Fundamental limitations on multiple-antenna wireless links in Rayleigh fading

Multiple-antenna wireless links have been shown theoretically to sustain enormous data rates in Rayleigh flat-fading, provided that the propagation coefficients between pairs of transmitter and receiver antennas are statistically independent and known to the receiver. It is not always possible for the receiver to learn the coefficients. Without assuming any knowledge of the fading coefficients and without imposing any ad hoc training schemes, we examine the capacity of the link as a function of the fading rate and SNR. We first look at piecewise constant fading processes where we compute the capacity at high SNRs. We then look at continuous fading processes, and it is shown that the capacity cannot be increased by increasing the number of transmitter antennas beyond a certain fading coherence time. This is radically different from the case when the fading coefficients are known, where the capacity increases indefinitely by increasing the number of transmitter and receiver antennas.