Theory and analytical performance evaluation of generalized correlation beamformers

Traditionally, passive detection and localization of an acoustic source has been based on exploiting the relative differences in temporally averaged power outputs of contiguous beams of an element-weighted beamformer. An alternate approach, the generalized correlation beamformer (GCBF), is proposed where a weighted Toeplitz-averaged (spatially averaged) correlation function is used to estimate the beamformer output power. All element-weight sequences can be transformed into correlation-weight sequences through a convolution operation. Additional weight sequences which cannot be generated from a convolution of real element-weight sequences are available for use in the GCBF. A special case of the GCBF was proposed by Wilson et al. (1995) in which the correlation-weights are set to unity, a correlation-weight sequence which cannot be obtained from any classical element-weight sequence. Although such a "boxcar" correlation-weight sequence produces a sharper main peak power response (improved resolution), it has the undesirable effect of producing abnormally high (positive and negative power) sidelobes. General analytical performance bounds are developed that accurately reflect the GCBF detection and bearing localization performance for a noise model that includes spatially white noise and spatially discrete interferers (clutter). Analysis results indicate that the GCBF with Bartlett correlation-weights outperformed the GCBF with unity correlation-weights for both detection and bearing estimation except when the clutter bearing is close to the signal bearing.