Lower bounds on the channel estimation error for fast-varying frequency-selective Rayleigh MIMO channels

In this paper, we derive a lower bound on the MSE matrix of training-based channel estimators for MIMO systems over fast-varying fading channels. To this end, we consider an ideal estimator that is able to estimate the long-term features of the channel (e.g., second order statistics, delays...) with high accuracy while tracking the fast-varying fading fluctuations in an optimum (MMSE) way. The bound on the MSE matrix is a valuable tool as a reference to assess the performance of any proposed estimator and it is proved to reduce to known results for simplified settings.