Performance sensitivity of optimum beamformers

The objective of this work is to study the effect of arbitrary and small look-direction errors on the gain-pattern of the Capon (1969) beamformer and on the optimum interference notch for the general case any number of sensors and sources, and to compare their relative performance. In this analysis, explicit expressions for the sensitivity functions, defined as the derivative of the array response with respect to look-direction errors, were derived. Using these expressions, the perturbations in the array gains at the source directions were evaluated and compared with the actual ones and they were found to be very close.<>