Finite blocklength analysis of the MISO Coherent Block Fading Channel

Abstract

The Coherent MISO Block Fading Channel is a wireless communication channel model in which the transmitter has access to multiple antennas while the receiver has access to one. This model is becoming increasingly important in communication networks because a base station is often able to use many antennas whereas smaller receivers, such as mobile devices, have a strict size limitation. The capacity of this channel is known, but the finite blocklength limits of codes over this channel is still unknown. In this thesis, we analyze these finite blocklength fundamental limits. Specifically, we give the coding theorem showing the achievable dispersion of this channel. We identify that this channel has non-unique capacity achieving input distributions, and although these distribution all yield the same capacity, some distributions in this set yield a better dispersion than others. We show that orthogonal design input distributions achieve capacity in dimensions where they exist, and that they strictly outperform schemes that purely aim to maximize multiplexing gain from a finite blocklength perspective.