Ergodic capacity of frequency selective block fading MIMO channels

We derive ergodic capacity of frequency selective block fading multiple input multiple output (MIMO) channels using limiting eigenvalue distribution function (LEDF) of channel matrices of increasing size. We derive capacity for arbitrary number of transmit and receive antennas and for two cases: side information to receiver only (RSI), and side information to transmitter and receiver (TRSI). When MIMO channel coefficients on different lags are correlated, the statistics of MIMO transfer functions computed at different frequency bins differ, and, as a result, capacity differs from the capacity of frequency non-selective Rayleigh fading MIMO channel. In the RSI case we prove that there is performance loss for any SNR, and in the TRSI case we prove that there is performance loss in the high SNR region and performance gain in the low SNR region, compared to the non-correlated case. We estimate the asymptotic gain and loss and show that they are equal as in the single input single output (SISO) case.