Antenna array design for music in the presence of spatially distributed sources

Abstract

In this paper, the impact of array geometry on the direction of arrival (DOA) estimation of spatially distributed sources impinging on a sensor array is considered. Taking into account the coherently distributed source model proposed in [1], we establish closed-form expressions of the MUSIC-based DOA estimation error as functions of the positions of the array sensors in the presence of model errors due to the angular dispersion of the signal sources. The impact of the array geometry is studied and particular array designs are proposed to make DOA estimation more robust to source dispersion. The analytical results are validated by numerical simulations.

Array geometry impact on music in the presence of spatially distributed sources

“…In order to explore the peak separation, let us consider the sign of ∆θ 1 . Firstly,Π is Hermitian, so the denominatorȧ H iΠȧ i in (11) is non-negative, it is enough to focus on the numerator in (11) for θ 1 which yields 1 2 2 (see (A.5) in appendix) after some straightforward calculus. Secondly with a small δ, 18φ 2 (1) − 3δ 2φ2 (1) +φ 4 (1) can be approximated by 18φ 2 (1) which is positive, and obviously (φ 2 (1) −φ 2 (1) ) 2 is positive.…”

“…In our work, we focus on the impact of the array geometry on the performance of the MUSIC estimator with the CD source model, in the presence of errors due to modeling mismatch of source dispersion. Let us first briefly review our work in [8] and [1]. In [8], the point source MUSIC has been extended into CD-MUSIC (coherent source MUSIC), the first order Talyor approximation DOA estimation bias is proposed in the case that the steering vectors in the model and of the actual sources are mismatched.…”

“…In [8], the point source MUSIC has been extended into CD-MUSIC (coherent source MUSIC), the first order Talyor approximation DOA estimation bias is proposed in the case that the steering vectors in the model and of the actual sources are mismatched. In [1] we make use of the theoretical estimation bias expression in [8], and express the DOA estimation bias as a function of the sensor positions. Impacts of particular array geometries on the estimator performances are studied in the scenario of single source and multiple sources, respectively.…”

“…Impacts of particular array geometries on the estimator performances are studied in the scenario of single source and multiple sources, respectively. In this paper, besides the results in the conference papers, our contributions consist of: firstly, a general condition for canceling the DOA estimation bias in the case of one source is derived; secondly, the condition for canceling the cross terms of the DOA and the angular dispersion parameter in Cramer-Rao bound in the case of one source is derived; thirdly, for the results concerning UCA in the case of two source in [1], the calculation details are given in 6.1.…”