A robust sparse optimization for pattern synthesis with unknown manifold error

The performance of synthesis pattern with sparse arrays is known to degrade in the presence of errors in the array manifolds. This paper introduces a beampattern synthesis approach with uncertain manifold vectors perturbation for linear array. In order to match the desired pattern and minimize the elements simultaneously, the convex optimization of minimizing a reweighted l₁-norm objective based on the weights of elements is proposed. The superposition sampling is used for select the elements. The excitation weights and sensor positions of an array radiating pencil beampatterns are obtained. This method is demonstrated through numerical simulations. The results show the maximally sparse array in beampattern synthesis with manifold vectors perturbation is obtained and the method is effective.