AN APPROXIMATE EXPRESSION FOR THE CRAMER-RAO BOUND ON DIRECTION-OF-ARRIVAL ESTIMATION WITH SMALL RING ARRAYS

It is demonstrated that the Cramer-Rao lower bound on direction-of-arr ival estimation with two uncorrelated but closely spaced narrow-band s ources impinging on a small circular array is well approximated by a m odification of a recently published, extremely simple, nonmatrix, line -array formula. The approximation is demonstrated to be useful for a n umber of sensors from about 5 to 30, SNR's from -30 to +30 dB, source separations down to about 0.1 beamwidths, and radius-to-wavelength rat ios from 0.1 to 2. The rms error is about 30%.