the kth user. Thus, the probability of symbol error would be the same as in the single user AWGN case for QAM symbols [1], [44]. Figure 2.2, 2.3 and 2.8 have provided a detailed structural realization of the OWSS transreceiver, however si mpler realization is possible as illustrated in Figure 2.9. This is a ROM based design, where the S/P and P/S conversions have been omitted for simplicity. Here the PN code has already been imbibed in the transmit pulse (i)(t) for the ith transmitterreceiver pair.. Also, Decision Feedback Equalizer (DFE) [44] has been added, which will be discussed in the next s ubsection. Also note that the wavelet pulse set {(i)(t)} is common to all users. It is only the PN codes that are different for each user pair, as signified by the superscript i in equation (2.10). 2.1.5 Equalization in the OWSS Receiver To surmount the ISI introduced by a time varying multipath channel [1], [44], a powerful adaptive equalizer [44] structure ha s been developed for the OWSS system. The
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Z n a n r(t) Channel T S T ST Detect & DFB Error Adaptation s(t) p(t) Symbols Out ^ a n Corr TX pulse (i) (i) FE DFE + Figure 2.9 Simplified ROM Based OWSS Signaling System baseband part of an OWSS receiver is shown in Figure 2.10. It deploys an adaptive Forward Equalizer (FE) and a Decision Feedback Equalizer (DFE), both of finite impulse response (FIR) form [45]. Not shown is th e adaptation mechanism, which will not be discussed here but can be found in [29], [30] The receiver also uses a correlator, a decision device, and an upsampler. Indeed, the output of the equalizer is correlated with an OWSS pulse, which is specific to the user, thus despreading it for detection. Note also that the correlator generates its output every Mth sample. Therefore, the decision device [1] and error computations operate at a lo wer rate than does the equalizer. Thus the OWSS receiver is a multi rate system [51]. Since the DFE ope rates at the same speed as the FE, an upsampler [45] is needed, as shown in the figure. Initially, the coefficients of the FE and DFE are obtained through a trai ning phase (using a pr estored sequence of symbols and the LMS [44] algorithm for update ). Subsequently, the receiver goes into maintenance mode. Of course, the equalizer coe fficients are updated in this mode as well. The training phase begins with an arbitrary set of equalizer weights. These weights tend to converge to minimize the Mean Square Er ror (MSE) [44]. The final weights obtained at the end of the training are then used to initialize the maintenance phase. As stated will
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earlier, the theory of the adaptive equalizer, in particular the adaptation mechanism, will not be discussed here. Readers can refer to [26], [39] and [30] for further details. q(k)+ a((kL)/M)^ b 2 p(k) q(kL+1) b 3 Delay line Correlator F/M + r(k1) 0 1 2 r(k2) r(k) w w w M F + e((kL)/M) M v(k/M) e((kL)/M 1) z 1 z 1 F/M F/M F/M a((kL)/M 1)^ e((kL)/M2) z 1 z 1 a((kL)/M 2)^ b 1 f(k) Figure 2.10 Details of the Baseba nd Portion of the OWSS Receiver 2.1.6 Bandwidth Estimate and Multiple Access Capability of OWSS The transmission bandwidth of the 108 Mbps OWSS System will now be discussed. Let us assume a 108 Mbps gross bit ra te, of which 8 Mbps is to be set aside for overhead. A 64QAM modulation [44] is assume d, so that the symbol rate becomes Rs = 108/log216 = 108/6= 18 Msps. For M wavelet channels the symbol rate on each channel becomes Rsc= 18/M Msps with a corresponding supersymbol interval T = M/18. Then the bandwidth of each of the underlying M wavelets is f = 18/M MHz. Correspondingly,
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the baseband bandwidth becomes BWBB = (M)( 18/M) MHz. Finally, th e transmission bandwidth is given by BT = (18)((M+l)/M). Due to the overlap be tween the spectra of the wavelet pulses, the bandwidth expansion takes place only for the boundary wavelets, giving rise to the factor (M+l)/M. Thus For M=4, T=3.5555 s and BT = 18.28125 MHz. For M=8, T=0.44444 s and BT = 20.25 MHz. As mentioned earlier the OWSS scheme can be used for multiple access, from a high singleuser data rate to various shades of multiuser and correspondingly reduced data rates. Denote the overall system bit rate R. Then any of the combinations, U = 1, U = 2, U = 4, U = M can be incorporated. For example, if the number of users is U = 8, the bit rate for each would be R/8 and the number of codes allocated to each M/8; needless to say, M should be chosen to be greater than or equal to 8 (e.g., 16). It is useful to remark that in the single user case, ra ndom access sharing of the channel could well be done using CSMA/CA [40] at the MAC layer. Thus, the term single user must be interpreted carefully. It simply means that only a single user can access the bandwidth at a time (whereas with U = 8, up to eight users can access the channel simultaneously).
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2.2 Background on MIMOSTCOFDM The prevailing 54Mbps WLAN standards, 802.11a/g [4], [5] ar e based on OFDM [6][8]. Next generation WLAN standards are also expected to be based on OFDM and the Industry is specifically in terested in Multiple Input Mu ltiple Output (MIMO) systems [9] [16] which are compatible with OFDM, namely current legacy systems. This would allow reuse of functionality and existing standard protocols. A high data rate extension 802.11 n targeting bit rates of over 100 Mbps is due in 2009 and will probably combine concepts of OFDM with Multiple Input Mu ltiple Output (MIMO) algorithms. A novel MIMOSTCOFDM system [33] [35] has been developed whic h is capable of targeting bit rates upwards of 108 Mbps. This system combines basically combines OFDM technology with Space Time Block Coding (ST BC) [38], [39], [52], [53] in a MIMO environment. We begin with an analysis of OFDM. 2.2.1 Background on OFDM In early systems high data rates of th e time were obtained by achieving parallel transmissions of data the frequency domai n. This was achieved by dividing the total signal frequency band into nonoverlapping fr equency subchannels or subcarriers, a technique called Frequency Division Multiplexing (FDM) [ 44]. FDM however was spectrally inefficient due to the use of guard sp aces to eliminate ICI. A more efficient use of the spectrum can be achieved if the subc hannels in FDM are able to overlap. This would however require the subchannels to be mutually orthogonal and this was the basic concept behind OFDM. OFDM is a multi carrier (MC) technique [44], that operates with
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specific orthogonality constraints between the subcarriers. Due to this, OFDM achieves high spectral efficiency. In OFDM the subcarrier pulse is chos en to be rectangular and number of subcarriers is selected to be a power of 2. This has the a dvantage that the pulse shaping and modulation can be done by a simple inve rse discrete fourrier transform (IFFT) [5][8], resulting in remarkable reduction of hardware complexity. A simple baseband OFDM transreceiver is illus trated below in Figure 2.11. Figure 2.11 Simple Baseband OFDM Transreceiver OFDM converts serial data stream X (n) into parallel blocks of size K (where K is the number of subcarriers), and uses IFFT to obtain timedomain signal x (n). Before transmission, the inverse FFT (IFFT) described by matrix FH to applied to the QAM symbols, to obtain (n)XF(n)xH (2.14) where F is a K K FFT matrix.
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Let h(l), l=0,,L be the chip rate sample discretetime baseband equivalent Lth order FIR channel between the transmit and rece ive antenna. Knowledge of the channel is not required, except for the upper bound L on its maximum channel order. In order to eliminate the interblock interference (IBI) ca used by the FIR channel, the cyclic prefix (CP) of length L is inserted at the beginning of x (n) which is discarded at the receiver. Time domain OFDM signal is cyclically extended to mitigate the effect of time dispersion [5][8]. The length of cyclic prefix (CP) [5] has to exceed the maximum excess delay of the channel in order to avoid IBI. Basic idea of cy clic extension is to replicate part of the OFDM timedomain symbol from back to the front to create a guard period. As long as maximum excess delay is smaller than the le ngth of the cyclic extension, the signal distortion stays within the guard interval which is removed later at the receiver. Hence, ISI is prevented at the expense of a spectral efficiency loss. The CP insertion can be described by P = [IP T IK T], where IP is formed by the last rows of the KK identity matrix I. The operation of discarding the first L receiver symbols in the receiver can be described by the matrix Q =[0KL IK]. The FIR channel is described by the (K+L)(K+L) Toeplitz matrix Hi with the (k,l) entry h(kl).Let G=PHQ denote the equivalent channel matrix in the receiver after eliminating the IBI. The K IBIfree received symbol block y (n) is given by (n)wQ(n)XGF(n)yH (2.15) is the received symbol block from the transmit antenna. w (n) is the AWGN vector.
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Given y (n), the FFT described by the matrix F is performed on y(n) to obtain (n)W(n)XDQw(n)F(n)XD(n)yF(n)Y (2.16) where D is the diagonalized equivalent channel matrix by preand postmultiplication of the circulant matrix G with F and FH. The diagonalized channel matrix can now be equalized by the Zero Forcing (ZF) [44] approach and fed to symbol decision device like a slicer to recover the QAM symbols at the receiver. In the OFDM transmitter, the subcarriers at the ends of the spectrum are usually set to zero in order to simplify the spectru m shaping requirements at the transmitter, e.g. IEEE 802.11a [4]. These subcarriers are used as frequency guard bands and are referred as virtual carriers or null subcarriers in literature [4]. To av oid difficulties in D/A and A/D converter offsets, and to avoid DC offset the center subcarrier falling at DC is not used as well. The power spectrum for a 54 Mbps 802.11a OFDM spectrum is shown in Figure 2.12. The system has 64 subcarriers, uses 64QAM modulation and number of subcarriers that are set to zero at the sides of the spectrum is 11. In the figure the 802.11a OFDM spectrum has been simulated, the associated spectrum mask and spectrums provided by the 802.11a standard and Richard Van Nee. For a more detailed review of the OFDM and the 802.11a standard, refer to [4],[8]. 2.2.2 Background on MIMO and STC Physical limitations on wireless channels present a fundamental challenge to the reliability of wireless communications. Factors such as bandwidth limitations, propagation loss, time variance, noise, interf erence, offsets and multipath channel fading limit the capacity of the wireless channel making it a narrow pipe that has limited ability
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accommodate the flow of data. Further challe nges come from power limitation as well as size, shape and speed of devices in wireless portables. In orde r to achieve very high data 5750 5760 5770 5780 5790 5800 5810 5820 60 50 40 30 20 10 0 Windowed and Smoothed IEEE 802.11a OFDM Spectrum with Transmit MaskPower(dB)Freq. (MHz) Sim. OFDM Spectrum with prefix OFDM Transmit Mask Spectrum IEEE 802.11a Std. Richard van Nee Figure 2.12 802.11a OFDM Passband Spectrum and Spectrum Mask rates on narrowband wireless channels, many antennas at both transmitter and receiver will be needed. Deploying multiple antennas at both the base and remote stations, i.e. Multiple Input Multiple Output (MIMO) [9], [10] systems, increases the capacity [11], [12] of wireless channels and information th eory provides measures of this increase. MIMO technology has attracted significant attention in wireless communications, since it offers significant increases in data th roughput and link range without additional bandwidth or transmit power. It achieves this by higher spectral efficiency (more bits per second per hertz of bandwidth) and link reliab ility or diversity (reduced fading). Because of these properties, MIMO is the current theme of international wireless research.
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2.2.2.2 Basic Mathematical Model of MIMO Systems Consider a wireless co mmunication systems with n transmit and m receive antennas where the channel between each tran smit and receive antenna is quasistatic Rayleigh [1], flat and mutually independe nt. This is illustra ted in Figure 2.13. If n is fixed, then the capacity increases only logarithmically with m. If m is fixed, the mathematics of outage capacity proves th at there comes a point when adding more transmit antennas will not make much difference. n Transmitter Antennas m Receiver Antennash11h21hn1h12h22hn2h1mh2mhnm c1c2r1r2rm cnn Transmitter Antennas m Receiver Antennash12h22hn2h11h21hn1h1mh2mhnm c1c2r1r2rm cn Figure 2.13 Basic MIMO System For instance, if there is one transmit antenna i.e. n = 1, then Foschini et al. [11] prove that the capacity of the system is a random variable of the form log2(1 + (x2m 2/2m) SNR) where x2m 2 is a random variable formed by summing the squares of 2m independent Gaussian random variables with mean zero and variance one. This means
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that by the strong law of large num ber in distribution, in the limit (x2m 2/2m) tends to 1. Practically speaking, for m = 4, (x2m 2/2m) 1, and the capacity is the familiar Gaussian capacity log2(1 + SNR) per complex dimension. Thus in the presence of one receive antenna, little can be gained in terms of outage capacity by using more than four transmit antennas. A similar argument s hows that if there ar e two receive antennas, almost all the capacity increase can be obtai ned using transmit antennas If m increases and n m, then information theory [11], [12] shows that the capacity of the system increases at least linearly as a function of m. Therefore by using multiple transmitter and receiver antennas to create multipleinput multipleoutput (MIMO) systems to obtain higher capacities. Th e number of degrees of freedom is given by the product n m. Consider the wireless communication system with n antennas at the base station and m antennas at the remote. At each time slot t, signals are transmitted simultaneously from n transmit antennas. i tc,i1,2,.......,n (2.17) n signals are transmitted simultaneously each from a different antenna and all these signals have the same transmission period T. The channel is assumed to be flat fading [1], and the path gain from transmit antenna i to receiver antenna j is defined to be hi,j j t is the noise for channel between transmit antennas and receive antenna j at time t. The path gains are modeled as samples of independent complex Gaussian random
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variables with variance 0.5 per real dimension. The wireless channel is assumed to be quasistatic so that path gains ar e constant over a frame of length l and vary from one frame to another. The noise samples are independent samples of a zero mean complex Gaussian random variable with variance n/(2 SNR) per complex dimension. At time t, t=1,2,3,..,l the signals received at antenna j, j=1,2,3,,m is given by n tt ji,ji i1rhct j (2.18) Using matrices and vectors, the ab ove relation can be expressed as r t = Hc t + t (2.19) where the received signal vector, transmitted signal vector, channel matrix and noise vector are expressed as 12mT ttttr(r,r,....,r) ; ; (2.20) 12nT ttttc(c,c,....,c) 12lT tttt(,,....,)1,12,1 n,1 1,22,2 n,2 1,m2,m n,mhh......h hh......h :::: H :::: hh......h (2.22) Mathematically MIMO transmissions can be seen as a set of m equations (received signals) with a number of n unknowns (transmitted signals). To solve a problem of m equations and n unknowns, m should be at least equal to n. If m = n, there exists a unique solution to the problem and if m > n, a solution can be found by performing a
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projection using a least square s method, also known as the Zero Forcing (ZF) method. If m = n, ZF gives the unique solution. For (2.19), you can recover the transmitted signals by ZF and using a decision device (slicer). In this case assume m = n and H is invertible, the ZF equalization [44] of the channel matrix can be carried out by multiplying both sides of (2.19) by the hermitian transpose HH. HHHH H cHrHHcHIcH ccH (2.23) The output of the ZF equalizer is fed to the slicer to recover the original QAM symbols. Minimum Mean Squared Error (MMSE) equaliza tion [44] can also be used for better performance. 2.2.2.2 MIMO Technologies MIMO technologies can be subdivided in to three main categories: (1) Precoding, (2) Spatial Multiplexing (SM) and (3) Diversity Coding. Precoding can be interpreted as multilayer beamforming in a narrow sense. Beamforming is a signal proces sing technique used in sensor arrays for directional signal transmission or reception. In (singlelayer) beamforming, the same signal is emitted from each of the transmit antennas with appropriate phase weighting (sometimes with gain) such that the signal power is maximized at the receiver input The benefits of beamforming are to increase the signal gain from constructive combining and to reduce the multipath fading effect. The improvement compared with an omnidirectional
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reception/transmission is known as the receive/ transmit gain (or loss). In a wide sense precoding means that all spatial processing is done at the transmitter. When the receiver has multiple antennas, the transmit beamforming cannot simultaneously maximize the signal level at all of the r eceive antenna and precoding is used. Note that precoding requires knowledge of the channel state information (CSI) at the transmitter. Spatial multiplexing (SM) requires actual MIMO antenna configuration, i.e. multiple antennas at the transmitter and receiver. In SM, a high rate signal is split into multiple lower rate streams and each stream is transmitted from a different transmit antenna in the same frequency channel. If these signals ar rive at the receiver antenna array with sufficiently different spatial signatures, the r eceiver can separate these streams, creating parallel channels for free. Spatial multip lexing algorithms like BLAST [56][58] are a very powerful technique for increasing channe l capacity at higher Signal to Noise Ratio (SNR). The maximum number of spatial stream s is limited by the lesser in the number of antennas at the transmitter or receiver. Spat ial multiplexing can be used with or without transmit channel knowledge. Diversity coding techniques are used when there is no channel knowledge at the transmitter. In diversity methods a single st ream (unlike multiple streams in SM) is transmitted, but the signal is coded using techniques called spacetime coding [52], [53]. The signal is emitted from each of the transmit antennas using certain principles of full or near orthogonal coding. Diversity exploits the independent fading in the multiple antenna
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links to enhance signal diversity. Because there is no channel knowledge, there is no beamforming or array gain from diversity coding. Combinations of the three different technol ogies are possible. Spatial multiplexing can also be combined with precoding when th e channel is known at the transmitter or combined with diversity coding when decodi ng reliability is in tradeoff. In this dissertation new MIMOSTCOFDM system [3 3][35] is being presented combining concepts of MIMO systems, OFDM and STC. Hence the concepts of STC, especially Space Time Block Coding (STBC) will now be reviewed. 2.2.2.3 Space Time Coding (STC) Space Time Codes [52], [53] are basically of two type s : (1) Space Time Trellis Codes (STTC) (2) Space Time Block Codes (S TBC). In this dissert ation STBC has been used and as such the terms STC and STBC are interchangeable. However from now on STC will be used to denote space time block codes. Spacetime block coding is a coding technique used in wireless communications to transmit multiple copies of a data stream (generally QAM symbols) across a number of antennas and to exploit the various received vers ions of the data to improve the reliability of the communication. The transmitted signal traverses a difficult environment with fading, scattering, reflection, refraction and is further corrupted by thermal noise (AWGN) in the receiver, which means that some of the received copies of the data will be 'better' or less corrupted than others. This redundancy results in a higher chance of
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being able to use one or more of the receiv ed copies to correctly decode the received signal. In fact, spacetime coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible. Originally proposed by Tarokh et al., these spacetime bl ock codes (STCs) achieve significant error rate improvements over singleantenna (SISO) systems. Their original scheme was based on trellis codes (STTC) but the simpler block codes were first uti lized by Alamouti [39], and later by Tarokh et al. [38] to deve lop spacetime blockcodes (STBCs). STC nowadays primarily refers to STBC. STC invol ves the transmission of multiple redundant copies of data to compensate for channel fading and AWGN in the hope that some of them may arrive at the receiver less corr upted than others. In the case of STBC in particular, the data stream to be transmitted is encoded in blocks, which are distributed across space (transmit antennas) and time (tim e instant slots). While it is necessary to have multiple transmit antennas, it is not necessary to have multiple receive antennas, although to do so improves performance. This process of receiving diverse copies of the data is known as diversity reception. A STC is usually represented by a matr ix. Each row represents a transmission from an antenna over time and each column represents a time slot as shown below in (2.24). 1112 1T 2122 2T n1n2 nT 1 2 T s ss 1 s ss 2 s ss n (2.24)
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Here, sij is the modulated symbol to be transmitted in time slot j from antenna i. There are to be T time slots and n transmit antennas as well as m receive antennas. This block is usually considered to be of 'length' T. The code rate of an STC measures how many sy mbols per time slot it transmits on average over the course of one block If a block encodes k symbols, the coderate is k r T (2.25) STCs as originally introduced, and generally studied as orthogonal This means that the STC is designed such that the vectors representing any pair of rows taken from the coding matrix are orthogonal. This results in simple, linear optimal decoding at the receiver. Its most serious disadvan tage is that all but one of the codes that satisfy this criterion must sacrifice some proportion of their data rate. The design of STC is well documented in literature and readers can refer to [52][53], fo r further details. Alamouti [39] invented the simplest of all the STC. It was designed for a twotransmit antenna system and has the coding matrix: 12 2 21ss C ss where denotes complex conjugate .This is a rate1 code an d it takes two timeslots to transmit two symbols. Using the optimal decoding scheme discussed below, the biterror rate (BER) of this STC is equivalent to 2mbranch (2 receiver antennas) maximal ratio
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combining (MRC). This is a result of the perf ect orthogonality betwee n the symbols after processing at the receiver there are tw o copies of each sym bol transmitted and m copies received. Alamoutis STC is a very special STC. It is the only orthogonal STBC that achieves rate1. That is to say that it is th e only STC that can achieve its full diversity gain without needing to sacrifice its data rate. Strictly, this is only true for complex modulation symbols. Since almost all constellation diagrams rely on complex numbers (QAM sym bols) however, this property us ually gives Alamouti's code a significant advantage over the higherorder STBCs ev en though they achieve a better errorrate performance. The significance of Alamouti' s proposal is that it was the first demonstration of a m ethod of encodi ng which enables full diversity with linear processing at the receiver. Fu rthermore, it was the first openloop transmit diversity technique which had this capab ility. Subsequent generalizat ions of Alamouti's concept have led to a tremendous impact on the wireless communications industry. Higher STC for more than 2 transmit antennas have been designed. However none of them are full rate codes. For exampl e, the m aximum rate for 3 transmit antennas is One particularly attractive f eature of orthogonal STCs is that maximum likelihood decoding can be achieved at the receiver with only linear processing. For further details on higher order STCs and decoding of STCs, refer to [38], [52], [53].
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2.3 Conclusion In this chapter, a background on the OW SS, MIMO systems, OFDM and STC has been provided. OWSS is a promising technolog y for the next generation of high speed WLANs due to the unique advantages it en joys over current WLAN signaling schemes like OFDM. Another promising technology fo r the next generation of high speed WLANs is the combination of MIMO sy stems and OFDM. MIMO algorithms are generally narrowband and the combination of OFDM with MIMO can deal with the wideband frequency selective fading channels of the future.
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CHAPTER 3 MEDIUM ACCESS CONTRO L IN OWSS WLANs 3.1 Medium Access Control in WLANs The Medium Access Control (MAC) [59] pr otocol sublayer, is the lower sublayer of the Data Link Layer (DLL) [59], specified as the second layer above the PHY layer in the seven layer OSI model [59] In WLANs, the MAC Layer manages and maintains communications between the wireless stations (radio network cards and access points) by controlling and coor dinating access to the shared radio channel and utilizing protocols that enhance the transfer of data packets over the wireless medium. The 802.11a [4] standard specifies a common MAC Layer, which provides a variety of functions to support the operati on of different 802.11 PHY laye r specifications, such as 802.11a/g [4], [5] and the eagerly awaited 802.11n standard [17], [18], [60]. The channel access control mechanisms provided by the MAC layer are generally known as a multiple access protocols. Th e multiple access protocols are broadly classified into circuit mode [59] (like FDMA, TDMA, CDMA etc.) or packet mode methods [59] (like CSMA/CA, Slotted ALOH A). Hybrids of these techniques are also frequently used. In wireless networks, especially 802.11 WLANs, the packet mode method called Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) [40] is the basic channel access pr otocol in the MAC layer.
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OWSS offers multiplexing capability either at the PHY layer or at the MAC layer. The primary advantage of using the MAC laye r approach is that users can transmit and receive data packets at the fu ll system bit rate, which is th is paper, is 108 Mbps. Thus efficient resource sharing can occur for bursty users. Towards this end, OWSS will use a MAC protocol similar to that of the 802.11 WLAN Standard. Called the distributed coordination function (DCF) [4], it is a car rier sense multiple access with collision avoidance (CSMA/CA) scheme with bi nary slotted exponential backoff. 3.2 CSMA/CA: The Basic Access Method The IEEE 802.11 standard [4], [5] uses CSMA/CA MAC protocol with binary exponential backoff algorithm to access the medium, called Distributed Coordination Function (DCF). DCF defines two methods two way handshaking basic access (for broadcast frames) illustrated in Figure 3.1 a nd optional four way handshaking technique known as requesttosend and cleartosend (R TSCTS) technique, illustrated in Figure 3.2. A summary of the two DCF access methods is given here. DIFS Busy Medium DIFS Defer Access Contention Window Back Off Window SIFS Slot Time Select slot and decrement backoff as long as medium is idle Figure 3.1 CSMA/CA
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Access Point Mobile Node ACK DATA CTS RTS Figure 3.2 Four Way Handshake RTSCTS Scheme The basic access method is a twoway ha ndshaking technique. A station with a packet to transmit persistently senses the ch annel and waits until a idle period equal to a distributed interframe space (DIFS) is detecte d. After an idle DIFS, the station waits for a random backoff interval before transmitting. This is a collision avoidance feature, which minimizes the probability of collision with packets transmitted from other stations. DCF has adopted a very efficient exponential bac koff scheme. The time after DIFS is slotted and a station can transmit only at the beginni ng of each slot time as shown in Figure 3.1. Slot time () is the time that a station takes to de tect a transmission from another station and it depends on the physical layer. Slot time is the sum of the medium propagation delay, the receiver to transmitter turnaround time and the time taken to sense the state of the channel. A collision occurs only when tw o or more packets are transmitted in the same time slot.
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At each packet transmission, the backoff time is uniformly chosen in the range (0,w1). The, value w, called the contention window, at the first transmission attempt is equal to the minimum contention window CWmin. After each unsuccessful attempt, w is doubled, up to a maximum value CWmax =2mCWmin. CWmin, CWmax and m, the number of retry attempts are PHYspecific. The backo ff interval is equal to the product of the selected random contention window CW and slot time. The backoff time counter is decremented as long as an idle channel is de tected, frozen when the channel is sensed busy and reactivated again when the channel is sensed idle again for a time period more than DIFS. After the backoff timer expires, the station transmits the packet. Unlike CSMA/CD, CSMA/CA cannot detect a collision and has to rely on a positive acknowledgement (ACK) from the destination sta tion to signal successful packet reception. At the end of a successfully tr ansmitted packet, the destination station transmits ACK to the source station after a period of time called short interframe space (SIFS), which is shorter than DIFS. If th e transmitting station does not receive the ACK within a specified ACK timeout, or it detect s the transmission of another packet on the channel, it reschedules the packet transmission according to the above backoff scheme shown in Figure 3.3. DCF defines an additional fourway hands haking technique to be optionally used for a packet transmission, known by the na me RTS/CTS shown in Figure 3.4. A station that wants to transmit a packet, waits for an idle DIFS and follows the backoff rules explained above, and then, instead of the pack et, first transmits a special short frame
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called request to send (RTS). When the receiving st ation detects an RTS frame, it responds, after a SIFS, with a clear to send (CTS) frame. If the CTS frame is correctly received, the transmitting station is ready to transmit its packet after a SIFS. The RTS/CTS scheme also handles the problem of system degradation due to hidden terminals. The RTS and CTS frames car ry information regarding the length of the packet to be transmitted. This information ca n be read by all stations, which then update their network allocation vector (NAV). NAV contains specifi c information about the period of time the channel would be sensed busy. Thus a hidden station can suitably delay transmission and avoid collision, by dete cting one of the RTS and CTS frames. The RTS/CTS scheme is very effective in terms of system performance for large packets, by reducing the length of frames involved in the contention process. For a more detailed explanation of the Basic Access and RTSCTS scheme refer to the 802.11a standard [4]. Data ACK DIFS SIFS Next MPDU Contention Window Defer Access Backoff after Defer Figure 3.3 Basic Access Mechanism
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Source Destination Other Data ACK Next MPDU CW Defer Access Backoff after Defer CTS RTS NAV (RTS) NAV (CTS) SIFS SIFS SIFS DIFS Slot Time Figure 3.4 RTS/CTS Mechanism 3.3 Performance Analysis of the Distributed Coordination Function This analysis is based on Bianchis Mode l [41], [42]. The anal ysis is carried out as follows. First the behavior of a single st ation is analyzed usi ng a Markov model [44], and two critical probabilitie s are obtained, which are independent of the DCF mechanism employed: stationary probability that the stati on transmits a packet in a generic slot time (q) and the probability that a transmitted packet collides (p). Then, by studying the events that can occur within a generic slot time the saturation throughput of both Basic and RTS/CTS access methods can be expressed as function of the probability q. Finally the packet delay can be calculated based on the model above.
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3.3.1 Markov Model Consider a fixed number of n contending wireless stations operating under saturation conditions. Let b(t) be the stochastic process re presenting the size of the back off window for a given st ation at slot time t (the time is stopped when the channel is sensed busy). The station transmits when the back off time reaches zero. At each transmission, the back off time is uniformly chosen in the range (0,w1). At the first transmission attempt, w=W, namely the minimum back off window. After each unsuccessful transmission, is doubled, up to a maximum value 2 m W. The maximum number of retry attempts is m. Let W i =2 i W, where i lies in the range (0,m), is called backoff stage, and let s(t) be the stochastic process re presenting the back off stage (0,,m) of the station at time t. The key approximation in Bianchis model is that at each transmission attempt and regardless of the number of atte mpts at retransmission, the probability p that a transmitted packet collides is constant and independent of the state s(t) of the station (this is more accurate when W and n are larger). In this condition, it is possible to model the bidimensional process {s(t),b(t)} with a discretetime Markov chain illustrated below in Figure 3.5.
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In this Markov chain, the only non null onestep transition probabilities are )1W,0(k, W p 0,mk,mP )m,1(i&)1W,0(k, W p 0,1ik,0P )m,0(i&)1W,0(k, W p1 0,ik,0P )m,0(i&)2W,0(k,11k,ik,iPm m i i 0 0 i (3.1) Let )1W,0(k&)m,0(i},k)t(b,i)t(s{Plimbi t k,i (3.2) be the stationary distribution of the chain. 0, 0 i, 0 m, 0 i, 1 m,1 (1p)/W0p/W1 1 1 p/Wi+1 0, 1 0, W01 (1p)/W0 i1, 0 i, Wi1 p/Wi m, Wm1 p/Wmp/Wm 111 1 11 1 0, 0 i, 0 m, 0 i, 1 m,1 (1p)/W0p/W1 1 1 p/Wi+1 0, 1 0, W01 (1p)/W0 i1, 0 i, Wi1 p/Wi m, Wm1 p/Wmp/Wm 111 1 11 1 Figure 3.5 Markov Chain Model for the Backoff Window Size
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Owing to the chain regularities, the following relations hold 0, ,0,0 0, 0,0 0,; 1 ;)1,0(,i i i ki m m i ib W kW bb p p bmibpb (3.3) The value of b0,0 is determined by imposing the normalization condition 1bm 0i 1W 0k k,ii From which ))p2(1(pW)1W)(p21( )p1)(p21(2 bm 0,0 (3.4) Let q be the probability that a station transmits in a generic slot time. As any transmission occurs when the back off window is equal to zero, regardless of the back off stage, it is ))p2(1(pW)1W)(p21( )p21(2 p1 b bqm m 0i 0,0 0,i (3.5) However in general, q depends on the conditiona l collision probability p. To finally compute the probability p, that a transmitted packet collides, note that p is the probability that, in a time slot, at least one of the remaining n1 stations transmits. p = 1 (1 q)n1 (3.6) Equation (3.5) and (3.6) represent a nonlinear system with two unknowns p and q can be solved using numerical techniques. 3.3.2 Throughput Analysis Given n active stations contend on the same channel, and each transmits with a probability q, the probability Ptr that there is at least one tr ansmission in a considered slot
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time is given by n trq P )1(1 (3.7) Given that a transmission has occurred the probability Ps, that the transmission is successful is given by n n tr n sq qnq P qnq P )1(1 )1()1(1 1 (3.8) Let u be the random variable representing the nu mber of consecutive idle slots between two consecutive transmissions on the channel 1 1 P E[u]tr (3.9) Finally the normalized system throughput S can be determined, defined as the fraction of time the channel is used to successfully transmit payload bits. As the instants of time right after the en d of a transmission are renewal points, it is sufficient to analyze a single renewal interval between two consecutive transmissions, and express as the ratio cs ss sTPTPvE PEP E E S 1 interval revewalaoflength intervalinntranmissio successful fortime (3.10) where E[P] is the average packet length, TS is the average time the channel is sensed busy because of a successful transmission, and T c is the average time the channel is sensed busy by the stations during a collision. The times E[P], TS and T c must be measured in slot times, as this is the time unit of E[u].
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To conclude the analysis, it remains only to specify the values TS and T c Let H=PHY hdr + MAC hdr be the packet header, and d be the propagation delay. For the basic access method it is TSB = H + E[P] + SIFS + d + ACK + DIFS + d T cB = H + E[P *] + DIFS + d (3.11) where E[P *] is the average length of the longest p acket payload involved in a collision, in the case all packets have the same fixed size, E[P *]= E[P] =P. Tc is the time in which the channel is sensed busy by the noncolliding stations. For the RTS/CTS access method, d DIFS RTS T d DIFS ACK d SIFS E[P].......... .... H d SIFS CTS d SIFS RTS TR C R S (3.12) 3.3.3 Delay Analysis The packet delay is another critical pa rameter in performance evaluation of the MAC layer [12] For this another probability Pa is calculated, the probability that a specific station in n active stations transmits successfully n 1n s a)q1(1 )q1(q n P P (3.13) R is the number of attempts at resensing the channel and Tf the expected time between two consecutive attempts at channel sensing. Then
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c a s s a as f aT P P T P PP T P R 1 1 1 1 1 (3.14) The average delay time equals the average renewal cycle time plus the successful transmission time for the packet. D=R(Tf + E(u))+Ts (3.15) 2.4 Performance of CSMA/CA MAC Layer in OWSS WLANs In this analysis a robust transfer of th e header and the preamble has been adopted; i.e., the PHY preamble (96 bits) and header (32 bits) are BPSK modulated with the concomitant transfer rate of only 18 Mbps. The use of the strategy shown in Figure 3.6 enhances the probability th at even the far away stations receive the handshaking messages reliably so as to update thei r NAV (Network Allocation Vector) [4] for CSMA/CA access. Figure 3.6 also shows the inhe rent plumes of the OWSS pulses; as can be seen, all of these plumes are hi dden except for the very last one. A system throughput and delay analysis was carried out for OWSS based on Bianchis Model. The numerical results are obtained according to the system parameters listed in Table 3.1. From the throughput analysis in Figure 3.7, it is evident that for a large number of stations, the RTSCTS sche me performs significantly better than the basic access scheme. For the basic access sc heme the throughput has an exponentially decaying profile, whereas for RTSCTS it is generally constant at about 66%. The
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average packet delay time, plotted in Figure 3.8, is proportional to the number of stations when the number of stations is small. Howeve r, it increases rapidly for large number of stations. At 20 stations, the packet delay is around 5 ms for both RTSCTS and basic access; at 50 stations it increases to 12.5 ms for RTSCTS and 15 ms for basic access. OWSS Pulses BPSK modulation 64QAM modulation DATA Header Preamble 1 2 3 Plume 1 Plume 2 Plume 18 Mbps 108 Mbps N Figure 3.6 OWSS Frame Format Table 3.1 MAC Attributes of OWSS Attribute Value 96 bits OWSS preamble OWSS header 48 bits 160 bits RTS size CTS size 128 bits ACK size 112 bits 272 bits MAC header SIFS time (SIFS) 2 s 9 s DIFS time (DIFS) 5 s SLOT time () Retry Attempts (m) 5 Payload 2312 bytes CWMIN (W) 32
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5 10 15 20 25 30 35 40 45 50 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 Saturation Throughput (S)Number of Stations (n) Basic RTSCTS Figure 3.7 System Throughput for 108 Mbps OWSS WLAN 5 10 15 20 25 30 35 40 45 50 0 5 10 15 Average Packet Delay (ms)Number of Stations (n) Basic RTSCTS Figure 3.8 Average Delay for 108 Mbps OWSS WLAN
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3.5 Conclusion The OWSS signaling system w ith bit rates of 108 Mbps and beyond is directed at the next generation of high speed WLANs. OWSS offers multiplexing capability both at the PHY and MAC layers. However, multiplexing at the MAC layer is more preferable, as it would enable full rate shared access of the bandwidth (in this case 108 Mbps) to bursty users. Towards this end, OWSS will use a CSMA/CA based MA C protocol similar to the IEEE 802.11a standard to access the medium. A frame format for OWSS data packets in the MAC layer and MAC attributes of OWSS in terms of DCF parameters are proposed. Using a simple theoretical model for performance analysis, the MAC layer of OWSS has indicated a saturati on throughput of 66% and an aver age packet delay of 5 ms using RTSCTS for a moderate number of stations (say, less than 50).
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CHAPTER 4 SPECTRAL CHARACTERISTICS OF THE OWSS SIGNAL Unlike the pulses used in OFDM [6] a nd TDMA [1], the OWSS pulses have both a wide time support and a wide frequency s upport, thereby lending the transmitted signal to effective multipath equalization at the recei ver. However intrinsic to the design of the transmission system is the specification of th e bandpass filter at its front end and the need to meet the emission mask requirements. For both these specifica tions, the study of the spectral characteristics of the OWSS signal is critical. The spectrum of a WLAN transmission system is one of its most important characteristics. It provides information about spectral leakages by the transmitted signal into adjacent bands. This chapter elaborates on the beneficial spectral propert ies of the OWSS transmitted signal. It shows that the baseband spectrum is perfectly fl at, and that the passband signal requires a bandwidth 3040% less than that required by OFDM. As an example, for 54 Mb/s operation, OWSS requires only 13 MHz bandwidth compared to 20 MHz for 802.11a OFDM [4], [5]. This is due primarily to the avoidance of overhead (prefix and channel coding), while still achieving BERs of 104 to 105 (at practical delay spreads of 50100 ns and SNRs of 1922 dB), and a sharp roll off of the spectrum. The analysis also confirms that the broadband nature of th e OWSS baseband signal is preserved in the passband. This enables the OWSS system to transmit data successfully over a frequency
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selective multipath channels [1] with deep fades, unlike comparatively narrowband systems like OFDM. OWSS also extends to hi gher bit rates such as 108 Mbps, in a bandwidth efficient manner. 4.1 Baseband Spectrum of OWSS Signal Assuming only a single supersymb ol for OWSS and that all M virtual channels are active. The corresponding baseband signal in the time and frequency domains are given by )f(cA)f(S )t(A)t(sT)i( )i( 1M 0i 0 )i()i( 1M 0i 0 (4.1) Therefore the power of th e baseband signal is 2 2 1M 0i )i( 2 M H 2 1M 0i T)i()i(H 2 2 0M )f(M )f(IM)f( )f(cc)f( )f(SE (4.2) where IM is an identity matrix of size MM and 2 E  Ai 2. For example, for 64QAM, 2 = 42. Note that in (4.2) the power comple mentary properties of the OWDM pulses is used, (see top trace of Figure 4.1), and the fact that the Hadamard [25] codes are orthogonal; indeed orthonormal if the code vectors are norma lized to unit energy. In the
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latter case, the factor M on th e right hand side of (4.2) may be replaced by unity. Clearly, the baseband spectrum is flat, regardless of the value of M. A simulated spectrum is shown in the lower trace of Figure 4.1. It follows in an analogous manner that the theoretical baseba nd spectrum of the complete signal, with an infinite symbol stream, n T n n i i n M inTtAnTtAts )( )( )()( )( 1 0 (4.3) is also flat. Here, the vector of symbols An = [An (o) An (1) An (M1) ]T is called the nth supersymbol. Figure 4.1. Baseband Spectrum of OWSS 4.2 Passband Spectrum of the OWSS Signal In a typical WLAN system, the transmitted passband RF signal [44] is analog while the baseband signal is a discrete time signal generate d by DSP [45]. Therefore the
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baseband signal must be conve rted into an analog signal. The passband analog OWSS signal used for spectral analysis is given by tj M i icets tx)(Re)(1 0 )( (4.4) As passband modulation is performed by a complex analog carrier signal (with frequency fc), D/A conversion of th e discrete time baseband OWSS signal is required. This can be achieved by means of a simp le passband OWSS transmission system for spectral analysis, illustrated in Figure 4.2. This analog signal is produced through an upconversion process. Prior to upconversion, a pseudo D/A [45] conversion (upsampling by a factor U followed by low pass filtering) of the discrete time baseband signal is performed. Thereupon, in the simulations for the passband spectrum, an FFT is performed, its magnitudesquare calculated, then smoothed (using a moving average filter [45] of length W as shown in Figure 4.3), and finally sh ifted to the carrie r frequency (for example, 5.785 GHz). s S Figure 4.2 Simple Passband OWSS Transmi ssion System for Spectral Analysis M U LPF D/A Conversion Re {} a A U Z X fc
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Figure 4.3 Simulated Baseband and Passband Spectrum of OWSS Signal 4.2.1 Passband Spectrum of 108 Mbps OWSS The 108 Mbps OWSS system has a sampling rate of 18 Msps and uses a 64QAM constellation. The passband spectrum of the 108 Mbps OWSS transmitted signal is shown in Figure 4.4. The spectral plot is obtained for M=64 (all virtual channels or users active). For D/A conversio n, a combination of upsampling, by U = 8, JIF filtering [61] (LPF), followed by smoothing (W = 200) is used. The solid line shows the passband spectrum and the suggested emission mask is shown by the dotted line. The response of the filter was finally shifte d to the carrier frequency of 5.785 GHz. The OWSS spectrum for 108 Mbps has a 3dBr pa ssband bandwidth of about 16 MHz, 10 dBr bandwidth of 18 MHz and 40dBr bandwidth of 25 MHz. Also notice the sharp roll off at the edges of the spectrum, indicating a low spectral leakage into adjacent bands. An emission mask is also suggested, shown by a dotted line. The emission mask has been
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specified generously to account for nonlinea rities and impairments. However certain changes may be necessary to account for PA nonlinearities. The resultant spectrum bandwidth and suggested emission mask is tabulated in Table 4.1. Figure 4.4 Spectrum and Emission Mask for 108 Mbps OWSS Signal Table 4.1 Spectrum and Emission Mask BW of 108 Mbps OWSS Signal 30 21.7 20.1 19.6 18.6 18 17.2 15.5 Spectrum BW ( MHz ) 50 25 20 Suggested Mask BW ( MHz ) 40 50 3 6 30 20 10 0 Average Spectral Density ( dBr )
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4.2.2 Bandwidth Efficiency of OWSS visvis OFDM Now the bandwidth efficiency of OWSSS visvis OFDM will be compared by studying the passband spectrum a nd emission masks of both the signaling schemes for 54 Mbps operation. Figure 4.5 co mpares the passband spectra and emission masks of 60 Mbps (10 Msps sampling rate and 64QAM modulation) OWSS and 54 Mbps 802.11a OFDM system. 60 Mbps OWSS gives a ne t rate of about 54 Mbps with adaptive loading (use of lower constellation training symbols for equalization in poor channels) and a comparable BER. The spectral plot for OWSS shown in Figure 1.5 is obtained for M=64 (all virtual channels active). For D/A conversion, a combination of upsampling, by U = 8, 129 tap JIF filtering [61] (LPF), followed by smoothing (W = 200) is used. The spectrum and emission mask for 802.11a OFDM is specified in the standard. An an emission mask for 54 Mbps OWSS is also suggested. As is evident from the plots, OWSS spectrum requires only 9.5 MHz for OFDM s 16.3 MHz at dBr and 10.3 MHz for OFDMs 17 MHz at dBr. This represents a spectrum bandwidth efficiency of about 40% for OWSS over OFDM. At 10 dBr, OW SS emission mask requires only 12 MHz bandwidth as compared to 20 MHz for 802.11a OFDM emission mask [5], [6]. This represents a significant bandw idth advantage of roughly 40% for both the spectrum and the emission mask. See Table 4.2 and Table 4.3 for details. This advantage arises due to (1) the avoidance of the pref ix, channel coding, and guard ze rocarriers in OWSS and (2) a compact brickwall like ch aracteristic of the base band OWSS spectrum. PA nonlinearities and other impairments such as tim ing and carrier phase errors have been ignored in this simulatio n, though the emission mask for 54 Mbps OWSS has been defined generously to account for such impairments.
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Figure 4.5 Comparison of OWSS and 802.11a OFDM. Table 4.2 Comparison of 54 Mbps OWSS and 802.11a OFDM Spectrums 78.5% 56 12 40 57% 26 11.2 30 43.15% 19 10.8 20 39.41% 17 10.3 10 40.12% 16.7 10 6 41.46% 16.4 9.6 3 Efficiency (%) BW 54 Mbps OFDM Spectrum (MHz) BW 60 Mbps OWSS Spectrum (MHz) Average PSD (dBr)
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Table 4.3 Comparison of OWSS and 802.11a OFDM Emission Masks 65 % 40 14 28 63 % 60 22 40 41 % 22 13 20 40 % 20 12 10 39 % 18 11 0 Efficiency (%) BW 54 Mbps OFDM Mask (MHz) BW 60 Mbps OWSS Mask (suggested) (MHz) Average PSD (dBr) 4.3 Compensation of PA NonLinearity in OWSS WLAN systems PA nonlinearity in the transmitter leads to spectral broadening in the passband which can exacerbate adjacent channel interfer ence [71]. This spectral regrowth depends on the level of output backoff and can severe ly affect the performance of the system. Backoff [72] is an important parameter for a practical power amplifier to attain an acceptable level of out of band radiation. Backof f is used to shift the operating point of a nonlinear PA so as to operate it in the linear (actually, less nonlinear) region. To simulate the PA, a Rapp Model [72] is used for AM/AM conversion given by p pAAAf2 1 21 )( where A is the input amplitude A good approximation to existing amplifiers is obtained by choosing p in range of 2 to 3. We chose p =2.2. Figure 4.6 illustrates the effect of PA nonlinearit y on the passband spectra of 108 Mbps (18 Msps sampling rate, 64 active users, 64QAM modulation and smoothing window W=200) OWSS. The figure also shows the spectral regrowth for backoff values of 10dB,
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7dB and 5dB on the 108 Mbps OWSS spectrum. It is observed that for 6 dB backoff, any significant distortion occurs only at 28 dBr. Notice that the 108 Mbps OWSS bandwidth has broadened from 22 MHz (linear) to 26 MHz (6 dB backoff) at 30 dBr, and from 26 MHz (linear) to 54 MHz (6 dB backoff) at 40 dBr. Figure 4.6 Passband 108 Mbps OWSS spectrum with PA Nonlinearity using Rapp Model To compensate for this spectral regrowth a novel predistortion [70], [73] scheme is employed based on the inverse function [70] of the Rapp PA Model which is illustrated in Figure 4.7. The analog OWSS signal is norm alized and appropriate backoff is applied. The magnitude and phase are extracted from the signal and the magnitude is clipped (if required) and passed through the inverse Rapp function model given by p pAAAg2 1 21 )( The predistorted magnitude is then combined with the phase to get the predistorted OWSS signal. This signal is then modulated by a carrier frequency
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and the Rapp model f(A) is applied to simulate the eff ect of PA nonlinea rity. Figure 4.8 shows the effect of predistortion on the OWSS signal for 6 dB backoff. As can be seen, with compensation (using predistortion) any significant distortion o ccurs only at 38 dBr as compared to 28 dBr without compensation. This represents a significant improvement of 10 dB [70] in spectral re growth distortion levels in the passband for the 108 Mbps OWSS signal. The 108 Mbps OWSS bandwidth with 6 dB backoff shows no broadening at 30 dBr and has broadened to only 30 MHz at 40 dBr, compared to 54 MHz (without predistortion). Figure 4.7 Novel Predist ortion Scheme for PA N onLinearity Compensation g fc f Re() Predistortion Rapp PA Model BO NORM u/rms(u) 10^(bo/20) QAM OWSS signal MAG ph sqrt(2) / sqrt(2) x u y y v zx ^ y v g fc f Re() Predistortion Rapp PA Model BO NORM u/rms(u) 10^(bo/20) QAM OWSS signal MAG ph sqrt(2) / / sqrt(2) x u y y y v zx ^ y ^ y v
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Figure 4.8 Compensated 108 Mbps Passb and Spectrum using PreDistortion 4.4 Conclusion OWSS can avoid substantial overhead pe nalties through the e limination of the prefix, the guard zerocarriers, and channel. coding, while still providing a desired BER performance at practical SNRs. It was show n that the theoretical baseband spectrum is perfectly flat, and the passband spectrum o ffers a 3040% bandwid th advantage over 802.11a OFDM. OWSS readily extends to hi gher bit rates, such as 108 Mb/s, in a bandwidth efficient manner. PA nonlinearity can lead to spectral regrowth in the passband spectrum of the OWSS signal. This sp ectral regrowth which increases with the output backoff level, can be compensated to a large extent using a predistortion scheme based on the Rapp model. At 6 dB backoff in 108 Mbps OW SS, this scheme yields an improvement of 10 dB in spectral regrowth distortion levels.
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CHAPTER 5 PERFORMANCE LIMITS OF THE OWSS WLAN SYSTEM OWSS WLAN System is based on a new fami ly of pulses which have both a wide time support and a wide frequency support, a nd is 30% more bandwidth efficient than OFDM. As a consequence of the wide frequenc y support, effective equalization [44] in a multipath environment [1] can be achieved using a Forward EqualizerDecision Feedback Equalizer (FEDFE) structure [29], [30] together with the LMS adaptation algorithm [29] as explained in Chapter 2. Th e purpose of this chapter is to explore the fundamental limits to OWSS performance. To wards this purpose, a multilevel matrix formulation [27], [31] is employed to mode l the signal processing system. The total minimum meansquare error (TMSE) [44] fo r the FEDFE structure is derived in a closed form, and thereupon minimized rigorously. The TMSE governs the BER performance of the system, and is the sum of the MSE of the unequalized residual error and the MSE due to the channel noise amplified by the FE. Simulation results on a 108 Mbps system will demonstrate the effectiveness of this theory. Although a symbollevel formulation is generally performed in the equalization literature, the problem is formulated at the chip level for the following reason. The peak of the channel response can occur at instants that are not integer multiples of the supersymbol interval, and therefore the best delay for optimum detection in the FEDFE is not
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necessarily an integer multiple of the symbol interval. A downsampled low rate symbolinterval formulation could actually easily miss the real optimum. Since the goal of this paper is to explore the fundamental limits to the performance, a ch iplevel formulation will be studied. The matter of reduced complexity can be addressed in the future. 5.1 Multi Level Matrix Formulation of OWSS Receiver The OWSS transmitterreceiver system is illust rated in Figure 5.1. The equalizer structure consists of two adaptive FIR [4 5] components: FE a nd DFE. LMS algorithm [29] is used as the adaptation mechanism to update the FE and DFE. The receiver also uses an OWSS correlator, an upsampler and a decision device (slice r) [44]. The output of the equalizer is correlated with a user spec ific OWSS pulse, thus generating a statistic for detection. Note also that the correlator generates its output every M th sample, or chip. Therefore, the decision device and error computa tions operate at a lower rate compared to the equalizer. The OWSS Receiver is thus a multi rate signal processing system [51]. Since the DFE operates at the same speed as th e FE, an upsampler is needed as shown in the figure. Initially, the coeffi cients of FE and DFE are obta ined through a training phase (using a previously stored sequence of sy mbols, and the LMS algorithm for update). Subsequently, the receiver goes into a ma intenance mode. Of course, the equalizer coefficients are updated in this mode as well. The training phase begi ns with an arbitrary set of equalizer weights. These weights tend to converge so as to minimize the MSE. The final weights obtained at the end of the tr aining are then used to initialize the maintenance phase.
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Figure 5.1 OWSS Transreceiver System After the FEDFE, the equalized output is fed to the slicer to rec over the QAM symbols. To minimize its receiver BER, the TMSE (T otal Mean Square Error) needs to be minimized, which is the subject of the disc ussion below. The TMSE governs the BER performance of the system, and is the sum of the MSE of the unequalized residual error and the MSE due to the channel noise amplified by the FE. The TMSE will be derived in closed form using a multi level matrix formulation [27], and thereupon minimized rigorously to give an estimate of the optimum FE and DFE weights. 5.1.1 TMSE in the OWSS Receiver The definitions of the QAM symbol vector a (of length D ), OWSS transmit filter ( L taps, assumed to be an integer multiple of M by zero padding if necessary), multipath channel c ( Nc taps), FE w ( Nw taps ) and DFE b ( Nb taps ) are given below c w bTT 012D1012L1 TT 012N1012N1 T 012N1aaaaa; ; ccccc;wwwww bbbbb ; (5.1)
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The symbol stream upsampled by a factor M (of length MD = M D ) is given by T up 012D1 1M11M11M11M1aa0..0a0..0a0..0.....a0..0 (5.2) The symbol matrix input A1 to the FE, OWSS filter matrix H1, multipath channel matrix C and the adaptive white Gaussian noise (AWGN) matrix N are given by up 11 up 00 MDMDMDMD00 00 a0 0 A ;H ; __a __ __a __ w w0 10 0MD1MD20 M DN MDN00n00 c0nn0 C; N __c __c nnn (5.3) The output of the FE, including th e contribution of noise, is pAHCNwAGwNw11 11 where G1 = H1C (5.4) The symbol matrix input to the DFE (with delay L due to the correlator) and the OWSS correlatordownsampler matrix H2 are given by
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1ML1 upL1 2 up L1 0 MDNb T 1M 1M T 1M 1M T 2 1M1M 1M T 1M1M1M DMD000 00 Aa0 ; __a:0 __...a 00 00 H 000 000 (5.5) The output of the DFE is given by fA2b (5.6) The input to the slicer (decision device), from the correlator, after th e sliding correlation and downsampling operation is 2 2 2112vHq Hpf HAGwNwAb (5.7) The error signal e (assuming perfect detection of QAM symbols, = a) is eva (5.8) Neglecting the effect of noise temporarily, th e error signal can be expressed as follows 2112 12eHAGwAba VwVba where V1 = H2A1G1 and V2 = H2A2. (5.9)
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Correspondingly, the TMSE is given by 2 H E eEe e (5.10) 5.1.2 Optimum FEDFE receiver Now, to find the optimum FED FE [27] to minimize the MSE, is differentiated with respect to w and b and set the two terms to zero. H w112 HHH 11121 H b212 HHH 21222E2VVwVba 2E(VV)w2E(VV)b2E(Va)0 E2VVwVba 2E(VV)w2E(VV)b2E(Va)0 (5.11) In matrixvector form, the above equations can be written as EVVEVV EVVEVV w b EVa EVa QQ QQ w b QHH HH H H H H()() ()() () ()1112 1222 1 2 23 34 10 (5.12) Hence the optimum FE and DFE can be estimated (for the noiseless case) as follows w b QQ QQ QH H 23 34 1 10 (5.13) Here, QEaHAG QEGARAGGEARAGGFG QEGARAGEARAGF QEARAEARAFH HHHHH HHHHH HH12 1 1 21111111111 311211212 422123 (); ()() ()(); ()()1 (5.14)
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A symbol correlator matrix for M symbols is shown below T T T all T M (M1)LM000 000 P 000 000 (5.15) Blocks p of size M M are extracted. Now let m = L/M. (Note L should be a multiple of M). So pi blocks of size M M ( i = 1, 2, ...I) where I = m + (M1) will be created. Also let Ip = I/m. Additional p blocks pi ( i = I+1 ...I+(Ip 1) M) = ZM M are then defined, so as to complete the polyphase sequences given below (5.16) pppp123I 1M2M3MIM 12M22M32M I2M 1(I1)M2(I1)M3(I1)MI(I1)M Now using the above polyphase sequences, R can be expressed (neglecting edge effects) as H 22 T 11 2 3 TT 21 12 I TTT 321 1 I T I T I T I 11RHH pppp ppppp00 ppppp0 p 0p p 000pp Ip 0 0
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(5.17) KJ J JKJ J J KJJ JK JJJ KI T I I T MMMIM M I T I T MIM M MDXMD111 11 11221 22 21 1 11 1122 ,, ,, , ,, ,,, Note the repeating blocks whose components are given below p pI T iik*Mik*M k0 I T i,jik*Mijk*M k0Kpp; J pp;i1,2,,M,j1,2,,I1 (5.18) The matrix Q1 can be expressed statistically in terms of symbol energy H 1211 2 0M1M2M1(I1)M1QE(aHA)G D..D(D1)..(D1)..(DI)G 1 1 (5.19 ) The matrix Q2 is given by (5.20) QGEARAGGFGHHH2111111()
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The diagonal and off diagonal terms of the matrix F1 = E(A1 HRA1) are given by M 2 1nn n1nmod(i/M)1 M 2 1n,jM(mod(i/M)1),j n1jnmod(i/M)1 M 2TT 1n,jM(mod(i/M)1) n1Di F(i,i)1KK MM Di F(i,ij)1JJJ MM Di F(ij,i)1JJ MM T ,jn,j jnmod(i/M 11MXMJ giveni1,2,....,D,j1,2,...,I1andijD elseF(i,ij)F(ij,i)Z,where Z is a zero matrix whengiveni1,2,....,DthenjI1,ijD n j ) 123 (5.21) The matrix Q3 can also be defined as QGEARAGFHHH31121() (5.22) Note that the matrix A1 is MD MD (i.e., D D blocks), and the matrix A2 is MD Nb, (D nb blocks) therefore the final matrix is of size MD Nb (i.e., D nb blocks), where nb Nb/M. Also note that the first l L/M block rows of A2 are zero rows. Then F2 = E(A1 HRA2) can be obtained from F1 by removing the first l block columns from F1 extracting the next nb block columns and removing the remaining block columns. The matrix Q4 can also be determined similarly QEARAFH422() (5.23) The final matrix F3 is of size Nb Nb (i.e., nb nb blocks), Also note that the first l block rows of A2 are zero rows. Then F3 is a submatrix of F2 and can be obtained from F2 by removing the first l block rows from F2 extracting the next nb block rows and removing the remaining block rows.
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Now to consider the effect of AWGN, another matrix Q5 will be incorporated in the estimation, from (5.13). Thus the optimum FE and DFE can be estimated (for the AWGN case) as follows w b QQQ QQ QH H 253 34 1 10 (5.24) The matrix Q5 is similar to Q1 and uses AWGN energy HH 522N MDMD 222 N M DMDQENHHNRS; where SdiagMDMD1 (5.25) 5.2 Simulation Results on the Performance Limits 5.2.1. Experiment 1 (100 ns DelaySpread Channel): Consider a 108 Mbps, 64 QAM (18 Msps), four users (M=4, L=12) OWSS system over a 100 ns rms delayspread multipath channe l [1]. A Naftali channel model [62], [63] is used which results in a 9tap structure. The receivers FEDFE are optimized for Nw = 4 and Nb = 8. Adaptive loading [64], [65] is also used based upon the total meansquared error. That is, if the TMSE is below a threshold thr64, 64QAM transmission is used; if it is at or above thr64 but below another threshold thr16, 16QAM transmission is used; otherwise QPSK transmission is used. Tabl e 5.1 shows the bit error rate for two scenarios. In the first case delayed decisi on is used which is simulated by accepting only those channels for which the peak occurs at th e zeroth bin; this is a simplified approach which can be made more rigorous either by incorporating the delay into the algorithm itself, or by LMS algor ithm [3]. This delay is bounded by the channel memory, i.e., eight samples. The second case is where the deci sion is not delayed. Also shown are the
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aggregate bit rates as a result of the adap tive strategy. The results are given for the following SNRs: Eb/No = 19 dB, 22 dB, and 25 dB with a 2:1 selection diversity at the receiver. Due to a very sharp rolloff of the spectrum, a bandwidth expansion ratio of just 1.1, and a corresponding bandwidth of 18*1.1=19.8 MHz are assumed in the calculation of the spectral efficiency. Figure 5.2 show s the BER curve for fixed 64QAM symbol constellation. Note that this represents the performance in the limit. 5.2.2 Experiment 2 (50 ns DelaySpread Channel) Consider again a 108 Mbps, 64 QAM (18 Msps), four user (M=4) OWSS system. However, now a 50 ns rms delayspread multipath channel (5 taps) will be considered. As before, an adaptive loading st rategy is used based upon the total meansquared error. The equalizer parameters are Nw=7, Nb=4. Table 5.2 shows the bit error rate for the situation where delayed decision is used which is simulated by accepting only those channels for which the peak occurs at the zeroth bin. This is a simplified approach which can be made more rigorous either by in corporating the delay into th e algorithm itself, or by LMS algorithm.
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Figure 5.2 BER for 108 Mbps 64QAM with 2: 1 Selection Diversit y (over 100 ns DelaySpread Channels) It is also useful to remark that Maximal Ratio Combining (MRC) [9] on a diversity of 2:1 is used at the receiver. Using this scheme in a 50ns delay spread channel, a low BER of 105 is achieved at an Eb/No of 19 dB for an aggregate bit rate of 103.3 Mbps and a spectral efficiency of 5.2 bits/s/Hz. Of course, this represents performance in the limit.
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Decision Eb/No (dB) 64QAM (%) thr64 TMSE 16QAM (%) thr16 TMSE QPSK (%) Aggregate bit rate (Mbps) BER Bits/s Table 5.1 Simulation Results with Adaptive Loading for 100 ns DelaySpread Channels Table 5.2 Simulation Results with Adaptive Loading for 50 ns DelaySpread Channels /Hz 19 dB 59 0.15 12 0.2 29 82.8 76 4.2 22 dB 82 0.15 14 0.2 4 100.1 66 5.0 Delayed 25 dB 90 0.1 7 0.15 3 103.3 37 5.2 19 dB 28 0.15 13 0.2 59 60.8 33 3.1 22 dB 51 0.15 10 0.2 39 76.3 64 3.8 Decision Eb/No (dB) 64QAM % thr64 TMSE 16QAM % thr16 TMSE QPSK % Aggregate bitrate (Mbps) BER Bits/s/ Not Delayed 25 dB 58 0.1 17 0.15 25 83.9 25 4.3 Hz Delayed 19 dB 91.5 0.2 4.5 0.25 5 103.3 105 5.2
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5.3 Conclusions This chapter has presented a theoretical basis for understanding the limits to the ormance of OWSS systems. Multilevel matrix formulation was used in determining um receiver for OWSS. Experime nts on 108 Mbps (64 QAM) indicate that a f 10 5 and spectral efficiencies up to 5.2 b its/s/Hz can be achieved for 50 ns delay annels at an SNR of 19 dB. This illustrates the effectiveness of this multilevel atrix formulation in determining the optimum receiver for OWSS. For practical plementation, future work should atte mpt an analogous development on a symbol rval basis. perf the optim BER o spread ch m im inte
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CHAPTER 6 A Novel MIMOSTCOFDM WLAN System 6.1 Introduction Fourth generation (4G) wireless tec hnology [2] will provide high bitrate multimedia communication capability, thereby enabling numerous advanced services that will significantly benefit the industry, busine ss, government, and the society in general. For example, info stations will become pervasive as are todays beveragevending machines, and highquality mobile video comm unication will become widespread as is todays cell telephony. Such path breaking changes are expected to have a major economic impact, nationally as well as gl obally. This chapter presents a novel MIMO STCOFDM technique [33][35] targeted towa rds 4G data rates, and at the same time achieve both high spectral efficiency and high performance (high data rate and low BER) over frequency selective channels. This new system is accomplished by a combination, or layering [36], of MIMO OFDM [12][16] (for high spectral efficiency), group transmit signals and antennas (for reduced complex ity) [37], space time block coding [38], [39] (for reliability), array proce ssing at the receiver [37] (for interference s uppression on a per carrier basis), and a new Least Squares (LS) decoding sc heme (for high performance) [33]. The overall approach is por trayed graphically in Figure 6.1.
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Figure 6.1 The Overall Approach Grouped Antennas (for reducing complexity) Array Processing (for interference suppression) Space Time Block Coding (for reliability) Jain Decoding (for high performance) Novel MIMOSTCOFDM System High Data Rate High Spectral Efficiency High Performance Low Error Rate Low overhead Low Complexity MIMO OFDM (for spectral efficiency) Originally proposed by Tarokh et al. [37] for flat fading MIMO system s, the group coding of transmit antennas reduces th e complexity of receivers in space time coded MIM O systems. It partitions transm it antennas into small groups. The received signals are then proces sed by a technique called group interference suppression method or array processing. By using interference suppression on a per carrier basis after the FFT at the receiver, as suggested by Boubaker et al [57], the t echnique also lends itself to frequency selective multipath channels. Fina lly, a novel decoding scheme is employed. It uses samples from frequencies that are K/2 apart, where K is the total number of FFT frequencies, in order to introduce another el ement of diversity, and then uses least squares estimation to yield reliable statistics for symbol detection. Note that this diversity is achieved without any cost. The frequency diversity is i llustrated in Figure 6.2.
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b 1 b 2 b2 b1 a1 a2 a2 a1 b1 b2 a1 a2 K/2 half block by IFFT half block seperation freq. freq. Figure 6.2. Frequency Di versity in New System At 22 dB, this new scheme achieves a BER of 4 x 105, without coding or interleaving. The data rate achieved, over a bandwidth of 20 MHz, is 144 Mbps with a corresponding spectral efficiency of 7.2 bits /s/Hz. If channel coding and interleaving gains of 8 dB and 4 dB, resp ectively, are assumed the propos ed technique can achieve a BER of 4 x 105 at 10 dB and a BER of 105 at about 13 dB. However, the data rate would then be reduced to 108 Mbps with a spectral e fficiency of 7.2 bits/s/Hz. In addition, the scheme is a relatively low complexity scheme, e.g., far lower compared to that in [66] which uses linear precoding and space frequency block coding. 6.2 Group Coded Antennas and Array Pro cessing in Flat Fading Channels In this section, the scheme proposed by Tarokh et al. [37] to reduce the complexity of receivers in space time code d MIMO systems, will be reviewed. It partitions the transmit antennas into small groups. The received signals are then processed by a technique called group interference suppression or array processing. It suppresses the signals from all other groups of antennas as interference, other than the specific group of interest which is to be decoded. Consider, for example, a 4 MIMO
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system shown in Figure 6.3. The four tran smit antennas are divided into two groups of two antennas each, and each of these groups uses the Alamouti STC code [39]. At the receiver the null space of the transpose of the second groups channel matrix is used to extract first groups signals (fro m the received signals). Conv ersely, the null space of the first groups channel matrix is us ed to extract second groups signals. ChannelsH Q1 TQ2 TQ1=Nullity matrix of L1 TQ2=Nullity matrix of L2 T s 1 s 2 s 3 s 4 Group 1 Group 2 + Decoder / Detector Decoder / Detector noise noise 4 Rx antennas ChannelsH Q1 TQ2 TQ1=Nullity matrix of L1 TQ2=Nullity matrix of L2 T s 4 Rx antennas Decoder / Detector Decoder / Detector Decoder / Detector Decoder / Detector + + 1 s 2 s 3 s 4 Group 1 Group 2 Matrix Q1 T ann T ihilates the contributions of TX signals s3and s 4and s Matrix Q2 annihilates the contributions of TX signals s1 2 Matrix Q1 T ann T Matrix Q2 ihilates the contributions of TX signals s3and s annihilates the contributions of TX signals s1 4and s 2 Figure 6.3 Grouped Antennas and Array Processing for 4 4 System To elaborate on the theory, consider a MIMO system with N transmit and M receive antennas, with the model r = H s + n (6.1) Where the vector s denotes the transmitted signals, r the received signals, and n the AWGN. The MN matrix H = [hij], represents the multiple flatfading channels. Assume that the N transmit antennas at the transmitter are partitioned into q groups G1, G2,.,Gq, comprising N1, N2,.,Nq antennas, respectively. Using array
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processing, the transmitted signals from antenna group g (g=1,2,.., q) are decoded/detected separately while suppre ssing signals from all other groups. For simplicity, focus on the detection of signals from group 1. The channel matrix H is partitioned into two sub matrices, namely V1 which consists of the first N1 columns and L1 which contains the remaining NN1 columns. Note that V1 corresponds to the transmission of the desired group signals, and L1 to the transmission of all other group signals, which may be interpreted as interferen ce. To annihilate this interference, Tarokh et al. compute a set of orthonorma l vectors in the null space of L1 T assembled into a matrix Q1. Multiplying both sides of (6.1) by its transpose Q1 T r = Q1 T H s + Q1 T n (6.2) Since Q1 T L1 = 0 i.e., a zero matrix, (2) can be written as Q1 T r = Q1 T H1 s 1 + Q1 T n (6.3) where s 1 represents the vector of all signals from group 1. Setting TT 111rQr;HQH;nQn T 1 (6.4) equation (3) can be rewritten as 1rHsn (6.5) Here all signalstreams out of transmit antennas N1 + 1 ., N are suppressed. That is, the matrix Q1 T annihilates the contributions of signals transmitted from N1+1,.., N; similarly Q2 T annihilates the contributions of signals transmitted from 1,..., N1, and N1+N2+1,, N ; and so on. Any of the various schemes could then be used for decoding/detection. The performance of the system can be enhanced considerably by
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using space time codes on each group, codes that are often called component codes [37],[38]. Using array processing [37] each code is decoded separately while suppressing signals from the other component codes. This combination of component codes and array processing can provide reliable and high data rate communication. 6.3 Grouped Antennas and Array Processing in MIMOOFDM. 6.3.1 Frequency Selective Channels in MIMOOFDM. Referring to Figure 6.3, consider an NM MIMOOFDM system with K subcarriers. The MIMO channel is modeled as L tap frequency selective channel hi,j(l) with l=0,1,,L1, i=1,2,..,M and j=1,2,..,N. Suppose hi,j(l) is the (i,j) th element of the matrix H(l), then the discrete time MIMO baseband signal model at time instant n is given by )()()()(1 0nwlnslHnxL l pfx pfx (6.6) where x pfx(n) is the M dimensional received signal with prefix, s pfx(n) is N dimensional transmitted signal with prefix and w (n) represents the additive noise. Here the underbar connotes a vector. This OFDM system utilizes K sub carriers per an tenna transmission and a cyclic prefix of G samples to avoid the socalled "InterBlockInterference". The received MIMO OFDM symbol, after remova l of the cyclic prefix, is given by x sw (6.7) Here s is the transmitted vector of size KN given by TT T TGKsGsGss ])1(....)1()([ with s (n) being an N subvector of the nth sample. Similarly x is the KM received vector given by
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TT T TGKxGxGxx ])1(....)1()([ with x (n) being an M subvector of the nth sample. is a KMKN block circulant matrix of the form (6.8) 0K1K2 10K1 210 K1K2K30 1 2 3 where each individual block k k = 0, 1 2, K1, is of size M N. The KMN dimensional first blockcolumn of is B = [ H(0)MN T H(1)MN T H(L1)MN T ZM(KL)N T ]T where Z represents a zero matrix. The transmitted signal can be represented as aIFsNN H (6.9) where F is a KK FFT matrix (the superscript H denotes hermitian transpose), a is the KN dimensional QAM symbol input given by T T K TTaaaa ]....[1 10 where a k is an N symbol vector of the kth subcarrier. Here denotes the Kronecker product. At the receiver, after the removal of cyclic prefix and conversion to frequency domain the signal is given by H MMMMNNMMyFIxFI FIaFI an w (6.10) where T T K TTyyyy ]....[1 10 is the frequency domain KM vector, n is the additive frequency domain noise and is a block diagonal matrix. 0 1 H MMNN K1H00 0H0 FIFI 00H (6.11)
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The kth block diagonal element is the NM MIMO channel of the kth subcarrier and can be shown to be L1 k l0kl HH(l)expj2 K So for this subcarrier the received frequency domain signal can be expressed as kk kyHan k (6.12) As shown above, the resulting MIMO channel model in the frequency domain on a per subcarrier basis is flat. 6.3.2. Array Processing for Fre quency Selective Channels In this section, the discussion on ar ray processing is extended to MIMOOFDM systems over frequency selective ch annels. Frequency dom ain equalization for frequency selective channels on a per subcar rier basis was proposed by Boubaker et al. [57] in the context of a VBLASTOFDM syst em. Their concept of per subcarrier based MIMO processing is adapted, combined with array processi ng, thereby extending it to MIMOOFDM systems in frequency selective channel environments. In the frequency domain each OFDM subcarrier undergoes (very nearly) flat fading [6][8], and as such array processing can be used to separate group signals on a per subcarrier basis. After group interference suppression, further processing such as equalization and decoding/detection can be carried out depending on the particular scheme. Consider equation (13), where Hk =[hij k] the MN kth subcarrier channel matrix. The channel matrix is partitioned into tw o sub matrices, namely the desired group matrix Vk g and interferer group matrix Lk g, whereupon array processing is applied to separate out
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the desired group of interest. Without loss of generality, further details are provided below only for group 1. kkk kk k 1,11,2 1,N1 1,N111,N12 1,N kkk kk k 2,12,2 2,N1 2,N112,N12 2,N kk 11 kkk kk k M ,1M,2 M,N1 M,N11M,N12 M,Nhhhhhh hhhhhh V;L hhhhhh T) (6.14) Note that the columns of V1k and those of L1k when adjoined, form the complete matrix Hk. Similar definitions hold for other groups. Now let kk 11Qnull((L) (6.15) Then Qk 1 T can be used for group in terference suppression to ex tract the signals of group 1, while suppressing the contributions of all ot her groups. Multiplying both sides of (12) by its transpose Q1 k y k = Q1 k Hk s k + Q1 k n k (6.16) Since Q1 k L1 k = 0 i.e., a zero matrix, (16) can be written as Q1 k y k = Q1 k H1 k s 1 k + Q1 k n k (6.17) where s 1 k represents the vector of all signals from group 1. Setting kk k kkkk 1 1 11111rQk k y ;U=QH;n=Qn (6.18) equation (3) can be rewritten as kk k 1 11 1r=Us+nk (6.19) As shown in Figure 6.4, all signa lstreams out of transmit antennas N1 + 1 ., N are suppressed. That is, the matrix Q1 k annihilates the cont ributions of signals (for subcarrier k) transmitted from N1+1,.., N; similarly Q2 k annihilates the contri butions of signals
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FFT FFT ARRAY PROC. CP CP1 CP CP1 IFFT IFFTf0fK1 CP CP IFFT IFFT FFT FFT ARRAY PROC. CP CP CP1 CP1 CP CP CP1 CP1 IFFT IFFT IFFT IFFTf0fK1 CP CP CP CP IFFT IFFT IFFT IFFT Figure 6.4 Array Processing in Frequency Selective MIMOOFDM Channels transmitted from 1,..., N1, and N1+N2+1,, N ; and so on. In general, Qg k is defined for the various other groups to facil itate signal extr action for group g. It is interesting to observe that each group g could, in the limit, contain only one antenna, i.e., each antenna could be transmitting independently. In such a case the transmission capacity would increase by N times over a SISO OFDM system. However, such a system would suffer in terms of perf ormance and reliability A reasonable solution would be to introduce diversity by use of component codes and array processing, which would provide a reliable and performance orient ed system with adequa te increase in data rate. 6.4 Novel MIMOSTCOFDM System A new system is proposed here system which combines the concepts of grouped
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antennas, component STC, array proces sing, MIMO OFDM and a new decoding algorithm. The objective is to achieve both high sp ectral efficiency and high performance. A block diagram of the system is shown in Figure 6.5. The approach is the following. The transmit antennas are divided into groups, each of which uses a component STCOFDM (block) code. At the receiver each component code is decoded by group interference suppression method that suppresses signals from other antenna groups as interference. This is followed by reassembly of carriers and a novel Least Squares (LS) decoding process called Jain decoding to recover the original QAM symbols. For definitiveness, consider a 4 system (N=4, M=4). The transmit antennas are divided into two groups of two each a nd the input stream of D QAM symbols to each group is space time block coded using the blockby half block Alamouti code [39]. n)(a)n(a )n(an)(ag g g g2*12 12* 2 (20) where n is halfblock index. Note that the underbar connotes a vector. Specifically, here the size of each of the symbol vectors is K/2. Also note that the symbol and its associate (complex conjugate of the symbol transmitted from the other antenna at the same time) are K/2 subcarrier frequencies apart which provides frequency diversity over symbolbysymbol scheme. From (6.12), on a per subcarrier basis the ve ctor of received signals can be written as kk ky=Hs+nk
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Figure 6.5 Novel MIMOSTCOFDM system where s k is the transmitted signal vector, n k the noise and Hk =[hij k] the MN subcarrier channel matrix. The channel matrix is partitioned into two sub matrices, namely the desired group matrix Vk g and the interferer groups matrix Lk g. The array processing matrix Qk g is applied to separate out the desi red group of interest, as shown below kk kk g k k g gg gr=Qg y ;U=QH (6.21) Now considering the structure of the Alamou ti space time block code, the symbol and its conjugate are K/2 subcarrier frequencies apart. Th is fact is used in the novel LS decoding scheme. The group index (g) details have been omitted below and only two symbols a1 and a2 are considered which are carri ed over frequencies that are K/2 subcarrier frequencies apar t in a single group. K K k+ k+ k 1 k 2 2 2 12 2 1 KK KK *k+ k+ *k+ k+ ** 1 2 22 22 22 2 1a a r=U+n;r=U+n a a a a r=U+n;r=U+n a a (6.22) f 0 FFT Jain Decoder FFT ARRAY PROC. CP CP1 CP CP1 IFFT IFFT f K 1 f0fK 1 CP CP IFFT IFFT STC STC f 0, f K./2f K/2 1 f K 1 f K./2 f K/2 1 Jain Decoder f 0 FFT Jain Decoder FFT f 0, f K./2CP CP ARRAY PROC. CP1 CP1 CP1 1CP CP CP IFFT IFFT IFFT IFFT CP CP IFFT IFFT IFFT IFFT STC STC CP CP f0f K 1 f K/2 1 f K 1 Jain Decoder f K./2 f K/2 1 fK 1
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The above terms can be grouped below as k k 1 1 K K k+ k+ 2 2 2 2U r n a =+ a n U r (6.23) (6.22) and (6.23) can also be explained in detail as follows 2 2 1 ~ 41 42 31 32 2 K k 2 1 2 42 41 32 31 2 K k* 2 1 2 42 41 32 31 2 K k 1 2 1 42 21 12 11 kn a a hh hh r ~ n a a hh hh r n a a hh hh r n a a hh hh r2 K k 2 K k* 2 K k k U U U U 1112 k 1 2122 1 K ** k 2 2 3231 2 ** 4241 k 1 1 K k+ 2 2 2 Uhh r n hh a a hh n r hh U n a + a n U The above equation can also be written as R=Ua+n (6.24) Finally frequency domain equalization is carried out using th e pseudoinverse and slicing is done to recover the received QAM symbols. dpinv(U)*Raslicer(d) (6.25) Although a 4 4 system with groups of 2 antennas and Alamouti coding has been discussed, however larger systems using va rious space time block coding schemes are possible. To compare the weak diversity (symbol by symbol separation) and strong diversity
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(half block by half block), the conditioning of the array processed 2 channel matrix (Uk ) is studied by comparing their eigenvalues. Recall that the minimum eigenvalue [68] of a matrix is a direct measure of its conditionality. Figure 6.6a shows the minimum eigenvalues for the weak diversity case while Figure 6.6b shows results for the strong diversity scheme. For iteration no. 7, in Figure 6.6a, the minimum (over K sub carriers) channel eigenvalues for the symbolbysymbol case are poor, less than 0.2, for both sym bols, while in Figure 6.b, the associate symbol which is K/2 subcarrier frequencies apart has a good minimum eigenvalue of 0.7. As another example, for iteration no. 9, the minimum eigenvalues for the weak diversity case are below 0.4 for both symbols, while in the strong diversity case (Figure 6b), the associate symbol has a minimum eigenvalue of 1.5. Thus the halfblock by half block based system provides distinct performance advantage over the symbolsymbol scheme. Figure 6.6 Eigen Value Analysis of Fre quency Diversity for Novel MIMOSTCOFDM System
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6.5 Performance of the New MIMOSTCOFDM System 6.5.1 Simulation Results Simulation results on a 4 4 system using the new scheme, Alamouti code with 2 groups of 2 transmit antennas each are shown in Figure 6.7. The new scheme clearly outperforms VBLAST technique s in performance. For a 64QAM symbol constellation, and 50ns delay spread Naftali channel [62], [63] (5 tap) model, to achieve BER = 103, Group STCOFDM with Array Processing an d Jain Decoding requires only 17 dB (Eb/No) compared to 30dB (Eb/No) for an uncoded 802.11a based 64QAM OFDM system. At 19 dB (Eb/No) this new system achieves BERs on the order of 34, and at 22 dB on the order of 45. The spectral efficiency is 9.6 bits/s/Hz (assuming that only 48 carriers are used for data), which is more than two times that of an 802.11a SISO OFDM system. The data rate becomes 144 Mbps. The bandwidth used is 20 MHz. Higher spectral efficiencies could be atta ined with larger systems, say 6 4. Figure 6.7 MIMOSTCOFD M Simulation Results
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6.5.2. Comparison with Other MIMOOFDM techniques To compare the novel MIMO STCOFDM te chnique with others, the following figure of merit is proposed: FOM = Spectral Efficiency (log10BER) Eb/NodB where is a suitable positive number. van Zelsts MIMO space division multiplexed (SDM) OFDM [13] has a spectral efficiency of 1.2 bits/sec/Hz and a BER of 3 104 at Eb/No of 3 dB; correspondingly for = 0.2, FOM = 11.Shaos MIMO space freque ncy block coded (SFBC) OFDM [66] has a spectral efficiency of 4.8 bits/sec/ Hz with a corresponding BER of 5 105 at Eb/No of 19 dB; correspondingly for = 0.2, FOM = 44. The new technique with spectral efficiency of 7.2 bits/sec/Hz and BER of 3 104 at Eb/No of 19 dB, has a FOM = 55. Comparison with other MIMO OFDM schemes for WLANs based on the Figure of Merit is provided in Table 6.1. This is a preliminary Figure of Merit (FOM) definition; and can be studied further for its strengths and weaknesses. 6.5.3 Benefits of Channel coding and Interleaving In the previous section, a bandwidth of 20 MHz has been used which provisions a rate 3/4 channel coding. Therefore, the bene fit of channel coding must be taken into account. Further, interlea ving/deinterleaving can be incorporated at the transmitter/receiver which can yet improve the performance. Table 6.2 gives the predicted performance estimates using the upper limits GC 8 dB and GI 6 dB. Admittedly, the BER numbers in this table are only approximate estimates, but they do point to the attainable levels of performance.
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Table 6.1 Comparison of the New MIMOSTCO FDM System with Other MIMOOFDM Systems Author System Const. Eb/No (dB) BER Rate (Mbps) Spec. Eff. (bits/s/Hz) Channel Coding FoM = 0.2 FoM = 0.5 IEEE 802.11a SISOOFDM 64QAM 19 33 54 2.7 50 ns known channel rate 12 6 vanZelst 4 4 MIMO SDMOFDM BPSK 3 104 24 1.2 50 ns known channel rate 11 10 vanZelst 3 MIMO SDMOFDM 64QAM 26 101 162 8.1 100 ns known channel rate 14 6 Ogawa [69] 4 4 MIMO SDMOFDM QPSK 10 102 96 4.8 Known Multipath Rayleigh None 20 17 Boubaker 4 4 VBLAST OFDM 16QAM 10 42 192 9.6 50 ns known channel None 29 26 Stuber 4 4 STBCOFDM 16QAM 10 107 36 2.7 Known 3 tap SUI4 model rate STBC 42 39 Shao 2 MIMO SFBCOFDM 64QAM 19 55 96 4.8 50 ns known channel LCF precoding 44 38 Divakaran 4 4 MIMO STCOFDM 64QAM 19 34 144 7.2 50 ns with Channel estimation None 55 48
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6.6 Conclusion high spectral efficiency and high perfor accom signals and antennas, array per carrier basis, and a new decoding sc A novel MIMO STCOFDM technique has been presented that achieves both mance ove r frequency selective channels. This is plished by a combination, or layering, o f MIMO OFDM, group coded transmit processing at the receiver fo r interference suppression on a heme which uses components that are K/2 FFT frequencies apart and leastsquares estimati on to arrive at the decision statistics. Simultaneously, the scheme is a low complexity scheme. At 22 dB, this new scheme achieves a BER of 4 x 105, without coding or interleaving. The data rate achieved, over a bandwidth of 20 MHz, is 144 Mbps with a corresponding spectral efficiency of 9.6 bits/s/Hz. If channel coding and interleavi ng gains of 8 and 4 dB respectively, are assumed, the proposed technique can achieve a BER of 4x105 at 10 dB and a BER of Table 6.2 Coding and Interleaving Gains for MIMOSTCOFDM system SNR (Eb/No) dB Coded Rate Mbps Data Rate Mbps Spectral Efficiency (bps/Hz) Coding and Interleaving Gains (GC, GI) 10 dB 15 dB 19 dB 22 dB N/A 144 9.6 N/A (0,0) 2x102 2x103 3x104 4x105 (5,0) 2x103 2x104 3x105 4x106 (6,0) 1x103 104 105 (7,0) 8x104 5x104 8x106 144 108 7.2 (8,0) 3x104 2x105 4x106 (5,3) 3x104 2x105 4x106 (5,4) 2x104 105 (8,3) 8x105 8x106 144 108 7.2 (8,4)* 4x105 4x106
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105 at about 13 dB. Correspondingly, the data rate becomes 108 Mbps with a spectral efficiency of 7.2 bits/s/Hz. Future wo rk could involve studyi ng and minimizing the overhead and extension to other conf igurations, e.g., 4x3, 4x5, and 6x4.
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CHAPTER 7 CHANNEL ESTIMATION FOR THE NEW MIMOSTCOFDM SYSTEM 7.1 Introduction This chapter presents an efficient ch annel estimation technique for the novel MIMO STCOFDM system, a WLAN signaling scheme with hi gh spectral efficiency and high performance over frequency selectiv e channels. The new system employs a combination, or layering [36], of MIMO OFDM [12][16], group coded transmit signals and antennas [37], array proces sing at the receiver for inte rference suppression on a per carrier basis, frequency diversity which us es FFT components (for STC purposes) that are K/2 apart, and a new LS decoding scheme [33], [35] that uses leastsquares upon the these components. In term of MIMO classification, it is a 4 system, i.e., it has four transmit and four receive antennas. For a 50 ns delay spread WLAN, the time domain formulation [34], [35] for the unknown channel coefficients l eads to estimates that have an SNR on the order of 48 dB when just one block of 64 symbols per transmitter is used and while the receive signal SNR is 19 dB. (Actually, only 52 nonzero symbols, since there are twelve zero carriers; 11 at the guardbands, and one at zero frequency.) The final 4 equivalent channel matrix, for each of th e two component systems, is shown to have a corresponding SNR of 37 dB Most importantly, the impact on the system BER performance due to the channel estimation pr ocess (compared to the known channel case) is found to be negligible.
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The training symbol blocks transmitted for channel estimation, preceding the actual data transmission, use high power QPSK symbols [44], j, which are the outer corners of the 64QAM constellation. This l eads to a 3 dB advantage over high power BPSK symbols with no additi onal cost. Employing this channel estimation technique on a 50 ns delay spread WLAN, the new MIMO STCOFDM scheme [33], [35] achieves a BER of 3104 at 19 Db signal SNR, without the need for any channel coding or interleaving. The corre sponding data rate over a bandwidth of 20 MHz, is 144 Mbps with an associated spectral efficiency of 7.2 bits/s /Hz. If a combined 3/4rate channel coding and interleaving [1] gain of 10 dB is assu med, the proposed tec hnique could achieve a BER of 304 at 9 dB signal SNR. Then, the data rate would become 108 Mbps with a spectral efficiency of 5.4 bits/s/Hz. Befo re frequency selective channels, channel equalization scheme for Tarokhs [37] MIMO system using grouped antennas and array processing in flat fading cha nnels will be discussed. 7.2 Channel Estimation for Grouped Antenn as and Array Processed MIMO System in Flat Fading Channels In 6.2, a 4 MIMO system has been studied with group coded transmit antennas and array processing at the receiver. The f our transmit antennas are divided into two groups of two antennas each, a nd each of these groups uses the Alamouti STC code [39]. At the receiver, array processing was used to separate signals from different groups, i.e. the transmitted signals from one antenna gr oup were decoded/detected separately while suppressing signals from all other groups. In th e case of flat fading channels, the received signal is given by
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r = H s + n (7.1) Where the vector s denotes the transmitted signals, r the received signals, and n the additive white Gaussian noise. The MN matrix H = [ hij ], represents the multiple flatfading channels where M is number of receive antennas and N is number of transmit antennas. The channel matrix H is partitioned into tw o submatrices, namely L1 consisting of channels associated with group 2 and L2 with channels for group 1. The null space of the transpose of the second groups ch annel matrix is used to extract first groups signals (from the received signals). Conversely, the null space of the first groups channel matrix is used to extract second groups signals. Q1 is the null matrix of L2 t. Multiplying both sides of (5.1) by its transpose and noting that Q1 T L1 = 0. Q1 T r = Q1 T H s + Q1 T n = Q1 T H1 s 1 + Q1 T n (7.2) where s 1 represents the vector of all group 1 signals and H1 represents channel matrix for group 1. Setting TT 1 11t111rQr;HQH;nQ Tn The array processed input to the group 1 decoder is given by 1 1 1trHsn (7.3) Here all the signals from group 2 are suppre ssed. This process is repeated for group 2 where signals from group 1 will be suppressed. For decoding, channel estimation is necessary to cancel the effect of array processed matrices H1t and H2t. A channel estimation scheme is illustrated in Figure 5.1.
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Estimation Q1 T Q2 T R 2 R R Decoder / Detector R 1 Decoder / Detector +n oise (N ) 1 H) S H ^ =RS H(S Channel Estimation H Channels blocks (S ) Figure 7.1 Channel Estimation for Flat Fading Channels The channel estimation is done by transmitting a estimation block of data S of size 4 D preceding the transmission of the data bloc k. The estimation blocks use high power QPSK symbols {7+7j, 77j, 7+7j, 77j}. Th ese symbols provide an Eb/No advantage of approximately 17 dB over the normal QPSK symbols. The received signal after channel mitigation is given by R HSN (7.4) The channel matrix estimation is done in the frequency domain, and is given by [34], [35] = R SH (S SH)1 (7.5) For the 4 4 system the minimum size of estimation block S is 4 4. S matrices are designed to have a conditional number of 1 to enhance the es timation process. The SNR of the estimated flat channels for channel matrix H, array processed matrices H1t and H2t and BER results for the 4 4 64QAM system (Eb/No = 19 dB) are given in Figure 5.2 for various values of D. The SNR is calculates as given below 2 h ehhSNREhEe 2 For example, for D = 16; SNR for estimated channels {H, H1t, H2t} were {42.4 dB, 35.8 dB, 35 dB}. Using these estimated channels a
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D=16 D=16 Figure 7.2 SNR of Estimated Flat Channels and Associated BER for Varying Values of D in a 4 4 MIMOSTCOFDM System (Eb/No = 19dB)
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7.3 Frequency Domain Estimation for Multipath Fading Cha the New MIMOSTCOFDM system in nnels In the system the post FFT received signal on a per subcarrier basis (k) is kkk krHsn W here s k is the per carrier input to the IFFT block at transmitter and n k is the per carrier FFT of noise and Hk is the per subcarrier FFT of the frequency selective channel. The frequency domain channel estimation can also be done on a per subcarrier basis by using estimation frames S preceding the data. The process is illustrated in Figure 7.3. D estimation frames of size N K where K is the number of subcarriers. For a 4 4 64 subcarrier system D estimation frames of size 4 64 will be used. The estimation frames igh power symbols and the columns representing subcarrier k are collected over all D frames, they form a matrix Sk of conditional number 1. The received signals can also be collected into a similar matrix Rk, and channel estimation carried out on a per asis. also use h subcarrier b (7.6) 64QAM 4 4 system has a BER of 5 104. If the minimum D = 4 is used, a BER of 9.6 104 is obtained. For perfect channel info rmation, the BER achievable is 3.7 104, however a close performance of 4 104 can be achieved with D = 60.
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FFT FFT ARRAY PROC. CP CP1 CP CP1 IFFT IFFTf0fK1 CP CP IFFT IFFT Channel Estimation on per subcarrier basis H0HK1^ ^ FFT FFT ARRAY PROC. CP CP1 CP CP1 IFFT IFFTf0fK1 CP CP IFFT IFFT Channel Estimation on per subcarrier basis H0HK1^ ^ Figure 7.3 Frequency Domain Channel Estimation for the New MIMOSTCOFDM System kkkk kkHkkH k RHSNHR(S)[S(S)]1 (7.7) The estimated channel SNR using high power Q PSK symbols in the 4 x 4 system with 50 ns delay spread Naftali channels [ 62], [63] for va rying values of D are given below in Figure 7.4. The channel SNR for each subca rrier is constant and hence the average channel SNR over all carrier is plotted belo w in the figure. The SNR of the channel estimation for a 50ns delay spread Naftali chan nel in the 4 4 system using 4 estimation frames (size 4 64) of high power QPSK sy mbols was found to be 33.4 dB, for 8 frames it was 36.4 dB and for16 frames it was 39.4 dB. This represents a drop of 3 dB in performance as compared to the flat fading channel case.
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Figure 7.4 SNR of Estimated Fl at Channels for Varying Values of D in a 4 4 MIMOSTCOFDM System (Eb/No = 19dB) 7.4 Time Domain Channel Estimation fo r the New MIMOSTCOFDM System in Multipath Fading Channels Consider the N M OFDM system as illustrated in Figure 7.5. The input to the IFFT block for the jth transmitter a j j=1,2,3,..N. The estimation blocks use high power QPSK symbols 7 7j. The output of the corresponding IFFT operation is s j =ifft (a j) = [ sj(1) sj(2) sj(K) ]T where K is the number of subcarrier frequencies. Cyclic prefix is then prepended to these signals before transmission. The M N channel impulse responses, each of length L, are denoted as h i,j i=1,2, ..M ; j=1,2,3,..N. Note that h i,j is a
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column vector of length L. The received signal at the ith receive antenna after removal of cyclic prefix is given by )()()())(*)(()(1 1 ,knkrknkskhkri N j ji ij N j ji i (7.8) CP CP1 CP CP1 IFFT IFFT CP CP IFFT IFFT TIME DOMAIN CHANNEL ESTIMATOR TIME DOMAIN CHANNEL ESTIMATOR a 1a 2a 3a 4s 1s 2s 3s 4r 1r M CP CP CP1 CP1 CP CP CP1 CP1 IFFT IFFT IFFT IFFT CP CP CP CP IFFT IFFT IFFT IFFT TIME DOMAIN CHANNEL ESTIMATOR TIME DOMAIN CHANNEL ESTIMATOR a 1a 2a 3a 4s 1s 2s 3s 4r 1r M Figure 7.5 Time Domain Channel Estimation for the New MIMOSTCOFDM System where ni is the noise. The channels associated with the ith receiver can be collected in a vector of size NL T T TT ii,1i,2i,Nhhhh (7.9) The time domain convolution can be expresse d as a matrix vector product. The known OFDM symbols can be collected in a circular convolution (r ectangular) matrix as shown below
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LK j jj j j j j j j jLKs KsKs LKs ss LKsKss S )1()1()( )3( )1()2( )2( )()1( (7.10) Then the convolution expression for the received signal can be written as i ii 12N ii K(NL)rSSShn Shn (7.11) The matrix SK(NL), applicable to a single frame of channel estimation phase symbols, is shown in equation (7.12). NNN 111 NNN 111 K(NL) NNN 111s(1)s(K)..s(KL2) s(1)s(K)..s(KL2) s(2)s(1)..s(KL3) s(2)s(1)..s(KL3) S..   s(K)s(K1)..s(KL1) s(K)s(K1)..s(KL1) (7.12) If more than one frame is used, SK(NL) matrices for each frame are stacked one on top of the other to create a matrix S(BK)(NL) where B is the number of frames. This is shown in (7.13) after two pages. Then th e channel impulse response for the ith receiver can be estimated using the least square s criterion, as follows H1H i i h(SS)Sr (7.14) The components of the channel impulse re sponse can be separated into individual four channels associated with the ith receiver. The process is repeated for each receiver, to estimate all sixteen channel in the 4 4 system and thereupon, FFT of the individual channel impulse responses will be used for a rray processing, equalization and decoding.
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From (7.14), the estimated channel ve ctor can clearly be written as i i hCr (7.15) where H 1HC(SS)S (7.16) The matrix C of equations (7.15) and (7.16) is known and can therefore be prestored. The channel estimation process then involves the matrixvector multiplication C*r i. The matrix C has a size (NL)K. For a 50ns delay spread (5 tap channel) 4 4 MIMO WLAN (K=64), C would be a 20 64 matrix. High power BPSK symbols were tried in the estimation process. However they suffered from a 3dB SNR loss. If it were possible to design a matrix S, whose columns are orthogonal, then SHS will become a diagonal matrix [3 4], [35]. This may simplify the matrixvector multiplication process in (7.15).
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(7.13)NNN 111 NNN 111 NNN 111s(1)s(K)s(KL2) s(1)s(K)s(KL2) s(2)s(1)s(KL3) s(2)s(1)s(KL3)   s(K)s(K1)s(KL1) s(K)s(K1)s(KL1) ________________________ S NNN 111 NNN 111 NN 111____________________ __________ _________ s(1)s(K)s(KL2) s(1)s(K)s(KL2) s(2)s(1)s(KL3) s(2)s(1)s(KL3)   s(K)s(K s(K)s(K1)s(KL1) N 111 1111)s(KL1) ________________ _________________________ _____________ ___________ ____________________ ____________________________ ____________ s(1)s(K)s(KL2) s(2)s(1)s(KL3) NNN NNN NNN 111 (BK)(NL)Frame1 Frame2 s(1)s(K)s(KL2) FrameB s(2)s(1)s(KL3)   s(K)s(K1)s(KL1) s(K)s(K1)s(KL1)
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7.5 Simulations based on the Time Domain Channel Estimation The channel estimation can be done using B frames of known time domain OFDM symbols (IFFT of hi gh power QPSK symbols) of size K before the actual transmission of data symbols. The SNR (SNRh) of estimated channel parameters (Hk) and estimated array processed channel parameters (Uk) using varying number of frames is shown in Figure 7.6 (for signal Eb/No = 19 dB). The SNR is calculates as 2 2 ,,,ji jih jijijieEhESNR hheparam param frequency dom m figure also shows the SNR of dom based STCOFDM. For channels is 48 dB. F or ex ample, for one frame (K=64) and 5 tap channel, the SNR of the estimated channel eters is 49 dB and for two frames it is 52 dB. The SNR of estimated channel eters for the time domain translates in the frequency domain for a per subcarrier ain channel matrix, as FFT of the carrier frequency domain channel atrix, as FFT of the estimated time domain channels is a orthogona l transformation. The estimated array processed channels in the frequency ain, taking into account the inherent frequency diversity of the system by using block example for one frame the SNR of estimated array processed
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Figure 7.6 SNR of Time Domain Estimated Channel Parameters at 19 dB Signal SNR Simulation results on a 4 system usi ng the time domain estimation scheme and Alamouti STC codes with 2 groups of 2 transm it antennas each is s hown in Figure 7.7. System parameters are as follows: B=1, K=64, 64QAM symbol constellation, and 50ns delay spread Naftali channel [62], [63] (5 tap) model. The spectral efficiency is 9.6 bits/s/Hz (assuming that only 48 carriers are used for data), which is more than two times that of an 802.11a SISO OFDM system [4], [8]. The data rate becomes 144 Mbps. The bandwidth used is 20 MHz with K=64 subcarrier frequencies. These input parameters generally conform to the 802.11a standard [4], [8]. The figure shows the BER curves with channel estimation and with perfect know ledge of the channel, showing that highly efficient results are obtained using a single frame.
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Figure 7.7 System Performance with Know n Channels and Time Domain Channel Estimation 7.6 Conclusions An efficient time domain formulation for cha nnel estimation has been presented, for the new high performance MIMO STCOFDM system, which uses high power QPSK symbols. Four matrixvector multiplications enable high accuracy estimation of all sixteen MIMO channels. For a 50 ns delay sp read WLAN, at 22 dB signal SNR this new scheme, together with channel estimati on incorporation, achieves a BER of 45 without coding or interleaving. The correspondin g data rate over a bandwidth of 20 MHz, is 144 Mbps with a corresponding spectral efficien cy of 7.2 bits/s/Hz. Further work could involve improvising on the fre quency domain channel estima tion and optimizing the time domain estimation block.
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CHAPTER 8 CONCLUSIONS AND FUTURE WORK In this dissertation, two different techologies are presented for the next n generation of high speed WLANs, OW SS and MIMOSTCOFDM. OWSS, or O rthogonal W avelet Division Multiplexed S pread S pectrum was first introduce new class of pulses and a corresponding si gnaling system which can be a candidate signaling scheme for the next generation high speed WLANs. OWSS offers multiple capability both at the PHY and MAC layers. However, multiplexing at the MAC layer is more preferable, as it would enable full rate shared access of the bandw idth (in this case 108 Mbps) to bursty users. Towards this e nd, it was proposed that OWSS will use a CSMA/CA based MAC protocol similar to the IEEE 802.11a standard to access the medium. A frame format for OWSS data packets in the MAC layer and MAC attribu of OWSS in terms of DCF parameters was also proposed. Using a simple theoretical model for performance analys is, the MAC layer of OWSS sh owed excellent performa results, a saturation throughput of 66% and an average packet delay of 5 ms using RTSCTS for a moderate number of stations (say, less than 50) At the PHY layer, a critical attribute of OWSS was looked at, its spectral characteristics. OWSS can avoid substantial overhead penalties through the elimination of the prefix, the guard zerocarriers, and channel. coding, while still providing a desired BER performance at practical SNRs. I was shown that the theoretical baseband sp ectrum is perfectly flat, and the passband d as a xing tes nce t
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spectrum offers a 3040% bandwidth a dvantage over 802.11a OFDM for 54 Mbps operation. OWSS readily extends to higher bit rates, such as 108 Mbps, in a bandwi efficient manner. Spectrum masks for 54 M bps and 100 Mbps OWSS operation were als proposed. dth o Unlike the pulses used in OFDM, CD MA, and TDMA, OWSS pulses are based al meane y low BER on a new family of pulses which have both a wide time support and a wide frequency support. As a consequence of the wide frequency support, effectiv e equalization in a multipath environment can be achieved using an FEDFE structure in the receiver together with the LMS adaptation algorithm. The fundamental limits to its system performance is investigated out by formul ating the system as a multirate signal processing system, using hierar chical matrices, and thereupon minimizing the tot square error (TMSE). The TMSE governs the BER performance of the system, and is defined as the sum of the MSE of the unequa lized residual error and the MSE due to th channel noise amplified by the forward equalizer The problem is formulated at the chip level so as to truly discern the fundamental limits to the performance of the equalizer. This approach enables estimation of the optim um equalizer for mitigating the effect of the multipath channel, prior to correlation a nd detection blocks embedded in the FEDFE loop, and thereby the system performan ce. Simulation results demonstrate its effectiveness. For a 108 Mbps sy stem with a 50 ns delay spr ead channel, a ver of 105 and high spectral efficiency up to 5.2 bi ts/s/Hz can be achieved at a bit SNR of 19 dB.
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Moving away from OWSS, a new MIMOSTCOFDM system was then of me h a Finally the frequency selective channel for the new 4 4 system was modeled. nted, introduced that achieves both high spectral efficiency and high perform a nce over frequency selective channels. This is accomp lished by a combination, or layering, MIMO OFDM, group coded transm it signals and antennas, array processing at the receiver for interference suppression on a per carrier basis, and a new decoding sche which uses components that are K/2 FFT frequencies apart and leastsquares estimation to arrive at the decision statistics. Simultaneously, the scheme is a low complexity scheme. At 22 dB, this new scheme achieves a BER of 4 x 105, without coding or interleaving. The data rate achieved, over a bandwidth of 20 MHz, is 144 Mbps wit corresponding spectral efficiency of 9.6 bits/s /Hz. If coding and interleaving gains of 8 and 4 dB respectively, are assumed the proposed technique can ach ieve a BER of 4x105at 10 dB and a BER of 105 at about 13 dB. Correspondingly, the data rate will become 108 Mbps with a spectral efficiency of 7.2 bits/s/Hz. Frequency domain equalization using high power QPSK symbols provided excellent results for flat fading channels but did not port too well to the frequency selective channels. So an efficient time domain formul ation for channel estimation was prese for the new high performance MIMO STCOF DM system, which uses high power QPSK symbols. Four matrixvector multiplications and a single estimation data frame enabled high accuracy estimation of all sixteen MIMO channels.
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To summarize we again list the specific c ontributions of this dissertation below. idates for the next d SS to access the medium. A alyzed visavis OFDM. The OWSS 54 eme was develope d to compensate for the passband spectral cture was matrix g Following this, possible extensions of the work done are discussed. (1) O WSS and MIMOS TCO FDM are both pr e sen ted as viable cand generation of high speed WLANs. OWSS is a new modulation technique capable of high data rates without using multiple antennas at the transmitter and receiver. MIMOSTCOFDM on the other hand, achieves next gene ration data rates by combining transmit an receive diversity techniques w ith legacy OFDM systems. (2) A CSMA/CA based MAC protocol is pr oposed for OW frame format for OWSS data packets and MA C attributes of OWSS are also proposed. Performance of OWSS at the MAC layer in terms of saturation throughput and average delay was analyzed using Bianchi's model. (3) The spectrum efficiency of OWSS was an passband spectrum is found to have 3040% bandwidth advantage over OFDM for Mbps operation. OWSS also readily extends to higher bit rates, such as 108 Mbps, in a bandwidth efficient manner. (4) A novel predistortion sch regrowth due to PA nonlin earity. At 6 dB backoff in 108 Mbps OWSS, this scheme yields an improvement of 10 dB in spectral regrowth distortion levels. (5) A Forward Equalizer Decision Feedback Equalizer (FEDFE) stru originally proposed for the OWSS receiver. To wards this end, a novel multilevel formulation has been conceptualized to model the entire OWSS transreceiver and establish its fundamental theoretical pe rformance (BER) in random multipath fadin
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channels. This formulation can also be used for channel estimation, i.e. to estimate the optimum channel equalizer (weights of th e FE and DFE) for these channels. (5) A new MIMOSTCOFDM system has been developed that achieves both high spectral efficiency and high performance over frequency selective channels. This new system was achieved combining MIMOOFDM, group coding antennas using STC, array processing at the receiver (for interference suppression) and new LS decoding technique. (6) A highly effective channel equalization te chnique in the time domain has also been developed for the new MIMOSTCOFDM system. The multipath channel model for the system was also conceptualized. OWSS achieves high data rates without the use of MIMO technology and if combined with MIMO technology is capable of data rates in excess of 200 Mbps within current bandwidth limitations. The potent mixture of MIMO, OWSS and STC could make these data rates possible with high pe rformance and bandwidth efficiency. Future work in OWSS could include a MIMOOWSS sy stem and reducing the complexity of the OWSS receiver. Researchers could also l ook into other PHY issues related OWSS namely effect of offsets, effects of clipping to reduce PAPR etc. MIMOSTCOFDM is a new system base d on current trends of R&D for 4G WLANs. The 4 4 MIMOSTCOFDM system is capable both of high performance and high spectral efficiency at a data rate of 108 Mbps. Future work could involve extending the 4 4 systems to larger systems such as 6 6, capable of even higher data rates. With the current system, researchers could l ook into improvising on the frequency domain
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channel estimation and optimizing the time domain estimation frames so as to reduce overhead and complexity. The susceptibility of MIMOSTCOFDM to general OFDM impairments like frequency offset should also be explored.
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APPENDICES
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Appendix A An Example Based on th e Multi Level Matrix Formulation For a single stage ( M = 2) OWDM synthesizer, the OWDM pulses generated using a 4 tap Daubecheis filter is given by 0 =[0.3415 0.5915 0.1585 0.0915] and 1 = [0.0915 0.1585 0.5915 0.3415]. The above OWDM pulses are spread in the wavelet domain by using Hadamard codes given by [1 1] and [1 1]. The single stage OWSS pulses thus generated, are [0.433 0.75 0.433 0.25] and [0.25 0.433 0.75 0.433]. For this example, the first pulse,=[0.4330 0.7500 0.4330 0.2500] will be used. The channel is a real 3 tap channel ( L = 3), given by ]10.81[ c. For simplicity of presentation, only 4 BPSK symbols (D = 4, 2 = 1) will be used to estimate the equalizer, with Nw = 2 and Nb = 2. The effect of noise will also be neglected. The OWSS filter matrix H1 and multipath channel matrix C from (5.3), are given by 1 0.8 1 0 0 0 0 0 0 1 0.81 0 0 0 0 0 0 1 0.81 0 0 0 0 0 0 1 0.81 0 0 0 0 0 0 1 0.81 0 0 0 0 0 0 1 0.81 0 0 0 0 0 0 1 0.80 0 0 0 0 0 0 1 0.4330.75 0.433 0.25 0 0 0 0 0 0.4330.75 0.433 0.25 0 0 0 0 0 0.4330.75 0.433 0.25 0 0 0 0 0 0.4330.75 0.433 0.25 0 0 0 0 0 0.4330.75 0.433 0.25 0 0 0 0 0 0.4330.75 0.433 0 0 0 0 0 0 0.4330.75 0 0 0 0 0 0 0 0.4331C H
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Appendix A (Continued) The correlator matrix, from (5.5), is given by 0.6250 0.21650.1875 0.10830 0 0 0 0.21650.3750 0.3248 0.18750 0 0 0 0.1875 0.3248 0.6250 0.21650.1875 0.10830 0 0.10830.18750.21650.3750 0.3248 0.18750 0 0 0 0.1875 0.3248 0.6250 0.21650.1875 0.10830 0 0.10830.18750.21650.3750 0.3248 0.18750 0 0 0 0.1875 0.3248 0.5625 0.32480 0 0 0 0.10830.18750.32480.1875 2H Neglecting the edge effects, the repetitive component blocks, from (5.18), are given by 0.1875 0.3248 0.10830.1875; 00 00 ; 0.1875 0.3248 0.10830.18750.6250 0.21650.21650.3750 ; 0.6250 0.21650.21650.3750 1,2 2,1 1,1 2 1J J J K K Using (5.21), matrix F1 can be calculated 0.6250 0.21650.1875 0.10830 0 0 0 0.21650.3750 0.3248 0.18750 0 0 0 0.1875 0.3248 1.2500 0.43300.3750 0.21650 0 0.10830.18750.43300.7500 0.6495 0.37500 0 0 0 0.3750 0.6495 1.8750 0.64950.5625 0.32480 0 0.21650.37500.64951.1250 0.9743 0.56250 0 0 0 0.5625 0.9743 2.5000 0.86600 0 0 0 0.32480.56250.86601.5000 1F
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Appendix A (Continued) F2 and F3 are submatrices of F1 1.2500 0.43300.43300.7500 ; 0.1875 0.10830.3248 0.18751.2500 0.43300.43300.7500 0.3750 0.6495 0.21650.37500 0 0 0 3 2F F The matrices Q1, Q2 Q3 and Q4 given in equations (5.19), (5 .20), (5.22) and (5.23) can now be calculated 1.2500 0.43300.43300.7500 ; 0.37290.45840.5866 0.7160 ; 1.7119 2.13432.13435.7987 ;0.3248 3.754 3 2 1Q Q Q QUsing the above matrices, the optimum FE and DFE are estimated to be w = [1.1302 0.8508] and b = [0.8983 0.5877] Using the above equalizer, the normalized MSE of the unequalized error is found to be 0.010174. Note that the decision boundary for correct detecti on of a BPSK symbol is a unit distance away from either BPSK symbol, 1 or 1. An MSE of 0.010174 represents a standard deviation of approxi mately 0.1, around the transmitted symbols 1 and 1. If 8 BPSK symbols are used to estimate the equalize r, the FE and DFE are found to be w = [1.1053 0.7902] and b = [0.90298 0.62995] and the normalized MSE improves to 0.0068931. Finally if 100 BPSK sy mbols are used, the FE and DFE are
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Appendix A (Continued) estimated to be w = [1.0894 0.55148] and b = [1.112 0.76697] and the normalized MSE is further reduced to 0.0044986. For illustration purposes, a Nw = 2tap FE is used. For a longer 5tap FE and 100 symbols for estimation, the optimum equalizer turns out to be w = [1.1394, 0.57591, 0.31036, 0.037525, 0.12544] and b = [0.80517, 0.3338], with a corresponding MSE = 6.7 105. The feedback equalizer was still maintained at a length Nb = 2. This success, even for a difficult channel, may be attributed to the wide frequency support of the OWSS pulses. As a reminder, in this simple example, the effect of AWGN was ignored.
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ABOUT THE AUTHOR
