Spatial blocking filter derivative constraints for the generalized sidelobe canceller and MUSIC

The paper presents a new approach to spatial derivative constraints for the generalized sidelobe canceller (GSC). Spatial derivative constraints have been applied to linearly constrained minimum variance beamformers to reduce the sensitivity to steering error. Earlier approaches to this problem constrained derivatives of the beamformer power and phase response, leading to beamformer performance that depended on the coordinate reference location of the array. Current approaches constrain only the beamformer power response, eliminating the problem with phase dependence. However, nonlinear minimization is required in order to solve for the linear constraint equations. An alternative approach for the GSC, which is presented in the paper, is to use derivative constraints to flatten the null of the spatial blocking filter power response. Thus, for a small steering error, the desired signal is still blocked from the noise cancelling filter, and the GSC output is unaffected by the steering error. These derivative constraints can be used with wideband array calibration, leading to effective performance in the presence of array errors. This same approach to derivative constraints can be used in other applications involving spatial blocking filters, such as the constrained MUSIC direction finding algorithm to give robustness against direction error of the known signal subspace.