Optimal Synthesis of Sum and Difference Beam Patterns with a Common Weight Vector for Symmetric and Asymmetric Antenna Arrays

To alleviate the complexity of feeding network design and reduce the dependence of sum and difference beam pattern synthesis on the central symmetric antenna arrays, a method generating a common weight vector to simultaneously produce these two beam patterns for symmetric and asymmetric antenna arrays is proposed. By considering the main-lobe radiation power of the sum beam pattern, sidelobe level (SLL), null depth of the difference beam pattern at the direction of the target, and difference-to-sum ratio as design parameters in the beam pattern synthesis, a new optimization problem with a nonconvex objective function and two quadratic fractional constraints is formulated. To tackle it, we first use the variant penalty method to convert the original constrained optimization problem into a nonsmooth unconstrained one and then adopt smooth functions to approximate the nonsmooth components to obtain a smooth unconstrained optimization problem that is then solved by steepest descent. Four representative examples, namely, symmetric linear, asymmetric linear, asymmetric rectangular, and symmetric flower arrays, are implemented to demonstrate that our algorithm can simultaneously synthesize the sum and difference beam patterns with accurately controlled SLLs even in asymmetric array configurations.