In this paper, an optimal far-field radiation pattern synthesis by using time modulation technique is carried out for a compact circular antenna array (CAA) design using a stochastic optimization method called krill herd (KH) optimization. A compact antenna array is achieved by reducing the inter-element spacing between the array elements, which leads to the miniaturization of the size of the array. On the other hand, an improved far-field radiation characteristic is achieved with a low side lobe level (SLL) and narrow first null beam width (FNBW). A low SLL is an essential requirement to reduce the interference with the other systems operating in the same frequency band. A narrow FNBW is necessary to obtain a high directivity. In time modulation technique, ‘time’ has the most significant role. It is considered the fourth-dimensional parameter, which plays the role of an additional degree of freedom to achieve an improved radiation pattern. The time-modulated antenna array (TMAA) radiates at various harmonic frequencies for the periodic switching time sequence. In this paper, the generation of the radiation pattern at the fundamental/central frequency only is considered. The KH algorithm is a flexible and robust search algorithm. It is applied here to find out the optimum sets of switching on-time duration for each array element and to determine the optimum inter-element separation between two array elements of the 20- and 36-element time-modulated circular antenna array (TMCAA). Particle swarm optimization (PSO) and differential evolution (DE) optimization techniques are also individually applied for the same design purpose to prove the superiority of the KH algorithm–based design. Finally, statistical analysis is performed to ensure the significance of the numerical results.

在本文中，使用一种称为磷虾群（KH）优化的随机优化方法，对紧凑型圆形天线阵列（CAA）设计进行了使用时间调制技术的最佳远场辐射方向图综合。通过减小阵列元件之间的元件间间隔来实现紧凑的天线阵列，这导致了阵列尺寸的小型化。另一方面，在低旁瓣电平（SLL）和较窄的第一空波束宽度（FNBW）的情况下实现了改进的远场辐射特性。低SLL是减少对在相同频带中运行的其他系统的干扰的基本要求。窄的FNBW是获得高方向性所必需的。在时间调制技术中，“时间”具有最重要的作用。它被认为是第四维参数，它起到额外的自由度的作用，以实现改善的辐射方向图。对于周期切换时间序列，时间调制天线阵列（TMAA）以各种谐波频率辐射。在本文中，仅考虑在基频/中心频率处产生辐射图。KH算法是一种灵活而强大的搜索算法。在此应用该算法找出每个阵列元件的最佳接通时间持续时间，并确定20元素和36元素时间调制圆形天线阵列（TMCAA）的两个阵列元件之间的最佳元素间间隔。粒子群优化（PSO）和差分进化（DE）优化技术也分别用于同一设计目的，以证明基于KH算法的设计的优越性。