Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
SPARLS: the sparse RLS algorithm
IEEE Transactions on Signal Processing
Coherence-based performance guarantees for estimating a sparse vector under random noise
IEEE Transactions on Signal Processing
Toeplitz compressed sensing matrices with applications to sparse channel estimation
IEEE Transactions on Information Theory
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In this paper, we study the problem of anomaly detection in sparse channel tracking applications via the l1-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.