為了滿足下一代5G行動通訊系統高資料傳輸速率的要求，巨量天線多重輸入多重輸出系統為目前最合適的選擇。但是使用巨量天線多重輸入多重輸出系統會使天線間距必須大幅縮小，否則沒有足夠空間擺放上百根的天線。這也同時代表著必須使用高頻段來傳輸。在5G行動通訊系統中，不同國家會使用不同頻帶來傳輸。例如，若使用頻段為24 GHz，而設計頻段為28 GHz，波瓣會產生變化並導致傳輸失敗。因此，我們將討論操作頻段差異造成的影響。首先，在均勻天線架構下比較不同天線間距造成的影響，並發現天線間距不足時會導致波瓣變寬，而天線間距過大時會導致光柵波瓣出現。我們認為光柵波瓣會造成極大的干擾，但在均勻天線架構下無法解決，因此嘗試非均勻天線架構。再來，比較了四種天線架構，包含了左右型、高頻對應天線間距在兩側的中間型、低頻對應天線間距在兩側的中間型與交錯型。並得出左右型天線架構效果最好。最後討論若在上述四種非均勻天線架構下，調整部分天線相位來壓制光柵波瓣，並得出左右型可以較好的壓制光柵波瓣。

To meet the high data rate requirements in the next generation 5G mobile communication system, massive multiple-input multiple-output (MIMO) systems is currently the most suitable choice. However, in massive MIMO systems, antenna spacing requires a significant reduction, or there is not enough space for hundreds of antennas. Simultaneously, it means that high frequency must be used for transmission. In the 5G mobile communication system, different countries provide different frequency bands for transmission. For example, if an operation band is 24 GHz, and the design band is 28 GHz, the beam will change that cause unsuccessful transmission. As a result, we discussed the influence of frequency discrepancy. First, we compared different antenna spacing on uniform antenna structure. We found the beam become wider when antenna spacing is insufficient and found grating lobe appeared when antenna spacing is excessive. Then, we considered the grating lobe as severe interference and tried to suppress it. But it doesn’t work on uniform antenna structure, so we tried the non-uniform antenna structure. Second, we compared four different antenna structures and invented that one side antenna structure is better than others. At last, continue the above four antenna structures with adjusting part of the antenna phase to suppress the grating lobe, and invent that one side antenna structure is better than others.

Abstract
摘要
LIST OF FIGURES
Chapter 1 Introduction-----------------------------------------1
Chapter 2 System Model-----------------------------------------4
2.1 Massive MIMO System-----------------------------------------4
2.2 Beam Pattern Construction-----------------------------------5
Chapter 3 The Effect of Frequency Discrepancy------------------9
3.1 Problem Construction----------------------------------------9
3.2 Impact of Beam Pattern--------------------------------------14
Chapter 4 Solution of the Effect of Frequency Discrepancy------20
4.1 Adjustment for Beam Direction Offset------------------------20
4.2 Proposed Antenna Structure Design---------------------------21
4.2.1 Antenna Structure Design without Phase Adjustment---------22
4.2.2 Antenna Structure Design with Phase Adjustment------------28
Chapter 5 Numerical Results------------------------------------37
5.1 Uniform Antenna Structure-----------------------------------38
5.2 Non-uniform Antenna Structure-------------------------------41
5.3 Non-uniform Antenna Structure with Phase Adjustment---------48
5.3.1 Main Lobe to Grating Lobe Peak Ratio Metric---------------49
5.3.2 BLR Metric------------------------------------------------58
Chapter 6 Conclusion-------------------------------------------65
References------------------------------------------------------66

[1] J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun., vol. 32, Jun. 2014, pp. 1065–1082.
[2] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,” IEEE Commun. Mag., vol. 52, no. 2, pp. 186–195, Feb. 2014.
[3] E. Dahlman, S. Parkvall and J. Sköld, 4G: LTE/LTE-Advanced for Mobile Broadband, Oxford, Academic Press, 2011.
[4] J. Gorisse, D. Morche, and J. Jantunen, “Wireless transceivers for gigabit-per-second communications,” IEEE International NEWCAS, June 2012, pp. 545–548.
[5] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broadband systems,” IEEE Commun. Mag., vol. 49, no. 6, Jun. 2011, pp. 101–107.
[6] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wireless networks: Potentials and challenges,” in Proc. IEEE, vol. 102, no. 3, Mar. 2014.
[7] W. Roh, J. Y. Seol, J. Park, B. Lee, J. Lee, Y. Kim, J. Cho; K. Cheun, and F. Aryanfar, “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results,” IEEE Commun. Mag., vol. 52, no. 2, Feb. 2014, pp. 106–113.
[8] 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 Trans. Commun., vol. 61, no. 10, Oct. 2013, pp. 4391–4403.
[9] M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antennas Propag., vol. 50, no. 12, Dec. 2002, pp. 1732–1742.
[10] Z. Xiao, T. He, P. Xia, and X.-G. Xia, “Hierarchical codebook design for beamforming training in millimeter-wave communication,” IEEE Trans. Wireless Commun., vol. 15, no. 5, May 2016, pp. 3380–3392.
[11] D. Yang, L.-L. Yang, and L. Hanzo, “DFT-based beamforming weightvector codebook design for spatially correlated channels in the unitary precoding aided multiuser downlink,” in Proc. IEEE Intern. Conf. Commun, vol. 1, May 2010, pp. 1–5.
[12] D. Qiao, H. Qian, and G. Y. Li, ‘‘Multi-resolution codebook design for twostage precoding in FDD massive MIMO networks,’’ in Proc. 18th IEEE Int. Workshop Signal Process. Adv. Wireless Commun. (SPAWC), Jul. 2017, pp. 1–5.
[13] D. Tse and P. Viswanath, “MIMO I: Spatial multiplexing and channel modeling,” in Proc. Fundamentals of Wireless Communication, May 2005, pp. 290–331.
[14] M. Khodier and C. Christodoulou, “Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization,” IEEE Trans. Antennas Propag., vol. 53, no. 8, Aug. 2005, pp. 2674–2679.
[15] G. Hua and S. S. Abeysekera, “Receiver design for range and Doppler sidelobe suppression using MIMO and phased-array radar,” IEEE Trans. Signal Process., vol. 61, no. 6, Mar. 2013, pp. 1315–1326.
[16] S. K. Goudos, V. Moysiadou, T. Samaras, K. Siakavara, and J. N. Sahalos, “Application of a comprehensive learning particle swarm optimizer to unequally spaced linear array synthesis with sidelobe level suppression and null control,” IEEE Trans. Antennas Propag., vol. 9, Sep. 2010, pp. 125–129.
[17] I. Cosovic, S. Brandes, and M. Schnell, “Subcarrier weighting: a method for sidelobe suppression in OFDM systems,” IEEE Commun. Lett., vol. 10, no. 6, June 2006, pp. 444–446.
[18] J. Lee, E. Tejedor, K. Ranta-Aho, H. Wang, K.-T. Lee, E. Semaan, E. Mohyeldin, J. Song, C. Bergljung, and S. Jung, “Spectrum for 5G: Global status, challenges, and enabling technologies,” IEEE Commun. Mag., vol. 56, no. 3, Mar. 2018, pp. 12–18.
[19] R. Chang, X. Wang, Z. Xue, and J. Liu, “Investigation on grating lobe suppression of uniform antenna array,” in Proc. IEEE International Conference on Microwave Technology & Computational Electromagnetics, May 2011, pp. 285–288.