On the capacity of multi-antenna Gaussian channels

We investigate the use of multi-antennas at both ends of a point-to-point communication system over the additive Gaussian channel. We consider a system with t transmit antennas and r receive antennas in which the received vector v∈C^τ depends on the transmitted vector u∈C^τ via: v=Hu+w where H∈C ^r×t is the channel transfer matrix and w is zero-mean complex circular symmetric Gaussian noise. We assume that E[ww]=σ ²I_r. The transmitter is constrained in its total power, i.e., E[uu]⩽E_s. We assume that the channel matrix H is known at both ends of the communication system, and that the waveform channel is flat over the bandwidth of interest