Analyzing selective relaying for multiple‐relay–based differential DF‐FSO network with pointing errors

Abstract In this paper, we examine differential modulation for the decode‐and‐forward(DF) based cooperative free‐space optical (FSO) network. We consider multiple relays for transmitting differential binary phase‐shift keying (DBPSK) data from an optical source to destination along with a direct path between the two. The relays utilize the selective relaying protocol where the source data is forwarded to the destination only in the case of error‐free decoding by the relays. We derive the unified expression of probability density function (PDF) of the signal‐to‐noise ratio (SNR) for generalized‐ ( ) distribution with pointing error (PE) considering both intensity modulation/direct detection (IM/DD) and heterodyne detection techniques. The derived unified PDF of SNR for distribution is mathematically combined with the unified PDF of SNR for the Gamma‐Gamma (GG) distribution. This combining enables us to obtain a single closed‐form expression for a particular performance metric, which is applicable to both and GG distributions with PE and both IM/DD and heterodyne detection techniques. More specifically, we derive the average bit error rate (ABER) and outage probability(OP) for the considered multiple‐relay–based DF‐FSO network. Furthermore, we analyze the asymptotic BER and asymptotic outage performances for the considered system at high SNR of source to relay links and obtain the diversity order, analytically. The impact of different power allocation schemes on ABER and OP is determined by utilizing the power allocation factor. The derived results clearly demonstrate the impact of severe atmospheric conditions, PE, the type of detection scheme, and the number of relays on the network performance. All the derived analytical results are verified through simulations.