# Bayesian Compressive Sensing Approaches for Direction of Arrival Estimation with Mutual Coupling Effects

## TL;DR

This paper introduces two Bayesian compressive sensing methods for accurately estimating the direction of arrival of signals with mutual coupling effects, especially effective in challenging endfire regions.

## Contribution

It develops a Bayesian compressive sensing Kalman filter and a Gibbs sampling approach with explicit sparsity enforcement, advancing DOA estimation accuracy under mutual coupling.

## Key findings

- Achieved up to 86.36% reduction in RMSE with the Gibbs sampling method.
- Proposed methods outperform traditional relevance vector machine approaches.
- Enhanced DOA estimation accuracy in endfire regions of the array.

## Abstract

The problem of estimating the dynamic direction of arrival of far field signals impinging on a uniform linear array, with mutual coupling effects, is addressed. This work proposes two novel approaches able to provide accurate solutions, including at the endfire regions of the array. Firstly, a Bayesian compressive sensing Kalman filter is developed, which accounts for the predicted estimated signals rather than using the traditional sparse prior. The posterior probability density function of the received source signals and the expression for the related marginal likelihood function are derived theoretically. Next, a Gibbs sampling based approach with indicator variables in the sparsity prior is developed. This allows sparsity to be explicitly enforced in different ways, including when an angle is too far from the previous estimate. The proposed approaches are validated and evaluated over different test scenarios and compared to the traditional relevance vector machine based method. An improved accuracy in terms of average root mean square error values is achieved (up to 73.39% for the modified relevance vector machine based approach and 86.36% for the Gibbs sampling based approach). The proposed approaches prove to be particularly useful for direction of arrival estimation when the angle of arrival moves into the endfire region of the array.