巨量多輸入多輸出(Massive multiple-input multiple-output, Massive MIMO )系統可以提供高通訊可靠度、高效能、高頻譜效率和高容量，因此已經成為第五代(5G)行動通訊的研究熱點。在分時雙工模式中，用戶端發送領航序列進行通道估測時，為了避免細胞內干擾，用戶間的領航序列需要互相正交。但是由於時頻資源缺乏，相同的領航序列很可能在不同的細胞中重複使用，當基地台接收到這些來自相鄰細胞的非正交領航序列時就會造成干擾導致領航訊號污染(Pilot contamination)，此現象被認為是限制Massive MIMO系統性能的主要因素。本文針對具有領航訊號污染環境中，比較多種通道估測方法在不同環境下的通道估測性能。比較多種方法後，針對在多用戶及有限天線數場景中，本文提出協調式領航序列配置演算法搭配子空間投影方法的組合可以獲得較佳的估測性能。其概念就是利用無線訊號在角度域和功率域中的路徑分集，利用所有細胞基地台中的通道協方差訊息來最小化均方誤差，配置使用相同領航序列且彼此空間最不重疊的用戶，接著在利用貝葉斯方法消除在角度域中不重疊的干擾用戶，最後在透過子空間投影方法在功率域上抑制領航訊號汙染，增強通道估測的強健性。本文最後在未知通道資訊情況下，為了在領航訊號汙染環境中估測通道協方差訊息，將領航序列以兩階段式發送，並且對大維度的樣本通道協方差矩陣進行正規化，能夠以少量的觀測值估測樣本通道協方差矩陣，使得貝葉斯估測性能快速收斂。

Massive multiple-input multiple-output (Massive MIMO) system can provide high communication reliability, high performance, high spectral efficiency and high capacity, so it has become a research hotspot of the fifth generation (5G) mobile communication.In the time-division duplex mode, when the user sends the pilot sequence for channel estimation, in order to avoid intra-cell interference, the pilot sequences between users need to be orthogonal to each other. However, due to the lack of time-frequency resources, the same pilot sequence is likely to be reused in different cells. When the base station receives these non-orthogonal pilot sequences from adjacent cells, it will lead to the phenomenon of pilot contamination. This phenomenon is considered to be the main factor limiting the performance of Massive MIMO systems. This thesis compares the channel estimation performance of various channel estimation methods in different environments with pilot contamination. After comparing various methods, in the scenario of multi-user and limited number of antennas, this thesis proposes a combination of coordinated pilot assignment algorithm and subspace projection method to obtain better estimation performance. The concept is to use the path diversity of the wireless signal in the angle domain and the power domain, use the channel covariance information in all cell base stations to minimize the mean square error, configure the users who use the same pilot sequence and the least overlap each other in space, and then The Bayesian method is used to eliminate the least overlapping interfering users in the angle domain, and finally the pilot contamination is suppressed in the power domain through the subspace projection method to enhance the robustness of the channel estimation. Finally, in the case of unknown channel information, in order to estimate the channel covariance information in the pilot contamination environment, the pilot sequence is sent in two stages, and the large-dimensional sample channel covariance matrix is normalized. The sample channel covariance matrix can be estimated with a small number of observations, so that the Bayesian estimation performance converges quickly.

[1] G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Technical Journal , vol. 1, no. 2, pp. 41-59, 1996.
[2] G. J. Foschini and M. J. Gans, "On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas," Wireless Personal Communications, vol. 6, p. 311–335, Mar. 1998.
[3] P. Wolniansky, G. Foschini, G. Golden and R. Valenzuela, "V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel," Proc. URSI ISSSE, pp. 295-300, Sep. 1998.
[4] D. Tse and P. Viswanath, in Fundamentals of Wireless Communication, Cambridge University Press, 2005.
[5] L. Lu, G. Y. Li, A. L. Swindlehurst, A. Ashikhmin and R. Zhang, "An Overview of Massive MIMO: Benefits and Challenges," IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 5, pp. 742-758, Oct. 2014.
[6] N. Prasad, H. Zhang, H. Zhu and S. Rangarajan, "Multi-user MIMO scheduling in the fourth generation cellular uplink," Asilomar Conference on Signals, Systems and Computers, pp. 1855-1859, Nov. 2013.
[7] T. L. Marzetta, "Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas," IEEE Trans. Wireless Commun, vol. 9, no. 11, pp. 3590 - 3600, Nov. 2010.
[8] J. Hoydis, S. t. Brink and M. Debbah, "Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?," IEEE J. Sel. Areas Commun, vol. 31, no. 2, pp. 160 - 171, Feb. 2013.
[9] Cisco, "Cisco visual networking index: Global mobile data traffic forecast update , 2014–2019,," Feb 2015.
[10] E. Björnson, J. Hoydis and L. Sanguinetti, "Massive MIMO Has Unlimited Capacity," IEEE Trans. Wireless Commun, vol. 17, no. 1, pp. 574 - 590, Jan. 2018.
[11] E. G. Larsson, O. Edfors, F. Tufvesson and T. L. Marzetta, "Massive MIMO for next generation wireless systems," IEEE Commun. Mag., vol. 52, no. 2, pp. 186-195, Feb. 2014.
[12] H. Q. Ngo, in Massive MIMO: Fundamentals and System Designs, Linköping University Electronic Press, 2015.
[13] A. Tulino and S. Verdú, in Random Matrix Theory and Wireless Communications, Now Foundations and Trends, 2004.
[14] R. Knopp and P. Humblet, "Information capacity and power control in single-cell multiuser communications," in Proceedings IEEE International Conference on Communications ICC '95, Seattle, WA, USA, 1995.
[15] B. Hochwald, T. Marzetta and V. Tarokh, "Multiple-antenna channel hardening and its implications for rate feedback and scheduling," IEEE Transactions on Information Theory, vol. 50, no. 9, pp. 1893 - 1909, Sep. 2004.
[16] H. Huh, G. Caire, H. C. Papadopoulos and S. A. Ramprashad, "Achieving "Massive MIMO" Spectral Efficiency with a Not-so-Large Number of Antennas," IEEE Trans Commun, vol. 11, no. 9, p. 3226–3239, Sep. 2012.
[17] H. Q. Ngo, E. G. Larsson and T. L. Marzetta, "Energy and spectral efficiency of very large multiuser MIMO systems," IEEE Trans. Wireless Commun, vol. 61, no. 4, p. 1436–1449, Apr. 2013.
[18] J. Jose, A. Ashikhmin, T. L. Marzetta and S. Vishwanath, "Pilot contamination problem in multi-cell TDD systems," in 2009 IEEE International Symposium on Information Theory, Seoul, Korea (South), 2009.
[19] J. Jose, A. Ashikhmin, T. L. Marzetta and S. Vishwanath, "Pilot Contamination and Precoding in Multi-Cell TDD Systems," IEEE Trans. Wireless Commun., vol. 10, no. 8, p. 2640–2651, Aug. 2011.
[20] O. Elijah, C. Y. Leow, T. A. Rahman, S. Nunoo and S. Z. Iliya, "A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System," IEEE Communications Surveys & Tutorials, vol. 18, no. 2, pp. 905 - 923, SECOND QUARTER 2016.
[21] D. Chu, "Polyphase codes with good periodic correlation properties," IEEE Trans. Inf. Theory, vol. 18, no. 4, p. 531–532, Jul. 1972.
[22] S. Ali, Z. Chen and F. Yin, "Eradication of pilot contamination and zero forcing precoding in the multi-cell TDD massive MIMO systems," IET Journal on communications, vol. 11, no. 13, Sep. 2017.
[23] M. Hua, M. Wang, K. W. Yang and K. J. Zou, "Analysis of the frequency offset effect on Zadoff–Chu sequence timing performance," IEEE Trans Commun., vol. 62, no. 11, p. 4024–4039, Nov. 2014.
[24] S. Sesia, I. Toufik and M. Baker, LTE—The UMTS Long Term Evolution, Wiley online Library, 2009.
[25] A. J. Paulraj, R. Nabar and D. Gore, "Introduction to space-time wireless," Introduction to space-time wireless, Cambridge University Press, 2003.
[26] A. F. Molisch, Wireless Communications, New York, NY, USA:Wiley, 2010.
[27] S. M. Kay, in Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall, 1993.
[28] H. Q. Ngo, T. L. Marzetta and E. G. Larsson, "Analysis of the pilot contamination effect in very large multicell multiuser MIMO systems for physical channel models," in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’11), Prague, Czech Republic, May 2011.
[29] B. Gopalakrishnan and N. Jindal, "An analysis of pilot contamination on multi-user MIMO cellular systems with many antennas," in 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2011.
[30] F. Fernandes, A. Ashikhmin and T. L. Marzetta, "Inter-Cell Interference in Noncooperative TDD Large Scale Antenna Systems," IEEE Journal on Selected Areas in Communications, vol. 31, no. 2, pp. 192-201, Feb. 2013.
[31] Ö. Özdogan, E. Björnson and E. G. Larsson, "Massive MIMO With Spatially Correlated Rician Fading Channels," IEEE Transactions on Communications, vol. 67, no. 5, pp. 3234 - 3250, May. 2019.
[32] M. Schubert and H. Boche, "Solution of the multiuser downlink beamforming problem with individual SINR constraints," IEEE Transactions on Vehicular Technology, vol. 53, no. 1, pp. 18 - 28, Jan. 2004.
[33] X. Gao, O. Edfors, F. Rusek and F. Tufvesson, "Massive MIMO Performance Evaluation Based on Measured Propagation Data," IEEE Transactions on Wireless Communications, vol. 14, no. 7, pp. 3899 - 3911, Jul. 2015.
[34] H. Yin, L. Cottatellucci, D. Gesbert, R. R. Müller and G. He, "Robust Pilot Decontamination Based on Joint Angle and Power Domain Discrimination," IEEE Trans. Signal Process., vol. 64, no. 11, pp. 990-3003, Jun. 2016.
[35] J. H. L. S. Emil Björnson, in Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency, Now Publishers, 2018.
[36] H. Yin, D. Gesbert, M. Filippou and Y. Liu, "A Coordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems," IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp. 264 - 273, Feb. 2013.
[37] H. Yin, D. Gesbert and L. Cottatellucci, "Dealing with interference in distributed large-scale MIMO systems: A statistical approach," IEEE J. Sel. Topics Signal Process, vol. 8, no. 5, p. 942–953, Oct. 2014.
[38] M. A. Abu-Rgheff, in 5G Physical Layer Technologies, John Wiley & Sons Australia Lt, 2019.
[39] A. Adhikary, J. Nam, J.-Y. Ahn and G. Caire, "Joint Spatial Division and Multiplexing—The Large-Scale Array Regime," IEEE Trans. Inf. Theory, vol. 59, no. 10, p. 6441–6463, Oct. 2013.
[40] R. R. Müller, L. Cottatellucci and M. Vehkaperä, "Blind pilot decontamination," IEEE J. Sel. Topics Signal Process, vol. 8, no. 5, p. 773–786, Oct. 2014.
[41] L. Cottatellucci, R. R. Müller and M. Vehkapera, "Analysis of pilot decontamination based on power control," in Proc. IEEE Veh. Technol. Conf. (VTC), p. 1–5, Jun. 2013.
[42] H. Yin, L. Cottatellucci, D. Gesbert, R. R. Müller and G. He, "Pilot decontamination using combined angular and amplitude based projections in massive MIMO systems," Proc. IEEE 16th Workshop Signal Process. Adv. in Wireless Commun. (SPAWC), pp. 216-220, Jun. 2015.
[43] T.-L. Lee, T.-Y. Li and Z. Zeng, "A Rank-Revealing Method with Updating, Downdating, and Applications. Part II," SIAM. J. Matrix Anal. Appl., vol. 31, no. 2, 2009.
[44] Y. Deng and T. Ohtsuki, "Low-Complexity Subspace MMSE Channel Estimation in Massive MU-MIMO System," IEEE Access, vol. 8, pp. 124371 - 124381, Jul. 2020.
[45] V. Saxena, G. Fodor and E. Karipidis, "Mitigating Pilot Contamination by Pilot Reuse and Power Control Schemes for Massive MIMO Systems," in 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), Glasgow, UK, 2015.
[46] E. Björnson, L. Sanguinetti and M. Debbah, "Massive MIMO with imperfect channel covariance information," 2016 50th Asilomar Conference on Signals, Systems and Computers, pp. 974-978, Nov. 2016.
[47] N. Shariati, E. Björnson, M. Bengtsson and M. Debbah, "Low-complexity polynomial channel estimation in large-scale mimo with arbitrary statistics," IEEE J. Sel. Topics Signal Proc., vol. 8, no. 5, p. 815–830, Oct. 2014.
[48] O. Ledoit and M. Wolf, "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, vol. 88, no. 2, p. 365 – 411, 2004.
[49] T. S. Rappaport, in Wireless Communications: Principles and Practice, Englewood Cliffs, NJ, USA: Prentice-Hall PTR, 1996.