Left–Right Ambiguity Resolution Methods for Closely Spaced Arrays

Abstract

One linear array with omnidirectional sensors cannot discriminate between the azimuth angle and its complementary angle due to axisymmetry about the array axis. This article examines solutions to the bearing ambiguity problem known as left–right (LR) ambiguity resolution using two closely spaced parallel arrays. We design a second-order nulling (SoN) beamformer to produce a cardioid-type spatial response with a null electronically steered to the complementary angle of the direction of interest. Three methods—namely, SoN, null constrained beamformer (NCB), and 2-D direct beamformer (2-DDB), are studied. The performance is evaluated in correlated noise conditions modeled by a first-order auto-regressive process. This work establishes analytical results for the bound on the detection gain (DG) of the two parallel arrays in terms of the Rayleigh quotient of the circulant noise correlation matrix. A closed-form expression is developed for estimating the loss due to cardioid processing at closer inter-array spacing. The expressions are validated based on the deflection criterion. Twin-array processing using the 2-DDB method results in a higher DG, while cardioid-based beamformers give a higher rejection ratio (RR). Data from an at-sea experiment using a towed array are analyzed. Field results show that the deeper null achieved by the cardioid method results in a higher RR compared to 2-D direct beamformer. From the field data, approximately 19-dB LR discrimination is demonstrated at 1650 Hz for the broadside. Experimental results from a towed array corroborate theory and simulations.