On the sensitivity of a suboptimal precoding scheme for frequency-selective block-based channels with respect to channel inaccuracies
Water-filling is the precoding scheme that achieves capacity in Gaussian parallel or block-based channels. A suboptimal precording scheme, which 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. In this work, we consider the sensitivity of the suboptimal scheme when a channel estimate is used at the transmitter as if it were the true channel. Using tools from matrix perturbation theory, we derive closed-form expressions and bounds relating the channel estimation error covariance matrix with the mean mutual information decrease. We thus uncover the factors that determine the behavior of the suboptimal precoding scheme under channel uncertainties. Simulations are in agreement with our theoretical results.
precoding water-filling channel uncertainties invariant subspaces perturbation expansions