Information theoretic limits for non-coherent multi-antenna communications

In this paper, we study the capacity of multiple antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a block fading model proposed by Marzetta and Hochwald (see IEEE Trans. on Info. Theory, vol.45, no.1, p.139-57, 1999). The model does not assume any prior knowledge of the fading coefficients, but only assumes that the coefficients remain constant for a coherent interval T as an approximation of the continuously varying channel. We compute the asymptotic capacity of this channel at high SNR in terms of T, the number of transmit antennas M and the number of receive antennas N. While the capacity gain of the coherent multi-antenna channel is min{M,N} bps/Hz for every 3 dB increase in SNR, the corresponding gain for the non-coherent channel turns out to be M^*(1-M^* /T) bps/Hz, where M^*=min{M,N,[T/2]}. The capacity expression has a geometric interpretation of sphere packing in the Grassmann manifold