Array Synthesis With Low Sidelobe Level Using Two-Way Array Factor: A Mixed-Integer Programming Approach

In this paper, we consider the array synthesis with low sidelobe level using two-way array factor (AF), which is defined as the product of the factors in transmit and receive AFs. Utilizing the integer modeling techniques, we reformulate and simplify the non-convex constraint on sidelobe level, and the coupled variables are linearized according to the characteristics of binary vectors. This allows us to derive a mixed-integer programming (MIP) two-way array synthesis formulation with sidelobe suppression, which can be solved by MIP solvers. Compared to existing algorithms which rely on uniform transmit array or complex excitation distribution, the proposed algorithm yields more flexible arrays with uniform excitation. Moreover, the mainlobe width (MLW) of the two-way AF can be added to the constraints and adjusted as desired at the cost of an acceptable longer running time. Additionally, our algorithm can be extended to more scenarios due to the flexibility of the two-way array structure. Representative simulations are provided to demonstrate the effectiveness and superiority of the proposed algorithm in various scenarios.