On the performance of optimum noncoherent amplify-and-forward reception for cooperative diversity

In this paper, we present receiver structures for maximum-likelihood (ML) noncoherent amplify-and-forward (AF) communication links when multiple relay nodes are employed. We consider both on-off keying (OOK) and binary frequency shift keying (BFSK) modulation schemes on Rayleigh fading relay channels with no channel state information. Even for the simple case of having only one relay node, the optimum noncoherent receiver is quite involved, and the ML metric computation requires certain integral evaluations. To lower hound the average bit error rate (BER), we assume that the link between the relay and the destination node is unfaded, a reasonable assumption when there is a strong line-of-sight path between the relay and the destination, and obtain simple closed-form expressions for the average BER with an arbitrary number of relays. Upper bounds on the average BER are also presented by numerically evaluating the Bhattacharyya distance between the likelihood functions. Further, simple suboptimum receiver structures are proposed, for both OOK and BFSK, along with an analytical performance evaluation, and an asymptotic diversity order analysis.