Capacity of Ergodic MIMO Channels with Complete Transmitter Channel Knowledge

The purpose of this paper is to attack a common misconception regarding the capacity computation for multiple-input multiple-output channels whose gains follow ergodic laws and are known to both the transmitter and the receiver. Several researchers have reported results in which they first compute capacity of a time-invariant channel via application of water filling principles and proceed to average the result over various channel eigenvalue distributions. In this paper we show that this approach is incorrect, and outline the correct procedure, which in addition to spatial water filling makes use of temporal water filling