ML decoding in decode-and-forward based cooperative communication system

In this paper, we derive a maximum-likelihood (ML) decoder of the decode-and-forward (DF) protocol utilizing an arbitrary complex-valued M-point constellation. Existing decoders of the DF based cooperative systems are applicable only to real-valued constellations like BPSK and M-PAM, hence, also to square M²-QAM. We have considered a DF based cooperative system with a single source-destination pair and one relay. The ML decoder is obtained by maximizing the probability density function (p.d.f.) of the received signal at the destination. The proposed ML decoder provides lower decoding complexity than an existing decoder. We also propose an approximate piecewise linear (PL) decoder for M-PSK constellation which performs similar to the proposed ML decoder. The proposed PL decoder provides significant lower decoding complexity than the proposed ML decoder. We analytically derive the approximate symbol error rate of the proposed PL decoder. The DF based cooperative system with the proposed ML and PL decoders outperforms the same rate amplify-and-forward based cooperative communication system from moderate to high signal-to-noise ratio values.