Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrade when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1-D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators

Direction of arrival estimation using robust complex Lasso

The Lasso (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. In this paper, we propose a new novel approach for robust Lasso that follows the spirit of M-estimation. We define $M$-Lasso estimates of regression and scale as solutions to generalized zero subgradient equations. Another unique feature of this paper is that we consider complex-valued measurements and regression parameters, which requires careful mathematical characterization of the problem. An explicit and efficient algorithm for computing the $M$-Lasso solution is proposed that has comparable computational complexity as state-of-the-art algorithm for computing the Lasso solution. Usefulness of the $M$-Lasso method is illustrated for direction-of-arrival (DoA) estimation with sensor arrays in a single snapshot case.Comment: Paper has appeared in the Proceedings of the 10th European Conference on Antennas and Propagation (EuCAP'2016), Davos, Switzerland, April 10-15, 201