Abstract
The dynamic partially connected (DPC) structure can achieve the trade-off between hardware loss and precoding performance of millimeter-wave multi-input multi-ouput systems. Via convolutional neural network (CNN), a novel hybrid precoding approach is proposed for the DPC structure in this paper, namely CNN-DPC algorithm. Firstly, the Euler’s formula and identity matrix are used to construct a phase shift (PS) layer that handles diagonal constraints of the analog PS precoding matrix and constant modulus. Then, the state of the connection between the antennas the radio frequency (RF) chains is determined by the probability layer. On this basis, a lambda layer is established to output the vectorized hybrid precoding matrix, and a loss function is expressed as the minimization of the Euclidean distance between the optimal fully digital precoding matrix and the hybrid precoding matrix. Finally, after the CNN learns the mapping relationship between the hybrid precoding matrix and the channel characteristics, it can directly output the desired hybrid precoding matrix with the input of the channel matrix. The proposed CNN-DPC algorithm achieves higher energy efficiency and the spectral efficiency compared with the related algorithms is indicated in the simulations.
Similar content being viewed by others
Data availability
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
References
Wang, X., Kong, L., Kong, F., Qiu, F., Xia, M., Arnon, S., & Chen, G. (2018). Millimeter wave communication: a comprehensive survey. IEEE Communications Surveys Tutorials, 20(3), 1616–1653.
Han, S., Chih-Lin, I., Xu, Z., et al. (2015). Large-scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G. IEEE Communications Magazine, 53(1), 186–194.
Ayach, O. E., Rajagopal, S., Abu-Surra, S., et al. (2014). Spatially sparse precoding in millimeter wave MIMO systems. IEEE Transactions on Wireless Communications, 13(3), 1499–1513.
Yu, X., Shen, J., Zhang, J., & Letaief, K. B. (2016). Alternating minimization algorithms for hybrid precoding in millimeter wave MIMO systems. IEEE Journal of Selected Topics in Signal Processing, 10(3), 485–500.
Kasai, H. (2018). Fast optimization algorithm on complex oblique manifold for hybrid precoding in millimeter wave MIMO systems. In 2018 IEEE Global Conference on Signal and Information Processing , pp. 1266-1270.
Gao, X., Dai, L., Han, S., et al. (2016). Energy-efficient hybrid analog and digital precoding for mmWave MIMO systems with large antenna arrays. IEEE Journal on Selected Areas in Communications, 34(4), 998–1009.
Zhao, X., Lin, T., Zhu, Y., et al. (2021). Partially-connected hybrid beamforming for spectral efficiency maximization via a weighted MMSE equivalence. IEEE Transactions on Wireless Communications, 20(12), 8218–8232.
Pérez-Adán, D., González-Coma, J.P., Fresnedo, O., Castedo, L. (2019). Hybrid mmWave MIMO transceivers for the uplink of multiple correlated users. In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications , pp. 1-5.
Park, S., Alkhateeb, A., & Heath, R. W. (2017). Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems. IEEE Transactions on Wireless Communications, 16(5), 2907–2920.
Jin, J., Xiao, C., Chen, W., & Wu, Y. (2019). Channel-statistics-based hybrid precoding for millimeter-wave MIMO systems with dynamic subarrays. IEEE Transactions Communications, 67(6), 3991–4002.
Wang, D., Zhou, F., Lin, W., Ding, Z., & Al-Dhahir, N. (2022). Cooperative hybrid nonorthogonal multiple access-based mobile-edge computing in cognitive radio networks. IEEE Transactions on Cognitive, 8(2), 1104–1117.
Wang, D., Wu, M., He, Y., Pang, L., Xu, Q., & Zhang, R. (2022). An HAP and UAVs collaboration framework for uplink secure rate maximization in NOMA-enabled IoT networks. Remote Sensing, 14(18), 4501.
Wang, D., He, T., Zhou, F., Cheng, J., Zhang, R., & Wu, Q. (2022). Outage-driven link selection for secure buffer-aided networks. Science China Information Sciences, 65(8), 1–6.
Du, R., Liu, H., Guan, Z., et al. (2022). HP-SPC algorithm with dynamic partially connected structure for mmWave MIMO systems. Transactions on Emerging Telecommunications Technologies, 33(7), e4474.
Huang, H., Song, Y., Yang, J., et al. (2019). Deep-learning based millimeter-wave massive mimo for hybrid precoding. IEEE Transactions on Vehicular Technology, 68(3), 3027–3032.
Elbir, A. M. (2019). CNN-based precoder and combiner design in mmWave MIMO systems. IEEE Communications Letters, 23(7), 1240–1243.
Li, L., Ren, H., Li, X., Chen, W., & Han, Z. (2019). Machine learning-based spectrum efficiency hybrid precoding with lens array and low-resolution ADCs. IEEE Access, 7, 117986–117996.
Peken, T., Adiga, S., Tandon, R., et al. (2020). Deep learning for svd and hybrid beamforming. IEEE Transactions on Wireless Communications, 19(10), 6621–6642.
Alkhateeb, A., Alex, S., Varkey, P., et al. (2018). Deep learning coordinated beamforming for highly-mobile millimeter wave systems. IEEE Access, 6, 37328–37348.
Hojatian, H., Nadal, J., Frigon, J. F., et al. (2021). Unsupervised deep learning for massive MIMO hybrid beamforming. IEEE Transactions on Wireless Communications, 20(11), 7086–7099.
Bao, X., Feng, W., Zheng, J., & Li, J. (2020). Deep CNN and equivalent channel based hybrid precoding for mmWave massive MIMO systems. IEEE Access, 8, 19327–19335.
Chen, K., Yang, J., Li, Q., & Ge, X. (2021). Sub-array hybrid precoding for massive MIMO systems: A cnn-based approach. IEEE Communications Letters, 25(1), 191–195.
Saleh, A. A. M., & Valenzuela, R. (1987). A statistical model for indoor multipath propagation. IEEE Journal on Selected Areas in Communications, 5(2), 128–137.
Elbir, A. M. (2019). CNN-based precoder and combiner design in mmWave MIMO systems. IEEE Communications Letters, 23(7), 1240–1243.
Li, M., Wang, Z., Li, H., Liu, Q., & Zhou, L. (2019). A hardware-efficient hybrid beamforming solution for mmWave MIMO systems. IEEE Wireless Communications, 26(1), 137–143.
Feng, C., Shen, W., Gao, X., et al. (2020). Dynamic hybrid precoding relying on twin-resolution phase shifters in millimeter-wave communication systems. IEEE Transactions on Wireless Communications, 20(2), 812–826.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61971117), by the Natural Science Foundation of Hebei Province (Grant No. F2020501007) and by the S &T Program of Heibei (No.22377717D).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Du, R., Li, T., Li, X. et al. CNN-DPC algorithm for hybrid precoding in millimeter-wave massive MIMO systems. Wireless Netw 29, 2447–2456 (2023). https://doi.org/10.1007/s11276-023-03308-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11276-023-03308-6