Linear and Planar Array Pattern Nulling via Compressed Sensing

Authors

DOI:

https://doi.org/10.26636/jtit.2021.152921

Keywords:

compressed sensing, convex optimization, , iterative re-weighted l1- norm minimization, linear and planar arrays

Abstract

An optimization method based on compressed sensing is proposed for uniformly excited linear or planar antenna arrays to perturb excitation of the minimum number of array elements in such a way that the required number of nulls is obtained. First, the spares theory is relied upon to formulate the problem and then the convex optimization approach is adopted to find the optimum solution. The optimization process is further developed by using iterative re-weighted l1- norm minimization, helping select the least number of the sparse elements and impose the required constraints on the array radiation pattern. Furthermore, the nulls generated are wide enough to cancel a whole specific sidelobe. Simulation results demonstrate the effectiveness of the proposed method and the required nulls are placed with a minimum number of perturbed elements. Thus, in practical implementations of the proposed method, a highly limited number of attenuators and phase shifters is required compared to other, conventional methods.

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References

[1] M. Fakharzadeh, S. H. Jamali, P. Mousavi, and S. Safavi-Naeini, „Fast beamforming for mobile satellite receiver phased arrays: theory and experiment", IEEE Trans. Antennas Propag., vol. 57, no. 6, pp. 1645-1654, 2009. DOI: https://doi.org/10.1109/TAP.2009.2019911
View in Google Scholar

[2] Y. Dong, Z. Chen, P. Fan, and K. B. Letaief, „Mobility-aware uplink interference model for 5G heterogeneous networks", IEEE Trans. Wireless Commun., vol. 15, no. 3, pp. 2231-2244, 2016. DOI: https://doi.org/10.1109/TWC.2015.2500566
View in Google Scholar

[3] Z. Geng, H. Deng, and B. Himed, „Adaptive radar beamforming for interference mitigation in radar-wireless spectrum sharing", IEEE Signal Process. Letters, vol. 22, no. 4, pp. 484-488, 2015. DOI: https://doi.org/10.1109/LSP.2014.2363585
View in Google Scholar

[4] J. R. Mohammed, „Rectangular grid antennas with various Bondary square-rings array", Progress In Electromagnet. Res. Letters, vol. 96, pp. 27-36, 2021. DOI: https://doi.org/10.2528/PIERL20112402
View in Google Scholar

[5] J. R. Mohammed, „Obtaining wide steered nulls in linear array patterns by controlling the locations of two edge elements", AEU Int. J. of Electron. and Commun., vol. 101, pp. 145-151, 2019. DOI: https://doi.org/10.1016/j.aeue.2019.02.004
View in Google Scholar

[6] C. A. Balanis, Antenna Theory: Analysis and Design, Third Edition, Hoboken, New Jersey: John Wiley & Sons, 2005, pp. 385-424 (ISBN: 9780471667827).
View in Google Scholar

[7] W. P. M. N. Keizer, „Fast low sidelobe synthesis for large plan ar array antennas utilizing successive fast Fourier transforms of the array factor", IEEE Trans. Antennas Propag., vol. 55, no. 3, pp. 715-722, 2007. DOI: https://doi.org/10.1109/TAP.2007.891511
View in Google Scholar

[8] J. R. Mohammed and K. H. Sayidmarie, „Null steering method by controlling two elements", IET Microwaves, Antennas Propag., vol. 8, no. 15, pp. 1348-1355, 2014. DOI: https://doi.org/10.1049/iet-map.2014.0213
View in Google Scholar

[9] J. R. Mohammed and K. H. Sayidmarie, „Synthesizing asymmetric sidelobe pattern with steered nulling in non-uniformly excited linear arrays by controlling edge elements", Int. J. of Antennas and Propag., vol. 2017, 2017. DOI: https://doi.org/10.1155/2017/9293031
View in Google Scholar

[10] M. Dawoud and M. Nuruzzaman, „Null steering in rectangular planar arrays by amplitude control using genetic algorithms", Int. J. Electron., 2000, vol. 87, no. 12, pp. 1473-1484, 2010. DOI: https://doi.org/10.1080/00207210050192498
View in Google Scholar

[11] M. A. Mangoud and H. M. Elragal, „Antenna arrays pattern synthesis and wide null control using enhanced particle swarm optimization", Prog. in Electromag. Res. B, vol. 17, pp. 1-14, 2009. DOI: https://doi.org/10.2528/PIERB09070205
View in Google Scholar

[12] A. Trastoy and F. Ares, „Placing quasi-nulls in planar and conformal arrays", Electromagnetics, vol. 19, no. 4, pp. 373-383, 1999. DOI: https://doi.org/10.1080/02726349908908654
View in Google Scholar

[13] A. Slowik and H. Kwasnicka, „Evolutionary algorithms and their applications to engineering problems", Neural. Comput. Appl., vol. 32, no. 16, pp. 12363-12379, 2020. DOI: https://doi.org/10.1007/s00521-020-04832-8
View in Google Scholar

[14] J. R. Mohammed, „A new simple adaptive noise cancellation scheme based on ALE and NLMS filter", in Proc. 5th Annual Int. Conf. on Commun. Network and Service Res. (CNSR), Fredericton, New Brunswick, Canada, 2007, pp. 245-254. DOI: https://doi.org/10.1109/CNSR.2007.4
View in Google Scholar

[15] U. Singh and M. Rattan, „Design of linear and circular antenna arrays using Cuckoo optimization algorithm", Prog. in Electromag. Res. C, vol. 46, pp. 1-11, 2014. DOI: https://doi.org/10.2528/PIERC13110902
View in Google Scholar

[16] S. K. Mahto and A. Choubey, „A novel hybrid IWO/WDO algorithm for nulling pattern synthesis of uniformly spaced linear and non-uniform circular array antenna", AEU Int. J. of Electron. And Commun., vol. 70, no. 6, pp. 750-756, 2016. DOI: https://doi.org/10.1016/j.aeue.2016.02.013
View in Google Scholar

[17] P. Saxena and A. Kothari, „Optimal pattern synthesis of linear antenna array using Grey Wolf optimization algorithm", Int. J. Antennas Propag., vol. 2016, pp. 1-11, 2016. DOI: https://doi.org/10.1155/2016/1205970
View in Google Scholar

[18] A. J. Abdulkader, J. R. Mohammed, and R. H. Thaher, „Phase-only nulling with limited number of controllable side elements", Prog. In Electromag. Res. C, vol. 99, pp. 167-178, 2020. DOI: https://doi.org/10.2528/PIERC20010203
View in Google Scholar

[19] J. R. Mohammed, A. J. Abdulqader, and R. Hamdan, „Antenna pattern optimization via clustered arrays", Prog. in Electromag. Res. M, vol. 95, pp. 177-187, 2020. DOI: https://doi.org/10.2528/PIERM20042307
View in Google Scholar

[20] J. R. Mohammed, A. J. Abdulqader, and R. Hamdan, „Array pat tern recovery under amplitude excitation errors using clustered elements", Prog. In Electromag. Res. M, vol. 98, pp. 183-192, 2020. DOI: https://doi.org/10.2528/PIERM20101906
View in Google Scholar

[21] J. R. Mohammed, „Thinning a subset of selected elements for null steering using binary genetic algorithm", Prog. in Electromag. Res. M, vol. 67, pp. 147-155, 2018. DOI: https://doi.org/10.2528/PIERM18021604
View in Google Scholar

[22] J. R. Mohammed and K. H. Sayidmarie, „Performance evaluation of the adaptive sidelobe canceller with various auxiliary configurations", AEU Int. J. of Electron. and Commun., vol. 80, pp. 179-185, 2017. DOI: https://doi.org/10.1016/j.aeue.2017.06.039
View in Google Scholar

[23] A. Massa, P. Rocca, and G. Oliveri, „Compressive sensing in electromagnetics - a review", IEEE Antennas Propag. Mag., vol. 57, no. 1, pp. 224-238, 2015. DOI: https://doi.org/10.1109/MAP.2015.2397092
View in Google Scholar

[24] J. R. Mohammed, „High-resolution direction-of-arrival estimation method based on sparse arrays with minimum number of elements", J. of Telecommun. and Informat. Technol., vol. 1, pp. 8-14, 2021. DOI: https://doi.org/10.26636/jtit.2021.143720
View in Google Scholar

[25] F. Viani, G. Oliveri, and A. Massa, „Compressive sensing pat tern matching techniques for synthesizing planar sparse arrays", IEEE Trans. Antennas and Propag., vol. 6, no. 9, pp. 4577-4587, 2013. DOI: https://doi.org/10.1109/TAP.2013.2267195
View in Google Scholar

[26] J. Yang and Y. Zhang, „Alternating direction algorithms for ℓ1-problems in compressive sensing", SIAM J. on Scien. Comput., vol. 33, no. 1, pp. 250-278, 2011. DOI: https://doi.org/10.1137/090777761
View in Google Scholar

[27] H. Mohimani, M. Babaie-Zadeh, and C. Jutten, „A fast approach for over complete sparse decomposition based on smoothed norm", IEEE Trans. Signal Process., vol. 57, no. 1, pp. 289-301, 2009. DOI: https://doi.org/10.1109/TSP.2008.2007606
View in Google Scholar

[28] J. A. Tropp and A. C. Gilbert, „Signal recovery from random measurements via orthogonal matching pursuit", IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655-4666, 2007. DOI: https://doi.org/10.1109/TIT.2007.909108
View in Google Scholar

[29] F. Marvasti et al. „A unified approach to sparse signal processing", EURASIP J. Adv. Signal Process., vol. 2012, p. 44, 2012. DOI: https://doi.org/10.1186/1687-6180-2012-44
View in Google Scholar

[30] M. A. Abdelhay, N. O. Korany, and S. E. El-Khamy, „Synthesis of uniformly weighted sparse concentric ring arrays based on off-grid compressive sensing framework", IEEE Antenn. and Wireless Prop. Letters, vol. 20, no. 4, pp. 448-452, 2021. DOI: https://doi.org/10.1109/LAWP.2021.3052174
View in Google Scholar

[31] M. Khosravi, M. Fakharzadeh, and M. H. Bastani, „Large array null steering using compressed sensing", IEEE Sig. Process. Let., vol. 23, no. 8, pp. 1032-1036, 2016. DOI: https://doi.org/10.1109/LSP.2016.2580587
View in Google Scholar

[32] E. J. Candfies, M. B. Wakin, and S. P. Boyd, „Enhancing sparsity by reweighted ℓ1 minimization", J. Fourier Anal. Appl., vol. 14, no. 5, pp. 877-905, 2008. DOI: https://doi.org/10.1007/s00041-008-9045-x
View in Google Scholar

[33] M. Grant and S. Boyd, „CVX: Matlab software for disciplined convex programming, version 2.2", 2020 [Online]. Available: http://cvxr.com/cvx
View in Google Scholar

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Submitted

2023-05-15

Published

2021-09-30

Issue

No. 3 (2021)

Section

ARTICLES FROM THIS ISSUE

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Copyright (c) 2021 Journal of Telecommunications and Information Technology

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
J. R. Mohammed, R. H. Thaher, and A. J. Abdulqader, “Linear and Planar Array Pattern Nulling via Compressed Sensing”, JTIT, vol. 85, no. 3, pp. 50–55, Sep. 2021, doi: 10.26636/jtit.2021.152921.

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