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.

中文翻译：

---

用于对称和非对称天线阵列的具有公共权向量的和和差波束方向图的最佳合成

为了减轻馈电网络设计的复杂性并减少和和差波束图合成对中心对称天线阵列的依赖性，提出了一种生成公共权向量以同时产生对称和非对称天线阵列的这两种波束图的方法。通过考虑和波束图的主瓣辐射功率、旁瓣电平（SLL）、目标方向上差波束图的零位深度和差值比作为波束图合成中的设计参数，制定了一个具有非凸目标函数和两个二次分数约束的新优化问题。为了解决它，我们首先使用变体惩罚方法将原始的有约束优化问题转化为非光滑无约束优化问题，然后采用平滑函数对非光滑分量进行逼近，得到光滑无约束优化问题，然后通过最速下降求解。实施了四个代表性示例，即对称线性、非对称线性、非对称矩形和对称花阵列，以证明我们的算法即使在非对称阵列配置中也可以通过精确控制的 SLL 同时合成和和差波束模式。