Quasi-Static SIMO Fading Channels at Finite Blocklength

TL;DR

This paper analyzes the maximal achievable rate over quasi-static SIMO fading channels at finite blocklengths, revealing zero channel dispersion under mild conditions and demonstrating rapid convergence to outage capacity.

Contribution

It proves that the channel dispersion is zero for quasi-static SIMO channels under mild conditions, enabling faster convergence to capacity at finite blocklengths.

Findings

Zero dispersion holds under mild conditions on channel gains.

Fast convergence to outage capacity with increasing blocklength.

Significantly smaller blocklength needed to achieve near-capacity in SIMO channels.

Abstract

We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1*2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.