在毫米波 (millimeter wave) 在第五代以及未來行動通訊，扮演這個關鍵
角色。基於毫米波多輸入多輸出系統架構之下的混合式波束成形 (Hybrid
beamforming) 已被大量探討及研究。目前混合式波束成形皆以考量無限精
度的相移器，然而在混合式波束成使用無限精度的相移器是不切實際的其
原因為需要高成本以及高功率消耗。在本論文中，我們打算提出一個用於
為多用戶多輸入多輸出 (MU­MIMO) 系統下基於非監督式學習的方法，來
聯合設計類比預編碼器與結合器，並使使用低精度相移器來實現。我們先
原本類比預編碼器與結合器設計問題轉換成為角度分類問題並且提出一個
具有泛用性的神經網路架構，稱為角度分類網路 (PCNet)，能夠解決各精
度的相移器設計。最後模擬結果證明了所提出方法與現有的低精度相移器
混合式波束成形算法比較，並且所提出方法得到優越系統的總傳送速率
(sum­rate) 和復雜性。

Millimeter wave (mmWave) is a key technology for fifth­generation (5G) and
beyond communications. Hybrid beamforming has been proposed for large­scale
antenna systems in mmWave communications. Existing hybrid beamforming designs based on infinite­resolution phase shifters (PSs) are impractical due to power
consumption and hardware cost. In this paper, we propose an unsupervised­learningbased scheme to jointly design the analog precoder and combiner with low­resolution
PSs for multiuser multiple­input multiple­output (MU­MIMO) systems. We transform the analog precoder and combiner design problem into a phase classification
problem and propose a generic neural network architecture, termed the phase classification network (PCNet), capable of producing solutions of various PS resolutions. Simulation results demonstrate the superior sum­rate and complexity performance of the proposed scheme, as compared to state­of­the­art hybrid beamforming designs for the most commonly used low­resolution PS configurations.

摘要 i
Abstract ii
1 Introduction 1
1.1 Background and Related Works 1
1.2 Contribution 3
1.3 Organization of the Thesis 4
2 Technical Background 5
2.1 MIMO Systems 5
2.2 Deep Neural Network 9
2.2.1 Neural Network 9
2.2.2 Deep Residual Neural Network (ResNet) 9
3 Hybrid Beamforming Design Method 12
3.1 Signal Model 12
3.2 mmWave Channel Model 14
3.3 Problem Formulation 16
3.4 The Two­Stage Algorithm 17
3.4.1 The First Stage 17
3.4.2 The Second Stage 17
3.5 The Proposed Phase Classification Network (PCNet)­Based Analog Precoder and Combiner Design 18
3.5.1 The Proposed Method 18
3.5.2 Loss function 20
4 Simulations Results and Discussion 24
4.1 Simulation Environment 24
4.2 Simulation Setting 24
4.3 Performance of the Proposed Scheme and Different Algorithms 26
4.4 Execution Time Analysis 32
5 Conclusion 34
References 35

[1] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G. N. Wong, J. K. Schulz,M. Samimi, and F. Gutierrez, “Millimeter wave mobile communications for 5g cellular:It will work!” IEEE access, vol. 1, pp. 335–349, May 2013.
[2] C. X. Wang, F. Haider, X. Gao, X.­H. You, Y. Yang, D. Yuan, H. M. Aggoune, H. Haas,S. Fletcher, and E. Hepsaydir, “Cellular architecture and key technologies for 5G wireless communication networks,” IEEE Commun. Mag., vol. 52, no. 2, pp. 122–130, Feb. 2014.
[3] Z. Pi and F. Khan, “An introduction to millimeter­wave mobile broadband systems,” IEEE Commun. Mag., vol. 49, no. 6, pp. 101–107, Jun. 2011.
[4] R. W. Heath, N. González­Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An overview of signal processing techniques for millimeter wave MIMO systems,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 436–453, Apr. 2016.
[5] O. El Ayach, S. Rajagopal, S. Abu­Surra, Z. Pi, and R. W. Heath, “Spatially sparse precoding in millimeter wave MIMO systems,” IEEE Trans. Wireless Commun., vol. 13, no. 3,pp. 1499–1513, Mar. 2014.
[6] X. Gao, L. Dai, S. Han, C.­L. I, and R. W. Heath, “Energy­efficient hybrid analog and digital precoding for mmwave mimo systems with large antenna arrays,” IEEE Journal on Selected Areas in Communications, vol. 34, no. 4, pp. 998–1009, 2016.
[7] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Hybrid precoding for millimeter wave cellular systems with partial channel knowledge,” in 2013 Information Theory and Applications Workshop (ITA), 2013, pp. 1–5.
[8] F. Sohrabi and W. Yu, “Hybrid digital and analog beamforming design for large­scale antenna arrays,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 501–513, Apr. 2016.
[9] W. Ni and X. Dong, “Hybrid block diagonalization for massive multiuser MIMO systems,” IEEE Trans. Commun., vol. 64, no. 1, pp. 201–211, Jan. 2015.
[10] A. Alkhateeb, G. Leus, and R. W. Heath, “Limited feedback hybrid precoding for multiuser millimeter wave systems,” IEEE Trans. Wireless Commun., vol. 14, no. 11, pp. 6481–6494, Nov. 2015.
[11] D. H. N. Nguyen, L. B. Le, and T. Le­Ngoc, “Hybrid MMSE precoding for mmwave multiuser MIMO systems,” in 2016 IEEE international conference on communications (ICC), 2016, pp. 1–6.
[12] D. H. N. Nguyen, L. B. Le, T. Le­Ngoc, and R. W. Heath, “Hybrid MMSE precoding and combining designs for mmWave multiuser systems,” IEEE Access, vol. 5, pp. 19 167–19 181, 2017.
[13] S. Han, C.­l. I, Z. Xu, and C. Rowell, “Large­scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G,” IEEE Commun. Mag., vol. 53, no. 1, pp. 186–194, Jan. 2015.
[14] Z. Wang, M. Li, X. Tian, and Q. Liu, “Iterative hybrid precoder and combiner design for mmwave multiuser mimo systems,” IEEE Commun. Lett., vol. 21, no. 7, pp. 1581–1584, Jul. 2017.
[15] A. Li and C. Masouros, “Hybrid precoding and combining design for millimeter­wave multi­user MIMO based on SVD,” in 2017 IEEE international conference on communications (ICC), 2017, pp. 1–6.
[16] T. Lin, J. Cong, Y. Zhu, J. Zhang, and K. B. Letaief, “Hybrid beamforming for millimeter wave systems using the mmse criterion,” IEEE Transactions on Communications, vol. 67, no. 5, pp. 3693–3708, 2019.
[17] A. Li and C. Masouros,, “Hybrid analog­digital millimeter­wave MU­MIMO transmission with virtual path selection,” IEEE Commun. Lett., vol. 21, no. 2, pp. 438–441, Feb. 2017.
[18] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Hybrid precoding for millimeter wave cellular systems with partial channel knowledge,” in 2013 Information Theory and Applications Workshop (ITA). IEEE, 2013, pp. 1–5.
[19] X. Yu, J. Shen, J. Zhang, and K. B. Letaief, “Alternating minimization algorithms for hybrid precoding in millimeter wave MIMO systems,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 485–500, Apr. 2016.
[20] J.­C. Chen, “Hybrid beamforming with discrete phase shifters for millimeter­wave massive MIMO systems,” IEEE Trans. Veh. Technol., vol. 66, no. 8, pp. 7604–7608, Aug. 2017.
[21] L. Liang, W. Xu, and X. Dong, “Low­complexity hybrid precoding in massive multiuser MIMO systems,” IEEE Wireless Commun. Lett., vol. 3, no. 6, pp. 653–656, Dec. 2014.
[22] Y. Zhang, X. Dong, and Z. Zhang, “Machine learning­based hybrid precoding with low resolution analog phase shifters,” IEEE Commun. Lett., vol. 25, no. 1, pp. 186–190, Jan. 2021.
[23] H. Li, M. Li, and Q. Liu, “Hybrid beamforming with dynamic subarrays and low resolution PSs for mmWave MU­MISO systems,” IEEE Trans. Commun., vol. 68, no. 1, pp. 602–614, Jan. 2020.
[24] F. Dong, W. Wang, and Z. Wei, “Low­complexity hybrid precoding for multi­user mmWave systems with low­resolution phase shifters,” IEEE Trans. Veh. Technol., vol. 68, no. 10, pp. 9774–9784, Oct. 2019.
[25] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Communications of the ACM, vol. 60, no. 6, pp. 84–90, 2017.
[26] C. Szegedy, S. Ioffe, V. Vanhoucke, and A. A. Alemi, “Inception­v4, inception­resnet and the impact of residual connections on learning,” in Thirty­first AAAI conference on artificial intelligence, 2017.
[27] J. Hu, L. Shen, and G. Sun, “Squeeze­and­excitation networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 7132–7141.
[28] J. Redmon and A. Farhadi, “Yolov3: An incremental improvement,” arXiv preprint arXiv:1804.02767, 2018.
[29] F. Chollet, “Xception: Deep learning with depthwise separable convolutions,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp.1251–1258.
[30] G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 4700–4708.
[31] J. Redmon and A. Farhadi, “Yolo9000: better, faster, stronger,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 7263–7271.
[32] M.­Y. Liu, T. Breuel, and J. Kautz, “Unsupervised image­to­image translation networks,”in Advances in neural information processing systems, 2017, pp. 700–708.
[33] S. Sun, T. S. Rappaport, R. W. Heath, A. Nix, and S. Rangan, “Mimo for millimeter­wave wireless communications: Beamforming, spatial multiplexing, or both?” IEEE Communications Magazine, vol. 52, no. 12, pp. 110–121, 2014.
[34] A. Lozano and N. Jindal, “Transmit diversity vs. spatial multiplexing in modern mimo systems,” IEEE Transactions on wireless communications, vol. 9, no. 1, pp. 186–197,2010.
[35] E. Fishler, A. Haimovich, R. S. Blum, L. J. Cimini, D. Chizhik, and R. A. Valenzuela, “Spatial diversity in radars—models and detection performance,” IEEE Transactions on signal processing, vol. 54, no. 3, pp. 823–838, 2006.
[36] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on selected areas in communications, vol. 16, no. 8, pp. 1451–1458, 1998.
[37] X. Bao, W. Feng, J. Zheng, and J. Li, “Deep CNN and equivalent channel based hybrid precoding for mmwave massive mimo systems,” IEEE Access, vol. 8, pp. 19 327–19 335,2020.
[38] Z. Wang, M. Li, Q. Liu, and A. L. Swindlehurst, “Hybrid precoder and combiner design with low­resolution phase shifters in mmWave MIMO systems,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 2, pp. 256–269, May 2018.
[39] F. Sohrabi and W. Yu, “Hybrid beamforming with finite­resolution phase shifters for largescale MIMO systems,” in 2015 IEEE 16th International Workshop on Signal Processing
Advances in Wireless Communications (SPAWC), Stockholm, Sweden, Jun. 2015, pp. 136–140.
[40] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR),June 2016, pp. 770–778.
[41] D.­A. Clevert, T. Unterthiner, and S. Hochreiter, “Fast and accurate deep network learning by exponential linear units (elus),” arXiv preprint arXiv:1511.07289, 2015.
[42] S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” in Proceedings of the 32nd International Conference on Machine Learning, 2015, pp. 448–456.
[43] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” The journal of machine learning research, vol. 15, no. 1, pp. 1929–1958, 2014.
[44] M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard et al., “Tensorflow: A system for large­scale machine learning,” in Proc. USENIX Symp. Oper. Syst. Design Implement. (OSDI), vol. 16, 2016, pp. 265–283.
[45] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” Int. Conf. Learning Representations (ICLR), 2014.