Deep-Learning-Driven Adaptive Filtering for Non-Stationary Signals: Theory and Simulation

Adaptive filtering remains a cornerstone of modern signal processing but faces fundamental challenges when confronted with rapidly changing or nonlinear environments. This work investigates the integration of deep learning into adaptive-filter architectures to enhance tracking capability and robustness in non-stationary conditions. After reviewing and analyzing classical algorithms—LMS, NLMS, RLS, and a variable step-size LMS (VSS-LMS)—their theoretical stability and mean-square error behavior are formalized under a slow-variation system model. Comprehensive simulations using drifting autoregressive (AR(2)) processes, piecewise-stationary FIR systems, and time-varying sinusoidal signals confirm the classical trade-off between performance and complexity: RLS achieves the lowest steady-state error, at a quadratic cost, whereas LMS remains computationally efficient with slower adaptation. A stabilized VSS-LMS algorithm is proposed to balance these extremes; the results show that it maintains numerical stability under abrupt parameter jumps while attaining steady-state MSEs that are comparable to RLS (approximately 3 × 10−2) and superior robustness to noise. These findings are validated by theoretical tracking-error bounds that are derived for bounded parameter drift. Building on this foundation, a deep-learning-driven adaptive filter is introduced, where the update rule is parameterized by a neural function, Uθ, that generalizes the classical gradient descent. This approach offers a pathway toward adaptive filters that are capable of self-tuning and context-aware learning, aligning with emerging trends in AI-augmented system architectures and next-generation computing. Future work will focus on online learning and FPGA/ASIC implementations for real-time deployment.