2D-DOA Estimation for Coherent Signals via a Polarized Uniform Rectangular Array

This letter aims to estimate the 2-D direction-of-arrival (DOA) using a polarized uniform rectangular array (URA) under multipath propagation. To leverage the tensorial nature, a parallel factor (PARAFAC) model is established, in which it comprises two spatial response matrices, the polarization response matrix, and the source matrix. Unfortunately, the source matrix exhibits rank-deficiency, hindering effectively PARAFAC decomposition. Our analysis reveals that the rank-deficiency can be easily resolved by taking the KhatriRao product with a full column rank factor matrix. Consequently, three rearranged PARAFAC tensors are obtained that are free of the source matrix's rank-deficiency. The estimation of 2D-DOA is then performed using the vector cross product-auxiliary rotational invariance technique (VCPARIT). The proposed algorithms are insensitive to inter-sensor distance and are suitable for a one-snapshot scenario. Furthermore, they outperform existing smoothing methods from the perspective of estimation accuracy. Theoretical advantages of the proposed algorithms are corroborated by the simulations.

I. Introduction

2-D direction-of-arrival (DOA) estimation is a crucial topic in the fields of wireless communications, radar, navigation, etc. Typically, a 2-D scalar sensor array, such as an L-shaped array [1], [2], a uniform circular array [3], or a uniform rectangular array (URA) [4], is used to estimate the 2D-DOA. However, there is a tradeoff between estimation accuracy and computational complexity. To mitigate angular ambiguity, it is necessary to have an inter-element distance smaller than (or equal to) half the wavelength. Meanwhile, achieving high-resolution 2D-DOA estimation typically requires a large number of sensors. Unfortunately, too small of an element distance would result in severe mutual coupling effects, which require complex array calibration. Massive antennas would exacerbate the computational burden. Sparse geometries, for instance, coprime/nested array, can reduce the mutual coupling effect [5], [6], but they impose strict constraints on the quantity of sensors and the spacing between them, making them unsuitable for scenarios with limited space or limited numbers of sensors.