Direction of arrival estimation using robust complex Lasso

TL;DR

This paper introduces a robust complex Lasso method based on M-estimation for direction-of-arrival estimation with complex measurements, providing an efficient algorithm and demonstrating its effectiveness in sensor array applications.

Contribution

It presents a novel robust complex Lasso approach using M-estimation, with an explicit algorithm for complex data and application to DoA estimation.

Findings

Effective for direction-of-arrival estimation with complex data

Comparable computational complexity to standard Lasso algorithms

Demonstrated usefulness in sensor array single snapshot scenarios

Abstract

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.