針對多重輸入輸出天線系統，許多低複雜度之偵測演算法相繼被提出以克服傳統 ML 解碼搜尋上的高複雜度問題。然而目前許多研究，都顯示ML解碼方法已經遇到瓶頸，故本篇論文將會討論近似ML解碼效能的演算法在多重輸入多重輸出系統。
在本篇論文中，首先我們將介紹幾種低運算複雜度的偵測定理，包含 ZF 和MMSE，我們將結合ZF和MMSE的想法介紹連續干擾消除 (SIC) 的方法來改善偵測錯誤的機率。另一方面，在本篇論文介紹到球體解碼，球體解碼為目前簡化多輸入輸出系統之運算搜尋的理想演算法，同時也能達到最佳的 ML 偵測效能。
在介紹完傳統的解碼方法後，本篇論文將會介紹三種方向的演算法，第一個方向就是探討如何降低球體解碼的尋找點數，第二種方向將會介紹許多接近ML解碼效能的解碼方法，第三種方向將會介紹接近傳統OSIC演算法效能的方法
最後，本論文將會做個總整理，整理出每一種演算法優點缺點，且將來可以發展的方向。以提供以後對本篇論文有興趣者，繼續研究之目標。

For multiple-input multiple-output (MIMO) antenna systems, there are many low complexity detection algorithms mentioned by everyone in order to solve the traditional high complexity ML decoder algorithm.
However, most of the researches indicate that it is difficult to reduce the complexity of the traditional high ML decoder algorithm, so in this thesis, we will discuss that the algorithm of near ML performance for multiple-input multiple-output (MIMO) antenna systems.
In this thesis, we give a brief introduction to suboptimal MIMO detection including zero-forcing (ZF) and minimum mean-square error (MMSE) to reduce the high complexity of ML detection. And then, successive interference cancellation (SIC) technique is applied to improve the bit error rate performance. To achieve the ML detection, we will introduce sphere decoding.
After introducing traditional detection algorithm, in this thesis, we will introduce three algorithms. At first, we propose sphere decoding combined with re-arranged search order, such that the tree-search complexity can be further reduce, the second we will propose near ML performance, the third we will propose near OSIC performance.
Finally, we focus on the advantage and disadvantage of the detection algorithm we propos, and the directions in the future in order to offer the researchers who are interested to my thesis.

[1] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun., vol.6, no.3, pp.311-335, 1998.
[2] S.M. Alamouti, “A simple transmit diversity technique for wireless communication ,”Selected Areas in Communication, IEEE Jounal on, vol. 16, pp. 1451-1458, 1998.
[3] D. Gesbert, M. Shafi, S. Da-shan, P.J. Smith, and A. Naguib, “From theory to practice: an overview of MIMIO space-time coded wireless systems ,” Selected Areas in Communication, IEEE Jounal on, vol. 21, pp. 281-302, 2003.
[4] J. Benesty, Y. Huang, and J. Chen, “A fast recursive algorithm for optimum sequential signal detection in BLAST system,” IEEE Trans. Signal Process., vol. 51, pp. 1722-1731, Jul. 2003.
[5] M. Damen, H.El Gamal, and G. Caire, “On maximum-likelihood detection and the search for the closest lattice point,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2389-2402, Oct. 2003.
[6] B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm I. Expected complexity,” Signal Processing, IEEE Transactions on see also Acoustics, Speech, and Signal Processing, IEEE Transactions on], vol. 53, pp. 2806-2818, 2005.
[7] Thomas J. Richardson and Rüdiger L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding ,” IEEE Trans. on Information Theory, vol. 47, no. 2, pp. 599-616, February 2001.
[8] J. Chen and M. P. C. Forssorier, “Near-optimum universal belief propagation based decoding of low-density parity check codes,” IEEE Commun. Letters, vol. 10, no.6, June 2006.
[9] H. Vikalo, B. Hassibi, and P. Stoica, “Efficient joint maximum-likelihood channel estimation and signal detection,” Wireless Communications, IEEE Transactions., vol. 5, no. 7, July 2006.
[10] A. M. Chan, and I. Lee, “A new reduced-complexity sphere decoder for multiple antenna systems,” in Proc. IEEE Int. Conf. Commun., vol. 1, pp. 460-464, 28 Apr.-2 May 2002.
[11] D. Pham, K. R. Pattipati, P. K. Willett, and L. Jie, "An improved complex sphere decoder for V-BLAST systems," Signal Processing Letters, IEEE, vol. 11, pp. 748-751, 2004.
[12] B.Kim and I.-C. Pack "K-best MIMO detection base on interleaving of distributed sorting," Electronics Letters, IEEE, vol. 44 No. 1 3rd. January 2008.