Sparse wideband array design with reweighted iterative optimisation and frequency invariant response

Sparse wideband sensor (such as microphones) array design for sensor location optimisation is traditionally solved by genetic algorithms, simulated annealing or other similar methods. Recently, a compressive sensing based approach has been proposed by minimising a modified l₁ norm of the weight coefficients. To have a closer approximation to the original l₀ norm minimisation, in this work, we further modify the design by adding a reweighting term to the modified l₁ norm and propose a reweighted optimisation process for a design result with much improved sparsity. Moreover, the formulation can further be extended to give a frequency invariant (FI) response by considering the idea of response variation (RV). Limiting RV to a small value as an added constraint, we can obtain a sparse design result according to the frequency invariance criterion.