目前行動通訊系統越來越普及的情況下，使用無線通訊的人日益增加，對於有限的無線頻譜來說除了進行有效的頻譜分配，要再更近一步的最大化頻譜利用率於是使用multi-input multi output(MIMO)技術，使能夠在空間中產生多個獨立且並行的無線通道同時傳輸資料，在頻寬不增加的情況之下進而提高了頻譜利用率並且再結合orthogonal frequency-division multiplexing(OFDM)調變技術，組成現在4G行動通訊實體層所使用的MIMO-OFDM系統。
現今較為廣泛討論的偵測器演算法可分為Mean Square Error-Successive Interference Cancellation (MMSIC)與LSD，而本論文主要研究List Sphere
Decoder LSD，並用更進一步的遞迴式偵測器(Detection)與解碼(Decoder)架構，在MIMO-OFDM的環境下使用LSD偵測器的演算法則，搭配上了外部編碼，目標在於能夠逼近最佳偵測器的效果。在多根天線傳送與接收的架構下，接收機若採用理想偵測器MAP，複雜度會隨著天線數成指數次方成長，不利於實際的應用，所以提出Sphere Decoder接收機的演算法，目標在於能夠接近MAP的效率，又可以減少其複雜度。並針對多天線展頻 (MIMO-Spreading) 環境下，提出LSD PLUS NLOGN解法，利於硬體實現。MIMO架構中再搭配外部編碼，接收端偵測機利用List Sphere Decoder 與外部解碼器做Soft的資訊交換，並做遞迴的動作，能達到最好的效果。
藉著特性曲線來分析LSD 接收機的特性，選擇適當的Candidates數搭配外部編碼。最後介紹MIMO-OFDM架構下，LSD PLUS NLOGN有效的分工解符碼及展頻碼。並且有效的趨近MAP 的效能。

Since the popularity of wireless online and wireless communications is increasing, the number of users has also increased. For the finite wireless spectrum, we have to divide wireless spectrum effectively and maximize spectrum efficiency. Then we can generate multiple independent parallel channels and transmit data simultaneously by using the multi-input multi-output (MIMO).Therefore using MIMO improves spectrum efficiency without increasing bandwidth. We can obtain the physical layer for 4G wireless communications by combining MIMO with orthogonal frequency-division multiplexing (OFDM).

There are two popular detection algorithms which are discussed widely, Minimum Mean Square Error-Successive Interference Cancellation (MMSE-SIC) and List Sphere Decoder (LSD). In this thesis, we focus on researching LSD in iterative detection and decoding schemes. The objective of my research is to approach the performance of MAP when LSD combined with outer encoder in MIMO-OFDM systems. In multiple-in multiple-out antennas environment, the complexity of MAP detector grows exponentially with the number of transmitter antennas, so we use the Sphere Decoder to reduce the complexity. In MIMO spreading situation, we proposed LSD PLUS NLOGN detection, which is also easier to implement in a practical hardware application. By using iterative methods with LSD, “soft” information were exchanged between detector and decoder, and the performance can be increased.

Finally, in MIMO-OFDM systems, LSD PLUS NLOGN detects the symbol and decodes spreading code efficiently. Moreover, it approaches the performance of MAP efficiently.

[1] G. J. Foschini, “Layered Space-Time Architecture for Wireless Communication in a Fading Environment When using Multiple Antennas,” Bell Labs Technical Journal, Vol.1, No.2, pp41-59, Autumn 1996.
[2] G.Caire, G. Taricco, and E.Biglieri, "Bit-interleaved coded modulation," IEEE Trans. Inf, Theory, vol.44, no.3, pp.927-946, May 1998.
[3] B.B. Hochwald and S. ten Brink, "Achieving near-capacity on a multiple-antenna channel," Communications, IEEE Trans. Commun., vol.51, no.3, pp. 389- 399, March 2003
[4] T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
[5] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1," in Proc. Int. Conf. Communications, pp.1064-1070, May 1993
[6] S. ten Brink, "Convergence behavior of iteratively decoded parallel concatenated codes," IEEE Trans. Commun., vol.49, no.10, pp.1727-1737, Oct 2001
[7] A.M. Chan, Inkyu Lee, "A new reduced-complexity sphere decoder for multiple antenna systems," IEEE Conf. Communications, vol.1, pp.460-464, 2002
[8] Jin Lee, Sungchung Park, Yuping Zhang, K.K.Parhi, and Sin-Chong Park, “Implementation Issues of a List Sphere Decoder” IEEE Conf, Signal process., vol.03, pp.3, 2006
[9] M. Myllyla, J. Antikainen, M. Juntti, and J.R. Cavallaro, "The effect of LLR clipping to the complexity of list sphere detector algorithms," IEEE Conf, Signals, Systems and Computers, pp.1559-1563, Nov. 2007
[10] L. G. Barbero and J. S. Thompson, “A fixed-complexity MIMO detector based on the complex sphere decoder,” IEEE Workshop on Signal Processing Advances forWireless Communications (SPAWC ’06). IEEE 7th Workshop on , pp.1-5, July 2010
[11] L. G. Barbero and J. S. Thompson, "Performance Analysis of a Fixed-Complexity Sphere Decoder in High-Dimensional Mimo Systems," Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference , vol.4, pp.4 , May 2006
[12] P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, “V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel,” in Proc. URSI International Symposium on Signals, Systems and Electronics (ISSSE ’98), Atlanta, pp. 295–300. Sept. 1998
[13] D. Wubben, R. Bohnke, V. Kuhn, and K. D. Kammeyer, "MMSE extension of V-BLAST based on sorted QR decomposition," Vehicular Technology Conference, 2003. VTC 2003-Fall. 2003 IEEE 58th , vol.1, pp. 508- 512, Oct. 2003
[14] M. Mohaisen, KyungHi Chang, "On Improving the Efficiency of the fixed-Complexity Sphere Decoder," Vehicular Technology Conference Fall (VTC 2009-Fall), 2009 IEEE 70th , pp.1-5, 20-23 Sept. 2009
[15] 3GPP, "3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 6)", TR 25.996 V6.1.0, 2003-09.
[16] WiMAX,“WiMAX Forum Mobile RCT- Wave 2 Amendment”, 2007-07
[17] Yu, Kai, Ottersten, Bjorn, “Models For MIMO Propagation Channels, A Review Summary”, Wiely Journal on Wireless Communications and Mobile Computing, July 2002
[18] D.S. Baum, J. Hansen, J. Salo, "An interim channel model for beyond-3G systems: extending the 3GPP spatial channel model (SCM)," Vehicular Technology Conference, 2005. VTC 2005-Spring. 2005 IEEE 61st , vol.5, pp. 3132- 3136, June 2005
[19] Barbero, L.G., Ratnarajah, T., Cowan, C., "A low-complexity soft-MIMO detector based on the fixed-complexity sphere decoder," IEEE Conf. Acoustics, Speech and Signal Processing, pp.2669-2672, April 2008
[20] B. Hassibi, H. Vikalo, "On the expected complexity of sphere decoding," IEEE Conf. Signals, Systems and Computers, vol.2, pp.1051-1055, 2001
[21] P. Robertson, E. Villebrun, P. Hoeher, "A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain," IEEE Conf. Communications, vol.2, pp.1009-1013, Jun 1995
[22] Ren Chien Chen, “Optimal design of iterative detection and decoding receivers
for MIMO-OFDM systems”, NTUST, July 2009
[23] De-Jhen Huang, “Gaussian Approximation MAP Decoder”,NTUST,EE
MC-LAB,July 2007.
[24] Huan-Chun Wang and De-Jhen Huang, “An Extremely Low Complexity MAP
Detector for Complex Signal”,NTUST.EE.MC-LAB,Jul.2007
[25] Hoondong Noh, Myoungseok Kim, Jaesang Ham Chungyong Lee, "A practical MMSE-ML detector for a MIMO SC-FDMA system," IEEE Communications Letters, vol.13, no.12, pp.902-904, Dec. 2009.