On the performance of hybrid-ARQ with code combining over double rayleigh fading channels

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with code combining (CC) over double Rayleigh channels. This channel can be utilized to model the fading envelope of vehicle-to-vehicle (V2V) channels. We derive analytical solutions for the characteristic quantities of double Rayleigh channels, such as the outage probability, the ergodic capacity, and the bit error probability (BEP). Moreover, we study the performance of HARQ with CC. Our analysis focuses on information theoretic aspects of HARQ with CC. closed-form analytical approximations are derived for the ε-outage capacity, the average number of transmissions, and the average transmission rate of HARQ with CC assuming a maximum number of rounds M 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 ε is not exceeded. This setting is conform with modern communication systems, in which a quality of service should be ensured independently of the channel conditions. We demonstrate that HARQ with CC allows to communicate at a rate close to the ergodic capacity, especially at low and medium SNR. This rate is achieved in absence of channel state information (CSI) at the transmitter. This feature makes HARQ very attractive for V2V communications. In fact, in V2V channels, the coherence time is too short to allow for feedback of the instantaneous channel conditions from the receiver to the transmitter.