Rate Selection for Cooperative HARQ-CC Systems over Time-Correlated Nakagami-m Fading Channels

TL;DR

This paper derives analytical expressions for rate selection in cooperative HARQ-CC systems over time-correlated Nakagami-m fading channels, optimizing throughput and outage probability.

Contribution

It introduces a closed-form CDF for combined SNRs using Fox's H function, enabling precise rate selection in correlated fading environments.

Findings

Less correlated channels yield higher diversity gain.

Outage probability decreases as the Nakagami-m parameter increases.

Optimal rate increases with retransmissions and decreases with channel correlation.

Abstract

This paper addresses the problem of rate selection for the cooperative hybrid automatic repeat request with chase combination (HARQ-CC) system, where time correlated Nakagami-m fading channels are considered. To deal with this problem, the closed-form cumulative distribution function (CDF) for the combine SNRs through maximal ratio combining (MRC) is first derived as a generalized Fox's $\bar H$ function. By using this result, outage probability and delay-limited throughput (DLT) are derived in closed forms, which then enables the rate selection for maximum DLT. These analytical results are validated via Monte Carlo simulations. The impacts of time correlation and channel fading-order parameter $m$ upon outage probability, DLT and the optimal rate are investigated thoroughly. It is found that the system can achieve more diversity gain from less correlated channels, and the outage probability of cooperative HARQ-CC system decreases with the increase of $m$, and etc. Furthermore, the optimal rate increases with the number of retransmissions, while it decreases with the increase of the channel time correlation.