Sensitivity analysis of a suboptimal precoding scheme for block channels with respect to channel inaccuracies

Water-filling is the technique that computes the input data covariance matrix that achieves capacity in Gaussian parallel or block channels. A suboptimal precoding scheme, that has been observed to perform quite close to water-filling in some cases of great interest, is when all "active" eigenvectors of the input data covariance matrix receive the same power. Both techniques require perfect channel knowledge at the transmitter. We consider the suboptimal precoding scheme when, at the transmitter, we use a channel estimate as if it were the true channel and we derive a closed form expression relating the channel estimation error covariance matrix with a mean mutual information decrease. We observe that serious error magnification may happen if the channel matrix is badly conditioned and the SNR is high.