Statistical Model of Combining Efficiency for Digital Phase Alignment in Multi-Aperture Free-Space Coherent Optical Receivers

In order to eliminate the impact of atmospheric turbulence on the performance of free-space optical (FSO) communication systems, the multi-aperture receiving technique is wildly recognized as a powerful fading-mitigation technology. As one of the essential technologies in the multi-aperture receiver, digital coherent beam combining relies on the digital phase alignment algorithm to align the different versions of signals in phase. In this paper, the statistical model of combining efficiency for digital phase alignment is derived in multi-aperture FSO receivers by considering the phase alignment errors at each receiving aperture. It can be expressed as a linear function of chi-square distribution by Satterthwaite approximation. Based on this statistical model, we derive the exact expressions of the mean, variance, and probability density function of the combining efficiency. The simulation results show that this model is valuable and practical under the condition of the different number of aperture and signal-to-noise ratio combinations. Combining efficiency is also compared for equal gain combining diversity FSO systems with or without considering aperture selection.