An Improved Adaptive Dot-Shape Beamforming Algorithm Research on Frequency Diverse Array

Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

Abstract:

Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: Multi-carrier frequency diverse array, adaptive beamforming, correction index, limited snapshot, robust.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3299801

References:

[1] Butt F A, Jalil M. An overview of electronic warfare in radar systems(C)// International Conference on Technological Advances in Electrical. IEEE, 2013.
[2] Xiaodong Li. Research on Modern Radar Jamming Technology (D). University of Electronic Science and Technology of China, 2011.
[3] Veen B D V, Buckley K M. Beamforming: a versatile approach to spatial filtering(J). IEEE Assp Magazine, 2002, 5(2):4-24.
[4] Heer C, Schaefer C. Digital Beam Forming technology for phased array antennas(C)// International Conference on Space Technology. IEEE, 2011.
[5] P. Antonik, M. C. Wicks, C. J. Baker, et al. Frequency diverse array radars(C). Proceedings of the IEEE Radar Conference, Verona, NY, April 2006, 215–217.
[6] M. C. Wicks and P. Antonik. Frequency diverse array with independent modulation of frequency, amplitude, and phase(P). U.S.A Patent 7,319,427, January 15, 2008.
[7] Wang W, Shao H, Chen H. Frequency Diverse Array radar: concept, principle and application(J). Journal of Electronics & Information Technology, 2016.
[8] Huang J, Tong K F, Baker C J. Frequency Diverse Array with Beam Scanning Feature(C)// IEEE Antennas And Propagation Society International Symposium. IEEE, 2008.
[9] Huang J, Tong K F, Baker C. Frequency diverse array: Simulation and design(C)// Antennas & Propagation Conference, 2009. LAPC 2009. Loughborough. IEEE, 2009.
[10] Zhuang L, Liu X, Yu W. Precisely beam steering for frequency diverse arrays based on frequency offset selection(C)// Radar Conference - Surveillance for a Safer World, 2009. RADAR. International. IEEE, 2009.
[11] Gao K, Xiong J, Cai J, et al. Decoupled frequency diverse array range–angle-dependent beampattern synthesis using non-linearly increasing frequency offsets(J). Iet Microwaves Antennas & Propagation, 2016, 10(8):880-884.
[12] Yao A, Wu W, Fang D G. Frequency Diverse Array Antenna Using Time-Modulated Optimized Frequency Offset to Obtain Time-Invariant Spatial Fine Focusing Beampattern(J). IEEE Transactions on Antennas & Propagation, 2016, 64(10):4434-4446.
[13] Shao H, Dai J, Xiong J, et al. Dot-Shaped Range-Angle Beampattern Synthesis for Frequency Diverse Array(J). IEEE Antennas & Wireless Propagation Letters, 2016, 15:1703-1706.
[14] Xiong J, Wang W Q. Sparse reconstruction-based beampattern synthesis for multi-carrier frequency diverse array antenna(C)// IEEE International Conference on Acoustics. IEEE, 2017.
[15] Hoshuyama O, Sugiyama A. Robust Adaptive Beamforming(J). IEEE Transactions on Acoustics Speech & Signal Processing, 2008, 35(10):1365-1376.
[16] Carlson, B. D. Covariance matrix estimation errors and diagonal loading in adaptive arrays(J). IEEE Transactions on Aerospace and Electronic Systems, 1988, 24(4):397-401.
[17] Goldstein J S, Reed I S, Scharf L L. A multistage representation of the Wiener filter based on orthogonal projections(J). IEEE Transactions on Information Theory, 1998, 44(7):2943-2959.
[18] Gui-Yu L. A Robust Beamforming Method in the Situation of Sample Pollution and Limited Snapshots(J). Journal of Electronics & Information Technology, 2009, 31(1):192-195.