The capacity of the MIMO channel can be calculated under various conditions and different assumptions. Depending on whether the receiver has perfect channel knowledge or whether the channel exhibits a flat fading or frequency-selective fading behavior, different expres- sions for the channel capacity can be obtained. The MIMO channel capacity can be ana- lyzed under two different assumptions: (1) transmitter has no channel knowledge and (2) the transmitter has perfect channel knowledge through feedback from the receiver or reci- procity of the downlink and uplink channels. Let us denote by E the NTX X NTX covariance matrix of the channel input vector X and let further assume that the channel is unknown to the transmitter then it can be shown that the MIMO channel capacity can be written as CMIMO = log2 (det[I+HEH") where tr(E) V V ensures the total signal-power does not exceed a certain limit. It can be shown that for equal transmit power and uncorrelated sources E = (y/NTx)I. This is true when the channel matrix is unknown to the transmitter and the input signal is Gaussian-distributed, maximizing the mutual information. If the receiver measures and sends channel quality feedback or CSI to the transmitter, the covari- ance matrix E is not proportional to the identity matrix, rather it is constructed from a water-filling algorithm. If one compares the capacity achieved assuming equal transmit- power and unknown channel with that of perfect channel estimation through feedback then the capacity-gain due to use of feedback is obtained. New Radio Access Physical Layer Aspects (Part 2) 555 For the independent identically distributed Rayleigh fading scenario, the linear capacity growth discussed earlier will be observed. It is shown that MIMO channel capacity can be written as CMIMO = min(NTx,NRX) where li, i = 1, 2, min(NTx,NRX) are the non-zero eigenvalues of HHH. We can decompose the MIMO channel into K < min(NTx,NRX) equivalent parallel SISO channels using the singular value decomposi- tion (SVD) theorem. Let y = H