Book contents
- Frontmatter
- Dedication
- Contents
- Figures
- Tables
- Preface
- Acknowledgments
- Abbreviations
- 1 Introduction to MIMO Systems
- 2 Classical and Generalized Fading Distributions
- 3 Analytical MIMO Channel Models
- 4 Power Allocation in MIMO Systems
- 5 Channel Capacity of Simplified MIMO Channels
- 6 MIMO Channel Capacity
- 7 Introduction to Space-Time Codes
- 8 Space-Time Block and Trellis Codes
- 9 Introduction to MIMO Detection
- 10 Advanced MIMO Detection Techniques
- 11 Antenna Selection and Spatial Modulation
- 12 Advanced Topics in MIMO Wireless Communications
- Appendix A Matrices
- Appendix B MGF of Hermitian Quadratic Form in Complex Gaussian Variate
- Appendix C Basics of Information Theory
- Appendix D Basics of Convolutional Codes
- Appendix E Basics of Turbo Codes
- Appendix F Algebraic Structures
- Appendix G An Introduction to Game Theory
- Index
4 - Power Allocation in MIMO Systems
Published online by Cambridge University Press: 23 July 2017
- Frontmatter
- Dedication
- Contents
- Figures
- Tables
- Preface
- Acknowledgments
- Abbreviations
- 1 Introduction to MIMO Systems
- 2 Classical and Generalized Fading Distributions
- 3 Analytical MIMO Channel Models
- 4 Power Allocation in MIMO Systems
- 5 Channel Capacity of Simplified MIMO Channels
- 6 MIMO Channel Capacity
- 7 Introduction to Space-Time Codes
- 8 Space-Time Block and Trellis Codes
- 9 Introduction to MIMO Detection
- 10 Advanced MIMO Detection Techniques
- 11 Antenna Selection and Spatial Modulation
- 12 Advanced Topics in MIMO Wireless Communications
- Appendix A Matrices
- Appendix B MGF of Hermitian Quadratic Form in Complex Gaussian Variate
- Appendix C Basics of Information Theory
- Appendix D Basics of Convolutional Codes
- Appendix E Basics of Turbo Codes
- Appendix F Algebraic Structures
- Appendix G An Introduction to Game Theory
- Index
Summary
Introduction
Since using SVD, we can decompose a MIMO channel into RH parallel Gaussian channels, where RH is the rank of the MIMO channel matrix, we will use the knowledge on the capacity of the parallel Gaussian channel (see Appendix C) to find the capacity of a MIMO channel for uniform and adaptive power allocation scheme. Uniform power allocation is employed when the channel state information (CSI) is available at the receiver but not at the transmitter (open loop MIMO system). We can use adaptive power allocation based on Water-filling algorithm when CSI is available at the receiver as well as the transmitter (closed loop MIMO system). We will also discuss near optimal power allocation for high and low SNR cases.
Note that power allocation plays a significant role in deciding MIMO capacity. Power allocation was not an important issue in SISO since only single antenna was employed at the transmitter and receiver. Usually we allocate all the power to the single transmit antenna. But for MIMO it is one of the most important factors for increasing capacity. We have numerous antennas at the transmitter and receiver for MIMO case. The fundamental question is how much power we allocate to each transmit antennas. Hence if we allot power equally to all transmit antennas or unequally to each transmit antenna, capacity of the MIMO channel will be definitely different. If this is the case, then how we optimally allocate power to MIMO channels can be considered as an optimization problem to maximize capacity. To allocate power adaptively we need the CSI at the transmitter, also since power allocation is done at the transmitter. Intuitively we will allocate more power to better channels than the bad channels. We may not allocate any power at all to some of the worst channels. We will discuss these in detail in the following sections. In practical scenarios, we can allocate power near optimally for MIMO channels for two cases: high and low SNR regimes.
Uniform power allocation
The capacity indicates the best viable transmission data rate over the channel for miniscule probability of error. Shanon provided the expression of the achievable communication rate of a channel with noise (C. E. Shanon, 1948).
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- Fundamentals of MIMO Wireless Communications , pp. 70 - 79Publisher: Cambridge University PressPrint publication year: 2017