在5G毫米波通信中，波束對齊（BeamAlignment, BA）是確保高數據傳輸速率和可靠連接的關鍵技術。由於毫米波的波束窄、頻段高，傳統的2D波束對齊演算法（如HBA和2PHT&S）在 3D 波束成形的場景中性能受限，難以應對更多方向的搜索需求。本研究針對3D波束成形提出了一種全新的波束對齊演算法，稱為QSA（Quadrant Search Algorithm）。 QSA 基於象限搜索的思想，通過結合目標區域劃分與階段性細化搜索，能顯著縮短波束對齊時間，同時保持高準確率。我們在不同天線數與不同碼本波束數量下進行了模擬測試，結果顯示QSA在時間成本、準確率和計算複雜度方面均優於現有方法。此外，QSA在多路徑（LOS+NLOS）場景中有效應對了雜訊和干擾，展現了穩健的對齊性能。為進一步探討，本文還對適應性波束成形（AdaptiveBeamforming）中的RLS方法進行了比較，指出其時間成本與實現複雜度較高，而QSA在靜態場景中具顯著優勢。本研究提供了一種可行的方法，為毫米波通信的3D波束對齊問題提供了新的參考方向。

In 5G millimeter-wave communications, Beam Alignment is a key technology to ensure high data transmission rates and reliable connectivity. Due to the narrow beams and high frequency bands of millimeter waves, traditional 2D beam alignment algorithms, such as HBA and 2PHT&S, face limitations in 3D beamforming scenarios, where the search space expands to more directions. This study proposes a novel beam alignment algorithm, termed the Quadrant Search Algorithm (QSA), specifically designed for 3D beamforming. QSA is based on the concept of quadrant search, combining target region division and progressive refinement to significantly reduce beam alignment time while maintaining high accuracy. We conducted simulations under various antenna configurations and codebook sizes, and the results demonstrate that QSA outperforms existing methods in terms of time cost, accuracy, and computational complexity. Furthermore, QSA effectively handles noise and interference in multipath (LOS + NLOS) environments, showcasing robust alignment performance. To further investigate, we compared the Recursive Least Squares (RLS) method in adaptive beamforming with QSA, highlighting the higher time cost and implementation complexity of RLS. Incontrast, QSA exhibits significant advantages in static scenarios. This study provides a feasible approach and offers a new perspective for addressing the 3D beam alignment challenges in millimeter-wave communications.

[1] M. Vaezi et al., "Cellular, Wide-Area, and Non-Terrestrial IoT: A Survey on 5G Advances and the Road Toward 6G," IEEE Communications Surveys & Tutorials, vol. 24, no. 2, pp. 1117-1174, Secondquarter 2022.

[2] B. K. J. Al-Shammari, I. Hburi, H. R. Idan, and H. F. Khazaal, "An Overview of mmWave Communications for 5G," 2021 International Conference on Communication & Information Technology (ICICT), Basrah, Iraq, 2021, pp. 133-139.

[3] Z. Xiao et al., "A Survey on Millimeter-Wave Beamforming Enabled UAV Communications and Networking," IEEE Communications Surveys & Tutorials, vol. 24, no. 1, pp. 557-610, First quarter 2022.

[4] M. Klemm, I. J. Craddock, J. A. Leendertz, A. Preece, and R. Benjamin, "Radar-Based Breast Cancer Detection Using a Hemispherical Antenna Array—Experimental Results," IEEE Transactions on Antennas and Propagation, vol. 57, no. 6, pp. 1692-1704, June 2009.

[5] A. Kammoun, H. Khanfir, Z. Altman, M. Debbah, and M. Kamoun, "Preliminary Results on 3D Channel Modeling: From Theory to Standardization," IEEE Journal on Selected Areas in Communications, vol. 32, no. 6, pp. 1219-1229, June 2014.

[6] N. Seifi, J. Zhang, R. W. Heath, T. Svensson, and M. Coldrey, "Coordinated 3D Beamforming for Interference Management in Cellular Networks," IEEE Transactions on Wireless Communications, vol. 13, no. 10, pp. 5396-5410, Oct. 2014.

[7] N. Seifi, R. W. Heath, M. Coldrey, and T. Svensson, "Adaptive Multicell 3-D Beamforming in Multiantenna Cellular Networks," IEEE Transactions on Vehicular Technology, vol. 65, no. 8, pp. 6217-6231, Aug. 2016.

[8] L. Zhu, J. Zhang, Z. Xiao, X. Cao, D. O. Wu, and X.-G. Xia, "3-D Beamforming for Flexible Coverage in Millimeter-Wave UAV Communications," IEEE Wireless Communications Letters, vol. 8, no. 3, pp. 837-840, June 2019.

[9] W. Yi, Y. Liu, E. Bodanese, A. Nallanathan, and G. K. Karagiannidis, "A Unified Spatial Framework for UAV-Aided MmWave Networks," IEEE Transactions on Communications, vol. 67, no. 12, pp. 8801-8817, Dec. 2019.

[10] A. B. Shallah et al., "Recent Developments of Butler Matrix From Components Design Evolution to System Integration for 5G Beamforming Applications: A Survey," IEEE Access, vol. 10, pp. 88434-88456, 2022.

[11] Y. Huang, Q. Wu, T. Wang, G. Zhou, and R. Zhang, "3D Beam Tracking for Cellular-Connected UAV," IEEE Wireless Communications Letters, vol. 9, no. 5, pp. 736-740, May 2020.

[12] C. You and R. Zhang, "3D Trajectory Optimization in Rician Fading for UAV-Enabled Data Harvesting," IEEE Transactions on Wireless Communications, vol. 18, no. 6, pp. 3192-3207, June 2019.

[13] C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. Hoboken, NJ, USA: Wiley, 2016.

[14] C. You and R. Zhang, "Hybrid Offline-Online Design for UAV-Enabled Data Harvesting in Probabilistic LoS Channels," IEEE Transactions on Wireless Communications, vol. 19, no. 6, pp. 3753-3768, June 2020.

[15] Y. Zhang, Z. Mou, F. Gao, J. Jiang, R. Ding, and Z. Han, "UAV-Enabled Secure Communications by Multi-Agent Deep Reinforcement Learning," IEEE Transactions on Vehicular Technology, vol. 69, no. 10, pp. 11599-11611, Oct. 2020.

[16] B. Ning, Z. Chen, Z. Tian, C. Han, and S. Li, "A Unified 3D Beam Training and Tracking Procedure for Terahertz Communication," IEEE Transactions on Wireless Communications, vol. 21, no. 4, pp. 2445-2461, April 2022.

[17] W. Tang, H. Zhang, Y. He, and M. Zhou, "Performance Analysis of Multi-Antenna UAV Networks With 3D Interference Coordination," IEEE Transactions on Wireless Communications, vol. 21, no. 7, pp. 5145-5161, July 2022.

[18] N. Varshney and S. De, "Design Optimization for UAV Aided Sustainable 3D Wireless Communication at mmWaves," IEEE Transactions on Vehicular Technology, vol. 72, no. 3, pp. 3274-3287, March 2023.

[19] E. T. Michailidis, N. Nomikos, P. Trakadas, and A. G. Kanatas, "Three-Dimensional Modeling of mmWave Doubly Massive MIMO Aerial Fading Channels," IEEE Transactions on Vehicular Technology, vol. 69, no. 2, pp. 1190-1202, Feb. 2020.

[20] N. Seifi, R. W. Heath, M. Coldrey, and T. Svensson, "Adaptive Multicell 3-D Beamforming in Multiantenna Cellular Networks," IEEE Transactions on Vehicular Technology, vol. 65, no. 8, pp. 6217-6231, Aug. 2016.

[21] W. Junsheng, C. Yawen, L. Zhaoming, W. Xiangming, and W. Zifan, "A Low-Complexity Beam Searching Method for Fast Handover in MmWave Vehicular Networks," 2019 IEEE Wireless Communications and Networking Conference Workshop (WCNCW), Marrakech, Morocco, 2019, pp. 1-6.

[22] V. Kristem et al., "3D MIMO Outdoor-to-Indoor Propagation Channel Measurement," IEEE Transactions on Wireless Communications, vol. 16, no. 7, pp. 4600-4613, July 2017.

[23] S. Ju, Y. Xing, O. Kanhere, and T. S. Rappaport, "Millimeter Wave and Sub-Terahertz Spatial Statistical Channel Model for an Indoor Office Building," IEEE Journal on Selected Areas in Communications, vol. 39, no. 6, pp. 1561-1575, June 2021.

[24] P. Zhou, X. Fang, Y. Fang, Y. Long, R. He, and X. Han, "Enhanced Random Access and Beam Training for Millimeter Wave Wireless Local Networks With High User Density," IEEE Transactions on Wireless Communications, vol. 16, no. 12, pp. 7760-7773, Dec. 2017.

[25] B. You, I.-H. Lee, and H. Jung, "Optimal Subset Size Analysis of Randomized Analog Beamforming Using Uniform Planar Arrays in mmWave Networks," IEEE Wireless Communications Letters, vol. 10, no. 7, pp. 1414-1418, July 2021.

[26] Z. Lin, T. Lv, W. Ni, J. A. Zhang, J. Zeng, and R. P. Liu, "Joint Estimation of Multipath Angles and Delays for Millimeter-Wave Cylindrical Arrays With Hybrid Front-Ends," IEEE Transactions on Wireless Communications, vol. 20, no. 7, pp. 4631-4645, July 2021.

[27] Z. Wang, F. Zhang, H. Gao, O. Franek, G. F. Pedersen, and W. Fan, "Over-the-Air Array Calibration of mmWave Phased Array in Beam-Steering Mode Based on Measured Complex Signals," IEEE Transactions on Antennas and Propagation, vol. 69, no. 11, pp. 7876-7888, Nov. 2021.

[28] Q. Sultan, M. S. Khan, and Y. S. Cho, "Fast 3D Beamforming Technique for Millimeter-Wave Cellular Systems With Uniform Planar Arrays," IEEE Access, vol. 8, pp. 123469-123482, 2020.

[29] M. Sousa, A. Alves, P. Vieira, M. P. Queluz, and A. Rodrigues, "Analysis and Optimization of 5G Coverage Predictions Using a Beamforming Antenna Model and Real Drive Test Measurements," IEEE Access, vol. 9, pp. 101787-101808, 2021.

[30] Y. Lu, M. Koivisto, J. Talvitie, M. Valkama, and E. S. Lohan, "Positioning-Aided 3D Beamforming for Enhanced Communications in mmWave Mobile Networks," IEEE Access, vol. 8, pp. 55513-55525, 2020.

[31] W. Yi, Y. Liu, Y. Deng, and A. Nallanathan, "Clustered UAV Networks With Millimeter Wave Communications: A Stochastic Geometry View," IEEE Transactions on Communications, vol. 68, no. 7, pp. 4342-4357, July 2020.

[32] W. Wu, N. Cheng, N. Zhang, P. Yang, W. Zhuang, and X. Shen, "Fast mmWave Beam Alignment via Correlated Bandit Learning," IEEE Transactions on Wireless Communications, vol. 18, no. 12, pp. 5894-5908, Dec. 2019.

[33] J. Song, J. Choi, and D. J. Love, "Common Codebook Millimeter Wave Beam Design: Designing Beams for Both Sounding and Communication With Uniform Planar Arrays," IEEE Transactions on Communications, vol. 65, no. 4, pp. 1859-1872, April 2017.

[34] N. J. Myers, A. Mezghani, and R. W. Heath, "Swift-Link: A Compressive Beam Alignment Algorithm for Practical mmWave Radios," IEEE Transactions on Signal Processing, vol. 67, no. 4, pp. 1104-1119, Feb. 15, 2019.

[35] W. Attaoui, K. Bouraqia, and E. Sabir, "Initial Access & Beam Alignment for mmWave and Terahertz Communications," IEEE Access, vol. 10, pp. 35363-35397, 2022.

[36] J. Zhang, X. Yu, and K. B. Letaief, "Hybrid Beamforming for 5G and Beyond Millimeter-Wave Systems: A Holistic View," IEEE Open Journal of the Communications Society, vol. 1, pp. 77-91, 2020.

[37] X. Song, T. Kühne, and G. Caire, "Fully-/Partially-Connected Hybrid Beamforming Architectures for mmWave MU-MIMO," IEEE Transactions on Wireless Communications, vol. 19, no. 3, pp. 1754-1769, March 2020.

[38] A. Mazin, M. Elkourdi, and R. D. Gitlin, "Accelerating Beam Sweeping in mmWave Standalone 5G New Radios Using Recurrent Neural Networks," 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall), Chicago, IL, USA, 2018, pp. 1-4.

[39] J. Liu et al., "Initial Access Mobility and User-Centric Multi-Beam Operation in 5G New Radio," IEEE Communications Magazine, vol. 56, no. 3, pp. 35-41, March 2018.

[40] Amdocs, "Massive MIMO Beamforming Data Sheet," Nov. 2021.

[41] E. Rastorgueva-Foi, M. Costa, M. Koivisto, K. Leppänen, and M. Valkama, "User Positioning in mmW 5G Networks Using Beam-RSRP Measurements and Kalman Filtering," 2018 21st International Conference on Information Fusion (FUSION), Cambridge, UK, 2018, pp. 1-7.

[42] P. Auer, N. Cesa-Bianchi, and P. Fischer, "Finite-Time Analysis of the Multi-Armed Bandit Problem," Machine Learning, vol. 47, no. 2, pp. 235–256, 2002.

[43] M. B. Booth, V. Suresh, N. Michelusi, and D. J. Love, "Multi-Armed Bandit Beam Alignment and Tracking for Mobile Millimeter Wave Communications," IEEE Communications Letters, vol. 23, no. 7, pp. 1244-1248, July 2019.

[44] J. Zhang, Y. Huang, Y. Zhou, and X. You, "Beam Alignment and Tracking for Millimeter Wave Communications via Bandit Learning," IEEE Transactions on Communications, vol. 68, no. 9, pp. 5519-5533, Sept. 2020.

[45] M. Hashemi, A. Sabharwal, C. E. Koksal, and N. B. Shroff, "Efficient Beam Alignment in Millimeter Wave Systems Using Contextual Bandits," IEEE INFOCOM 2018 - IEEE Conference on Computer Communications, Honolulu, HI, USA, 2018, pp. 2393-2401.

[46] R. Gupta, K. Lakshmanan, and A. K. Sah, "Beam Alignment for mmWave Using Non-Stationary Bandits," IEEE Communications Letters, vol. 24, no. 11, pp. 2619-2622, Nov. 2020.

[47] C. Liu, L. Zhao, M. Li, and L. Yang, "Adaptive Beam Search for Initial Beam Alignment in Millimetre-Wave Communications," IEEE Transactions on Vehicular Technology, vol. 71, no. 6, pp. 6801-6806, June 2022.

[48] Y. Wei, Z. Zhong, and V. Y. F. Tan, "Fast Beam Alignment via Pure Exploration in Multi-Armed Bandits," IEEE Transactions on Wireless Communications, vol. 22, no. 5, pp. 3264-3279, May 2023.

[49] P. Susarla, B. Gouda, Y. Deng, M. Juntti, O. Silvén, and A. Tölli, "Learning-Based Beam Alignment for Uplink mmWave UAVs," IEEE Transactions on Wireless Communications, vol. 22, no. 3, pp. 1779-1793, March 2023.

[50] A. Sneh, S. Darak, S. S. Ram, and M. Hanawal, "Radar Enhanced Multi-Armed Bandit for Rapid Beam Selection in Millimeter Wave Communications," IEEE Communications Letters, vol. 27, no. 9, pp. 2441-2445, Sept. 2023.

[51] A. Kumar, A. Roy, and R. Bhattacharjee, "Actively Adaptive Multi-Armed Bandit Based Beam Tracking for mmWave MIMO Systems," 2024 IEEE Wireless Communications and Networking Conference (WCNC), Dubai, United Arab Emirates, 2024, pp. 1-6.

[52] G. Ghatak, "Best Arm Identification Based Beam Acquisition in Stationary and Abruptly Changing Environments," IEEE Transactions on Signal Processing, vol. 72, pp. 670-685, 2024.

[53] M. Arai and M. Hasegawa, "Two-dimensional Beam Selection for Multi-user Massive MIMO System Based on Multi-armed Bandit Algorithm," 2024 International Conference on Artificial Intelligence in Information and Communication (ICAIIC), Osaka, Japan, 2024, pp. 484-489.

[54] X. Song, S. Haghighatshoar, and G. Caire, "Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers," IEEE Transactions on Wireless Communications, vol. 18, no. 3, pp. 1518-1533, March 2019.

[55] "Introduction to Millimeter Wave Technology," 2CM Technology, available at: https://www.2cm.com.tw/2cm/zh-tw/tech/A540D94709A74EF7BE05F4BFF1D54451

[56] "Elevation Beamforming & Full Dimension MIMO," 3G4G Blog, available at: https://blog.3g4g.co.uk/2014/09/elevation-beamforming-full-dimension.html

[57] S. Yu, N. Kou, J. Jiang, Z. Ding, and Z. Zhang, "Beam Steering of Orbital Angular Momentum Vortex Waves With Spherical Conformal Array," IEEE Antennas and Wireless Propagation Letters, vol. 20, no. 7, pp. 1244-1248, July 2021.

[58] M. R. Akdeniz et al., "Millimeter Wave Channel Modeling and Cellular Capacity Evaluation," IEEE Journal on Selected Areas in Communications, vol. 32, no. 6, pp. 1164-1179, June 2014.

[59] S. He, J. Wang, Y. Huang, B. Ottersten, and W. Hong, "Codebook-Based Hybrid Precoding for Millimeter Wave Multiuser Systems," IEEE Transactions on Signal Processing, vol. 65, no. 20, pp. 5289-5304, 15 Oct. 2017.

[60] I. A. Hemadeh, K. Satyanarayana, M. El-Hajjar, and L. Hanzo, "Millimeter-Wave Communications: Physical Channel Models, Design Considerations, Antenna Constructions, and Link-Budget," IEEE Communications Surveys & Tutorials, vol. 20, no. 2, pp. 870-913, Secondquarter 2018.

[61] J. Cioffi and T. Kailath, "Fast, Recursive-Least-Squares Transversal Filters for Adaptive Filtering," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 2, pp. 304-337, April 1984.

[62] Alle-Jan van der Veen, "Array Signal Processing," Spring 2022.

[63] Simon Haykin, "Adaptive Filter Theory," 2002.

[64] https://www.mathworks.com/help/phased/ref/sensorarrayanalyzer-app.html