Noncoherent Amplify-and-Forward Cooperative Networks: Robust Detection and Performance Analysis

We develop closed-form generalized likelihood ratio test (GLRT) sequence detectors for multi-relay amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (M-DPSK) and noncoherent M-ary frequency-shift keying (M-FSK). The proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels, signal powers, noise variances, and relay functionalities is unavailable to the destination. A comprehensive error probability performance analysis is carried out in Rayleigh fading. Specifically, we derive unified pairwise error probability (PEP) expressions for both detectors in a dual-hop network, which are valid for arbitrary modulation order M and arbitrary sequence length N_s. We also derive unified bit-error probability (BEP) expressions for both detectors employing binary signalings in various networks for N_s = 1. It is further shown that both detectors achieve near full diversity orders. Finally, the superiorities of the proposed detectors over the state-of-the-art noncoherent detectors are justified through extensive comparisons in practical scenarios. For example, in a multi-relay network where the relays are uniformly distributed between the source and destination, the proposed detector for noncoherent FSK with N_s = 1 outperforms the well-known maximum energy selector by almost 15 dB in high signal-to-noise ratios.