Tensor DoA Estimation With Directional Elements

Directivity gain patterns are treated as a physical diversity for tensor array processing, replacing space diversity, in addition to time and space shift diversities. We show that the tensor formulation allows to estimate directions of arrival under the assumption of unknown gain patterns, improving the performance of the omnidirectional case. We propose a trilinear model where one dimension of the multiway data array is fully provided by gain patterns, allowing tensor approaches even when space diversity is missing due to sensor overlap.

I. Introduction

Direction of arrival (DoA) estimation is a central problem in array signal processing, e.g., for telecommunications, seismology, speech, biomedical engineering, etc. Acquisition systems are composed of multiple sensors that receive source signals from different directions [1], [2]. Directional sensor arrays have been used in the context of smart antennas, through beamforming techniques [3] and null-steering (see [4] and [5] for a list of examples). Several studies have investigated directional elements for DoA estimation, such as [6] and [7], both with uniform circular arrays (UCA). High resolution DoA estimation through the MUSIC algorithm [8] with known sensor gains has been further studied in [5], where the effects and advantages of different directivity patterns have been considered, as well as a realistic dipole array implementation. A derivation of the Cramér-Rao bound (CRB) for directional elements of a UCA can be found in [5].