A typical outcome of Collaborative Beamforming (CB) in Wireless Sensor Networks (WSNs) is the presence of relatively high radiation in undesired directions, an aspect attributed to the usual random arrangement of collaborating sensor nodes. High radiation in undesired directions and prominent sidelobes are bound to result in interference in adjacent co-channel networks. Research towards suppression of radiation in undesired directions in CB is active with a number of proposals already in place. Most of the proposals are in the domain/perspective of 2-dimension WSN configuration with a focus on suppressing the highest-leveled (peak) sidelobe only. Commonly, peak sidelobe suppression is achieved through nodes' transmission amplitude perturbation after a conventional phase steering based beamsteering procedure. In this paper, concurrent amplitude and phase perturbation at collaborating nodes has been utilized towards achieving concurrent beamsteering and suppression of radiation in an elaborate set of undesired directions. A variant of the Particle Swarm Optimization (PSO) algorithm has been applied in the node transmit amplitude and phase perturbation process. Selection of radiation suppression directions is done uniformly from the set of all possible undesired radiation directions. A WSN featuring planar node arrangement with the sink at an elevated plane has been used as the analysis platform. The proposed scheme outperforms the peak sidelobe suppression approach in terms of observed radiation in undesired directions and average sidelobe levels. It has also been established that increasing the number of collaborating nodes and/or the number of selected undesired radiation directions in the proposed CB scheme leads to undesired radiation performance improvement although at an exponentially decaying rate.
1. Jayaprakasam, S., S. K. A. Rahim, and C. Y. Leow, "Distributed and collaborative beamforming in wireless sensor networks: Classifications, trends, and research directions," IEEE Communications Surveys & Tutorials, Vol. 19, No. 4, 2092-2116, 2017. doi:10.1109/COMST.2017.2720690
2. Liang, S., T. Feng, G. Sun, J. Zhang, and H. Zhang, "Transmission power optimization for reducing sidelobe via bat-chicken swarm optimization in distributed collaborative beamforming," 2016 2nd IEEE International Conference on Computer and Communications (ICCC), 2164-2168, IEEE, 2016. doi:10.1109/CompComm.2016.7925083
3. Liang, S., Z. Fang, G. Sun, Y. Liu, G. Qu, S. Jayaprakasam, and Y. Zhang, "A joint optimization approach for distributed collaborative beamforming in mobile wireless sensor networks," Ad Hoc Networks, Vol. 106, 102216, 2020. doi:10.1016/j.adhoc.2020.102216
4. Sun, G., X. Zhao, G. Shen, Y. Liu, A. Wang, S. Jayaprakasam, Y. Zhang, and V. C. Leung, "Improving performance of distributed collaborative beamforming in mobile wireless sensor networks: A multiobjective optimization method," IEEE Internet of Things Journal, Vol. 7, No. 8, 6787-6801, 2020. doi:10.1109/JIOT.2020.2983519
5. Hasan, M. Z. and H. Al-Rizzo, "Beamforming optimization in internet of things applications using robust swarm algorithm in conjunction with connectable and collaborative sensors," Sensors, Vol. 20, No. 7, 2048, 2020. doi:10.3390/s20072048
6. Sun, G., X. Zhao, S. Liang, Y. Liu, Y. Zhang, and V. C. Leung, "A hybrid optimization approach for suppressing sidelobe level and reducing transmission power in collaborative beamforming," 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall), 1-6, IEEE, 2019.
7. Liang, S., Z. Fang, G. Sun, Y. Liu, X. Zhao, G. Qu, Y. Zhang, and V. C. Leung, "Joint sidelobe suppression approach for collaborative beamforming in wireless sensor networks," IEEE Access, Vol. 7, 803-817, 2019.
8. Bao, X., H. Liang, and L. Han, "A novel node selection algorithm for collaborative beamforming in wireless sensor networks," 2018 IEEE International Conference on Internet of Things, 345-349, IEEE, 2018.
9. Sun, G., Y. Liu, S. Liang, Z. Chen, A. Wang, Q. Ju, and Y. Zhang, "A sidelobe and energy optimization array node selection algorithm for collaborative beamforming in wireless sensor networks," IEEE Access, Vol. 6, 2515-2530, 2017.
10. Sun, G., Y. Liu, Z. Chen, A. Wang, Y. Zhang, D. Tian, and V. C. Leung, "Energy efficient collaborative beamforming for reducing sidelobe in wireless sensor networks," IEEE Transactions on Mobile Computing, 1-7, 2019.
11. Almagboul, M. A., F. Shu, Y. Qian, X. Zhou, J. Wang, and J. Hu, "Atom search optimization algorithm based hybrid antenna array receive beamforming to control sidelobe level and steering the null," AEU --- International Journal of Electronics and Communications, Vol. 111, 152854, 2019. doi:10.1016/j.aeue.2019.152854
12. Gravas, I. P., Z. D. Zaharis, T. V. Yioultsis, P. I. Lazaridis, and T. D. Xenos, "Adaptive beamforming with sidelobe suppression by placing extra radiation pattern nulls," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 6, 3853-3862, 2019. doi:10.1109/TAP.2019.2905709
13. Zhao, W., J. Lin, S. Chan, and H.-H. So, "A division-free and variable-regularized lms-based generalized sidelobe canceller for adaptive beamforming and its efficient hardware realization," IEEE Access, Vol. 6, 64 470-64 485, 2018. doi:10.1109/ACCESS.2018.2875409
14. Zhou, M., X. Ma, P. Shen, and W. Sheng, "Weighted subspace-constrained adaptive beamforming for sidelobe control," IEEE Communications Letters, Vol. 23, No. 3, 458-461, 2019. doi:10.1109/LCOMM.2019.2896578
15. Sun, G., Y. Liu, H. Li, S. Liang, A. Wang, and B. Li, "An antenna array sidelobe level reduction approach through invasive weed optimization," International Journal of Antennas and Propagation, Vol. 2018, 2018.
16. Yang, F., G. Pei, L. Hu, L. Ding, and Y. Li, "Joint optimization of sinr and maximum sidelobe level for hybrid beamforming systems with sub-connected structure," Digital Signal Processing, Vol. 109, 102917, 2021. doi:10.1016/j.dsp.2020.102917
17. Brooks, D., The Sampling Distribution and Central Limit Theorem, 1st Edition, Kindle, April 25, 2012.
18. Turner, J. R. and J. F. Thayer, Introduction to Analysis of Variance: Design, Analyis and Interpretation, 1st Edition, SAGE Publications, April 13, 2001.
19. Haynes, W., "Tukey's test," Encyclopedia of Systems Biology, Springer, New York, 2013.