# Optimal Pattern Synthesis of Linear Array Antennas Using the Nonlinear Chaotic Grey Wolf Algorithm
## 1 Introduction  
Array antennas are indispensable in present-day Wi-Fi verbal exchange systems. Compared to a single antenna, array antennas have greater directivities, greater gains, and higher competencies in beam control and null placement [1], which make them a crucial component in implementing fifth-generation (5G) and satellite communication systems [2]. Since environmental friendliness has become a significant theme of the current era, technological innovation is the ultimate solution to a green and sustainable system. A new track is opened by array antennas. For example, compared with the U.S. Arecibo array, the 500 m Aperture Spherical Radio Telescope of China has a 64% larger aperture, 2.5 times higher sensitivity, and 10 times higher comprehensive performance, and it can detect up to 13.7 billion light years away. Consequently, the efficiency enhancements of array antennas are apparent. In a broader context, array antenna elements can be structured in various configurations: linear, planar, and three-dimensional. When focusing on the pattern synthesis for linear array antennas (LAAs), there are two different types of LAAs: a uniform array with equal spacing and a nonuniform array. Furthermore, in the realm of planar arrays, the rectangular configuration stands out as a prevalent choice due to its geometric attributes and inherent traits [3]. Placing null placements in particular directions and reducing the sidelobe level (SLL) are essential methods to prevent the interference of array antennas [4]. However, in the pattern synthesis of array antennas, attaining a combination of low SLL, null control, and narrow main beam is challenging due to their inherent mutual constraints. The mutual coupling of array elements can affect the efficiency of array antennas, so the coupling effect between the elements should also be considered in the design to ensure better performance of the array antennas [2; 5; 6]. Previously, the conventional Taylor's method was employed for pattern synthesis with low SLL [7]. With the development of mathematics, several evolutionary algorithms have proven effective in the electromagnetic field, many of which are applied in the pattern synthesis of array antennas, such as the grey wolf optimization (GWO) algorithm [8], particle swarm optimization (PSO) algorithm [9], biogeography-based optimization (BBO) algorithm [10], firefly algorithm (FA) [11], genetic algorithm (GA) [12], difference evolution (DE) algorithm [13], exponential chaotic differential evolution (ECDE) [14], grasshopper optimization algorithm (GOA) [15], quantum particle swarm optimization (QPSO) algorithm [16], spider monkey optimization (SMO) algorithm [17], mayfly algorithm (MA) [18], wind-driven optimization (WDO) algorithm [19], invasive weed (IWO) algorithm [20], and atom search optimization (ASO) algorithm [21]. These algorithms have demonstrated commendable performance within their capabilities; however, the growing demand for anti-interference in information transmission has underscored the necessity for continuous research in the realm of intelligent antenna optimization. Hence, research on the enhancement of the current and new optimization methods has become active recently. The GWO algorithm was employed to optimize LAAs to synthesize optimal radiation patterns. The primary objective was to achieve an array pattern with a minimal SLL and place nulls in the specified directions. The GWO algorithm was successfully utilized to accomplish this goal [22]. The Improved Grey Wolf (IGWO) algorithm was previously utilized to optimize a uniform LAA for optimal pattern synthesis [23]. In this study, the original GWO algorithm has been reworked to an NCGWO algorithm, logistic-tent double mapping is adopted to generate initialized populations, and a convergence factor formula of the Gaussian function is used to enhance the overall performance of the GWO algorithm. The work proposes using the NCGWO algorithm for the pattern synthesis of LAAs and planar arrays.