Coherent Multiple-Antenna Block-Fading Channels at Finite Blocklength

Abstract

In this paper, we consider a channel model that is often used to describe mobile wireless scenarios: Multipleantenna additive white Gaussian noise channels subject to random (fading) gains with full channel state information at the receiver. The dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This paper 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. The multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding the channel dispersion. Alas, one difficulty remains: The converse (impossibility) part of our result holds under an extra constraint on the growth of the peak-power with blocklength. Our results demonstrate, for example, that while the capacities of nt × nr and nr × nt antenna configurations coincide (under fixed received power), the coding delay can be sensitive to this switch. For example, at the received SNR of 20 dB, the 16×100 system achieves capacity with codes of length (delay) which is only 60% of the length required for the 100×16 system. Another interesting implication is that for the MISO channel, the dispersionoptimal coding schemes require employing orthogonal designs such as Alamouti's scheme - A surprising observation considering the fact that Alamouti's scheme was designed for reducing demodulation errors, not improving coding rate. Finding these dispersion-optimal coding schemes naturally gives a criteria for producing orthogonal design-like inputs in dimensions where orthogonal designs do not exist.