A Distributed Step-Size Control Mechanism for Robust Set-Membership APA in Dynamic Channel Equalization

Abstract

The performance of the Affine Projection Algorithm (APA) and its Set-Membership (SM-APA) variants in adaptive channel equalization is limited by step-size selection. While fixed step-sizes offer a poor trade-off, many variable step-size (VSS) schemes fail to achieve optimal performance, particularly in nonstationary environments. This paper introduces a novel step-size control mechanism by integrating the Distributed Step-Size LMS (DSSLMS) strategy into APA and SM-APA frameworks. The method employs a two-stage process where a base step-size is dynamically adapted based on signal and error characteristics and then distributed to form an adaptive step-size vector, creating the DSSLMS-APA and two DSSLMS-SM-APA algorithms. The proposed algorithms are evaluated against conventional and state-of-the-art VSS benchmarks. Simulation results confirm superior performance. In a stationary environment, the proposed DSSLMS-SM-APA achieves a steady-state MSE of (2 × 10−3), outperforming both the conventional APA (3 × 10−3) and the benchmark VSS methods (VSS-APA-MSE and VSS-APAEC). In three distinct non-stationary scenarios, the proposed DSSLMS-based algorithms exhibit the fastest reconvergence and maintain the lowest post-change MSE, successfully tracking system dynamics where other methods struggle. The algorithms provide a robust, efficient solution for step-size adaptation that balances convergence speed, steady-state accuracy, and tracking agility, making them suitable for real-time channel equalization applications.

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