Algorithms and VLSI Implementations of MIMO Detection

✍ Scribed by Ibrahim A. Bello, Basel Halak

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 162
• Edition: 1st ed. 2022
• Category: Library

✦ Synopsis

This book provides a detailed overview of detection algorithms for multiple-input multiple-output (MIMO) communications systems focusing on their hardware realisation. The book begins by analysing the maximum likelihood detector, which provides the optimal bit error rate performance in an uncoded communications system. However, the maximum likelihood detector experiences a high complexity that scales exponentially with the number of antennas, which makes it impractical for real-time communications systems. The authors proceed to discuss lower-complexity detection algorithms such as zero-forcing, sphere decoding, and the K-best algorithm, with the aid of detailed algorithmic analysis and several MATLAB code examples. Furthermore, different design examples of MIMO detection algorithms and their hardware implementation results are presented and discussed. Finally, an ASIC design flow for implementing MIMO detection algorithms in hardware is provided, including the system simulation and modelling steps and register transfer level modelling using hardware description languages.

• Provides an overview of MIMO detection algorithms and discusses their corresponding hardware implementations in detail;
• Highlights architectural considerations of MIMO detectors in achieving low power consumption and high throughput;
• Discusses design tradeoffs that will guide readers’ efforts when implementing MIMO algorithms in hardware;
• Describes a broad range of implementations of different MIMO detectors, enabling readers to make informed design decisions based on their application requirements.

✦ Table of Contents

Preface
Acknowledgements
Contents
About the Authors
Acronyms
List of Figures
List of Tables
1 Introduction
1.1 Chapter Overview
1.2 Introduction
1.3 System Model
1.4 MIMO Detection
1.5 Hardware Implementation
1.6 Design Tradeoffs
1.7 Overview of the Book
1.8 Conclusion
References
2 Linear Detection Techniques for MIMO
2.1 Chapter Overview
2.2 Introduction
2.3 Zero-Forcing
2.4 Minimum Mean Square Error
2.5 Complexity of Linear Detection
2.6 Successive Interference Cancellation Aided Linear Detection
2.7 Lattice Reduction
2.7.1 Lattice Reduction Aided Linear Detection
2.7.2 Lattice Reduction with Successive Interference Cancellation
2.8 Linear Detection-Based Preprocessing
2.9 BER Simulation
2.10 Matrix Operations
2.10.1 Matrix Inversion
2.10.1.1 Cramer's Rule
2.10.1.2 Gaussian Elimination
2.10.1.3 LU Decomposition
2.10.2 QR Decomposition
2.10.2.1 Gram–Schmidt Orthogonalisation
2.10.2.2 Householder Transformations
2.10.2.3 Givens Rotation
2.10.2.4 Coordinate Rotation Digital Computer
2.10.2.5 CORDIC Hardware Implementation
2.11 Conclusion
Appendix
References
3 Algorithm and VLSI Implementation of Sphere Decoding
3.1 Chapter Overview
3.2 Introduction
3.3 Sphere Decoding Tree Search
3.4 Schnorr–Euchner Enumeration
3.4.1 Tabular Enumeration
3.4.2 Real-Valued Channel Decomposition
3.4.3 Orthogonal Real-Valued Channel Decomposition
3.5 Complexity of Sphere Decoding
3.5.1 Detection Ordering
3.5.2 Early Termination
3.6 Soft-Output Sphere Decoding
3.6.1 List Sphere Decoder
3.6.2 Single Tree-Search Soft-Output Sphere Decoder
3.7 Sphere Decoder Simulation
3.8 Hardware Implementation
3.8.1 Previous Works
3.8.2 Design Example
3.8.2.1 Fixed-Point Simulation
3.8.2.2 Hardware Implementation
3.8.2.3 Results and Discussion
3.9 Design Considerations
3.10 Conclusion
Appendix
References
4 Algorithm and VLSI Implementation of K-Best Detection
4.1 Chapter Overview
4.2 Introduction
4.3 K-Best Algorithm
4.4 Real-Valued Channel Model K-Best Detection
4.5 Non-constant K-Best Detection
4.6 Sorting
4.6.1 Bubble Sort
4.6.2 Multi-Cycle Merge
4.6.3 Batcher's Merge
4.6.3.1 Odd–Even Merge
4.6.3.2 Bitonic Merge
4.6.4 Relaxed Sort
4.6.5 Schnorr–Euchner Enumeration
4.7 Preprocessing
4.8 Complexity of the K-Best Algorithm
4.9 Hardware Implementation
4.9.1 Previous Works
4.9.2 Design Example
4.9.2.1 Approximate K-Best Algorithm
4.9.2.2 Hardware Architecture
4.9.2.3 Processing Element
4.9.2.4 Sorting Stage
4.9.2.5 Controller
4.9.2.6 Signal and Channel Inputs
4.9.2.7 Results and Discussion
4.9.2.8 Soft-Output K-Best Detection
4.10 Design Considerations
4.10.1 Throughput
4.10.2 Channel Model
4.10.3 Architecture
4.11 Conclusion
Appendix
References
5 Design Methodology for MIMO Detection
5.1 Chapter Overview
5.2 Introduction
5.3 Review of MIMO Detection
5.4 Modelling and Simulation
5.4.1 MATLAB Executable Files
5.4.2 Vectorised Operations
5.4.3 Multicore Operation
5.4.4 Computer Clusters
5.5 Register Transfer Level Implementation
5.5.1 Verilog
5.5.2 SystemVerilog
5.5.3 Number Representation
5.5.4 Integers
5.5.5 Fractional Numbers
5.5.5.1 Floating-Point Format
5.5.5.2 Fixed-Point Format
5.5.5.3 Complex Numbers
5.5.6 Arithmetic Operations
5.5.7 Relational Operations
5.5.8 Q Format Representation in SystemVerilog
5.5.9 Fixed-Point Simulation
5.5.10 Finite State Machines
5.5.11 State Encoding
5.5.12 Resets
5.6 Design Verification
5.6.1 Variable Assignments
5.6.2 Arithmetic Overflows and Underflows
5.6.3 Latches
5.6.4 Interconnections
5.7 Synthesis
5.7.1 Top-Down Approach
5.7.2 Bottom-Up Approach
5.7.3 Mixed-Mode Approach
5.8 Energy-Efficient MIMO Detection
5.8.1 Power Consumption
5.8.2 Throughput
5.8.3 Adaptive MIMO Detection
5.9 Conclusion
References
Conclusion of the Book
Index