Bayesian Linear Regression with Cauchy Prior and Its Application in Sparse MIMO Radar

TL;DR

This paper introduces a Bayesian linear regression algorithm with a Cauchy prior (BLRC) that improves sparse signal recovery in dynamic scenarios, outperforming existing methods in MIMO radar applications.

Contribution

The paper develops a practical BLRC algorithm with an AEM scheme, demonstrating superior performance over traditional sparse Bayesian learning and IR-l2 algorithms in sparse MIMO radar.

Findings

BLRC outperforms SBL and IR-l2 in noisy environments.

BLRC achieves higher resolution in target imaging.

Numerical results validate BLRC's robustness across various conditions.

Abstract

In this paper, a sparse signal recovery algorithm using Bayesian linear regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate expectation maximization(AEM) scheme, a systematic hyper-parameter updating strategy is developed to make BLRC practical in highly dynamic scenarios. Remarkably, with a more compact latent space, BLRC not only possesses essential features of the well-known sparse Bayesian learning (SBL) and iterative reweighted l2 (IR-l2) algorithms but also outperforms them. Using sparse array (SPA) and coprime array (CPA), numerical analyses are first performed to show the superior performance of BLRC under various noise levels, array sizes, and sparsity levels. Applications of BLRC to sparse multiple-input and multiple-output (MIMO) radar array signal processing are then carried out to show that the proposed BLRC can efficiently produce high-resolution images of the targets.