Optimum Distance and Power allocation Strategies for Quantum-limited Inter-Relayed FSO Communication System

In this work, we analyze the performance of a uni-directional quantum-limited inter-relay assisted free space optical link. We assume that there is no direct line of sight path between source and destination. The influence of path loss, atmospheric turbulence and pointing error impairments is considered for the analysis. The turbulence induced fading is modeled by independent but not necessarily identically distributed Gamma-Gamma fading statistics. The proposed system employs decode and forward relaying protocol assisted with channel state information. The approximate analytical expression for the probability of error is derived and illustrated by numerical plots. The asymptotic analysis for minimizing error probability in order to find optimum distance between the nodes for uniform power transmission, and for optimizing power allocated to different links, has been performed. It is shown that either distance between the nodes can be optimized for minimizing error probability when uniform power allocation is done, or optimum power allocation can be done for minimizing probability of error. Further, it helps to increase the distance for transmission between source and destination, and can make transmission possible in situations where direct link between source and destination can't be established due to high rise buildings and other obstacles, while keeping the total transmitted power within permissible levels.