A shrinkage adaptive filtering algorithm with graph filter models

In this study, we focus on an adaptive filtering algorithm that utilizes variable step-size and incorporates graph filter models within the realm of graph signal processing. The algorithm optimizes the step-size by minimizing the energy of the noise-free a posteriori error signal. To extract this noise-free signal from its noisy counterpart, we employ a shrinkage method. Through simulations involving zero-mean i.i.d. Gaussian input signals on a sensor network graph, we demonstrate that our graph-constrained shrinkage least-mean squares (GC-SHLMS) algorithm significantly outperforms traditional algorithms. Specifically, it excels in terms of both convergence speed and steady-state misalignment when compared to the centralized graph-LMS algorithm (GCLMS), the conventional variable-step-size graph-LMS algorithm (GVSSLMS) and the diffusion graph-LMS algorithm (GDLMS).