Regularized recursive least squares for anomaly detection in sparse channel tracking applications

Abstract

In this paper, we study the problem of anomaly detection in sparse channel tracking applications via the \(l_1\)-regularized least squares adaptive filter (SPARLS). Anomalies arise due to unexpected adversarial changes in the channel and quick detection of these anomalies is desired. We first prove analytically that the prediction error of the SPARLS algorithm can be substantially lower than that of the widely-used Recursive Least Squares (RLS) algorithm. Furthermore, we present Receiver Operating Characteristic (ROC) curves for the detection/false alarm trade-off of anomaly detection in a sparse multi-path fading channel tracking scenario. These curves reveal the considerable advantage of the SPARLS algorithm over the RLS algorithm.