# Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna
## 1 Introduction  
An active phased array antenna is composed of hundreds or thousands of radiating elements. The weighting and phase of the input signal are controlled with transmit-receive modules (TRMs) attached to each radiating element, and digital signal processing is performed through an analog-to-digital converter (ADC). However, due to the increased signals transmitted/received from numerous radiating elements, the computational speed of signal processing has been reduced [1]. In addition, given the significant number of TRMs, system construction costs have increased [2]. A subarray technique for grouping radiating elements has been applied to overcome these shortcomings. However, when the subarray is applied to an array antenna, problems can occur, such as the generation of a grating lobe or high sidelobe level (SLL). Therefore, various methods have been studied to solve these problems. In a previous study [3], a low SLL was achieved by using an overlapped subarray using a Butler matrix or a lens feed, and through various methods based on subarray rotation, the SLL was minimized [4]. In addition, the target SLL wasachieved by applying an aperiodic space to individual subarrays [5]. In [6], a study of the optimization of subarray weighting and size levels to achieve a target SLL using a hybrid genetic algorithm (GA) was performed. A GA was also utilized to optimize excitation amplitude and phase to increase transmission efficiency and to derive optimal antenna design parameters to increase gain [7; 8]. The particle swarm optimization (PSO) has been utilized to reduce beam scattering by optimizing the radome design parameters and to estimate the unknown parameters of the one-dimensional micro-Doppler frequency trajectories as a field of radar signal processing [9; 10]. Recently, a modified form of PSO was used to optimize the subarray weighting and achieve a low SLL [11]. In [12; 13], in order to reduce the SLL and form a narrow beam, linear programming was used. A radiation pattern with a low SLL was obtained by optimizing the shape of the subarray and the weighting applied to each subarray utilizing an excitation matching method [14]. In [15], the phase center of the subarray was irregular to achieve a low SLL by making the shape of subarrays tetromino and octomo. Additionally, how the shape of the subarray affects the gain was also investigated. The authors of [16] introduce the various methods to reduce the SLL regarding an unconventional phased array antenna. The SLL could be reduced by optimizing the subarray configuration and subarray excitation to a phased array antenna with subarrays applied. In [17], the characteristics of an array antenna including a low SLL were improved by designing a passive coherent location system with a non-uniform array environment of a space tapering. In this paper, we introduce a method by which to optimize the weighting of each subarray based on quadratic programming (QP) to acquire a low SLL. QP is a type of mathematical programming that determines an optimal value when a mathematical model defined as a quadratic function is given [18], and an optimization technique for the feeding signal of an array antenna using QP has been devised [19]. The subarray shape should be irregular to avoid the grating lobe when scanning [20; 21]. However, it is not easy to apply Taylor/Chebyshev weighting to an array antenna to which a non-periodic subarray is applied. Hence, weighting optimization for each subarray to secure a low SLL in an aperiodic array environment was conducted using QP. The array antenna configuration is a \(24\times 24\) rectangular lattice, the distance between the radiating elements operating at 30 GHz is \(0.72\lambda\) and the number of radiating elements is 576. This paper is organized as follows: Section 2 introduces the method to optimize the subarray shape and weighting to each subarray using genetic swarm optimization (GSO) and QP, respectively. Firstly, in order to achieve a low SLL and avoid a grating lobe, the shapes of 96 subarrays were optimized by GSO.