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2 MIMO Link with Perfect Channel State Information 2.1 Overview 59 2.2 Mathematical Model of the MIMO Link 60 2.2.1 Probabilistic Channels with States 61 2.2.2 General Transmission and CSI Feedback Model 64 2.2.3 Adaptive-Channel Encoding and Decoding 65 2.2.4 Transmit Power Constraint 66 2.2.5 Causal Feedback Constraint 67 2.3 Ergodic and Outage Channel Capacity 67 2.3.1 Ergodic Capacity 68 2.3.2 Outage Capacity 68 2.4 Channel Capacity with No CSIT and No CSIR 69 2.4.1 Fast Flat Fading MIMO Channels 70 2.4.2 Block Fading Channels 70 2.5 Channel Capacity with Perfect CSIR 72 2.5.1 Block Fading Channels 73 2.5.2 Fast Flat Fading MIMO Channels 76 2.5.3 Effect of Antenna Correlation on Ergodic MIMO Capacity 81 2.5.4 Slow Flat Fading MIMO Channels 87 2.6 Channel Capacity with Perfect CSIT Only 89 2.6.1 Discrete Block Fading Channels 91 2.6.2 Discrete Channel with Three States 93 2.6.3 Fast Flat Fading MIMO Channels 94 2.6.4 Slow Flat Fading MIMO Channels 94 2.7 Channel Capacity with Perfect CSIR and Perfect CSIT 95 2.7.1 Fast Flat Fading MIMO Channels 96 2.7.2 Slow Flat Fading MIMO Channels 100 2.8 Summary 101 Exercises 103
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3 MIMO Link with Imperfect Channel State Information 3.1 Overview 107 3.2 Effect of Imperfect CSI Estimation 108 3.2.1 CSI Estimation for MIMO Channels 108 3.2.2 Capacity Bounds of MIMO Link 109 3.3 Effect of Limited Feedback Optimizing for SNR 111 3.3.1 Introduction to Optimizing Effective SNR 112 3.3.2 Grassmannian Line Packing 112
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Grassmannian Precoding for MIMO Systems Spatial Diversity 115 3.3.4 Grassmannian Precoding for MIMO Systems Spatial Multiplexing 119 3.4 Effect of Limited Feedback Optimizing for Ergodic Capacity 3.4.1 Channel Capacity with Partial CSIT 124 3.4.2 Coding Theorem with Partial CSIT 125 3.4.3 Equivalence with Vector Quantization Problem 130 3.4.4 Fast Flat Fading MIMO Channels 130 3.4.5 Lloyd s Algorithm 132 3.4.6 Approximate Closed-Form Solution for Step 1 133 3.4.7 Complexity of the Online Adaptation Strategy 134 3.4.8 MMSE-SIC Receiver Structure 135 3.4.9 Numerical Results and Discussion 136 3.5 Summary 138 Exercises 140
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4 Spacetime Coding and Layered Spacetime Coding for MIMO with Perfect Channel State Information 143 4.1 Overview 143 4.2 Design of MIMO Links with Perfect CSIR 144 4.2.1 Spacetime Coding Spatial Diversity 147 4.2.2 Layered Spacetime Coding Spatial Multiplexing 154 4.2.3 Receiver Designs for Layered Spacetime Codes 159 4.2.4 Optimal Architecture for Fast Flat Fading Channels 166 4.2.5 Optimal Architecture for Slow Flat Fading Channels 168 4.2.6 Fundamental Tradeoff between Spatial Diversity and Spatial Multiplexing 170 4.3 Switching Threshold Design for MIMO Adaptation with Perfect CSIT and Perfect CSIR 175 4.3.1 MIMO Transmitter and Adaptation Designs 176 4.3.2 Optimization Problem Quasistatic Fading Channels 178 4.3.3 Equivalence to the Classical Vector Quantization Problem 179 4.3.4 Results and Discussion 180 4.4 Summary 183 Exercises 184 5 MIMO Constellation Design with Imperfect Channel State Information 189 5.1 Overview 189 5.2 Constellation Design for MIMO Channels with Imperfect CSIR 191 5.2.1 System Model 191 5.2.2 Design Criteria Based on Kullback Leibler Distance 191
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5.2.3 Constellation Design Optimization 195 5.2.4 Single-Transmit Antenna Example 197 5.2.5 Multitransmit Antenna Example 200 Spacetime Coding for MIMO Channels with Imperfect CSIR 200 5.3.1 Overview of Coded Modulation in AWGN Channels 203 5.3.2 Coded Modulation Design for MIMO Channels with Imperfect CSIR 207 Summary 211
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6 Cross-Layer Scheduling for Multiuser Systems with Multiple Antennas 6.1 Overview 215 6.2 Multiuser System Performance 217 6.2.1 Examples of System Utility 218 6.2.2 De nition of Network Capacity 220 6.2.3 De nition of Network Coverage 220 6.3 System Models 222 6.3.1 Multiuser MIMO Channel Model 223 6.3.2 Multiuser Downlink Physical Layer Model 224 6.3.3 MAC Layer Model 229 6.4 Cross-Layer Optimization with Perfect CSIT 229 6.4.1 Capacity-Optimized Scheduler Design 229 6.4.2 Coverage-Optimized Scheduler Design 231 6.4.3 Common Framework for Both Capacity-Optimized and Coverage-Optimized Scheduling 231 6.4.4 Optimal Solution Single-Antenna Systems 232 6.4.5 Optimal Solution Multiple-Antenna Systems with OTBF Processing 234 6.5 Low-Complexity Scheduling Algorithms 236 6.5.1 Suboptimal Solution A Greedy Algorithm 236 6.5.2 Suboptimal Solution B Genetic Algorithm 237 6.6 Results and Discussion 239 6.6.1 System Capacity Performance 239 6.6.2 Proportional Fairness Performance 241 6.6.3 Coverage Performance 242 6.6.4 Tradeoff between Capacity and Coverage 243 6.6.5 Ef ciency of Multiuser Diversity 244 6.6.6 Ef ciency of Spatial Multiplexing 244 6.6.7 Complexity Comparisons of Various Cross-Layer Algorithms 245 6.7 Cross-Layer Scheduling with Imperfect Channel State Information 245
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