在這篇論文中，我們考慮多輸入多輸出正交分頻多工(Multiple-Input-Multiple-Output Orthogonal Frequency Division Multiplexing, MIMO-OFDM) 的系統，並模擬由 IEEE 802.15.3c 工作團隊所制定毫米波(mmWave)頻帶的通道模型。在毫米波頻帶中混合式波束成形(hybrid beamforming)被視為一種有效率的技術，但是需要在功耗與頻寬效益之間作出取捨。
波束成形可以分為完全連接式(fully connected)跟部分連接式(partially connected)架構。其中部分連接式的架構雖然有較差的頻寬效益，但它使用了較少的移相器(phase shifter)，因此更為節能。在現有的部分連接架構的研究中，大多都只考慮發射端的系統，還使用了高複雜度的演算法進行設計。
我們考慮的部分連接架構將整個天線陣列分成數個子陣列，每個子陣列分別與一些射頻鏈(RF chain)互相連結。基於子系統奇異質分解(sub-system SVD)，我們提出了一個低複雜度的設計方法。為了提升系統的表現，我們套用了動態天線陣列結構(dynamic antenna array structure)。最後，我們與既有的演算法做比較，可以得到我們所提出的演算法會具有比較低的複雜度和相當的效能。而在我們討論的架構中，若是適當的調整部分連接的架構，可以讓表現大量提升並且維持高節能的特性。

Although hybrid beamforming is considered efficient for use in millimeter-wave (mmWave) multiple-input–multiple-output (MIMO) systems, it introduces a trade-off between achievable spectral efficiency and power consumption. Beamforming structures can be fully or partially connected. Partially connected structures use a low number of phase shifters and thus serve as an energy-efficient solution for hybrid precoding, even though performance degradation could be introduced. Most previous studies on partially connected structures have focused only on transmitter designs, and previous precoder designs include iterative calculation, leading to high computational complexity.

In this thesis, we consider a new partially connected architecture for hybrid beamforming, where the antennas of the transmitter and receiver are separated into several sub-arrays, each of which is connected to a radio frequency chain group. A low-complexity algorithm based on sub-system singular value decomposition (SVD) is developed for determining the solution for multicarrier systems. The solution is then extended to a dynamic antenna array structure for better performance. Finally, the results are compared with those from previous studies. The channel model employed is the indoor mmWave channel model established by the IEEE 802.15.3c Task group, which includes line-of-sight and non-line-of-sight enviroments.

[1] N. Guo, R. C. Qiu, S. S. Mo, and K. Takahashi, “60-GHz millimeter-wave radio: Principle, technology, and new results,” EURASIP J. Wireless Commun. and Networking, vol. 2007, pp. 1–8, 2007.

[2] http://www.ieee802.org/15/pub/TG3c.html.

[3] T. S. Rappaport, E. Ben-Dor, J. N. Murdock, and Y. Qiao, “38 GHz and 60 GHz angledependent propagation for cellular & peer-to-peer wireless communications,” in Proc. IEEE Int. Conf. Commum., Ottawa, ON, Candada, Jun. 2012, pp. 4568–4573.

[4] R. W. Heath, Jr., N. Gonzalez-Prelcic, 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] A. Alkhateeb, G. Leus, and R. W. Heath, Jr., “Limited feedback hybrid precoding for multi-user millimeter wave systems,” IEEE Trans. Wireless Commun., vol. 14, no. 11, pp. 6481–6494, Nov. 2015.

[6] O. El Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath, Jr., “Spatially sparse precoding in millimeter wave MIMO systems,” IEEE Trans. Wireless Commun., vol. 13, no. 3, pp. 1499–1513, Mar. 2014.

[7] T. E. Bogale, L. B. Le, A. Haghighat, and L. Vandendorpe, “On the number of RF chains and phase shifters, and scheduling design with hybrid analog digital beamforming,” IEEE Trans. Wireless Commun., vol. 15, no. 5, pp. 3311–3326, May 2016.

[8] J. Li, L. Xiao, X. Xu, and S. Zhou, “Robust and low complexity hybrid beamforming for uplink multiuser mmWave MIMO systems,” IEEE Commun. Lett., vol. 20, no. 6, pp. 1140–1143, Jun. 2016.

[9] F. Sohrabi and W. Yu, “Hybrid digital and analog beamforming design for large-scale antenna arrays,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 501–513, Apr. 2016.

[10] O. E. Ayach, R. W. Heath, Jr., S. Rajagopal, and Z. Pi, “Multimode precoding in millimeter wave MIMO transmitters with multiple antenna sub-arrays,” in Proc. IEEE Global Commun. Conf., Atlanta, GA, Dec. 2013, pp. 3476–3480.

[11] J. Singh and S. Ramakrishna, “On the feasibility of codebook-based beamforming in millimeter wave systems with multiple antenna arrays,” IEEE Trans. Wireless Commun., vol. 14, no. 5, pp. 2670–2683, May 2015.

[12] C. Kim, T. Kim, and J. Y. Seol, “Multi-beam transmission diversity with hybrid beamforming for MIMO- OFDM systems,” in Proc. IEEE Global Commun. Conf. Workshops, Atlanta, GA, Dec. 2013, pp. 61–65.

[13] X. Gao, L. Dai, S. Han, C.-L. I, and R. W. Heath, Jr., “Energy-efficient hybrid analog and digital precoding for mmWave MIMO systems with large antenna arrays,” IEEE J. Sel. Areas Commun., vol. 34, no. 4, pp. 998–1009, Apr. 2016.

[14] X. Yu, J.-C. 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.

[15] S. Park, A. Alkhateeb, and R. W. Heath, Jr., “Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems,” IEEE Trans. Wireless Commun., vol. 16, no. 5, pp. 2907–2920, May 2017.

[16] T.-H. Tsai and C.-C. Chao, “Hybrid beamforming for indoor mmWave multi-carrier systems under sub-system SVD,” in Proc. IEEE Int. Symp. Personal Indoor Mobile Radio Commun., Montreal, QC, Canada, Oct. 2017, pp. 1–6.

[17] S.-K. Yong, et al., “TG3c channel modeling sub-committee final report,” IEEE doc.:IEEE 802.15-07-0584 -01-003c, Sep. 2010.

[18] S. Yoon, T. Jeon, and W. Lee, “Hybrid beam-forming and beam-switching for OFDM based wireless personal area networks,” IEEE J. Sel. Areas Commun., vol. 27, no. 8, pp. 1425–1432, Oct. 2009.

[19] X. Yu, J. Zhang, and K. B. Letaief, “Partially-connected hybrid precoding in mm-wave systems with dynamic phase shifter networks,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Sapporo, Japan, Jul. 2017, pp. 1–5.

[20] “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 Std 802.15.3c-2009 (Amendment to IEEE Std 802.15.3-2003), pp. c1–187, Oct. 2009.