L0 Regularization parameter for sparse DOA estimation of coherent signals with modeling errors

Abstract

Sparse methods have been recently introduced in Direction-Of-Arrival (DOA) estimation as an alternative to subspace-based methods and Maximum Likelihood (ML) techniques. This paper proposes a low complexity sparse L0-regularized method for DOA estimation of coherent signals in multipath environment, a scenario in which subspace-based methods fail. The first eigenvector of the covariance matrix is used as an observation and its statistics in the presence of modeling errors are derived. Thanks to those statistics, we present a theoretical statistical analysis of an interval in which the regularization parameter, usually empirically tuned, should stand. For a regularization parameter in this interval, the global solution of the L0-regularized problem coincides with the solution of the deterministic ML. An off-line selection of the regularization parameter is therefore proposed. Simulations confirm the relevance of this interval and of the proposed method.