Finite-signal-to-noise ratio diversity-multiplexing-delay tradeoff in half-duplex hybrid automatic repeat request relay channels

In this study, the authors consider a delay-limited hybrid automatic repeat request (HARQ) protocol that makes use of incremental redundancy over the three-node decode-and-forward relay fading channel where one source cooperates with a relay to transmit information to the destination. They provide an estimate of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) based on tight bounds on outage probabilities for two channel models. The results for the long-term quasi-static channel highlight the distributed diversity, that is, the cooperative space diversity, and the HARQ coding gain, achieved by soft combining the successive transmitted punctured codewords via incremental redundancy. On the other hand, the results for the short-term quasi-static channel illustrate the diversity gains obtained, thanks to cooperative space diversity and time diversity, along with the HARQ coding gain. Using the DMT formulation, they show that equal power partitioning between the source and the relay nodes provides close to optimal performance. Furthermore, thanks to the extension of the finite-SNR DMT to the finite-SNR diversity-multiplexing-delay tradeoff, they show that, unlike the asymptotic SNR analysis, the ARQ delay, defined as the maximum number of retransmissions rounds, impacts the performance of the HARQ relay protocol for high effective multiplexing gain.