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).