Optimal Mode Set Selection for Free Space Optical Communications in the Presence of Atmosphere Turbulence

In this paper, the capacity of the free space optical communication system employing the general Laguerre Gaussian (LG) modes under random atmosphere turbulence is studied. A coupled mode theory is used to derive the coupled equations to evaluate the correlation matrix of the corresponding LG mode channels. It is found that the correlation term between the LG modes is nonzero if and only if the azimuth orders of the two LG modes are the same when the input sources are assumed to independent of each other. The results are compared with the Monte Carlo simulation results and a good agreement is observed. Based on the coupled mode theory as well as the Monte Carlo simulations, the system capacity is evaluated and the optimal mode set of the LG modes that maximizes the system capacity is determined. It is found that the LG modes with the lowest azimuth orders can be selected as the optimal mode set if the radial order p is fixed. For the general LG modes, one can classify the LG modes as different mode groups according to the radial order p. Within the same group, the lowest azimuth order modes selection rule can be applied. Therefore, the optimization process is simplified to the determination of the number of modes within the mode groups. The rule can be rigorously proved for the low signal-to-noise ratio (SNR) scenario and is found to be valid for the high SNR scenario as well.