Impact of relay placement on diversity order in adaptive selective DF relay-assisted FSO communications

The impact of relay placement on diversity order in adaptive selective decode-and-forward (DF) cooperative strategies is here investigated in the context of free-space optical (FSO) communications over atmospheric turbulence channels with pointing errors when line of sight is available. The irradiance of the transmitted optical beam here considered is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution together with a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Novel closed-form approximate bit error-rate (BER) expressions are obtained for a cooperative FSO communication setup with N relays, assuming that these relays are located in an area similar to an annulus around source or destination node. An analytical expression is here found that determines the best selection criterion based on the knowledge of the channel state information (CSI) of source-relay or relay-destination links in order to significantly increase the diversity order corresponding to the cooperative strategy under study. It is concluded that the highest diversity order is achieved when the relation β(SR(min)) > β(SD) + β(R(min)D) is satisfied, wherein β(SR(min)), β(R(min)D) and β(SD) are parameters corresponding to the atmospheric turbulence conditions of source-relay and relay-destination link with the greatest scintillation index, and source-destination link, respectively.