Heterogeneous-Gradient Phase--Polarization Alignment and Maximal-Ratio Weight Allocation for Multi-Aperture Coherent FSO Reception

Multi-aperture coherent reception can improve freespace optical (FSO) links by converting spatial diversity into coherent combining gain. In turbulent links, the aperture branches are simultaneously affected by relative phase errors, polarization mismatch, and unequal signal-to-noise ratios (SNRs). Existing methods treat phase/polarization alignment and branch-weight allocation as separate operations, or absorb all impairments into a high-dimensional MIMO equalizer that obscures the physical meaning of each aperture's contribution. This paper proposes a structured blind combining method based on heterogeneous gradient sources: phase and per-aperture polarization parameters are updated by closed-form analytical gradients that maximize the combined output power, while aperture weights and an optional global polarization angle are updated by gradients derived from the constellation-radius error. An exponential parameterization pn = eqn/N ensures positivity without clipping. The internal variable qn is adapted by radius-error gradients, thereby allocating maximal-ratio-combining-like weights according to the quality of the already aligned branches.