Nested Circular Array and Its Concentric Extension for Underdetermined Direction of Arrival Estimation

Abstract

In this paper, a new array geometry is proposed which is capable of performing underdetermined Direction-Of-Arrival (DOA) estimation for the circular array configuration. DOA estimation is a classical problem and one of the most important techniques in array signal processing as it has applications in wireless and mobile communications, acoustics, and seismic sensing. We consider the problem of estimating DOAs in the case when we have more sources than the number of physical sensors where the resolution must be maintained. The proposed array geometry called Nested Sparse Circular Array (NSCA) is an extension of the two level nested linear array obtained by nesting two sub-circular arrays and one element is placed at the origin. In order to extend the array aperture, a Khatri-Rao (KR) approach is applied to the proposed NSCA which yields the virtual array structure. To utilize the increase in the degrees of freedom (DOFs) that this new array provides, a subspace based approach (MUSIC) for DOA estimation and 1-based optimization approach is extended to estimate DOAs using NSCA. Simulations show that better performance for underdetermined DOA estimation is achieved using the proposed array geometry.

A note on CRLB formulation for underdetermined DOA estimation in circularly configured planar arrays

“…In order to validate our claims, we now conduct simulations and perform a CRLB performance comparison for uniform circular array and nested sparse circular array [12] as shown in Fig.1. We consider a six element NSCA (three dense and three sparse elements [12]), and a six, nine and twelve element UCA all with r = λ.…”

“…The detailed consideration of Fig. 1(b) can be found in [12]. We assume that D narrowband sources with the wavenumber k = 2π/λ are impinging on this array from the directions…”

“…We consider a six element NSCA (three dense and three sparse elements [12]), and a six, nine and twelve element UCA all with r = λ. The eight uncorrelated sources are located…”

“…In terms of underdetermined DOA estimation, many estimation methods use the KhatriRao subspace method. In array geometry consideration, there exists some 2-D non-uniform planar array configurations such as nested sparse circular arrays (NSCA) [12] which are capable of overdetermined and underdetermined DOA estimation. Thus, there is an existing gap for the derivation of the CRLB for planar arrays especially circularly configured arrays such as uniform circular array (UCA) and nested sparse circular array which are two examples of circularly configured arrays.…”

“…NSCA is a circularly configured array in which two sub-circular arrays are nested together. One part of the array is dense and the other is sparse [12].…”