Synthesis of arbitrary and conformal arrays using non-linear optimization techniques

Two related synthesis problems associated with coherent sensor array processing are discussed. The first problem concerns the determination of the geometric arrangement of a fixed number of array elements to achieve an optimal response; the other is to find a set of shading weights for an array of predetermined geometry. The case of an array of sensors with arbitrary 3-D geometry or conformity to a curved sheet in space, which in general do not have analytic solutions, is treated. These synthesis problems are solved by the application of nonlinear optimization techniques. Methods are presented that are suitable for configuring arrays of arbitrary geometry, applicable for most coherent signal-processing algorithms, along with a method for determining weights useful for conventional beamforming. As with most nonlinear optimization problems, the solutions represent only local optimality and not global optimality. The usual technique of reoptimization with random or perturbed initial values should be used to insure that suitable local minima are found