Synthesizing Linear-Array Patterns via Matrix Computation of Element Currents

The design of linear arrays to produce a desired radiation pattern, i.e., the pattern-synthesis problem, continues to be of interest, as demonstrated by the number of articles being published on this topic. Varieties of approaches have been developed to deal with this problem. The approach discussed here begins with a specified set of element currents - such as choosing all to be of unit amplitude, for example - the radiation pattern of which is computed. A matrix is constructed, the individual coefficients of which are comprised of the contribution each element current makes to the maxima of this initial radiation pattern. A vector, the entries of which are the desired amplitudes of each maxima in the radiation pattern, is then multiplied by the inverse of this matrix. This operation generates a new set of element currents, the pattern maxima of which may change somewhat in angle relative to those of the initial pattern. This requires that the process be repeated as an iterative sequence of element-current and pattern computations. When the locations of the pattern maxima no longer change in angle and the maxima converge to their specified values, the synthesis is complete. Results from this approach are demonstrated for several pattern types.