Luo Y. Sparse Antenna Array Design Based on Special Matrix Operations

The purpose of the research. The research focuses on developing new methods for constructing planar sparse antenna arrays (SAAs), specifically for radiotelescopes (8–80 MHz). Innovative techniques utilizing Latin squares and their triangular matrices have been proposed, providing satisfactory results. Key contributions include the inaugural use of Latin square matrices in SAA construction, pioneering the combination of circular difference sets and Latin square matrices, and integrating Latin square matrices with their lower triangular counterparts. The matrix method introduced is efficient, direct, and straightforward compared to iterative approaches. This novel approach achieves full spatial frequency coverage in planar SAAs designed for radio astronomy. The outline of the main content of the thesis is as follows: Chapter 1 provides a review of the research history in radio wave propagation and antenna theory. The thesis introduces key parameters, such as radiation pattern, main beam width (MBW), average side lobe level (SLL), filling factor, redundancy, and spatial frequency. Additionally, the traditional matrix-based method for constructing SAAs is explained. Chapter 2 explores constructing SAAs based on Latin squares. The algorithm uses matrix element values from "Latin" squares to compute SAA coordinates, forming an interferometer between adjacent elements. Synthesizing large SAAs based on component squares using embedded Latin squares is demonstrated, with characteristics analyzed under various shifts and rotations. Mutual rotations within the synthesized grid enhance its characteristics. The study suggests new possibilities for creating SAAs with low coefficients and acceptable side lobe levels, surpassing previous methods based on cyclic-difference sets (CDS). Chapter 3 focuses on the construction of SAAs using Latin squares with CDS as elements, employing the traditional algorithm from Chapter 1. The resulting arrays exhibit nearly complete spatial frequency coverage with minimal redundancy. SAAs based on Latin squares with CDS elements outperform other configurations, providing new prospects for large SAAs with reduced filling and redundancy coefficients. Chapter 4 introduces a novel SAA synthesis method based on the Latin square and its triangular matrix. This efficient approach ensures full spatial frequency coverage, reduces array compactness and overall numbers, while effectively reducing SLL. Despite the large number of elements, the SAA maintains a fixed geometry and consistent characteristics. Chapter 5 presents a comparative analysis using the 25MHz radio astronomical telescope antenna as SAA element. Novel approaches for constructing non-equidistant planar SAAs based on mathematical structures like Magic squares and Latin squares (including cyclic-difference sets as elements) exhibit unique properties. The methodology is characterized by simplicity and efficiency, avoiding intricate nonlinearity associated with traditional SAA design. It employs straightforward mathematical concepts like matrix multiplication, nesting, and element generation. Additionally, the approach is regular, scalable, combines nonlinearity and multidimensionality, and holds significant future potential for a comprehensive SAA optimization design system, paving the way for systematic studies and knowledge bases. The CONCLUSION provides a comprehensive overview of the thesis, introducing novel direct design methods for planar SAAs based on special matrices. Emphasizing their advantages (low cost, low SLL, low redundancy with complete spatial frequency coverage) and versatile applications (particularly in radio astronomy), the conclusion discusses prospects and potential benefits. However, critical shortcomings in current research are acknowledged, including the absence of pilot measurements, lack of understanding of specific application scenarios, the need for further mathematical development, and the importance of analyzing signal processing systems in SAA integration. These identified areas for improvement offer valuable directions for future research and development.