Dispersion of the Coherent MIMO Block-Fading Channel

In this paper we consider a channel model that is of'ten used to describe the mobile wireless scenario: multiple-antenna additive white Gaussian noise channels subject to random (fading) gain with full channel state information at the receiver. Dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropie block fading). This work addresses the finite blocklength fundamental limits of this channel model. Specifically, we give a formula for the channel dispersion - a quantity governing the delay required to achieve capacity - and present achievability and (partial) converse bounds. Multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding channel dispersion. Knowledge of channel dispersion opens the possibility for studying the impact of channel dynamies, antenna selection rules, etc on the communication rate.