Cramer–Rao lower bounds on the angle-of-arrival estimates for a wave propagating in a random medium: Geometric acoustics regime

Abstract

In the geometric acoustics regime, a propagating wave is weakly diffracted and weakly scattered by the medium. The variance of the real component of the signal is much less than the variance of the imaginary component, thus the signal may not be modeled as a complex Gaussian random variable (whose real and imaginary components have equal variance), as is often done in the Rytov extension region, where both scattering and diffraction are strong. A statistical model for a signal in the geometric acoustics regime has been previously developed [S. L. Collier and D. K. Wilson, J. Acoust. Soc. Am. 111, 2379 (2002)] and its properties have been further investigated [S. L. Collier and D. K. Wilson, ASA April 2003 Meeting on Signal Processing (submitted)]. This statistical model is applied here to an acoustic wave propagating in a random medium with fluctuations described by von Kármán’s spectrum. Additive white Gaussian noise is also considered. The correlation functions of the phase and log-amplitude fluctuations for a von Kármán spectrum are derived in the geometric acoustics limit. The Cramer–Rao lower bounds (CRLBs) on the angle-of-arrival estimates are calculated assuming multiple unknown parameters. The range dependence of the CRLBs is studied in detail.