Robust adaptive beamforming using modified constant modulus algorithms

Ahmad, Zeeshan; Jaffri, Zain ul Abidin; Hassan, Najam ul; Chen, Meng

doi:10.2478/jee-2022-0033

Abstract

This paper addresses the self-nulling phenomenon also known as the self-cancellation in adaptive beamformers. Optimum beamforming requires knowledge of the desired signal characteristics, either its statistics, its direction-of-arrival, or its response vector. Inaccuracies in the required information lead the beamformer to attenuate the desired signal as if it were interference. Self-nulling is caused by the desired signal having large power (high SNR) relative to the interference signal in case of the minimum variance distortion less response beamformer, and low power desired signal in the case of the constant modulus algorithm (CMA) beamformer, which leads the beamformer to suppress the desired signal and lock onto the interference signal. The least-square constant modulus algorithm is a prominent blind adaptive beamforming algorithm. We propose two CMA-based algorithms which exploit the constant modularity as well as power or DOA of the desired signal to avoid self-nulling in beamforming. Simulations results verify the effectiveness of the proposed algorithms.

References

[1] A. Elnashar, S. Elnoubi, and H. Elmikati, “Sample–by–sample and block–adaptive robust constant modulus–based algorithms”, IET Signal Processing, vol. 6, no. 8, pp. 805–813, 2012.10.1049/iet-spr.2011.0430
Search in Google Scholar Back to article
[2] M. Wax and Y. Anu, “Performance analysis of the minimum variance beamformer in the presence of steering vector errors”, IEEE Transactions on Signal Processing, vol. 44, no. 4, pp. 938–947, 1996.10.1109/78.492546
Search in Google Scholar Back to article
[3] C.–Y. Chen and P. P. Vaidyanathan, “Quadratically constrained beamforming robust against direction–of–arrival mismatch”, IEEE Transactions on Signal Processing, vol. 55, no. 8, pp. 4139–4150, 2007.10.1109/TSP.2007.894402
Search in Google Scholar Back to article
[4] Q. Du, Y. Song, C. Ji, and Z. Ahmad, “Digital beamforming for ultra–wideband signals utilizing an extrapolated array generated by carathodory representation combining fractional delay filters based on high–order hermite interpolation”, IEEJ Transactions on Electrical and Electronic Engineering, vol. 13, no. 12, pp. 1760–1768, 2018.10.1002/tee.22738
Search in Google Scholar Back to article
[5] Z. Jaffri, Z. Ahmad, A. Kabir, and S. Bukhari, “A novel miniaturized Koch–Minkowski hybrid fractal antenna”, Microelectronics International, vol. 39, no. 1, pp. 22–37, 2021.10.1108/MI-07-2021-0069
Search in Google Scholar Back to article
[6] Z. Ahmad, M. Chen, and S.-D. Bao, “Beampattern analysis of frequency diverse array radar: a review”, EURASIP Journal on Wireless Communications and Networking, no. 1, pp. 189, 2021.10.1186/s13638-021-02063-6
Search in Google Scholar Back to article
[7] J. Wang and M. G. Amin, “GPS interference cancellation performance in single and multiple MVDR beamforming methods”, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers, pp. 2300–2304, 2006.10.1109/ACSSC.2006.355180
Search in Google Scholar Back to article
[8] X. Song, J. Wang, and Y. Han, “Robust LSCMA under quadratic constraint”, 2010 IEEE International Conference on Automation and Logistics, pp. 464–467, 2010.10.1109/ICAL.2010.5585327
Search in Google Scholar Back to article
[9] J. Mguez and L. Castedo, “A constant modulus blind adaptive receiver for multiuser interference suppression”, Signal Processing, vol. 71, pp. 15–27, 1998.10.1016/S0165-1684(98)00131-5
Search in Google Scholar Back to article
[10] Z. Ahmad, Y. Song, and Q. Du, “Adaptive wideband beamforming based on digital delay filter”, Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 15, no. 3, pp. 262–274, 2016.10.1590/2179-10742016v15i3630
Search in Google Scholar Back to article
[11] Z. Ahmad, S. Yaoliang, and Q. Du, “A robust adaptive beam-forming algorithm based on LSCMA”, 2017 2nd Workshop on Recent Trends in Telecommunications Research (RTTR), pp. 1–6, 2017.10.1109/RTTR.2017.7887861
Search in Google Scholar Back to article
[12] H.–S. Lui, H. T. Hui, and M. S. Leong, “A Note on the mutual–coupling problems in transmitting and receiving antenna arrays”, IEEE Antennas and Propagation Magazine, vol. 51, no. 5, pp. 171–176, 2009.10.1109/MAP.2009.5432083
Search in Google Scholar Back to article
[13] A. J. Kerkhoff and H. Ling, “A simplified method for reducing mutual coupling effects in low frequency radio telescope phased arrays”, IEEE Transactions on Antennas and Propagation, vol. 59, no. 6, pp. 1838–1845, 2011.10.1109/TAP.2011.2122215
Search in Google Scholar Back to article
[14] W. P. M. N. Keizer, “Fast and accurate array calibration using a synthetic array approach”, IEEE Transactions on Antennas and Propagation, vol. 59, no. 11, pp. 4115–4122, 2011.10.1109/TAP.2011.2164171
Search in Google Scholar Back to article
[15] Y. Li and M. H. Er, “Theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array”, IEEE Transactions on Signal Processing, vol. 54, no. 2, pp. 712–723, 2006.10.1109/TSP.2005.861892
Search in Google Scholar Back to article
[16] A. Young, M. V. Ivashina, R. Maaskant, O. A. Iupikov, and D. B. Davidson, “Improving the calibration efficiency of an array fed reflector antenna through constrained beamforming”, IEEE Transactions on Antennas and Propagation, vol. 61, no. 7, pp. 3538–3545, 2013.10.1109/TAP.2013.2255577
Search in Google Scholar Back to article
[17] H. Pawlak and A. F. Jacob, “An external calibration scheme for DBF antenna arrays”, IEEE Transactions on Antennas and Propagation, vol. 58, no. 1, pp. 59–67, Jan 2010.10.1109/TAP.2009.2036195
Search in Google Scholar Back to article
[18] Z. Jaffri, Z. Ahmad, A. Kabir, and S. Bukhari, “A novel compact stair–shaped multiband fractal antenna for wireless communication systems”, Journal of Electrical Engineering–Elektrotechnicky Casopis, vol. 72, no. 5, pp. 306–314, 2021.10.2478/jee-2021-0043
Search in Google Scholar Back to article
[19] Z. Ahmad, Z. Jaffri, S.–D. Bao, and M. Chen, “Frequency diverse array radar with non–uniform array spacing based on sigmoid function”, Journal of Electrical Engineering, vol. 73, no. 1, pp. 36–42, 2022.10.2478/jee-2022-0005
Search in Google Scholar Back to article
[20] H.L. van Tress, Optimum array processing, Wiley, New York, NY, USA, 2002.10.1002/0471221104
Search in Google Scholar Back to article
[21] S. A. Vorobyov, A. B. Gershman, and Z.–Q. Luo, “Robust adaptive beamforming using worst–case performance optimization: a solution to the signal mismatch problem”, IEEE Transactions on Signal Processing, vol. 51, no. 2, pp. 313–324, 2003.10.1109/TSP.2002.806865
Search in Google Scholar Back to article
[22] S. A. Vorobyov, A. B. Gershman, Z.–Q. Luo, and N. Ma, “Adaptive beamforming with joint robustness against mismatched signal steering vector and interference nonstationarity”, IEEE Signal Processing Letters, vol. 11, no. 2, pp. 108–111, 2004.10.1109/LSP.2003.819857
Search in Google Scholar Back to article
[23] R. G. Lorenz and S. P. Boyd, “Robust minimum variance beam-forming”, IEEE Transactions on Signal Processing, vol. 53, no. 5, pp. 1684–1696, 2005.10.1109/TSP.2005.845436
Search in Google Scholar Back to article
[24] L. C. Godara, “Application of antenna arrays to mobile communications. II. Beam–forming and direction–of–arrival considerations”, Proceedings of the IEEE, vol. 85, no. 8, pp. 1195–1245, 1997.10.1109/5.622504
Search in Google Scholar Back to article
[25] A. B. Gershman, N. D. Sidiropoulos, S. Shahbazpanahi, M. Bengtsson, and B. Ottersten, “Convex optimization–based beam-forming”, IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 62–75, 2010.10.1109/MSP.2010.936015
Search in Google Scholar Back to article
[26] A. Elnashar, S. M. Elnoubi, and H. A. El–Mikati, “Further study on robust adaptive beamforming with optimum diagonal loading”, IEEE Transactions on Antennas and Propagation, vol. 54, no. 12, pp. 3647–3658, 2006.10.1109/TAP.2006.886473
Search in Google Scholar Back to article
[27] S. D. Somasundaram, “Linearly constrained robust capon beam-forming”, IEEE Transactions on Signal Processing, vol. 60, no. 11, pp. 5845–5856, 2012.10.1109/TSP.2012.2212889
Search in Google Scholar Back to article
[28] J. Li, P. Stoica, and Z. Wang, “Doubly constrained robust Capon beamformer”, IEEE Transactions on Signal Processing, vol. 52, no. 9, pp. 2407–2423, 2004.10.1109/TSP.2004.831998
Search in Google Scholar Back to article
[29] J. Xiang, L. Guo, and Q. Liu, “Study of GPS nulling antenna based on space–time processing algorithm”, 2009 5th International Conference on Wireless Communications, Networking and Mobile Computing, pp. 1–4, 2009.10.1109/WICOM.2009.5302363
Search in Google Scholar Back to article
[30] A.Özen, I. Kaya, and B. Soysal, “Variable step–size constant modulus algorithm employing fuzzy logic controller”, Wireless Personal Communications, vol. 54, no. 2, pp. 237–250, 2009.10.1007/s11277-009-9723-2
Search in Google Scholar Back to article
[31] M. Yan, W. Jin–kuan, and Z. Jun, “A linearly constrained LSCM algorithm based on subspace”, Journal of Electronics and Information Technology, vol. 31, no. 1, pp. 49–52, 2009.
Search in Google Scholar Back to article
[32] B. Agee, “The least–squares CMA: A new technique for rapid correction of constant modulus signals”, IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 953–956, 1986.
Search in Google Scholar Back to article
[33] X. Jiyao and F. Hongliang, “An improved constant modulus beam–forming algorithm”, Communications Technology, vol. 42, no. 8, pp. 181–191, 2008.
Search in Google Scholar Back to article
[34] X. Rui, Research on adaptive beamforming algorithm of smart antenna, Doctoral Dissertation: North China Electric Power University.
Search in Google Scholar Back to article
[35] N. Li, Y. Guo, and S.–R. Zheng, “Preprocessing LS–CMA in highly corruptive environment”, Journal of Army Engineering University of PLA, vol. 5, pp. 37–40, 2001.
Search in Google Scholar Back to article
[36] Tang Ling, Research on smart antenna beamforming technology, Doctoral Dissertation: Southwest Jiaotong University, 2007 DOI:10.7666/d.y1131389.
Search in Google Scholar Back to article
[37] Y. Guo, D. Fang, T. N. C. Wang, and C. Liang, “A preprocessing LS–CMA in highly corruptive environment”, Journal of Electronics (China), vol. 19, no. 3, pp. 248–254, 2002.10.1007/s11767-002-0045-8
Search in Google Scholar Back to article
[38] X. Mestre and M. A. Lagunas, “Finite sample size effect on minimum variance beamformers: optimum diagonal loading factor for large arrays”, IEEE Transactions on Signal Processing, vol. 54, no. 1, pp. 69–82, 2006.10.1109/TSP.2005.861052
Search in Google Scholar Back to article
[39] Z. Hao, X. Qian, Y. Qingkun, and F. Linfeng, “Model–switched beamformer with large dynamic range”, International Journal of Antennas and Propagation, pp. 625259, 2014.10.1155/2014/625259
Search in Google Scholar Back to article

Robust adaptive beamforming using modified constant modulus algorithms

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