Optimal and suboptimal decoding for SIM-BPSK over Gamma-Gamma FSO links with an erroneous relay

In this paper, we analyze a free space optical (FSO) cooperative communication system utilizing the Gamma-Gamma fading optical links and a single decode-and-forward (DF) erroneous relay. We adopt the subcarrier intensity modulation (SIM) technique for transmission of the binary phase shift keying (BPSK) modulated data over an optical link. For the considered DF-FSO cooperative system, we derive a maximum-likelihood (ML) decoder and a sub-optimal piecewise linear (PL) decoder in the destination of the system. The proposed PL decoder performs very close to the ML decoder with a significant reduction in the decoding complexity. Both the ML and the PL decoders incorporate the possibility of erroneous transmission by the DF relay and require the average statistics of the source-relay link for decoding the data of the source in the destination. Moreover, we also derive the closed-form expression for the average bit error rate (BER) of the proposed PL decoder.