Integration of Bayesian Inference Principles in the Development of Modern Adaptive Equalization Algorithms

Abstract

Adaptive equalization has long been a central mechanism for mitigating intersymbol interference and time variability in communication channels, with classical approaches relying on stochastic gradient and recursive least-squares recursions. Over the last decades, Bayesian inference has provided a complementary perspective that treats equalizer coefficients, latent channel states, and nuisance parameters as random variables with structured prior distributions. This perspective enables uncertainty quantification, principled regularization, and data-driven adaptation without ad hoc tuning. The present study examines the integration of Bayesian principles into modern adaptive equalization design under practical constraints of nonstationary propagation, non-Gaussian disturbances, finite-precision arithmetic, and stringent latency budgets. The discussion develops a modeling pipeline that connects parametric and nonparametric priors to state-space channel descriptions, explores online posterior inference via conjugate updates, Kalman-type filters, particle methods, and variational approximations, and evaluates robustness through heavy-tailed likelihood models and scale-mixture priors. Emphasis is placed on sparse and structured representations that align with wideband and millimeter-wave propagation, on hyperparameter learning through online evidence maximization, and on computational architectures that exploit matrix identities, low-rank structure, and streaming operators. The study also sketches links to coded and multicarrier systems, multiantenna processing, and differentiable implementations that borrow from probabilistic deep learning while preserving posterior interpretability. The treatment aims to remain neutral regarding algorithmic preferences, highlighting trade-offs among statistical fidelity, stability, and complexity, and it underscores regimes in which Bayesian equalizers can complement or subsume classical rules through calibrated uncertainty and regularized adaptation.