Circulant ADMM-Net for Fast High-resolution DoA Estimation

TL;DR

This paper presents CADMM-Net and CHADMM-Net, deep neural networks based on structured ADMM unfolding with circulant matrices, achieving fast, memory-efficient high-resolution DoA estimation with competitive accuracy.

Contribution

The paper introduces two novel deep unfolding neural networks leveraging circulant structures for efficient DoA estimation within the LASSO framework.

Findings

Computational complexity per layer is $ ext{O}(N ext{log}(N))$.

Memory footprint is significantly reduced compared to ADMM-Net.

Performance is competitive with existing methods in detection and error metrics.

Abstract

This paper introduces CADMM-Net and CHADMM-Net, two deep neural networks for direction of arrival estimation within the least-absolute shrinkage and selection operator (LASSO) framework. These two networks are based on a structured deep unfolding of the alternating direction method of multipliers (ADMM) algorithm through the use of circulant as well as Hermitian-circulant matrices. Along with a computational complexity of $\mathcal{O}(N\log(N))$ per layer for the inference, where $N$ is the length of the dictionary $\mathbf{A}$, they additionally exhibit a memory footprint of $N$ and approximately half of $N$ for CADMMNet and CHADMM-Net, respectively, compared with $N^{2}$ for ADMM-Net. Furthermore, these structured networks exhibit a competitive performance against ADMM-Net, LISTA, TLISTA, and THLISTA with respect to the detection rate, the angular root-mean square error, and the normalized mean squared error.