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.

[1]  Jalil Rashed-Mohassel,et al.  Cosecant-squared pattern synthesis using a weighted alternating reverse projection method , 2011 .

[2]  Xin-He Xu,et al.  Face recognition base on KPCA with polynomial kernels , 2007, 2007 International Conference on Wavelet Analysis and Pattern Recognition.

[3]  O. Bousquet,et al.  Kernel methods and their potential use in signal processing , 2004, IEEE Signal Processing Magazine.

[4]  Zhi-Quan Luo,et al.  Semidefinite Relaxation of Quadratic Optimization Problems , 2010, IEEE Signal Processing Magazine.

[5]  Wang Wen-jian.  Kernel parameter selection method based on estimation of convex , 2006 .

[6]  Hsuan-Tien Lin.  A Study on Sigmoid Kernels for SVM and the Training of non-PSD Kernels by SMO-type Methods , 2005 .

[7]  Jean-Philippe Thiran,et al.  Kernel matching pursuit for large datasets , 2005, Pattern Recognit..

[8]  Minghao Yin,et al.  Hybrid differential evolution with artificial bee colony and its application for design of a reconfigurable antenna array with discrete phase shifters , 2012 .

[9]  T. Isernia,et al.  An Effective Approach to the Synthesis of Phase-Only Reconfigurable Linear Arrays , 2012, IEEE Transactions on Antennas and Propagation.

[10]  Jian Yang,et al.  KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  T Isernia,et al.  On the optimal synthesis of phase-only reconfigurable antenna arrays , 2011, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP).

[12]  B. Fuchs.  Application of Convex Relaxation to Array Synthesis Problems , 2014, IEEE Transactions on Antennas and Propagation.

[13]  J Rashed-Mohassel,et al.  Flat-Top Footprint Pattern Synthesis Through the Design of Arbitrary Planar-Shaped Apertures , 2010, IEEE Transactions on Antennas and Propagation.

[14]  Pong C. Yuen,et al.  Interpolatory Mercer kernel construction for kernel direct LDA on face recognition , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  Marianna V. Ivashina,et al.  Reconfigurable aperiodic array synthesis by Compressive Sensing , 2016, 2016 10th European Conference on Antennas and Propagation (EuCAP).

[16]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[17]  P. Angeletti,et al.  Aperiodic Arrays for Spaceborne SAR Applications , 2012, IEEE Transactions on Antennas and Propagation.

[18]  K. N. Sherman,et al.  Phased array shaped multi-beam optimization for LEO satellite communications using a genetic algorithm , 2000, Proceedings 2000 IEEE International Conference on Phased Array Systems and Technology (Cat. No.00TH8510).

[19]  Yaohui Wang,et al.  Application of SVM in Object Tracking Based on Laplacian Kernel Function , 2016, 2016 8th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC).

[20]  P. L. Metzen.  Globalstar satellite phased array antennas , 2000, Proceedings 2000 IEEE International Conference on Phased Array Systems and Technology (Cat. No.00TH8510).

[21]  D. Pozar.  The active element pattern , 1994 .

[22]  Weixing Sheng,et al.  Multibeam Pattern Synthesis With Adaptive Finite Excitation Amplitude Levels , 2016, IEEE Communications Letters.

[23]  Wen Tao Li,et al.  Synthesis of multiple-pattern planar arrays with A hybrid generalised iterative fast Fourier transform algorithm , 2016 .

[24]  Didier Auroux,et al.  Large Multibeam Array Antennas with Reduced Number of Active Chains , 2007 .

[25]  K. Kim,et al.  Face recognition using kernel principal component analysis , 2002, IEEE Signal Process. Lett..

[26]  Daoqiang Zhang,et al.  Learning the kernel parameters in kernel minimum distance classifier , 2006, Pattern Recognit..