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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∈Cτ depends on the transmitted vector u∈Cτ 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 2Ir. The transmitter is constrained in its total power, i.e., E[uu]⩽Es. 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