A multiple time scale modularized adaptive beamformer

This paper analyzes the cascaded equivalent form of the minimum variance distortionless response (MVDR) beamformer. A unique feature of the modularized MVDR (M²VDR) beamformer is the ability to distribute adaptive degrees of freedom (DOF) among beamformer stages. This property of the M²VDR beamformer allows DOF to be adapted over different time scales. As a consequence of the multiple stage decomposition adaptive beamformer weights appear in a form which suggest an apparent increase in the number of DOF. To properly analyze this ease an alternative interpretation of adaptive DOF is introduced to establish the equivalence between the MVDR beamformer and its cascaded realization. In the second part of this paper the distribution for the output power estimate of a P stage M²VDR beamformer is derived. Analysis reveals the necessity of placing constraints on the adaptation time assigned to each beamformer stage. Simulation experiments are presented that demonstrate the applicability of the M ²VDR beamformer in resolving closely spaced sources under impulsive interference conditions