Full diversity decoding in differential DF cooperative system with unitary constellations

We derive a maximum likelihood (ML) decoder in the differential decode-and-forward (DF) based cooperative communication system utilizing complex-valued unitary constellations like M-PSK. We also derive a low complexity piecewise linear (PL) decoder of the differential data transmitted in the DF based cooperative system. The proposed ML and PL decoders are applicable to the complex-valued unitary constellations suitable for differential modulation, whereas, the existing ML and PL decoders of the differentially modulated data in the DF based cooperative communication system are only applicable to binary modulated signals like binary phase shift keying (BPSK) and binary frequency shift keying (BFSK). An approximate average symbol error rate (SER) of the proposed PL decoder is also obtained by ignoring the higher order noise terms. Based on this approximate SER, it is analytically shown that the proposed PL decoder provides full diversity of second order in the DF based differential cooperative system with one source-destination pair and a single relay.