Average approach to amplify-and-forward relay networks

In this paper, the analysis of an average received signal-to-noise ratio (SNR) for a cooperative communication network with amplify-and-forward (AF) relays is presented. In AF systems, the overall instantaneous SNR at the receiving end can be expressed as the form of a harmonic mean of per-hop SNRs. This means that the received SNR can be analyzed by applying the statistical expectation of the harmonic mean of two exponential random variables, which was derived in a closed-form expression. The proposed result can help examining the performance of AF relay systems by using the average sense approach. The simulation results demonstrate the exact derivation of the expectation of harmonic means. The result also shows that the destination node can obtain larger average received SNR as the number of relay nodes is increased.