Variational Blind Equalization for Dual-Polarization Free-Space Quantum Communications

Overview & Synopsis

Dual-polarization free-space quantum communication links require receiver equalization under polarization mixing, fading, phase variation, and limited channel supervision. This paper investigates variational blind and semi-blind equalization using VISTA (Variational Inference for Signal Tracking and Adaptation), a variational autoencoder-based probabilistic physical parameter estimator. In the semi-blind branch, channel-relevant statistics are mapped to the underlying 2x2 complex polarization channel. We compare forward KL, reverse KL, Average Jeffreys, Max-KL, and Adaptive Jeffreys regularization and analyze directional KL asymmetry and the local effect of the regularization weight zeta. Over 500 paired Monte Carlo trials, forward KL is nearly insensitive to zeta, whereas reverse and symmetric objectives exhibit low-error regions followed by degradation under stronger regularization. At zeta = 3 x 10^-5, Average Jeffreys reduces median channel NRMSE by approximately 4.8% relative to forward KL at the same weight. Reduced KL asymmetry does not necessarily imply lower channel error. A separate fully blind QPSK receiver estimates a direct equalizer from received data only. Over 3000 paired trials, the VISTA variants have nearly identical median aligned block-NMSE, while their lower mean aligned block-NMSE relative to the CMA-plus-separation baseline is concentrated in difficult, large-error trials. Direct-W optimization with Adam reproduces most of this mean reduction. In the fully blind benchmark, the tested weak regularizers provide no resolved improvement over unregularized VISTA.