Beamforming With Small-Spacing Microphone Arrays Using Constrained/Generalized LASSO

In this letter, we develop an approach to the design of beamformers with small-spacing uniform linear microphone arrays by incorporating sparseness constraints for attenuating scattered interference incident from some pre-specified ranges of directions of arrival. The design process is formulated as a constrained LASSO problem. By adjusting the value of a tuning parameter, the proposed method can make compromises among three important yet conflicting (especially at low frequencies) performance measures of small-spacing microphone arrays, i.e., the directivity factor (DF), which quantifies the array spatial gain, the white noise gain (WNG), which evaluates the robustness of the beamformer, and the signal-to-interference-ratio (SIR) gain with respect to scattered interference. Simulation results illustrate the properties of the developed approach.