Performance of Hybrid-ARQ with Incremental Redundancy over Double Rayleigh Fading Channels

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy (IR) over double Rayleigh channels. Such channels can be used to model the fading amplitude for vehicle-to-vehicle (V2V) communications. We study the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the $\epsilon$-outage capacity, the average number of transmissions, and the average transmission rate for HARQ with IR, assuming a maximum number of rounds for the HARQ protocol. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability is not exceeded. This setting conforms with communication systems in which a quality of service is expected regardless of the channel conditions. It is well known that the ergodic capacity is achievable only if the power is adapted to the channel conditions, which requires channel state information (CSI) at the transmitter. We demonstrate that HARQ allows to communicate at a rate close to the ergodic capacity even in absence of CSI at the transmitter. Our analysis underscores the importance of HARQ in improving the spectral efficiency and reliability of communication systems.