A method for the optimal pattern synthesis of linear arrays with prescribed nulls

A new L_∞ optimal method for the synthesis of equispaced linear array functions with asymmetrical far-field pattern functions is proposed. This iterative method provides for the exact specification of the beam width, while at the same time allowing for the specification of the relative levels of individual sidelobes by index or as a function of bearing (e.g., angularly-extended nulls), as well as the realization of specified narrowband nulls. The resulting array factors are optimal in the weighted L_∞ sense and, in general, have complex coefficients. This new Remez-type method employs multiple objective functions to provide the degrees of freedom that are required for exact null placement. Examples which demonstrate the design flexibility offered by the method are included for various sum and difference patterns, including superdirective and shaped-beam arrays