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 [1]). In this framework, several procedures have been proposed to reduce the complexity of the beam forming network aimed at generating at least a couple of radiation patterns. Among them, the generation of an optimal sum pattern and a difference one has been carried out by means of a sub‐arraying strategy [2,3]. The simplification of the hardware complexity has also been addressed by sharing some excitations for the sum and difference channels [4]. 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 [5]. The discrete linear arrays have been successively obtained by sampling the resulting continuous apertures. In this work, the same array synthesis problem dealt with in [5] 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 proposed in [6] and [7] for the optimal synthesis of sum and difference patterns respectively, the proposed method allows one to synthesize patterns with arbitrary sidelobes (unlike [5]).