Real-Valued Khatri-Rao Subspace Approaches on the ULA and a New Nested Array

TL;DR

This paper introduces real-valued Khatri-Rao subspace methods for underdetermined DOA estimation using ULA and nested arrays, reducing computational complexity and enhancing source resolution.

Contribution

It develops a novel real-valued Khatri-Rao approach with a special transformation matrix, improving efficiency and source detection in underdetermined scenarios.

Findings

Reduced complexity in subspace decomposition and spectral search.

Enhanced source resolution with new nested array design.

Numerical results demonstrate performance improvements.

Abstract

In underdetermined direction-of-arrival (DOA) estimation using the covariance-based signal models, the computational complexity turns into a noticeable issue because of the high dimension of the virtual array manifold. In this paper, real-valued Khatri-Rao (KR) approaches are developed on the uniform linear array (ULA) and the nested array. The complexities of subspace decomposition and spectral search are reduced compared with the complex-valued KR approach. By designing a special transformation matrix, the influence of the noise is removed in the mean time while the data is transformed from the complex domain to the real domain. Deploying the sensors with nonuniform spacings can raise the degree of freedom (DOF) and hence help detect more sources in the underdetermined situation. To increase the DOF further, a new nested array geometry is designed. The real-valued denoising KR approach developed on the new nested array can resolve more sources with reduced complexities. The performance improvement is demonstrated by numerical studies.