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

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