978-1-7281-7312-2/20/$31.00 ©2020 IEEE Design and Optimization of Sparse Planar Antenna Arrays Based on Special Matrices Yiyang Luo Department of theoretical radiophysics V. N. Karazin Kharkiv National University Kharkiv, Ukraine yiyangluo@163.com Vladislav Lusenko Department of Radiophysicintroscopy O. Ya. Usikov Institute for Radiophysics and Electronics of NASU Kharkiv, Ukraine lutsenko@ire.kharkov.ua Sergey Shulga Department of theoretical radiophysics V. N. Karazin Kharkiv National University Kharkiv, Ukraine sergeyshulga@karazin.ua Abstract— As sparse arrays can cover a large space with relatively few elements, their low cost and undegraded radiation patterns have attracted more and more interest. And also due to the randomness of antenna locations, sparse arrays can avoid the generation of grating lobes while the spacing between adjacent antenna is greater than half a wavelength. However, the locations of the antenna need to be carefully considered to ensure its acceptable level of performance. And Formally, the design of sparse arrays can be expressed as a constrained multidimensional nonlinear optimization problem. However, due to the lack of convexity, using deterministic optimization methods to solve this kind of multi-extremity problem is very tricky, and non-deterministic optimization methods (such as iterative methods) that are very time-consuming and wasteful of resources are always used to solve the problem. In this work, a simple and time-saving method for designing a two-dimensional planar antenna array using a deterministic method based on special matrices (including, Magic square, Latin square, and triangular matrix) are proposed. And the detailed design process, MATLAB simulation verification and comparative analysis are presented in the paper. Keywords—antenna design, latin square, magic square,, MATLAB simulation, radiation pattern, sparse planar antenna arrays, spatial frequencies, triangular matrix. I. INTRODUCTION Compared with the limited directivity of a single antenna, the antenna array can be widely used in various occasions, including telecommunication, wireless 3D local positioning system, and radio astronomy. And also antenna arrays have the potential to meet the stringent requirements on the multibeam, multichannel, and beam reconfigurability in many communication, sensor, and radar systems. However, the trade-off between the desired accuracy and a minimal antenna element number filling the antenna aperture needs to be considered in the design of an antenna array in order to reduce the electronic beamforming cost, the power consumption, and overall design complexity. The aperiodic arrays introduced by Unz [1] may meet the above requirements. Usually, the Sparse Array approach and the Thinned Array approach used to design such arrays. Unlike the Thinned Array approach, where the optimization starts from a densely filled regular array, after which some elements are removed to obtain an aperiodic array layout while meeting certain specifications [2], the Sparse Array approach directly positions the minimum antenna elements optimally based on specific criteria [3]. And several ways of implementing these approaches have been proposed, which are based on analytical (Almost Difference Sets [3], Matric Pencil Method [4]), stochastic (Genetic Algorithms [5]), or deterministic methods (Taylor Taper [6]). Each of these methods has advantages and disadvantages and has its own unique scope of application. However, no matter which method is used, there are two aspects to consider array design: 1) According to different mission objectives, the antenna needs to achieve specific requirements in specific occasions, and at the same time, it needs to consider actual various cost issues and the balance of different parameters, such as, mainlode beamwidth (MBW), sidelobe level (SLL), the number of elements, calculating time etc. Antenna array design is actually a multi-dimensional nonlinear optimization problem. Unfortunately, there are no closed solutions [7]. And usually, this kind of multiextremal problem is difficult to solve due to lack of convexity. 2) The essence of the antenna array is a combination of different antenna units, which cannot be separated from the electromagnetic (EM) field characteristics of the antenna itself. And especially when there are non-negligible obstacles around the antenna (even indoors), and the signal source, echo and interference have to be considered. Moreover, effects like antenna feeding and mutual coupling (MC) that degrade antenna array performance should be taken into account in the array design. Considering the scenario used by our array, when analyzing the radiation pattern, the near-field effect or the far-field according to the distance between the antenna and the target also need to be considered. In turn, the electromagnetic field characteristics of the antenna itself also can be used to help design the antenna arrays to solve specific practical physical problems. Specific constraints will make our design problems more specific, and provide more conditions to solve the problem. For the authors, the issues considered are more inclined to the region of astronomical radio, the measured signals are from distant celestial bodies, the near-field effect is not considered, and the antenna array used is an array composed of sub-arrays of a large enough array aperture. The distance between each antenna element is greater than half of the wavelength, and the MC effect can be ignored. Because the signals from distant stars are weak and sensitive, the device needs to have higher sensitivity and lower interference, that is, an antenna array with a possible large physical size and a low side lobe level. And if possible, the array is as sparse as possible to reduce energy consumption and the system's own interference with the measurement. At the same time, it is necessary to ensure that the spatial frequency of the array is completely covered to reduce unwanted grading lobe and unpredictable side lobe [8]. Based on the above constraints, a method for directly designing sparse arrays with some mathematical concepts was proposed, which is simple and efficient. Unlike global optimization (GO), this is a design method that uses the physical properties of the antenna and combines the __________________________________________________________________________________________________________________ 2020 IEEE Ukrainian Microwave Week Kharkiv, Ukraine, September 21 - 25 79