A Lower Bound on the Noncoherent Capacity Pre-log for the MIMO Channel with Temporally Correlated Fading

We derive a lower bound on the capacity pre-log of a temporally correlated Rayleigh block-fading multiple-input multiple-output (MIMO) channel with T transmit antennas and R receive antennas in the noncoherent setting (no a priori channel knowledge at the transmitter and the receiver). In this model, the fading process changes independently across blocks of length L and is temporally correlated within each block for each transmit-receive antenna pair, with a given rank Q of the corresponding correlation matrix. Our result implies that for almost all choices of the coloring matrix that models the temporal correlation, the pre-log can be lower-bounded by T(1-1/L) for T <= (L-1)/Q provided that R is sufficiently large. The widely used constant block-fading model is equivalent to the temporally correlated block-fading model with Q = 1 for the special case when the temporal correlation for each transmit-receive antenna pair is the same, which is unlikely to be observed in practice. For the constant block-fading model, the capacity pre-log is given by T(1-T/L), which is smaller than our lower bound for the case Q = 1. Thus, our result suggests that the assumptions underlying the constant block- fading model lead to a pessimistic result for the capacity pre-log.