Lower Bound on Training-Based Channel Estimation Error for Frequency-Selective Block-Fading Rayleigh MIMO Channels

A lower bound on the error correlation matrix of training-based channel estimators is derived for multiple-input multiple-output (MIMO) systems over block-fading frequency-selective channels with symbol-spaced receivers. The bound is obtained in a constructive way by evaluating the asymptotic performance of an estimator that fully exploits the algebraic structure of the multipath channel. In particular, the estimator is assumed to be able to estimate the long-term features of the channel consistently (e.g., second order statistics of fading, delays, angles) while tracking the fast-varying fading fluctuations by Wiener filtering. Known estimators that are able to attain the bound under simplified settings are referred to, and general guidelines for designing novel estimators are discussed. Based on the simple analytical expression of the bound, the impact of channel estimation error on the link capacity is investigated for different system parameters and channel characteristics (e.g., Doppler shift, spatial correlation of fading). Numerical results are provided to corroborate the analysis.