Adaptive Least Mean Squares Estimation of Graph Signals

TL;DR

This paper introduces an adaptive LMS algorithm for estimating band-limited graph signals, enabling reconstruction and tracking from limited observations, with theoretical analysis and applications in cognitive network environments.

Contribution

It proposes a novel LMS-based method for adaptive graph signal estimation, including support detection and sampling strategy adaptation, with theoretical performance guarantees.

Findings

The method guarantees mean-square error performance.

Numerical results confirm theoretical predictions.

Application to power density mapping in cognitive networks.

Abstract

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.