Statistical Analysis of a Posteriori Channel and Noise Distribution Based on HARQ Feedback

TL;DR

This paper investigates how the posterior distributions of channel and noise in HARQ systems are affected by feedback, revealing that they largely remain similar to prior distributions unless the coherence interval is large.

Contribution

The study provides a statistical analysis showing that posterior distributions in HARQ systems are mostly unchanged from priors, or differ by parameter mismatch, depending on coherence interval size.

Findings

Posterior distributions often remain similar to prior distributions.

Differences can be modeled as parameter mismatches.

Impact on applications is minimal in most cases.

Abstract

In response to a comment on one of our manuscript, this work studies the posterior channel and noise distributions conditioned on the NACKs and ACKs of all previous transmissions in HARQ system with statistical approaches. Our main result is that, unless the coherence interval (time or frequency) is large as in block-fading assumption, the posterior distribution of the channel and noise either remains almost identical to the prior distribution, or it mostly follows the same class of distribution as the prior one. In the latter case, the difference between the posterior and prior distribution can be modeled as some parameter mismatch, which has little impact on certain type of applications.