On a rate region approximation of MIMO channels under partial CSI

When the receiver of a multiple-input multiple-output (MIMO) channel does not know the channel state, but only a linear estimate thereof, the rates achieved with (suboptimal) Gaussian codebooks become difficult to compute. However, one can resort to upper and lower bounds known from literature. Extending the ideas of earlier works on the resource allocation (time and energy) between pilot and data symbols, we first show that, at high SNR, the optimal training length is min(M,N) (where M and N are the number of receive and transmit antennas), and that in no case more than half the coherence time should be used for training. By simple arguments, we show that the basic training scheme-which allocates separate time slots for training and data transmission-achieves the diversity-multiplexing tradeoff of block-fading channels. In a second part, we propose a generalization of the mutual information bounds to inner and outer rate region bounds of the multiple-access channel.