On the pre-log of the asymptotic capacity of stationary frequency-flat multi-antenna channels

We continue previous work [1] in which we analyzed the Mutual Information of Frequency-Flat MIMO Channels with a Block Fading model. Absence of Channel State Information at Transmitter or Receiver (no CSIT/CSIR) was considered there. It was shown that implicitly a (semi-blind) channel estimate needs to be constructed that, in decision-feedback style, depends on the past (detected) inputs and outputs (training part) and on the future outputs (blind part). On the other hand, for peak-power limited SISO frequency- flat channels with stationary Gaussian fading, it has been shown by Lapidoth [2] that at high SNR, the capacity is determined by a pre-log factor that is equal to the bandwidth of frequencies where the channel Doppler spectrum is zero (the complementary part of the Doppler bandwidth). In this paper we extend Lapidoth\´s result to MIMO channels with bandlimited stationary fading. At high SNR, the absence of CSIR decreases the pre-log with a factor equal to 1 minus the average number of parameters per symbol period that parameterize the channel. This reduction term is proportional to the Doppler bandwidth and the number of transmit antennas. We introduce channel parameterizations that naturally induce a split in the transmitted symbols between "learning" symbols (that carry loglog(SNR) information) and "data" symbols (that carry log(SNR) information). The capacity pre-log factor is the proportion of "data" symbols.