Direction-of-Arrival Estimation for Constant Modulus Signals Using a Structured Matrix Recovery Technique

TL;DR

This paper introduces a novel structured matrix recovery method that exploits both Vandermonde and constant modulus structures for improved DOA estimation of CM signals, outperforming existing algorithms.

Contribution

The paper proposes a fully exploiting structured matrix recovery technique (SMART) that reformulates CM DOA estimation as a rank-constrained Hankel-Toeplitz matrix problem, solved via ADMM.

Findings

SMART outperforms state-of-the-art algorithms in source localization.

The method achieves higher maximum number of locatable sources.

Simulation results validate the effectiveness and efficiency of SMART.

Abstract

This paper addresses the problem of direction-of-arrival (DOA) estimation for constant modulus (CM) source signals using a uniform or sparse linear array. Existing methods typically exploit either the Vandermonde structure of the steering matrix or the CM structure of source signals only. In this paper, we propose a structured matrix recovery technique (SMART) for CM DOA estimation via fully exploiting the two structures. In particular, we reformulate the highly nonconvex CM DOA estimation problems in the noiseless and noisy cases as equivalent rank-constrained Hankel-Toeplitz matrix recovery problems, in which the Vandermonde structure is captured by a series of Hankel-Toeplitz block matrices, of which the number equals the number of snapshots, and the CM structure is guaranteed by letting the block matrices share a same Toeplitz submatrix. The alternating direction method of multipliers (ADMM) is applied to solve the resulting rank-constrained problems and the DOAs are uniquely retrieved from the numerical solution. Extensive simulations are carried out to corroborate our analysis and confirm that the proposed SMART outperforms state-of-the-art algorithms in terms of the maximum number of locatable sources and statistical efficiency.