Rules-of-thumb to design a uniform spherical array for direction finding-Its Cramer-Rao bounds' nonlinear dependence on the number of sensors

摘要

This paper discovers rules-of-thumb on how the estimation precision for an incident source's azimuth-polar direction-of-arrival (phi, theta) depends on the number (L) of identical isotropic sensors spaced uniformly on an open sphere of radius R. This estimation's corresponding Cramer-Rao bounds (CRB) are found to follow these elegantly simple approximations, useful for array design: (i) For the azimuth arrival angle: 2 pi(R/lambda) (sigma(s)/sigma(n))root 2LMCRB(phi) sin(theta) approximate to (Le(1/14))(-1) +root 3(L -infinity) -root 3, for all(phi, 0); and (ii) for the polar arrival angle: 2 pi(R/lambda) (sigma(s)/sigma(n))root 2LMCRB(0) approximate to root 3-(Le(6/7))(-1) (L -infinity) - root 3, for all(phi, 0). Here, M denotes the number of snapshots, lambda refers to the incident signal's wavelength, and (sigma(s)/sigma(n))(2) symbolizes the signal-to-noise power ratio. (C) 2019 Acoustical Society of America.