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/spl isin/C/sup /spl tau// depends on the transmitted vector u/spl isin/C/sup /spl tau// via: v=Hu+w where H/spl isin/C/sup r/spl times/t/ is the channel transfer matrix and w is zero-mean complex circular symmetric Gaussian noise. We assume that E[ww]=/spl sigma//sup 2/I/sub r/. The transmitter is constrained in its total power, i.e., E[uu]/spl les/E/sub 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.