Application of Differential Geometry to the Array Manifolds of Linear Arrays in Antenna Array Processing

Abstract

This article deals with the application of differential geometry to the array manifolds of non-uniform linear antenna array (NULA) when estimating the direction of arrival (DOA) of multiple sources present in an environment using far field approximation. In order to resolve this issue, we utilized a doublet linear antenna array (DLA) comprising two individual NULAs, along with a proposed algorithm that chooses correct directions of the impinging sources with the help of the prior knowledge of the ambiguous directions calculated with the application of differential geometry to the manifold curves of each NULA. The algorithm checks the correlation of the estimated direction of arrival (DOAs) by both the individual NULA with its corresponding ambiguous set of directions and chooses the output of the NULA, which has a minimum correlation between their estimated DOAs and corresponding ambiguous DOAs. DLA is designed such that the intersection of all the ambiguous set of DOAs among the individual NULAs are null sets. DOA of sources, which imping signals from different directions on the DLA, are estimated using three direction finding (DF) techniques, such as, genetic algorithm (GA), pattern search (PS), and a hybrid technique that utilizes both GA and PS at the same time. As compared to the existing techniques of ambiguity resolution, the proposed algorithm improves the estimation accuracy. Simulation results for all the three DF techniques utilizing the DLA along with the proposed algorithm are presented using MATLAB. As compared to the genetic algorithm and pattern search, the intelligent hybrid technique, such that, GA–PS, had better estimation accuracy in choosing corrected DOAs, despite the fact that the impinging DOAs were from ambiguous directions.