Blind Gradient-Ascent Phase Alignment for Multi-Aperture Coherent Digital Combining Under Aperture-Dependent Phase Disturbance

Abstract

Multi-aperture reception can provide spatial diversity in free-space optical (FSO) communication by collecting signal replicas at separate apertures. When the branches are accurately phase-aligned, their received optical fields can also be added constructively to obtain coherent-combining gain. In this paper, we propose blind gradient-ascent phase alignment (BGAPA), which iteratively adjusts one phase correction per aperture by directly maximizing the combined output power. Closed-form analytical gradients provide a deterministic update that requires no symbol decisions, unlike the stochastic perturbation-based estimate of SPGD or the decision-directed feedback of DD-LMS. To isolate phase-tracking capability, the numerical model includes independent aperture-dependent phase disturbance but excludes amplitude scintillation and polarization-dependent distortion. Under this controlled phase-only setting, BGAPA obtains an SNR improvement closer to the ideal 6.02~dB coherent-combining gain than block-wise cross-correlation, SPGD, DD-LMS, and CMA/RDE-based equalization when the aperture count is increased by a factor of four. In particular, increasing the aperture count from 64 to 256 yields an SNR improvement of about 5.7~dB. In a separate amplitude-tolerance test with $N=16$ and $f_{\max}=1$~MHz, the first observed BGAPA trial above the HD-FEC threshold of $3.8\times10^{-3}$ occurs at an actual phase RMS of approximately 278~rad, whereas DD-LMS becomes unreliable at substantially smaller phase excursions. The reported step size is optimized separately at each operating point. BGAPA is fully blind and updates its phase parameters directly from the received aperture fields without training symbols, pilots, or decision-directed feedback.