he Nr X N channel matrix. Note that both MISO and MIMO channel capacities are based on equal power uncorrelated sources. It is demonstrated in the literature that the capacity of the MIMO channel increases linearly with min(N, rather than logarithmically, as in case of MISO or SIMO channel capacity, since the determinant operator yields the product of non-zero eigenvalues of its channel-dependent matrix argument, each eigenvalue characterizing the SNR over a SISO eigen-channel. It will be shown later that the overall MIMO channel capacity is the sum of capacities of each of these SISO eigen-channels. The increase in capacity is dependent on the properties of the channel eigenvalues. If the channel eigenvalues decay rapidly, then linear growth in capacity will not occur. However, the eigenvalues have a known limiting distribution and tend to be spaced out along the range of this distribution. Hence, it is unlikely that most eigenvalues are very small and linear growth is indeed achieved. Figures 10-23 and 10-24 show the impulse responses and the frequency responses of large delay- spread MIMO channels (two transmit and two receive antennas) measured over the extent of a subframe. It is noted that channel characteristics vary from one path (between one transmit and one receive antenna) to another and across time from one symbol to another. 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 is flat-fading or frequency-selective fading, different expressions for the channel capacity can be obtained. The MIMO channel capacity in Equation (10-29) can be analyzed under two different assumptions: (1) the transmitter has no channel knowledge; and (2) the transmitter has perfect channel knowledge through feedback from the receiver or reciprocity of the downlink and uplink channels. Let's denote by E the N X N covariance matrix of the channel input vector X and let us further assume that