Performance Analysis of Hybrid ARQ with Incremental Redundancy over Amplify-and-Forward Dual-Hop Relay Channels

In this paper, we consider a three node relay network comprising a source, a relay, and a destination. The source transmits the message to the destination using hybrid automatic repeat request (HARQ) with incremental redundancy (IR). The relay overhears the transmitted message, amplifies it using a variable gain amplifier, and then forwards the message to the destination. This latter combines both the source and the relay message and tries to decode the information. In case of decoding failure, the destination sends a negative acknowledgement. A new replica of the message containing new parity bits is then transmitted in the subsequent HARQ round. This process continues until successful decoding occurs at the destination or a maximum number $M$ of rounds is reached. We study the performance of HARQ-IR over the considered relay channel from an information theoretic perspective. We derive exact expressions and bounds for the information outage probability, the average number of transmissions, and the average transmission rate. Moreover, we evaluate the delay experienced by Poisson arriving packets over the considered relay network. We also provide analytical expressions for the expected waiting time, the sojourn time, and the energy efficiency. The derived exact expressions are validated by Monte Carlo simulations.