Sparse microphone array design for wideband beamforming

The sparse wideband sensor/microphone array design problem is highly nonlinear and it is traditionally solved by genetic algorithms, simulated annealing or other similar optimization methods. This is an extremely time-consuming process and an optimum solution is not guaranteed. In this work, this problem is studied from the viewpoint of compressive sensing (CS) and a CS-based method is provided. Although there have been CS-based methods proposed for the design of narrowband arrays, its extension to the wideband case is not straightforward, as there are multiple coefficients associated with each sensor/microphone and it is not sufficient to simply minimize the l₁ norm of the weight coefficients to obtain a sparse array solution. To achieve this, a modified l₁ norm minimization method is derived and its effectiveness is verified by design examples.