Outage probability of multihop free space optical communications over nakagami fading channels

In this paper, the end-to-end outage probability of a multihop free space optical (FSO) communication system over N independent Nakagami fading relay channels are analyzed. We assume that the channel state information-based relays have the knowledge of the channel states in the preceding hops. The Laplace transform of the inverse end-to-end signal-to-noise ratio (SNR) is derived in a closed form. Based on this expression, the outage probability involving N statistically independent, but not necessarily identically distributed (i.n.i.d) Nakagami relay channels is evaluated numerically via the inverse Laplace transform. The results indicate that the outage probability improves as N decreases and/or the arbitrary fading parameter m increases. This is because the probability that any of the cascaded fading channels is in deep fade decreases significantly. Therefore, the smaller N and/or larger m, the better the multihop relay channel.