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This paper studies the detection and performance analysis problems for arelay network with $N$ parallel decode-and-forward (DF) relays. Due to thedistributed nature of this network, it is practically very challenging tofulfill the requirement of instantaneous channel state information for coherentdetection. To bypass this requirement, we consider the use of non-coherent DFrelaying based on a generalized differential modulation (GDM) scheme, in whichtransmission power allocation over the $M$-ary phase shift keying symbols isexploited when performing differential encoding. In this paper, a noveldetector at the destination of such a non-coherent DF relay network isproposed. It is an accurate approximation of the state-of-the-art detector,called the almost maximum likelihood detector (AMLD), but the detectioncomplexity is considerably reduced from $\mathcal{O}(M^2N)$ to$\mathcal{O}(MN)$. By characterizing the dominant error terms, we derive anaccurate approximate symbol error rate (SER) expression. An optimized powerallocation scheme for GDM is further designed based on this SER expression. Oursimulation demonstrates that the proposed non-coherent scheme can perform closeto the coherent counterpart as the block length increases. Additionally, weprove that the diversity order of both the proposed detector and the AMLD isexactly $\lceil N/2 \rceil + 1$. Extensive simulation results further verifythe accuracy of our results in various scenarios.

Detection and Performance Analysis for Non-Coherent DF Relay Networks with Optimized Generalized Differential Modulation