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Decode-and-forward (DF) protocol based cooperative communication is vulnerable to the erroneous relaying by the relay. In this paper, we derive a maximum-likelihood (ML) decoder for the DF protocol utilizing arbitrary complex-valued constellations including M-PSK, M-PAM, and M-QAM. A set-up of a single pair of source and destination with one relay is studied. The source and the relay utilize orthogonal uncoded transmissions. The relay performs ML decoding and forwards the decoded symbol to the destination, and it might commit errors in decoding the data. The ML decoder at the destination is obtained by maximizing the probability density function (p.d.f.) of the data received during two orthogonal transmissions at the destination under the assumption that the average probability of error of the source-relay link is known at the destination. The proposed ML decoder is a generalized decoder which is applicable to arbitrary constellations, whereas, one existing DF cooperative decoder is applicable to the real valued constellations like BPSK and M-PAM. One existing decoder is also applicable to M2-QAM constellations. We also derive a low-complexity piecewise linear (PL) decoder for arbitrary complex-valued M-point constellations which performs similar to the ML decoder for all signal-to-noise ratio values. An approximate expression of the symbol error rate (SER) of the PL decoder for M-PSK constellation is derived. By using the approximate SER expressions, it is proved that the proposed ML and PL decoders achieve full diversity of two in the cooperative system studied.
Date of Publication: December 2011