he conditional entropy between the random variables X and Y. The entropy of a random variable can be described as the measure of uncertainty in the random variable or the amount of information required on the average to describe the random variable. Thus the mutual information representation of channel capacity can be described as the reduction in the uncertainty of one random vari- able due to the knowledge of the other. Note that the mutual information between X and Y depends on the properties of the channel through a channel matrix H and the properties of X through the probability distribution of X [22]. Throughout this section, it is assumed that the channel matrix H is random and that the receiver has perfect channel knowledge. It is also assumed that the channel is memoryless, that is, for each use of the channel an independent realization of H is drawn. This means that the capacity can be computed as the maximum of the mutual information as defined earlier. The results are also valid when H is generated by an ergodic process because as long as the receiver observes the H process, only the first order statistics are needed to determine the channel capacity. The ergodic (mean) capacity of a random channel with NRX = NTX = 1 and an average transmit power constraint PT can be expressed as Cergodic EH where P is the aver- age power of a single codeword, transmitted over the channel, and EH{.} denotes the expecta- tion over all channel realizations. Compared to the generic definition, the capacity of the channel is now defined as the maximum of the mutual information between the input and the output over all statistical distributions on the input that satisfy the power constraint. In general, New Radio Access Physical Layer Aspects (Part 2) 557 the capacity of a random MIMO channel with power constraint PT can be expressed as where is the covariance matrix of the =E[xx"] transmit signal vector X. The total transmit power is limited to PT irrespective of the number of transmit antennas. For a fading channel the c