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WS-ICNN algorithm for robust adaptive beamforming

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Abstract

This paper presents a wideband signal (WS) beamforming method based on Inception convolutional neural network (ICNN), named as WS-ICNN algorithm. Firstly, an Inception module is constructed via some convolutional layers with feature maps of different sizes and a pooling layer. It can not only extract different scale information of covariance matrix, but also excavate the spatial correlation information about received wideband signals, so that the inception module can help neural network improve the beamforming output performance. On this basis, an ICNN model is established, which is suitable for wideband beamforming. Then, in order to obtain a good training label for the proposed ICNN model, a taper matrix and a second-order cone programming problem are introduced to calculate a wideband beamforming weight vector label. Based on this label, the training process of the proposed ICNN model is accomplished. Finally, the well-trained ICNN model accepts the input of the covariance matrix, and output the beamforming weight vector. Simulation results demonstrate the performance of the proposed algorithm in the cases of direction-of-arrival estimation error and sensor position error.

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References

  1. Liu, X., Sun, Q., Lu, W., Wu, C., & Ding, H. (2020). Big-data-based intelligent spectrum sensing for heterogeneous spectrum communications in 5g. IEEE Wireless Communications, 27, 67–73. https://doi.org/10.1109/MWC.001.1900493

    Article  Google Scholar 

  2. Liu, X., Hu, S., Li, M., & Lai, B. (2021). Energy-efficient resource allocation for cognitive industrial internet of things with wireless energy harvesting. IEEE Transactions on Industrial Informatics, 17(8), 5668–5677. https://doi.org/10.1109/tii.2020.2997768

    Article  Google Scholar 

  3. Ge, S., Fan, C., Wang, J., & Huang, X. (2022). Robust adaptive beamforming based on sparse Bayesian learning and covariance matrix reconstruction. IEEE Communications Letters, 26(8), 1893–1897. https://doi.org/10.1109/lcomm.2022.3175176.

    Article  Google Scholar 

  4. Wang, W., Yan, S., Mao, L., & Guo, X. (2021). Robust minimum variance beamforming with sidelobe-level control using the alternating direction method of multipliers. IEEE Transactions on Aerospace and Electronic Systems, 57(5), 3506–3519. https://doi.org/10.1109/taes.2021.3090903

    Article  Google Scholar 

  5. Meng, Z., & Zhou, W. (2021). Robust adaptive beamforming for coprime array with steering vector estimation and covariance matrix reconstruction. IET Communications, 14(16), 2749–2758. https://doi.org/10.1049/iet-com.2019.1314

    Article  Google Scholar 

  6. Allam, M., & Moghaddamjoo, A. (1995). Two-dimensional DFT projection for wideband direction-of-arrival estimation. IEEE Transactions on Signal Processing, 43(7), 1728–1732. https://doi.org/10.1109/78.398738

    Article  Google Scholar 

  7. Bai, Y., Li, J., Wu, Y., Wang, Q., & Zhang, X. (2019). Weighted incoherent signal subspace method for DOA estimation on wideband colored signals. IEEE Access, 7, 1224–1233. https://doi.org/10.1109/access.2018.2886250

    Article  Google Scholar 

  8. Li, L., Yin, H., Zhao, W., & Wu, Z. (2021). Research on ultrasonic array positioning of partial discharge in gis based on incoherent signal subspace method. In: 2021 International Conference on Advanced Electrical Equipment and Reliable Operation (AEERO), pp. 1–4 . https://doi.org/10.1109/AEERO52475.2021.9708338

  9. Liu, F., Du, R., Wu, J., Zhou, Q., Zhang, Z., & Cheng, Y. (2018). Multiple constrained \(\ell\)2-norm minimization algorithm for adaptive beamforming. IEEE Sensors Journal, 18(15), 6311–6318. https://doi.org/10.1109/jsen.2018.2848632

    Article  Google Scholar 

  10. Zhang, X., Jiang, W., Huo, K., Liu, Y., & Li, X. (2020). Robust adaptive beamforming based on linearly modified atomic-norm minimization with target contaminated data. IEEE Transactions on Signal Processing, 68, 5138–5151. https://doi.org/10.1109/tsp.2020.3021257

    Article  MathSciNet  MATH  Google Scholar 

  11. Huang, L., Zhang, J., Xu, X., & Ye, Z. (2015). Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method. IEEE Transactions on Signal Processing, 63(7), 1643–1650. https://doi.org/10.1109/tsp.2015.2396002

    Article  MathSciNet  MATH  Google Scholar 

  12. Zheng, Z., Yang, T., Wang, W.-Q., & Zhang, S. (2020). Robust adaptive beamforming via coprime coarray interpolation. Signal Processing, 169, 107382. https://doi.org/10.1016/j.sigpro.2019.107382

    Article  Google Scholar 

  13. Carlson, B. (1988). Covariance matrix estimation errors and diagonal loading in adaptive arrays. IEEE Transactions on Aerospace and Electronic Systems, 24(4), 397–401. https://doi.org/10.1109/7.7181

    Article  Google Scholar 

  14. Zheng, Z., Yang, T., Wang, W.-Q., & So, H. (2019). Robust adaptive beamforming via simplified interference power estimation. IEEE Transactions on Aerospace and Electronic Systems, 55(6), 3139–3152. https://doi.org/10.1109/taes.2019.2899796

    Article  Google Scholar 

  15. Huang, Y., Vorobyov, S., & Luo, Z.-Q. (2020). Quadratic matrix inequality approach to robust adaptive beamforming for general-rank signal model. IEEE Transactions on Signal Processing, 68, 2244–2255. https://doi.org/10.1109/tsp.2020.2981208

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang, H., Wang, P., & Ye, Z. (2021). Robust adaptive beamforming via covariance matrix reconstruction under colored noise. IEEE Signal Processing Letters, 28, 1759–1763. https://doi.org/10.1109/lsp.2021.3105930

    Article  Google Scholar 

  17. Du, L., Li, J., & Stoica, P. (2010). Fully automatic computation of diagonal loading levels for robust adaptive beamforming. IEEE Transactions on Aerospace and Electronic Systems, 46(1), 449–458. https://doi.org/10.1109/taes.2010.5417174

    Article  Google Scholar 

  18. Vorobyov, S., Gershman, A., & Luo, Z.-Q. (2003). Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem. IEEE Transactions on Signal Processing, 51(2), 313–324. https://doi.org/10.1109/tsp.2002.806865

    Article  Google Scholar 

  19. Zhang, Z., Liu, W., Leng, W., Wang, A., & Shi, H. (2016). Interference-plus-noise covariance matrix reconstruction via spatial power spectrum sampling for robust adaptive beamforming. IEEE Signal Processing Letters, 23(1), 121–125. https://doi.org/10.1109/lsp.2015.2504954

    Article  Google Scholar 

  20. Gu, Y., & Leshem, A. (2012). Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Transactions on Signal Processing, 60(7), 3881–3885. https://doi.org/10.1109/tsp.2012.2194289

    Article  MathSciNet  MATH  Google Scholar 

  21. Yang, X., Li, S., Liu, Q., Long, T., & Sarkar, T. (2020). Robust wideband adaptive beamforming based on focusing transformation and steering vector compensation. IEEE Antennas and Wireless Propagation Letters, 19(12), 2280–2284. https://doi.org/10.1109/lawp.2020.3029950

    Article  Google Scholar 

  22. Liu, Z.-M., Zhang, C., & Yu, P. (2018). Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections. IEEE Transactions on Antennas and Propagation, 66(12), 7315–7327. https://doi.org/10.1109/tap.2018.2874430

    Article  Google Scholar 

  23. Elbir, A. (2019). Cnn-based precoder and combiner design in mmwave mimo systems. IEEE Communications Letters, 23(7), 1240–1243. https://doi.org/10.1109/lcomm.2019.2915977

    Article  Google Scholar 

  24. Ramezanpour, P., Rezaei, M., & Mosavi, M. (2020). Deep-learning-based beamforming for rejecting interferences. IET Signal Processing, 14(7), 467–473. https://doi.org/10.1049/iet-spr.2019.0495

    Article  Google Scholar 

  25. Ramezanpour, M.-R., & Mosavi, M.-R. (2021). Two-stage beamforming for rejecting interferences using deep neural networks. IEEE Systems Journal, 15(3), 4439–4447. https://doi.org/10.1109/jsyst.2020.3034957

    Article  Google Scholar 

  26. Liu, X., Sun, C., Yau, K.-L.A., & Wu, C. (2022). Joint collaborative big spectrum data sensing and reinforcement learning based dynamic spectrum access for cognitive internet of vehicles. IEEE Transactions on Intelligent Transportation Systems. https://doi.org/10.1109/tits.2022.3175570.

    Article  Google Scholar 

  27. Liu, X., Sun, C., Zhou, M., Wu, C., Peng, B., & Li, P. (2021). Reinforcement learning-based multislot double-threshold spectrum sensing with bayesian fusion for industrial big spectrum data. IEEE Transactions on Industrial Informatics, 17, 3391–3400. https://doi.org/10.1109/TII.2020.2987421.

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61971117) and by the Natural Science Foundation of Hebei Province (Grant No. F2020501007).

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Authors and Affiliations

  1. Institute of Engineering Optimization and Smart Antenna, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Fulai Liu & Ruiyan Du

  2. School of Computer Science and Engineering, Northeastern University, Shenyang, 110819, China

    Fulai Liu, Dongbao Qin, Shuo Yang & Ruiyan Du

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  1. Fulai Liu
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  2. Dongbao Qin
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  3. Shuo Yang
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  4. Ruiyan Du
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Correspondence to Fulai Liu.

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Liu, F., Qin, D., Yang, S. et al. WS-ICNN algorithm for robust adaptive beamforming. Wireless Netw (2023). https://doi.org/10.1007/s11276-023-03260-5

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