Synthesis of arbitrary sidelobes sum and difference patterns with common excitation weights

The synthesis of sum and difference patterns is a canonical problem widely dealt with by researchers working on antenna array synthesis. As a matter of fact, they are used as transmitting/receiving devices for search-and-track systems (e.g., monopulse radars). Recently, the synthesis of low-sidelobe sum and difference patterns with a common aperture has been carried out by perturbing the roots of the Bayliss distribution to match as much as possible a given Taylor distribution. The discrete linear arrays have been successively obtained by sampling the resulting continuous apertures. In this work, the same array synthesis problem dealt with is addressed, and an innovative approach based on a deterministic optimization strategy is presented wherein the problem is formulated as the minimization of a linear function over a convex set. Taking advantage from the approaches for the optimal synthesis of sum and difference patterns respectively, the proposed method allows one to synthesize patterns with arbitrary sidelobes.