## 1 Introduction  
In recent years, the spaceborne array antenna has attracted increasingly extensive attention due to its beamforming, beam steering and high-gain capabilities. For array antenna pattern synthesis, the main concern is to search for the appropriate excitation amplitude and phase to obtain the desired radiation pattern. Various approaches, for example, traditional mathematical techniques and optimization algorithms, have been put forward to the array antenna pattern synthesis problem [1; 2; 3; 4]. Normally, Taylor weighting method and Chebyshev weighting method are commonly used to achieve sidelobe suppression. Nonetheless, the amplitude excitation range satisfying Taylor or Chebyshev distribution is too large to be controlled, leading to the difficulty in its application in practical engineering, whereas the global optimization algorithm can effectively limit the range of amplitude variation. Owing to the limitation of such a device design, in Wilkinson circuit, the signal combination efficiency will be affected when there is a large signal power difference. This study controls the maximum variation range of amplitude to 20 dB in this project. Undoubtedly, if the amplitude change is too small, the sidelobe suppression will be very poor. In practice, this paper has achieved the attenuation control by using attenuators. Low sidelobe level is one of the key technical indicators in the antenna pattern, which can effectively improve the communication quality by facilitating the signal-to-noise ratio, reducing the influence of the clutter signal outside the main beam and enhancing the anti-interference ability of the entire system [5; 6; 7; 8]. Genetic algorithm (GA) and particle swarm optimization (PSO) are the first two popular and classical optimization algorithms, which have been successfully applied to antenna synthesis for their high efficiency and simplicity [9; 10; 11; 12]. However, these two algorithms have the disadvantage of premature convergence in solving multi-parameter optimization problems. Therefore, an increasing number of improved algorithms based on classical GA and PSO have been employed to the antenna synthesis problem [13; 14], such as differential evolution algorithm (DE) [15], moth flame optimization algorithm (MFO) [16], fruit-fly optimization algorithm (FOA) [17], invasive weed optimization algorithm (IWO) [18], grey wolf optimization algorithm (GWO) [19], mayfly optimization algorithm (MOA) [20], compressed sensing (CS) [21], biogeography-based optimization (BBO) [22], firefly algorithm (FA) [23], ant colony optimization (ACO) [24], and so on. Despite the fact that these aforementioned algorithms can achieve favorable results in array antenna synthesis, the increase in parameters will lead to slower calculation speed and lower algorithm efficiency. Furthermore, these solutions easily fall into a local optimal solution when the number of phased array elements increases. Therefore, further improvement is needed. The whale optimization algorithm (WOA) [25] is type of simple but effective swarm optimization algorithm. The research concept originates from the hunting behavior of humpback whales, which was proposed by Australian researchers [PERSON] and [PERSON] in 2016. WOA has advantages of simple structure and fewer parameters, so it has a faster solving speed and higher precision in the process of solving multivariate functions. In 2018, [PERSON] applied WOA to the synthesis of wide-sided linear aperiodic arrays with minimum sidelobe level under uniform excitation [26]. It can be clearly seen from these publications that WOA significantly superior to several standard algorithms, both in terms of convergence speed and convergence precision. Therefore, this study investigates the future WOA-based enhancements. To further improve the global search ability and solution accuracy of the WOA, an improved whale optimization algorithm (IWOA) has been proposed in this paper and and applied to the synthesis of low-sidelobe planar array antennas.