A generalized approximation for the Cramer-Rao lower bound on direction-of-arrival estimates for a pair of closely spaced sources

It is demonstrated that the Cramer-Rao lower bound on direction-of-arrival estimation with two closely spaced, narrow-band plane waves, with an arbitrary correlation coefficient, impinging on a uniform line array, is well-approximated by an empirically derived, nonmatrix expression combining two previously published, special-case approximations. The approximation is useful for a number of sensors down to about 6, signal-to-noise ratios from about -30 to +30 dB, and source separations down to about one-sixth of a Rayleigh beamwidth. The root mean square error is about 11%. (C) 1996 Acoustical Society of America.