Non-Coherent Amplify-and-Forward Generalized Likelihood Ratio Test Receiver

This paper proposes a simple non-coherent amplify- and-forward receiver for the relay channel and evaluates its diversity performance for Rayleigh fading channels. We use the generalized likelihood ratio test to obtain the decision rule in closed form, independent of the fading distribution. The receiver is developed for M-ary orthogonal signals and multiple relays. The only side information required is the average noise energy at the receiver; no statistical knowledge of the channel gains is needed. We develop closed-form upper and lower bounds on the probability of error of this receiver for the case of binary signaling with a single relay and show that this receiver achieves near-full diversity, with the probability of error decreasing with increasing signal-to-noise ratio (SNR) as log² (SNR) /SNR² for large SNR. Additional results obtained by simulation demonstrate increasing diversity gain with additional relays.