Diversity Performance of a Practical Non-Coherent Detect-and-Forward Receiver

We propose a non-coherent receiver for the fixed detect-and-forward relay channel and derive a closed-form tight upper bound on its bit error probability in Rayleigh fading channels. Using this upper bound, we show that the receiver achieves nearly full, second-order diversity, and the gap from full diversity is quantified. While the general receiver depends on the source-relay channel statistics, we show that similar diversity performance can be achieved when only first-order statistics of the source-destination channel are known. The receiver is derived using the generalized likelihood ratio test to eliminate dependence on the channel gains, applies to M-ary orthogonal signal sets, and is independent of the fading distribution. The results demonstrate that low-complexity transceivers, such as those used in some sensor networks, can benefit from cooperative diversity.