Optimum beamforming performance degradation in the presence of imperfect spatial coherence of wavefronts

Optimum-adaptive beamforming is generally analyzed and used assuming perfectly known wavefronts. There are several applications involving propagation media that are neither isotropic, nor homogeneous, nor deterministic. There are also applications where the arrays may be nondeterministic and/or nonrigid or, more simply, are in motion. Typical examples of such applications are radar, sonar, underwater and satellite and, in general, wireless communication systems. In these cases, the resulting wavefronts can be randomly distorted. We analyze the performance of an optimum-adaptive beamformer when the desired signal component or the interference are not fully coherent over the array aperture. The effects of reduced spatial coherence, for both signal and interference cases, are evaluated in terms of output signal-to-interference-plus-noise ratio (SINR) degradation with respect to the ideal case where the reception of a fully coherent signal is only affected by the presence of a zero-mean additive white Gaussian noise. For this purpose, we provide a theoretical analysis, deriving analytical expressions for general models of spatial coherence loss, supported by numerical results.