Multi-beam pattern synthesis algorithm based on kernel principal component analysis and semi-definite relaxation

In this study, a novel multi-beam pattern synthesis algorithm is proposed. The algorithm is divided into three steps. First, the pattern synthesis is performed for each beam without element excitation amplitude constraints, and form a element excitations amplitude matrix (EEAM). Second, the kernel principal component analysis (KPCA) technique is used to acquire a group of common element excitation amplitudes (CEEA). Finally, the semi-definite relaxation technique is employed to obtain the element excitation phase of each beam. The KPCA is a kind of principal component extraction method. Compared with the traditional method, the kernel function and the kernel parameter selection criterion used in the proposed study are designed to ensure that the extracted principal component can hold more than 80% of the information of the EEAM, which means that the acquired CEEA can bestly characterise the EEAM, hence resulting in a better synthesised pattern. In addition, the use of KPCA is a quasi-analytical process, which also speeds up the overall algorithm. Compared to the iterative multi-beam pattern synthesis algorithm, nearly half of the synthesis time is reduced. Through several sets of synthesised examples, and compared with some classical algorithms, this algorithm proves its superiority in the comprehensive effect and calculation time.