毫米波 (Millimeter wave) 系統被視為未來無線通訊協定的重要應用，可以提供每秒十億位元的高資料速率傳輸性能，然而在此系統的高頻段中將引入巨大的傳輸損耗使得訊號品質大幅下降，則波束成型 (Beamforming) 被視為毫米波系統不可或缺的關鍵技術。此外，無線通訊會受到環境的影響產生多路徑傳播效應，尤當接收端屬移動目標源更會使通道衍生時變現象並迫使波束校準的困難度增加，因此訊號的出發角 (Angle of Departure, AoD) 與入射角 (Angle of Arrival, AoA) 的估計與追蹤儼然成為毫米波系統的核心議題。本論文考量一多輸入多輸出 (Multiple-Input MultipleOutput, MIMO) 的均勻線性陣列 (Uniform Linear Array, ULA) 的天線架構，以分時 (Time division) 波束搜索 (Beam searching) 的方式對空間進行初始的探測，進而透過輔助波束對 (Auxiliary BeamPair, ABP) 的數值技巧，根據訊號強度做多路徑的檢測並估計角度資訊。而為克服時變現象引發傳送及接收端的波束失準或不匹
配，我們以區塊衰弱通道的環境為基礎並提出無跡卡爾曼濾波器(Unscented Kalman filter) 自適應演算法逐每個傳輸資源塊進行高效
率的波束追蹤 (Beam tracking)，並利用模擬結果進行性能分析與討
論。

The millimeter wave (mmWave) communication is deemed as
a promising technology for the approaching generation of wireless communications, which can provide high data rate transmission over multi-gigabit per second. However, the mmWave spectrum introduces high propagation attenuation that significantly degrades signal quality, and thus, the beamforming technology becomes indispensable for a mmWave
system. Moreover, there are several uncertainties in wireless communications like the multipath propagation effect and especially, the moving mobile equipment generates fast time-varying channels and makes the beam alignment more inconvenient in the real time environment. Therefore, estimation and tracking of angle-of-departure (AoD) and angle-ofarrival (AoA) are obviously the major issue for a mmWave system. This thesis considers a multiple antennas system based on a uniform linear array (ULA) structure. We propose a beam search procedure in a time division manner for initialization, utilizing the auxiliary beam pair (ABP)
nu-merical technique to perform multipath detection and estimating angle information based on signal strength. Furthermore, to overcome the beam misalignment or mismatch resulted from the time-varying channel, we employ the unscented Kalman filter to adaptively perform efficient
beam tracking over a block fading channel. Finally, we demonstrate the proposed system with computer simulation results and performance analysis in a typical mmWave environment.

[1] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile
broadband systems,” IEEE Communications Magazine, vol. 49,
no. 6, pp. 101–107, 2011.
[2] 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, 2013.
[3] S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A. Thomas, and
A. Ghosh, “Millimeter wave beamforming for wireless backhaul
and access in small cell networks,” IEEE Transactions on Communications, vol. 61, no. 10, pp. 4391–4403, 2013.
[4] T. S. Rappaport, Y. Xing, G. R. MacCartney, A. F. Molisch, E. Mellios, and J. Zhang, “Overview of millimeter wave communications
for fifth-generation (5g) wireless networks—with a focus on propagation models,” IEEE Transactions on Antennas and Propagation,
vol. 65, no. 12, pp. 6213–6230, 2017.
[5] “Ieee draft amendment to ieee standard for information technology–
telecommunications and information exchange between systems–
local and metropolitan area networks–specific requirements–part
15.3: Wireless medium access control (mac) and physical layer
(phy) specifications for high rate wireless personal area networks
(wpans): Amendment 2: Millimeter-wave based alternative physical layer extension,” IEEE Unapproved Draft Std P802.15.3c/D08,
Mar 2009, 2009.
[6] “Ieee standard for information technology–telecommunications and
information exchange between systems–local and metropolitan area
networks–specific requirements-part 11: Wireless lan medium access control (mac) and physical layer (phy) specifications amendment 3: Enhancements for very high throughput in the 60 ghz band,”
IEEE Std 802.11ad-2012 (Amendment to IEEE Std 802.11-2012,
as amended by IEEE Std 802.11ae-2012 and IEEE Std 802.11aa2012), pp. 1–628, 2012.
[7] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath,
“Spatially sparse precoding in millimeter wave mimo systems,”
IEEE Transactions on Wireless Communications, vol. 13, no. 3, pp.
1499–1513, 2014.
[8] R. W. Heath, N. González-Prelcic, S. Rangan, W. Roh, and A. M.
Sayeed, “An overview of signal processing techniques for millimeter wave mimo systems,” IEEE Journal of Selected Topics in Signal
Processing, vol. 10, no. 3, pp. 436–453, 2016.
[9] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Channel
estimation and hybrid precoding for millimeter wave cellular systems,” IEEE Journal of Selected Topics in Signal Processing, vol. 8,
no. 5, pp. 831–846, 2014.
[10] L. Dai, X. Gao, S. Han, I. Chih-Lin, and X. Wang, “Beamspace
channel estimation for millimeter-wave massive mimo systems with
lens antenna array,” in 2016 IEEE/CIC International Conference on
Communications in China (ICCC), 2016, pp. 1–6.
[11] J.-J. Park, J. Lee, K.-W. Kim, and M.-D. Kim, “Large- and smallscale fading characteristics of mmwave hst propagation channel
based on 28-ghz measurements,” in 2021 15th European Conference on Antennas and Propagation (EuCAP), 2021, pp. 1–5.
[12] A. Alkhateeb, G. Leus, and R. W. Heath, “Compressed sensing based multi-user millimeter wave systems: How many measurements are needed?” in 2015 IEEE International Conference
on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp.
2909–2913.
[13] T. Kim and D. J. Love, “Virtual aoa and aod estimation for sparse
millimeter wave mimo channels,” in 2015 IEEE 16th International
Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2015, pp. 146–150.
[14] D. Zhu, J. Choi, and R. W. Heath, “Auxiliary beam pair enabled
aod and aoa estimation in closed-loop large-scale millimeter-wave
mimo systems,” IEEE Transactions on Wireless Communications,
vol. 16, no. 7, pp. 4770–4785, 2017.
[15] S. Noh, M. D. Zoltowski, and D. J. Love, “Multi-resolution codebook and adaptive beamforming sequence design for millimeter
wave beam alignment,” IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp. 5689–5701, 2017.
[16] J. He, T. Kim, H. Ghauch, K. Liu, and G. Wang, “Millimeter wave
mimo channel tracking systems,” in 2014 IEEE Globecom Workshops (GC Wkshps), 2014, pp. 416–421.
[17] S. Shaham, M. Kokshoorn, M. Ding, Z. Lin, and M. Shirvanimoghaddam, “Extended kalman filter beam tracking for millimeter
wave vehicular communications,” in 2020 IEEE International Conference on Communications Workshops (ICC Workshops), 2020, pp.
1–6.
[18] C. Zhang, D. Guo, and P. Fan, “Tracking angles of departure and
arrival in a mobile millimeter wave channel,” in 2016 IEEE International Conference on Communications (ICC), 2016, pp. 1–6.
[19] S. Jayaprakasam, X. Ma, J. W. Choi, and S. Kim, “Robust beamtracking for mmwave mobile communications,” IEEE Communications Letters, vol. 21, no. 12, pp. 2654–2657, 2017.
[20] P. Jungwirth and J. V. Monaco, “Digital signal processing: From
complex numbers to the hilbert transform,” in 2019 SoutheastCon,
2019, pp. 1–6.
[21] H. Van Trees, Optimum Array Processing: Part IV of Detection,
Estimation, and Modulation Theory, ser. Detection, Estimation, and
Modulation Theory. Wiley, 2002.
78
[22] Z. Sha, Z. Wang, and S. Chen, “Harmonic retrieval based baseband channel estimation for millimeter wave ofdm systems,” IEEE
Transactions on Vehicular Technology, vol. 68, no. 3, pp. 2668–
2681, 2019.
[23] P. Bello, “Characterization of randomly time-variant linear channels,” IEEE Transactions on Communications Systems, vol. 11,
no. 4, pp. 360–393, 1963.
[24] V. Va, H. Vikalo, and R. W. Heath, “Beam tracking for mobile millimeter wave communication systems,” in 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2016,
pp. 743–747.
[25] J. Lim, H.-M. Park, and D. Hong, “Beam tracking under highly
nonlinear mobile millimeter-wave channel,” IEEE Communications
Letters, vol. 23, no. 3, pp. 450–453, 2019.
[26] J. Meditch, Stochastic Optimal Linear Estimation and Control, ser.
Electronics Series. McGraw-Hill, 1969.
[27] M. Pätzold, Mobile Fading Channels, ser. Online access: EBSCO
Computers & Applied Sciences Complete. Wiley, 2002.
[28] S. Orfanidis, Electromagnetic Waves and Antennas. Sophocles J.
Orfanidis, 2016.
[29] K.-B. Yu and M. F. Fernández, “Robust adaptive monopulse processing for multiple observations with applications to ts-mimo
radar,” in 2020 IEEE 11th Sensor Array and Multichannel Signal
Processing Workshop (SAM), 2020, pp. 1–5.
[30] E. Wan and R. Van Der Merwe, “The unscented kalman filter for
nonlinear estimation,” in Proceedings of the IEEE 2000 Adaptive
Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 2000, pp. 153–158.
[31] S. G. Larew and D. J. Love, “Adaptive beam tracking with the unscented kalman filter for millimeter wave communication,” IEEE
Signal Processing Letters, vol. 26, no. 11, pp. 1658–1662, 2019.
[32] D. Yang, L.-L. Yang, and L. Hanzo, “Dft-based beamforming
weight-vector codebook design for spatially correlated channels in
the unitary precoding aided multiuser downlink,” in 2010 IEEE International Conference on Communications, 2010, pp. 1–5.
[33] F. W. Vook, A. Ghosh, E. Diarte, and M. Murphy, “5g new radio:
Overview and performance,” in 2018 52nd Asilomar Conference on
Signals, Systems, and Computers, 2018, pp. 1247–1251.
[34] K. Gao, M. Cai, D. Nie, B. Hochwald, J. N. Laneman, H. Huang,
and K. Liu, “Beampattern-based tracking for millimeter wave communication systems,” in 2016 IEEE Global Communications Conference (GLOBECOM), 2016, pp. 1–6.
[35] S. Wikipedia, Information Theory: Quantum Computer, NyquistShannon Sampling Theorem, Kolmogorov Complexity, Entropy,
Bra-Ket Notation, Metcalfe’s Law, Shannon-Hart.