在大規模的多輸入-多輸出系統上，當訊雜比(SNR)很大時，傳統的線性預編碼方法像是Zero-forcing(ZF)有著近乎最佳化的效能表現，但對於大型矩陣來說，矩陣逆運算的複雜度通常會隨矩陣大小成立方性的增加。為了解決這個問題，我們提出了一個基於Neumann級數以及Jacobi迭代的預編碼方法，來趨近矩陣的逆運算，進而達到和傳統ZF預編碼幾乎一樣的效果。最後根據模擬結果，我們引入了曲線配適(Curve Fitting)，因應各種情況下找出最佳迭代數值的封閉表達式，並且比較其求出的數值與實際模擬結果之均方根誤差。

Conventional linear precoding schemes in massive multiple-input-multiple-output (MIMO) systems, such as Zero-forcing (ZF) precoding, have near-optimal performance but suffer from cubically-increased computational complexity due to the direct matrix inversion of large size. To solve this problem, we propose a modifying Neumann series and Jacobi iterative based precoding scheme to approximate the matrix inversion. The proposed precoding can approach the classical ZF precoding with negligible performance loss. According to simulation results, we conducted curve fitting to find a closed form which can provide the best iteration number for each case then we calculated the minimum root-mean-square error. Finally we also proposed a closed form for the best iteration number.

目錄
第一章 研究背景	1
第二章 簡介	4
2.1 現有技術介紹	4
2.2 主要技術優點	5
第三章 多使用者-大規模-多輸入-多輸出系統架構	7
3.1 系統架構介紹	7
3.3 混合類比和數位的波束成型架構	10
第四章 近乎最佳化預編碼器用於大規模-多輸入-多輸出系統	16
4.1迭代的方法	17
4.2基於Neumann級數的近似方法	19
4.3 提升近似 的準確度	21
4.4 降低複雜度的多項式配適	23
第五章 實驗模擬結果	25
5.1 模擬結果比較圖	25
5.2 觀察與發現	28
第六章 結論與未來研究方向	31
6.1結論	31
6.2未來研究方向	31
第七章 參考資料	32

 
圖目錄
圖1.1 5G的要求([2])	2
圖1.2 比較3G、4G、5G的最大資料傳輸量([2])	3
圖3.1多使用者-大規模-多輸入-多輸出系統架構([28])	7
圖3.2 多使用者-大規模-多輸入多輸出系統的全數位傳送端波束成型	9
圖3.3(a) 混合式預編碼裝載被動相位陣列天線架構	11
圖3.3(b) 混合式預編碼裝載主動相位陣列天線架構	12
圖5.1(a)N=256  K=16 Q=3 16QAM  SNR=0-30 dB	25
圖5.1(b)N=256  K=16 Q=3 64QAM  SNR=0-30 dB	26
圖5.2(a)N=64   K=16 Q=6 16QAM  SNR=0-30 dB	26
圖5.2(b)N=64   K=16 Q=6 64QAM  SNR=0-30 dB	27
圖5.3(a)N=128  K=16 Q=4 16QAM  SNR=0-30 dB	27
圖5.3(b)N=128  K=16 Q=4 64QAM  SNR=0-30 dB	28
圖5.4 三種配適方法在不同情況下所找出的最佳迭代數值(Q)	29

 
表目錄
表3.1 不同預編碼方法下的射頻元件總數量比較	15
表5.1 三種曲線配適的封閉表達式	29
表5.2 三種曲線配適求得的最佳和實際迭代數值之間的誤差值	30

[1] https://www.nttdocomo.co.jp/english/corporate/technology/whitepaper_5g“, DOCOMO
   5G White paper”, 2014
[2] http:// workshop.fantastic5g.com/wp-content/uploads/2015/06/“, 5G Vision: Services,
   Requirements and Key Enabling Technologies”, IEEE Vehicular Technology
   Conference(VTC),May 2015
[3] http://www.huawei.com/5gwhitepaper,“5G: A Technology Vision”, 2013
[4] 2016版通訊產業關鍵報告
[5] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, K.Higuchi,“Non-Orthogonal
   Multiple Access (NOMA) for Cellular Future Radio Access”, IEEE 77th Vehicular
   Technology Conference (VTC), pp. 1-5, June 2013
[6] M. Prytz, P. Karlsson, C. Cedervall, A. Bria, “Infrastructure Cost Benefits of Ambient
   Networks Multi-Radio Access”, IEEE 63rd, Vehicular Technology Conference (VTC), 
   pp. 648-652, May 2006
[7] G. Yuan et al., “Carrier Aggregation for LTE-Advanced Mobile Communication 
   Systems”, IEEE Communication Magazine, vol. 48, no. 2, pp. 88–93, Feb. 2010
[8] M. Jain et al., K.  Srinivasan, P. Sinha, “Practical, Real-time, Full Duplex Wireless”,
   IEEE 17th Annual International Conference on Mobile Computing and Networking 
   (MOBICOM), Sept. 2011
[9] S. F. Chou, T. C. Chiu, Y. J. Yu, A. C. Pang, “Mobile small cells deployment for next
   generation cellular networks”, IEEE Global Communications Conference
    (GLOBECOM), pp. 4852-4857, Dec. 2014
[10] P. M. Roodaki, F. Taghian, S. Bashirzadeh, M. Jalaali, “A survey of millimeter-wave
    technologies”, IEEE International Conference on Electrical and Control
    Engineering(ICECE), pp. 5726-5728,Sept. 2011
[11] W. Roh et al., “Millimeter-wave beamforming as an enabling technology for 5G
    cellular communications: Theoretical feasibility and prototype results”, IEEE
    Communications Magazine, vol. 52, no. 2, pp. 106–113, Feb. 2014
[12] E. G. Larsson, O. Edfors, F. Tufvesson, T. L. Marzetta, “Massive MIMO for Next
    Generation Wireless Systems”, IEEE Communications Magazine, vol.52, no. 2, pp.
    186-195, Feb. 2014
[13] L. Lu, G. Y. Li, A. L. Swindlehurst, A. Ashikmin, 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, April 2014
[14] K. J. Kim, K. J.Choi, S. R. Lee, K. S. Kim, “Multi-user massive MIMO for 
 	next-generation WLAN systems”, IET Electronics Letters, vol. 51, no. 10,pp.792-794,
    May 2015
[15] Q. H. Spencer, A. L. Swindlehurst, M. Haardt, “Zero-forcing methods for downlink
 	spatial multiplexing in multiuser MIMO channels”, IEEE Trans. on Signal 
    Processing, vol. 52, no. 2, pp. 461-471, Jan. 2004
[16] G. D. Galdo, M.Haardt, “Comparison of Zero-Forcing Methods for downlink spatial
 	multiplexing  multiuser MIMO channel”, IEEE 59thVehicular Technology Conference (VTC) , pp. 299-303, May 2004
[17] J. Hoydis, S. T. Brink, and M. Debbah, “Comparison of Linear Precoding Schemes
 	for Downlink Massive MIMO”, IEEE International Conference on Communications 	(ICC), pp. 2135-2139, June 2012
[18] P. Luo, M. Zhang, X. Zhang, G. Cai, D. Han, Q. Li, “Low Complexity Detection and
 	Precoding for Massive MIMO Systems”, IEEE Wireless Communications	and
	Networking Conference (WCNC), pp. 2857-2861, April 2013
[19] Y. Li, Y.H. Nam, B.L. Ng, “Zero-forcing Receiver in Uplink Massive MIMO” , IEEE
	Globecom Workshops (GC Wkshps), pp. 140-144, Dec. 2013
[20] S. Zarei, and W. Gerstacker, R.R. Muller, R. Schober, “Low-complexity linear			precoding for downlink large-scale MIMO systems”, IEEE 24th International  		Symposium on Personal Indoor and Mobile Radio Communications(PIMRC) ,
    pp.1119-1124,	Sept. 2015
[21] Y. Chen, C. Tellambura, “Performance Analysis of Maximum Ratio Transmission 
	with Imperfect Channel Estimation”, IEEE Communications Letters, vol. 9, no. 4, pp. 
    322-324, April 2005
[22] Z. Lu, J. Ning, Y. Zhang, T. Xie, W. Shen, “Richardson Method Based Linear 		    Precoding with Low Complexity for Massive MIMO Systems”, IEEE 81stVehicular Technology Conference (VTC), pp. 1-4, May 2015
[23] C.S. Park, Y.S. Byun, A. M. Bokiye, Y.H. Lee, “Complexity reduced zero-forcing
	beamforming in Massive MIMO systems”, IEEE Information Theory and
    Applications Workshop (ITA), pp. 1-5, Feb. 2014
[24] T. E. Bogale, L. B. Le, “Beamforming for Multiuser Massive MIMO Systems: Digital 	versus Hybrid Analog-Digital”, IEEE Global Communications Conference
    (GLOBECOM) , pp. 4066-4071, Dec. 2014
[25] S. Han, C. Lin, C. Rowell, Z. Xu, S. Wang, Z. Pan, “Large Scale Antenna System with
 	Hybrid Digital and Analog Beamforming Structure”, IEEE International Conference 
    on Communications. (ICC), pp.842-847, June 2014
[26] Y. Ren, Y. Wang, G. Xu, “Two-Stage Hybrid Precoding for Massive MIMO Systems 	”, IEEE 22nd International Conference on Telecommunications (ICT), pp. 294-297,
    April 2015
[27] L. Liang, W. Xu, X. Dong, “Low-Complexity Hybrid Precoding in Massive Multiuser 	MIMO Systems”, IEEE Wireless Communications Letters, vol. 3, no. 6, pp. 653-656, 
    Oct. 2014
[28] J. Ning, Z. Lu, T. Xie, J. Quan, “Low Complexity Signal Detector Based on SSOR 		Method for Massive MIMO Systems”, IEEE International Symposium on Broadband 	Multimedia Systems and Broadcasting (BMSB), pp. 1-4, June 2015
[29] L. Dai, X. Gao, X. Su, S. Han, Z. Wang, “Low-complexity soft-output signal detection 
based on Gauss-Seidel method for uplink multi-user large-scale MIMO systems”, IEEE Trans. on Vehicular Technology, vol. 64, no. 10, pp.4839-4845, Nov. 2014 
[30] H. Prabhu, F. R. Rusek, J. N.  Rodrigues, O. Edfors, “High Throughput Constant 		Envelope Pre-coder forMassive MIMO Systems”, IEEE International Symposium on 	Circuits and Systems (ISCAS), pp. 1502-1505, May2015
[31] Y. Ren, G. Xu, Y. Wang, X. Su, C. Li, “Low-complexity ZF precoding method for 		downlink of massive MIMO system”, IET Electronics Letters, vol. 51, no. 5, 
    pp.421-423, March 2015
[32] W. Shen, “An Introduction to Numerical Computation”, World Scientific Publishing.
    2015