Improving Performance of Affine Projection–Like Algorithm Using Two Combination Methods

The affine projection–like (APL) algorithm has garnered significant attention due to its low steady-state mean-square deviation and simplicity. However, its performance is limited by a fixed step-size, which forces a trade-off between fast convergence and low steady-state error. To overcome this limitation, this paper introduces two novel variants of the APL algorithm: the convex combination affine projection–like (CC-APL) and the combined step-size affine projection–like (CSS-APL) algorithms. The CC-APL algorithm leverages a convex combination of adaptive filters with different step-sizes, allowing for dynamic adjustment between convergence speed and accuracy. The CSS-APL algorithm optimizes performance by integrating multiple step-sizes directly into the adaptation process. Both algorithms are designed to enhance the balance between convergence rate and steady-state mean-square deviation, addressing a key drawback of the traditional APL. Simulation results demonstrate that the proposed algorithms significantly improve performance compared to the conventional APL algorithm, especially in scenarios requiring both fast adaptation and low mean-square deviation.