A stochastic approach for the apodization of very short arrays

The problem addressed in this paper is the synthesis of the weight coefficients to be assigned to the elements of a linear array that has a spatial aperture shorter than one wavelength. The aim is to obtain a data-independent beam pattern that fulfills some a priori fixed constraints. The analytical approach, expressed in terms of a linear least-squares problem, has been attempted, resulting in very large noise sensitivity and beam pattern instability. To overcome this problem a mixed methodology, based on a combination of a stochastic technique and a local descent method that provides very robust weight coefficients with reduced noise sensitivity, is proposed. Here, robust means that, even if unavoidable fluctuations occur in the transducer gains, the beam pattern obtained maintains the desired features.