Throughput and energy optimization of a cooperative ARQ scheme using analog network coding

In this paper, we propose to improve a Cooperative Automatic Repeat reQuest (C-ARQ) scheme through the optimization of the distribution of the average relay energy cost in a two sources one destination wireless system. We consider a BPSK modulated transmission over Rayleigh fading channels. We propose to use specific relay and destination treatment for different possible cases: both received packets are error free, only one received packet is detected erroneous or both received packets are detected erroneous at the destination. We derive semi-analytical bounds of the throughput and the average relay energy. We find the optimal relay energy distribution which maximizes the throughput by using dichotomy search. Numerical results confirm the accuracy of the derived closed form expressions and show the throughput improvement due to the relay energy optimization compared to the conventional cooperative ARQ scheme.