Minimum variance distortionless response (MVDR) beamformer is an adaptive beamforming technique that provides a method for separating the desired signal from interfering signals. Unfortunately, the MVDR beamformer may have unacceptably low nulling level and high sidelobes, which may lead to significant performance degradation in the case of unexpected interfering signals such as the rapidly moving jammer environments. Via support vector machine regression (SVR), a novel beamforming algorithm (named as SVR-CMT algorithm) is presented for controlling the sidelobes and the nullling level. In the proposed method, firstly, the covariance matrix is tapered based on Mailloux covariance matrix taper (CMT) procedure to broaden the width of nulls for interference signals. Secondly, the equality constraints are modified into inequality constraints to control the sidelobe level. By the ε-insensitive loss function for the sidelobe controller, the modified beamforming optimization problem is formulated as a standard SVR problem so that the weight vector can be obtained effectively. Compared with the previous works, the proposed SVR-CMT method provides better beamforming performance. For instance, (1) it can effectively control the sidelobe and nullling level. (2) it can improve the output signal-to-interference-and-noise ratio (SINR) performance even if the direction-of-arrival (DOA) errors exist. Simulation results demonstrate the efficiency of the presented approach.
2. Wang, L. and C. Andrea, "Microphone-array ego-noise reduction algorithms for auditory micro aerial vehicles," IEEE Sensors Journal, Vol. 17, No. 8, 2447-2455, 2017.
3. Hassanien, A. and G. Moeness, "Dual-function radar-communications: Information embedding using sidelobe control and waveform diversity," IEEE Transactions on Signal Processing, Vol. 64, No. 8, 2168-2181, 2016.
4. Capon, J., "High resolution frequency-wavenumber spectrum analysis," Processing of IEEE, Vol. 57, No. 58, 1408-1418, 1969.
5. Mailloux, R. J., "Covariance matrix augmentation to produce adaptive array pattern roughs," Electronics Letters, Vol. 31, No. 10, 771-772, 1995.
6. Zatman, M., "Production of adaptive array troughs by dispersion synthesis," Electronics Letters, Vol. 31, No. 25, 2141-2142, 1995.
7. Guerci, J. R., "Theory and application of covariance matrix tapers for robust adaptive beamforming," IEEE Transactions on Signal Processing, Vol. 47, No. 4, 977-985, 1999.
8. Liu, F., J. Wang, C. Y. Sun, and R. Du, "Robust MVDR beamformer for nulling level control via multi-parameteric quadratic programming," Progress In Electromagnetics Research C, Vol. 20, 239-254, 2011.
9. Li, W. X., X. J. Mao, and Y. X. Sun, "A new algorithm for null broadening beamforming," Journal of Electronics and Information Technology, Vol. 36, No. 12, 2882-2888, 2014.
10. Mao, X. J., W. X. Li, and Y. S. Li, "Robust adaptive beamforming against signal steering vector mismatch and jammer motion," International Journal of Antennas and Propagations, Vol. 10, 1-12, 2015.
11. Zhao, Y., W. X. Li, X. J. Mao, and N. Zhang, "Null broadening beamforming against array calibration errors," Journal of Harbin Engineering University, Vol. 39, No. 1, 163-168, 2018.
12. Li, S., "Robust beamforming algorithm based on nulls optimization," Signal Processing, Vol. 33, No. 12, 1542-1547, 2017.
13. Liu, J., A. B. Gershman, and Z. Q. Luo, "Adaptive beamforming with sidelobe control: A second-order cone programming approach ," IEEE Signal Processing Letters, Vol. 10, No. 11, 331-334, 2013.
14. Zaharis, Z. D., C. Skeberis, and T. D. Xenos, "Improved antenna array adaptive beamforming with low side lobe level using a novel adaptive invasive weed optimization method," Progress In Electromagnetics Research, Vol. 124, 137-150, 2012.
15. Huang, J., P. Wang, and Q. Wan, "Sidelobe suppression for blind adaptive beamforming with sparse constraint," IEEE Communications Letters, Vol. 15, No. 3, 343-345, 2011.
16. Liu, Y. and Q. Wan, "Sidelobe suppression for robust beamformer via the mixed norm constraint," Wireless Personal Communications, Vol. 65, No. 4, 825-832, 2012.
17. Vapnik, V. N., Statistical Learning Theory, Wiley, New York, 1998.
18. Salah, Z., M. Tarek, and A. Bechir, "Fault detection in wireless sensor networks through SVM classifier," IEEE Sensors Journal, Vol. 18, No. 1, 340-347, 2018.
19. Islam, M., G. Mallikharjunudu, A. S. Parmar, A. Kumar, and R. H. Laskar, "SVM regression based robust image watermarking technique in joint DWT-DCT domain," 2017 International Conference on Intelligent Computing, Instrumentation and Control Technologies, 1426-1433, 2017.
20. Ramon, M. M., N. Xu, and C. G. Christodoulou, "Beamforming using support vector machines," IEEE Antennas and Wireless Propagation Letters, Vol. 4, No. 1, 439-442, 2005.
21. Cesar, C. G. and S. Ignacio, "Robust array beamforming with sidelobe control using support vector machines," IEEE Transactions on Signal Processing, Vol. 55, No. 2, 574-584, 2007.
22. Lu, Y., J. An, and X. Bu, "Adaptive bayesian beamforming with sidelobe constraint," IEEE Communications Letters, Vol. 14, No. 5, 369-371, 2010.
23. Cui, L., Y. Li, and X. Li, "Application of support vector regression in beamforming," International Conference on Computer Science and Network Technology, 1270-1273, 2012.
24. Lin, C., Y. A. Li, Y. Y. Fang, and X. J. Bai, "The robust diagonal loading beamforming method using support vector machines," Acta Armamentarii, Vol. 34, No. 5, 598-604, 2013.
25. Ayestaran, R. G. and F. Las-Heras, "Support vector regression for the design of array antennas," IEEE Antennas and Wireless Propagation Letters, Vol. 4, No. 1, 414-416, 2005.
26. Ayestaran, R. G. and F. Las-Heras, "Support vector multi-regression and equivalent 2D modelling for 3D antenna array synthesis," European Conference on Antennas and Propagation, 1-5, 2008.
27. Ayestaran, R. G., J. Laviada, and F. Las-Heras, "Realistic antenna array synthesis in complex environments using a MOM-SVR approach," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 97-108, 2009.
28. Martinez-Ramon, M. and C. Christodoulou, "Support vector machines for antenna array processing and electromagnetics," Synthesis Lectures on Computational Electromagnetics, 1-120, 2006.
29. Perez-Cruz, F., "An IRWLS procedure for SVR," The 10th European Signal Processing Conference, 1-4, 2000.
30. Perez-Cruz, F., C. Bousono-Calzon, and A. Artes-Rodrıguez, "Convergence of the IRWLS procedure to the support vector machine solution," Neural Computation, Vol. 17, 7-18, 2005.
31. Sun, D. S., "The researches on support vector machine classification and regression methods," Central South University, 49-50, 2004.
32. Nocedal, J. and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.