Off-grid DOA Estimation Based on Analysis of the Convexity of Maximum Likelihood Function

TL;DR

This paper introduces a new off-grid DOA estimation method using analysis of the convexity of the maximum likelihood function, improving accuracy and efficiency over traditional grid-based methods.

Contribution

It provides a convexity analysis of the DML function for large arrays and proposes an efficient algorithm for off-grid DOA estimation.

Findings

The convexity range of the DML function is accurately characterized.

The proposed method outperforms existing techniques in accuracy and speed.

Numerical results confirm robustness and effectiveness of the approach.

Abstract

Spatial compressive sensing (SCS) has recently been applied to direction-of-arrival (DOA) estimation owing to advantages over conventional ones. However the performance of compressive sensing (CS)-based estimation methods decreases when true DOAs are not exactly on the discretized sampling grid. We solve the off-grid DOA estimation problem using the deterministic maximum likelihood (DML) estimation method. In this work, we analyze the convexity of the DML function in the vicinity of the global solution. Especially under the condition of large array, we search for an approximately convex range around the ture DOAs to guarantee the DML function convex. Based on the convexity of the DML function, we propose a computationally efficient algorithm framework for off-grid DOA estimation. Numerical experiments show that the rough convex range accords well with the exact convex range of the DML function with large array and demonstrate the superior performance of the proposed methods in terms of accuracy, robustness and speed.