本篇論文主要針對於大型Multiple Input Multiple Output (MIMO)系統提出新BP(Belief Propagation)檢測技術，傳統BP來解MIMO systems因loopy graph 而使傳遞的likelihood ratio彼此的相關性變強，所以會產生錯誤率表現不佳的問題，本論文是針對此問題提出新的BP演算法，新的演算法將原有可能產生通道矩陣轉作線性轉換，然後再針對轉換後的通道矩陣換來進行BP 檢測的動作，因此時轉換後的likelihood ratio彼此的相關性變小，所以會產生錯誤率表現也會比傳統的BP要好很多。並且另外使用EXIT chart估測模擬結果。模擬結果顯示我們所提出的新型BP在錯誤率接近 時，訊雜比(SNR)增益要比傳統的BP要好5dB以上，除此之外，我們所提出的BP演算法的收斂速度亦比傳統的BP收斂速度要快上兩倍以上，也與EXIT chart的估測結果符合。

This thesis proposes a new belief propagation (BP) detection algorithm for massive multiple input multiple output (MIMO) systems. The conventional BP detection algorithm for MIMO systems uses a loopy graph, which increases the mutual correlation of the likelihood ratios and thereby affecting BER performance. Our proposed BP algorithm addresses this problem by applying a linear transformation on the channel matrix before performing conventional BP detection. The likelihood ratios obtained by our proposed algorithm have lower mutual correlation and produce a much improved BER performance. We use EXIT charts to estimate simulation results. Simulation results show that, for 10-3≦BER≦10-4, our proposed BP detection algorithm has an SNR gain greater than 5 dB compared to the conventional BP algorithm. Besides, our proposed BP algorithm has a rate of convergence at least two times quicker than for conventional BP, which also corresponds to the results estimated by EXIT charts.

[1]3GPP, “Requirements for Further Advancements for E-UTRA,” TR36.913 v.8.0.0.
[2]IEEE 802.16 WG, “IEEE 802.16m System Description [Draft],” IEEE 802.16m-08/003r6, December 2008.
[3]A. Paulraj, R. Nabar, and D. Gore, Introduction to space-time wireless communication, New York: CAMBRIDGE University press,2003.
[4]H. Taoka and K. Higuchi, “Field experiment on 5-Gbit/s ultra-high-speed packet transmission using MIMO multiplexing in broadband packet radio access,” NTT DoCoMo Technical Journal, vol. 9, no. 2, pp. 25-31, Sep. 2007.
[5]J. Koivunen, “Characterisation of MIMO propagation channel in multi-link scenarios,” MS Thesis, Helsinki University of Technology, Dec. 2007.
[6]F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, “Scaling up MIMO: opportunities and challenges with very large arrays,” IEEE Signal Processing Mag., vol. 30, no1, pp. 40-60, Jan. 2013.
[7]T. Datta, N. Ashok Kumar, A. Chockalingam, and B. S. Rajan, “A novel monte-carlo-sampling-based receiver for large-scale uplink multiuser MIMO systems,” IEEE Trans. Veh. Technol., vol. 62, no. 7, pp. 3019-3037, Sep. 2013.
[8]M. Wu1, B. Yin, A. Vosoughi1, C. Studer, J. R. Cavallaro1, and C. Dick, “Approximate matrix inversion for high-throughput data detection in the large-scale MIMO uplink,” in Proc. IEEE Symposium on ISCAS, pp. 2155-2158, May2013.
[9]K. V. Vardhan, S. K. Mohammed, A. Chockalingam, and B. S. Rajan, “A low-complexity detector for large MIMO systems and multicarrier CDMA systems,” IEEE J. Sel. Areas Commun., vol. 26, no. 3, pp. 473-485, Apr. 2008.
[10]M. Wu, B. Yin, G. Wang, C. Dick, J. R. Cavallaro, and C. Studer, “Large-scale MIMO detection for 3GPP LTE：algorithms and FPGA implementations,” IEEE J. Sel. Areas Signal Processing, pp.1-15, 2013.
[11]S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, no.8, pp. 1451-1458, Oct. 1998.
[12]A. Bury, J. Egle, and J. Lindner, “Diversity comparison of spreading transforms for multicarrier spread spectrum transmission,” IEEE Trans. Commun., vol. 51, no5, pp. 774-781, May 2003.
[13]S. ten Brink and G. Kramer, “Design of repeat-accumulate codes for iterative detection and decoding,” IEEE Trans. Signal Processing, vol. 51, no. 11, pp. 2764-2772,Nov. 2003.
[14]S. ten Brink, G. Kramer, and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol. 52, no. 4, pp. 670-678, Apr. 2004.
[15]X. Wang and H.V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,”IEEE Trans. Commun, vol.47, no.7, pp.1046-1061,July 1999.
[16]J. Choi, “Acorrelation based analysis for approximate MAP detectors and iterative recievers,” IEEE Trans. Wireless Commun., vol.6, no.5, pp.1764-1773, May 2007.
[17]J.W. Choi, A.C. Singer , J. Lee, and N. I. Cho, “Improved linear soft-in soft-out detection via soft feedback successive interference cancellation, ”IEEE Trans. Comm.vol. 58, no.3, pp.1-12, March 2010.
[18]J. S. Yedidia, W. T. Freeman, and Y. Weiss, “Understanding belief propagation and its generalizations,” Mitsubishi Electric Research Labs, Tech. Rep. TR2001–22, Nov. 2001.
[19]B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel,” IEEE Trans. Commun., vol. 51, no. 3, pp. 389-399, Mar. 2003.
[20]W.R Gilks, S. Richardson, and D.J. Spiegelhalter, Markov Chain Monte Carlo in Pratice , U.K.: Chapman & hall, CAMBRIDGE , 1996.
[21]R. R. Chen, R. Peng, A. Ashikhmin, and B. Farhang-Boroujeny, “ Approaching MIMO capacity using bitwise markov chain monte carlo detection,” IEEE Trans. Commun., vol.58,no.2,pp. 423-428,Feb.2010.
[22]X. Mao, P. Amini, and B. F. Boroujeny, “Markov chain monte carlo MIMO detection methods for high signal-to-noise ratio regimes,” in Proc. Globecom, Washington, DC, USA, pp.3979-3983., Nov. 2007.
[23]R. J. McEliece, D. J. C. MacKay, and J.F. Cheng, “Turbo decoding as an instance of pearl’s belief propagation algorithm,” IEEE Jl. Sel. Areas in Commun., vol. 16, no.2, pp. 140-152, February 1998.
[24]D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399-431, March 1999.
[25]A. Montanari, B. Prabhakar, and D. Tse, “Belief propagation based multi-user detection,” in Proc. 43th Allerton Conf. on Commun., Control and Computing, Monticello, IL, USA, Sept. 2005.
[26]D. Guo and C.C. Wang. ”Multiuser detection of sparsely spread CDMA, ” IEEE
J. Select. Areas Commun., vol. 26, no.3, pp.421 - 431, April 2008.
[27]O. Shental, A. J. Weiss, N. Shental, and Y. Weiss, “Generalized belief propagation receiver for near-optimal detection of two-dimensional channels with memory,” in Proc. IEEE ITW 2004, pp. 225-229, Oct. 2004.
[28]G. Colavolpe and G. Germi, “On the application of factor graphs and the sum-product algorithm to ISI channels,” IEEE Trans. Commun., vol.53, no.5, pp. 818-825, May 2005.
[29]J.S. Garrido, R.J. Picchocki, and K. Maharatna. “Analog MIMO detection on the basis of belief propagation,” in Proc. IEEE IMS. in Circuits and Systems,, pp. 50-54, Aug. 2006.
[30]X. Yang and Y. Xiong, F. Wang, “An adaptive MIMO system based on unified belief propagation detection,” in Proc. IEEE ICC’2007, June 2007.
[31]M. Suneel, P. Som, A. Chockalingam, and B. S. Rajan, “Belief propagation based decoding of large non-orthogonal STBCs,” in Proc. IEEE ISIT2009, Seoul, pp.2003-2007,June-July 2009.
[32]P. Som, T. Datta, A. Chockalingam, and B.S. Rajan, “Improved large-MIMO detection based on damped belief propagation,” in Proc. IEEE ITW. 2010, pp. 1-5 , Jan. 2010.
[33]M. Pretti, “A message-passing algorithm with damping,” J. Stat. Mech., Nov. 2005, P11008.
[34]S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol.49, no.10, pp.1727-1737, Oct.2001.
[35]W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes, chap. 11, pp.564-574, New York: CAMBRIDGE University press,,2007.
[36]H. Bolcskei and A. J. Paulraj, “Fixed broadband wireless access: State of the art, challenges, and future directions, ”IEEE Comm. Mag., vol. 39, no. 1, pp. 100-108, 2001.
[37]M.R.D. Rodrigues, I. Chatzigeorgiou, I.J. Wassell, and R. Carrasco, “Performance analysis of turbo codes in quasi-static fading channels,” IET Commun., 2008, vol.2, no.3, pp. 449-461, Oct 2006.
[38]Z. Guo, and P. Nilsson, “Algorithm and implementation of the K-best sphere decoding for MIMO detection,” IEEE J. Select. Areas Commun., vol.24, no.3, pp.491-503, March 2006.
[39]A. D. Murugan, H. El Gamal, M. O. Damen, and G. Caire, “A unified framework for tree search decoding: rediscovering the sequential decoder,” IEEE Trans. Info. Theory, vol.52, no.3, pp.933-953, March 2006.