AN APPROXIMATE EXPRESSION FOR THE CRAMER-RAO BOUND ON DOA ESTIMATES OF CLOSELY SPACED SOURCES IN BROAD-BAND LINE-ARRAY BEAMFORMING

It is demonstrated that the CRLB on DOA estimation with two uncorrelat ed but closely-spaced wideband sources is well approximated by a strai ghtforward modification of a recently published, extremely simple, non -matrix, narrowband formula. The approximation is useful, in the conte xt of a uniform line array with constant SNR across the band, for a nu mber of sensors from about 6 to 60, SNR's from -30 dB to +30 dB, sourc e separations down to about 0.1 beamwidths and bandwidths approaching an octave. This covers many of the situations in the array processing literature. Variants of the basic formula are also discussed.