Mutual information bounds for MIMO channels under imperfect receiver CSI

We propose an upper and a lower bound on the mutual information of a pilot-aided MIMO link operating under imperfect receiver CSI. Said bounds depend on the linear channel estimator employed. They can be understood as a generalization of results from and. Furthermore, we prove that any bijective operation performed on the channel estimation does not modify the value of the mutual information bounds. Also, we prove that any sufficient channel estimator is equivalently optimal in terms of maximizing the upper and lower mutual information bounds. These two properties result to be identical to known properties of the true mutual information, namely the invariance against bijective (invertible) operations performed on the random variables, and the optimality of sufficient estimation (e.g.,). The study of these bound properties offers new insights and a deeper understanding of them, as compared to their original derivation in and. To complete the analysis, we show that the gap between the upper and lower bound (and thus also between the true mutual information and the lower bound) is generally upper-bounded by a constant which only depends on the number of receive antennas. This can be seen as a generalization of findings from. Additionally, we show that by taking certain parameter interdependencies more accurately into account, this bound gap becomes significantly smaller, and the mutual information bounds are thus shown to be even tighter.