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In this paper, a class of cooperative communication protocols with arbitrary N-relay nodes is proposed for wireless networks, in which each relay coherently combines the signals received from m (1lesmlesN-1) previous relays in addition to the signal from the source. Exact symbol-error-rate (SER) expressions for an arbitrary N-node network employing M'ary phase-shift-keying (MPSK) modulation or quadrature-amplitude modulation (QAM) are provided for the proposed class of protocols. Further, approximate expressions for the SER are derived and shown to be tight at high enough signal-to-noise ratio (SNR). Our analysis reveals an interesting result: The class of cooperative protocols shares the same asymptotic performance at high enough SNR and does not depend on m, the number of previous nodes involving in coherent detection, hence, the asymptotic performance of a simple cooperative scenario in which each relay combines the signals from the source and the previous relay is exactly the same as that for a much more complicated scenario in which each relay combines the signals from the source and all the previous relays. The theoretical results also confirm that full diversity equal to the number of cooperating nodes is indeed achievable by the proposed protocols. Finally, we formulate a power-allocation problem in order to minimize the SER of the system. The analysis shows that the optimum power allocation at different nodes follows a certain ordering, and that the power-allocation scheme at high SNR does not depend on the channel quality of the direct link between the source and the destination. Closed-form solutions for the optimal power-allocation problem are provided for some network topologies. Simulation results confirm our theoretical analysis
Sadek et al. (Tue,) studied this question.