《通信原理》课程教学资源（辅导资料）Selected MIMO Techniques and their Performance.pdf_大学文库

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 1 IST-2001-32125 FLOWS Deliverable Number: D14 Selected MIMO Techniques and their Performance Contractual Date of Delivery to the CEC: 31st December 2003 Actual Date of Delivery to the CEC: 9th January 2004 Author(s): Alister Burr, Yuriy Zacharov, Hendrik Troeger, Wei Qiu, Michael Meurer, Christian Stimming, Alexander Vanaev, Georg Tauboeck, Jia Shen, Huiheng Mai Participant(s) (partner short names): UoY, UKL, TUHH, FTW Workpackage: 5 Est. person months: 24 Security (Pub., FP5, IST, Rest., or Int.): Pub Nature of Deliverable (R, P, D, or O): R Version: 1.0 Total number of pages (including cover): 337 Abstract: This document is the final version of the FLOWS deliverable D14 “Report on selected MIMO techniques and their performance. It describes work performed under Activities A5.1 (“Survey of Multi-standard MIMO techniques”), A5.2 (“Development of selected MIMO techniques”), and part of that under A5.3 (“Performance evaluation of MIMO techniques”). The purpose of A5.1 was to survey and select MIMO techniques suitable for use within the FLOWS project; A5.2 is carrying out further development of these techniques, and A5.3 will evaluate their performance by simulation. The criteria for selection included the compatibility of the techniques with multiple wireless standards, and especially the standards selected for work in FLOWS, namely GSM-1800, UMTS and WLAN standards. The document divides into three main parts: chapters 2 and 3 describe work under A5.1, while chapters 4-7 describe further development of techniques under A5.2 and A5.3. Chapters 8 and 9 discuss the issue of channel estimation, identified as important for all such scheme during A5.1. Chapter 10 additionally covers some further issues which have arisen in WP5 which relate to linkages to other parts of the project. Keyword list: MIMO, space-time codes, joint transmission, OFDM, W-CDMA, eigenbeamforming, “Multi-standard friendliness

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 4 EXECUTIVE SUMMARY This document is the final version of the FLOWS deliverable D14 “Report on selected MIMO techniques and their performance”, previously issued in draft form in September 2002. It describes work performed under Activities A5.1 (“Survey of Multi-standard MIMO techniques”), A5.2 (“Development of selected MIMO techniques”), and part of that under A5.3 (“Performance evaluation of MIMO techniques”). The purpose of A5.1 was to survey and select MIMO techniques suitable for use within the FLOWS project; A5.2 is carrying out further development of these techniques, and A5.3 will evaluate their performance by simulation. The criteria for selection included the compatibility of the techniques with multiple wireless standards, and especially the standards selected for work in FLOWS, namely GSM-1800, UMTS and WLAN standards. This issue was described in the FLOWS Technical Annexe as “multi-standard friendliness”, building on the concept of “standard friendliness” introduced in the METRA project. The document divides into three main parts: chapters 2 and 3 describe work under A5.1, while chapters 4-7 describe further development of techniques under A5.2 and A5.3. Chapters 8 and 9 discuss the issue of channel estimation, identified as important for all such scheme during A5.1. Chapter 10 additionally covers some further issues which have arisen in WP5 which relate to linkages to other parts of the project. The main conclusions of A5.1 were to identify certain MIMO approaches as worthy of further consideration on the basis of a combination of “multi-standard friendliness” and performance. These included Joint Transmission, spatial multiplexing (such as BLAST), and various versions of linear beamforming, broadly understood. These schemes have been further developed, and the work is described as follows: • Joint Transmission, including channel-oriented joint transmission, in chapters 4 and 5; • A range of schemes related to spatial multiplexing and eigenbeamforming, providing a compromise between performance and extent of channel knowledge, in chapter 6; • Turbo parallel interference cancellation and chip equalisation for WCDMA, in chapter 7 A further important conclusion of A5.1 was to identify channel estimation for MIMO systems as an important and under-researched area, vital for nearly all MIMO techniques. Work in this area is described in chapters 8 and 9. Joint transmission, whose further development is described in Chapters 4 and 5, is a scheme developed originally for the downlink of the third generation system UMTS-TDD, where channel knowledge is available at the base station by exploiting the reciprocity of the channel, because the uplink is at the same frequency as the downlink. This allows the channel to be compensated in the base station transmitter, and reduces the complexity of the mobile terminal. However, the concept is based on a set of linear transformations which can readily be adapted to other air-interfaces, including those based on OFDM. Chapter 4 shows that the degradation of the scheme due to imperfect channel knowledge is reasonable, similar to joint detection. The performance of JT in a cellular system is examined by determining the intercellular interference it causes, and schemes are developed to improve this. It is also shown how JT and JD can coexist in a cellular system. Channeloriented joint transmission (CO-JT) optimizes the transformations in the transmitter and the receiver for energy efficiency. At the cost of increased complexity in the mobile terminal, this can greatly reduce the transmit power required, and hence the intercellular interference. Chapter 6 considers MIMO techniques particularly relevant to OFDM-based systems, especially WLAN (wireless local area networks) standards. The classification of chapter 3 is expanded to include the state of channel knowledge at transmitter and receiver – full, partial or none – which leads to six categories. Various practical schemes for OFDM with various degrees of channel knowledge are compared, and it is shown that performance degrades according to degree of knowledge: for a 2

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 5 × 2 systems there is about 7 dB between SVD and DSTC. However note that this takes no account of the overhead in terms of pilot symbols required to acquire the required channel knowledge. A novel scheme is also proposed that can exploit partial channel knowledge at the transmitter. The scheme allows whatever knowledge is available to be exploited, but does not degrade seriously in the absence of reliable information. Chapter 7 considers techniques specifically intended for WCDMA. Section 7.1 describes an iterative parallel interference cancellation (“Turbo-PIC”) using a space-time turbo-coding (STTuC) approach inspired by D-BLAST (Diagonal Bell Labs Space Time Architecture), applicable primarily to the WCDMA uplink. For a moderately-loaded 4 x 4 system with 10 users, the scheme can give performance within 1-2 dB of the single-input single-output (SISO) single-user bound, depending on fading. Section 7.2 describes the application of chip equalisation to the MIMO downlink, generalising the work already carried out for SISO systems to systems using space-time block codes such as the Alamouti scheme. The scheme is able to remove the error floor, but is much more sensitive to channel estimation error than the conventional RAKE receiver: in conventional pilot-based channel estimation a pilot of length 256 is required. Picking up on the need for further work on channel estimation identified in activity A5.1, chapters 8 and 9 describe further work in this area. Chapter 8 considers especially joint channel estimation and frequency estimation, and obtains Cramer-Rao bounds for the joint problem, and maximum-likelihood (ML) frequency estimation algorithms. The upper and lower bounds are tight and close to single tone Cramer-Rao lower bound (CRLB) if pilot sequence length is at least twice the number of transmit antenna elements. Chapter 9 develops an iterative technique for joint channel estimation and decoding, and evaluates its performance on time-variant channels. In a typical case, the performance is 2-3 dB better than pilot aided only, but still about 3 dB from performance with perfect channel knowledge. Finally, chapter 10 considers the interaction of baseband processing (FLOWS WP5) with, in turn, the channel models (WP2), the antenna arrays (WP3) and the RF processing (WP4). In respect of channel modelling, two types of model are identified, described as double-directional channel model and MIMO channel model. The former describes the radio channel itself in terms of multipath component directions and amplitudes, independent of the antenna arrays, thus allowing the performance of any arrays to be evaluated, while the latter describes the channel in terms of a matrix, including the arrays and RF processing chains. In FLOWS Deliverable D13 [FLOW03c] two FLOWS channel models are described, a double directional propagation model and a MIMO channel model, the latter being validated with reference to the information theoretic capacity results of the FLOWS measurement campaign carried out in Oslo (see D10 [FLOW03b]). Both these models are now available for use in evaluating MIMO transmission and baseband processing schemes. Further work will be carried out in WP5 to evaluate them for simulation purposes. The latter in particular, being validated in terms of capacity, needs also to be validated in terms of BER performance with specific MIMO transmission schemes. In respect of antenna arrays, the requirements of an array for MIMO purposes in general are discussed. These are not in fact very severe: relatively high coupling and fading correlation are acceptable, if not ideal. The characterisation of FLOWS antenna arrays to allow them to be incorporated in baseband simulations is discussed: steering vectors need to be determined either by direct measurement or by prediction from the element topology, directional properties of elements, and element coupling. It is important to separate the effects of element directional response and coupling, which can easily be compounded. The focus of continuing work in WP5, in A5.3, will in future shift towards the evaluation of MIMO techniques in the context of FLOWS scenarios, making use of the channel models developed in WP2, the antennas of WP3, and the limitations of the RF system as determined in WP4. The objective is to provide information on link level performance to inform work in WP6 on the performance of a complete wireless network. The work described in this report lays a sound basis for this

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 6 TABLE OF CONTENTS 1. INTRODUCTION............................................................................................................. 18 2. MIMO COMMUNICATION SYSTEMS: LITERATURE SURVEY ................................... 20 2.1 Introduction ...............................................................................................................................20 2.2 Flat fading channels..................................................................................................................20 2.2.1 Models of flat fading MIMO channels.....................................................................................20 2.2.2 Capacity of flat fading MIMO channels ..................................................................................21 2.2.3 MIMO techniques for flat fading channels..............................................................................22 2.3 Frequency-selective channels..................................................................................................25 2.3.1 Models of frequency-selective channels................................................................................25 2.3.2 Capacity of multipath MIMO channels ...................................................................................26 2.3.3 MIMO techniques for frequency-selective channels..............................................................26 2.4 Time-varying channels..............................................................................................................31 2.4.1 Model of time-varying MIMO channel ....................................................................................31 2.4.2 Capacity of time-varying MIMO channels ..............................................................................32 2.4.3 MIMO techniques for time-varying channels .........................................................................32 2.5 MIMO for UMTS and METRA project.......................................................................................34 2.5.1 MIMO channel characterization .............................................................................................34 2.5.2 Transmit techniques in the FDD mode of UMTS ...................................................................34 2.5.3 Transmit techniques in the TDD mode of UMTS ...................................................................35 2.5.4 Other detection techniques for UMTS....................................................................................35 2.6 MIMO for HIPERLAN/2 and SATURN project..........................................................................37 2.6.1 MIMO channel characterisation .............................................................................................37 2.6.2 Exploiting smart antenna technology .....................................................................................38 2.6.3 Performance analysis and validation of MIMO ......................................................................38 2.6.4 MIMO synchronisation ...........................................................................................................39 2.7 Conclusions ..............................................................................................................................39 3. CLASSIFICATION AND DESCRIPTION OF MIMO TECHNIQUES .............................. 42 3.1 Classification of MIMO techniques ...........................................................................................42 3.1.1 Spatial multiplexing ................................................................................................................42 3.2 Space-time coding....................................................................................................................43 3.2.2 Linear beamforming ...............................................................................................................44 3.3 Description of specific techniques ............................................................................................44 3.3.1 BLAST....................................................................................................................................44 3.3.2 Space-time trellis codes (STTC) ............................................................................................45 3.3.3 Space-time block codes (STBC)............................................................................................46 3.3.4 Joint Transmission (JT)..........................................................................................................47 3.3.5 MIMO WCDMA with multi-user detection ..............................................................................51 3.3.6 Eigenbeamforming.................................................................................................................53 3.4 “Multi-standard friendliness” .....................................................................................................54

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 7 3.4.1 The role of standards .............................................................................................................55 3.4.2 Compatibility across multiple standards.................................................................................56 3.4.3 Sharable features of standards..............................................................................................56 3.4.4 Standard-friendly MIMO techniques ......................................................................................56 3.5 Assessment and selection of techniques .................................................................................57 3.5.1 Multi-standard friendliness .....................................................................................................58 3.5.2 Performance...........................................................................................................................59 3.5.3 Recommendations .................................................................................................................60 4. JOINT TRANSMISSIONEQUATION SECTION 4 .......................................................... 61 4.1 Basics of Joint Transmission (JT).............................................................................................61 4.1.1 Introduction.............................................................................................................................61 4.1.2 Multi-user MIMO transmission model ....................................................................................62 4.1.3 Data transmission and detection............................................................................................63 4.1.4 Exemplary demodulator .........................................................................................................65 4.2 Influence of imperfect channel knowledge ...............................................................................66 4.2.1 Preliminary remark .................................................................................................................66 4.2.2 Generic model of linear MIMO transmission system .............................................................67 4.2.3 Performance analysis of the JT with perfect channel knowledge..........................................69 4.2.4 Imperfect channel knowledge versus transmission performance..........................................72 4.2.5 Exemplary numerical results..................................................................................................77 4.3 Appraisal of intercell interference .............................................................................................78 4.3.1 Introduction.............................................................................................................................78 4.3.2 Normalized transmission model and performance criterion ..................................................79 4.3.3 Appraisal of intercell interference caused by performing JT..................................................83 4.4 Intercell interference reduction .................................................................................................92 4.4.1 Preliminary remark .................................................................................................................92 4.4.2 Generalized JT.......................................................................................................................92 4.4.3 Energy reduced JT.................................................................................................................94 4.4.4 Other intercell interference reduction methods....................................................................113 4.5 Coexistence of JT and JD ......................................................................................................115 4.5.1 Introduction...........................................................................................................................115 4.5.2 Classification of MT..............................................................................................................116 4.5.3 Identification of different receiver structures ........................................................................120 4.5.4 Concurrent operation of JT and JD......................................................................................121 4.5.5 Symbiotic operation of JT and JD ........................................................................................124 4.5.6 Support of MTs without identification...................................................................................131 4.6 Appendix.................................................................................................................................134 4.6.1 Appendix I: Linear Taylor expansion....................................................................................134 4.6.2 Appendix II: Convariance matrix ..........................................................................................135 4.6.3 Appendix III: Transmit energy ..............................................................................................135 5. CHANNEL ORIENTED JOINT TRANSMISSION EQUATION SECTION 5 ................. 137 5.1 Channel oriented Joint Transmission (CO-JT).......................................................................137 5.1.1 Receiver oriented and channel multi-user MIMO downlinks ...............................................137

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 8 5.1.2 Energy efficiency..................................................................................................................140 5.1.3 CO-JT with beneficial choice of demodulators ....................................................................141 5.1.4 Performance study of CO-JT ...............................................................................................144 5.2 Enhanced CO-JT....................................................................................................................158 5.2.1 Dominant eigenvector vs. second strongest eigenvector ...................................................158 5.2.2 Enhanced CO-JT with eigenvector selection algorithm.......................................................161 5.2.3 Performance evaluation .......................................................................................................165 6. CLASSIFICATION AND PERFORMANCE COMPARISON OF MIMO TECHNIQUES FOR OFDM SYSTEMS................................................................................................. 170 6.1 OFDM Based Techniques ......................................................................................................170 6.1.1 Frequency Selective Radio Channels..................................................................................170 6.1.2 Basic OFDM System............................................................................................................170 6.1.3 MIMO and OFDM.................................................................................................................173 6.1.4 Subcarrier specific Linear MIMO Encoding .........................................................................176 6.1.5 Subcarrier specific Space-Time Coding ..............................................................................176 6.1.6 Space-Frequency Coding ....................................................................................................176 6.1.7 Coded MIMO-OFDM system ...............................................................................................177 6.2 Classification of MIMO-OFDM techniques according to the available channel knowledge...179 6.3 MIMO-OFDM with full channel knowledge at the transmitter and receiver............................180 6.3.1 Subcarrier specific SVD transmission system without bit loading .......................................180 6.3.2 OFDM-SVD transmission system with bit loading ...............................................................182 6.4 MIMO-OFDM with partial channel knowledge at the transmitter and full knowledge at the receiver ...................................................................................................................................182 6.4.1 Antenna selection.................................................................................................................183 6.4.2 A novel MIMO OFDM scheme with partial channel state information at the transmitter.....186 6.5 MIMO-OFDM with no channel knowledge at the transmitter and full channel knowledge at the receiver ...................................................................................................................................197 6.5.1 Space-time-frequency block code........................................................................................197 6.5.2 Spatial multiplexing(SM) ......................................................................................................199 6.6 MIMO-OFDM techniques with no channel knowledge at the receiver ...................................202 6.6.1 Differential space-time block code (DSTBC) .......................................................................202 6.7 Simulation results and comparison.........................................................................................204 7. MIMO TECHNIQUES FOR WCDMA ............................................................................ 207 7.1 MIMO WCDMA with multi-user detection...............................................................................207 7.1.1 Introduction...........................................................................................................................207 7.1.2 MIMO CDMA system model.................................................................................................208 7.1.3 Space-time Turbo codes......................................................................................................212 7.1.4 MMSE Multi-user-antenna receiver .....................................................................................212 7.1.5 Low Complexity Turbo Decoder...........................................................................................214 7.1.6 Turbo PIC STTuC CDMA receiver.......................................................................................216 7.1.7 Simulation results.................................................................................................................220 7.2 Chip Equalisation for the WCDMA Downlink..........................................................................227 7.2.1 Introduction...........................................................................................................................227 7.2.2 Receivers for WCDMA downlink..........................................................................................227

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 9 7.2.3 MIMO WCDMA receivers.....................................................................................................237 7.2.4 Pilot-aided channel estimation for WCDMA receivers.........................................................254 7.2.5 Chip equalisation for 3G systems ........................................................................................258 7.2.6 Conclusions..........................................................................................................................264 8. FREQUENCY AND CHANNEL ESTIMATION IN MIMO SYSTEMS............................ 266 8.1 Introduction ................................................................................................................................ 266 8.2 Signal and channel models ....................................................................................................... 268 8.2.1 SNR for deterministic MIMO channels.................................................................................. 271 8.2.2 SNR for MIMO fading channels ............................................................................................ 271 8.3 CRLB for deterministic channels .............................................................................................. 272 8.3.1 CRLB for channel estimation in deterministic MIMO channels ............................................ 274 8.3.2 CRLB for frequency estimation in deterministic MIMO channels ......................................... 278 8.3.3 Optimal pilot sequences for deterministic MIMO channels................................................... 281 8.4 MCRLB and ACRLB for fading channels .................................................................................. 286 8.4.1 MCRLB.................................................................................................................................. 286 8.4.2 ACRLB. ................................................................................................................................. 288 8.5 CRLB for Rayleigh fading channels .......................................................................................... 289 8.5.1 SISO fading channels with AWGN ....................................................................................... 290 8.5.2 MIMO fading channels with AWGN ...................................................................................... 292 8.5.3 MIMO channels with AWGN and independent fading of channel gains ............................... 292 8.5.4 MCRLB, ACRLB, and CRLB for orthogonal pilot signals...................................................... 293 8.6 ML frequency estimation in fading channels with known statistical characteristics ..................302 8.7 ML frequency estimation in fading channels with unknown variances of path amplitudes .......305 8.8 Frequency estimation when statistical characteristics of fading and noise are unknown ........307 8.9 Simulation results....................................................................................................................... 308 8.10 Conclusions ............................................................................................................................. 315 Appendix I .........................................................................................................................................316 9. ITERATIVE CHANNEL ESTIMATION FOR MIMO FLAT FADING CHANNELS .......... 20 9.1 Introduction .............................................................................................................................319 9.2 System model .........................................................................................................................319 9.2.1 Transmitter ...........................................................................................................................319 9.2.2 Channel model .....................................................................................................................320 9.2.3 Receiver structure................................................................................................................321 9.3 Channel estimator...................................................................................................................323 9.4 Simulation results ...................................................................................................................325 9.5 Conclusion ..............................................................................................................................327 10. LINKAGES WITH OTHER WORKPACKAGES ........................................................... 328 10.1 WP2: “Channel Modelling & Measurements” .........................................................................328 10.1.1 Nature of channel models ....................................................................................................328 10.1.2 Availability of channel models and measurements..............................................................329 10.1.3 FLOWS channel models ......................................................................................................330 10.2 WP3: “Antenna Design and Test”...........................................................................................330

FLOWS 1ST-2001-32125 Deliverable No:D14 LIST OF FIGURES 4445466441814444464454544444446464454444444444446144445481444461644… 19 8 FIgure 2.3 Pa c onne DFE scheme ....... Figure 2.4 Fully co IC DFE scheme... Figure 3.1 Principle of spatial multiplexing... 2 Figure 3.2 Principle of linear beamforming. Figure 3.3 Architecture of BLAST system.. 45 Figure 3.4 Mapping of coded data streams to antennas in BLAST... .45 Figure 3.5 Trellis for simple space-time code.... 45 Figure 3.6 Increase of the respectively;JT f omor Uand OL 0 Figure 3.7 Basic MAC frame structure [John99]..... 5 Figure 3.8 STTuC Uplink CDMA System(2-User,1-TC,2_2-Antenna Sample.. .51 Figure 3.9 STTuC Downlink CDMA System(2-User,2-TC,2_2-Antenna Sample).... .52 Figure 4.1 Structure of the demodulator matrix D of(4.14)for the example given by(4.21).....65 Figu re4.2 Different MT specific demodulator matrices Dof(4.12)conceming the air interfaces TDD and OFDM 66 Figure 4.3versus for N=4 and x=0.4;comparison between simulation results ( and analytical results (-). .78 Figure 4.4 Description of a mobile radio DL with the normalized matrices.andB...80 Figure 4.5 Three dimensional plot of of(4.119). .88 Figure 4.6 Three dimensional plot of of(4.124)for=5. Figure 4.7 Three dimensional plot of of (4.124)for =32.. 91 Figure 4.Three dimensional plot of of(4.126)for=32.. .92 Figure 4.9 Generic model of a linear transmission system. 9 Figure 4.10 Mean SNIR y of the TxMF,the TxZF and the TXMMSE,parameters: N=10,p=0.9 108 Figure 4.11 Energy of the desired data symbols for the TxMF the TxZF and the Figure 4.12 Er nergy of the interfe rence for the TxMF,the TxZF and the TxMM g Figure 4.13 Multiply connected decision regions G with partial decision regions G;M=4 111 Figure 4.14 Nassi Shneiderman diagram for the generation of the transmit signal in TXNZF112 Figure 4.15 Trans-cellular JT for 7 cells... 114 Figure 4.16 Considered scenario for the case,K=2........ 4.116 Figure 4.17 Normalised MT specific demodulator matrixof(4.237). …117 Figure 4.18 Illustration of the set formalism for various receiver structures. 119 Figure 4.19 Alternating time slot allocation to JT and JD....... .122 Figure 4.20 frequency slot allocation to JT and JD..... …122 Figure 4.21 Illustration of the spatial separation of JT and JD transmit signals.... .123 31 December 2003 Page 11

FLOWS IST-2001-32125 Deliverable No: D14 31st December 2003 Page 11 LIST OF FIGURES Figure 2.1 MIMO DFE scheme.............................................................................................................19 Figure 2.2 MISO DFE scheme ............................................................................................................20 Figure 2.3 Partly connected OSIC DFE scheme ...............................................................................20 Figure 2.4 Fully connected OSIC DFE scheme ................................................................................21 Figure 3.1 Principle of spatial multiplexing......................................................................................42 Figure 3.2 Principle of linear beamforming......................................................................................44 Figure 3.3 Architecture of BLAST system........................................................................................45 Figure 3.4 Mapping of coded data streams to antennas in BLAST ...............................................45 Figure 3.5 Trellis for simple space-time code..................................................................................45 Figure 3.6 Increase of the useful data rate using different burst formats for UL and DL, respectively; JT for DL transmission .........................................................................................50 Figure 3.7 Basic MAC frame structure [John99]...............................................................................50 Figure 3.8 STTuC Uplink CDMA System (2-User, 1-TC, 2_2-Antenna Sample .............................51 Figure 3.9 STTuC Downlink CDMA System (2-User, 2-TC, 2_2-Antenna Sample) .......................52 Figure 4.1 Structure of the demodulator matrix D of (4.14) for the example given by (4.21).......65 Figure 4.2 Different MT specific demodulator matrices ( ) k D of (4.12) concerning the air interfaces TDD and OFDM ...........................................................................................................66 Figure 4.3 Pb,n versus % i,n γ for t N = 4 and x = 0.4 ; comparison between simulation results (*) and analytical results ( ) − ............................................................................................................78 Figure 4.4 Description of a mobile radio DL with the normalized matrices M, H, and D ........80 Figure 4.5 Three dimensional plot of ( ) , rel k ηn of (4.119).......................................................................88 Figure 4.6 Three dimensional plot of ( ) , rel k η n of (4.124) for KB = 5. ...................................................90 Figure 4.7 Three dimensional plot of ( ) , rel k η n of (4.124) for Q = 32. ....................................................91 Figure 4.8 Three dimensional plot of ( ) , rel k η n of (4.126) for Q = 32. ....................................................92 Figure 4.9 Generic model of a linear transmission system.............................................................94 Figure 4.10 Mean SNIR γ of the TxMF, the TxZF and the TxMMSE, parameters: N = = 10, 0.9 ρ ..........................................................................................................................108 Figure 4.11 Energy of the desired data symbols for the TxMF, the TxZF and the TxMMSE ......109 Figure 4.12 Energy of the interference for the TxMF, the TxZF and the TxMMSE ......................109 Figure 4.13 Multiply connected decision regions Gm with partial decision regions Gm p, ; M = 4 111 Figure 4.14 Nassi Shneiderman diagram for the generation of the transmit signal t in TxNZF112 Figure 4.15 Trans-cellular JT for 7 cells ..........................................................................................114 Figure 4.16 Considered scenario for the case, K=2 .......................................................................116 Figure 4.17 Normalised MT specific demodulator matrix ( ) k D of (4.237) .....................................117 Figure 4.18 Illustration of the set formalism for various receiver structures..............................119 Figure 4.19 Alternating time slot allocation to JT and JD .............................................................122 Figure 4.20 frequency slot allocation to JT and JD........................................................................122 Figure 4.21 Illustration of the spatial separation of JT and JD transmit signals ........................123