Synthesis of linear arrays by optimization of weighted distance

We solve a synthesis problem for linear arrays which consists in determining an array pattern belonging to a given mask. As a first step, we assign a reference pattern, F/sub 0/, belonging to the mask; then we divide the interval [-/spl pi/, /spl pi/] of the space directions into small subintervals; this allows a weight to be introduced for each subinterval, thus determining a weighted mean-square distance between F/sub 0/ and the generic array pattern. Minimizing this distance gives an array pattern whose values in each subinterval can be controlled by modifying the weights. Starting from a set of unitary weights, we modify iteratively one weight at a time so as to control suitably the values of the pattern in the corresponding subinterval. This generates a sequence of array patterns which are closer and closer to the mask. A convergence test terminates the iteration and yields the solution.