近幾年來, 快速且可靠地傳送大量資料的需求巨大地增加，多輸入多輸出的天線系統能提供有效的頻譜使用和高吞吐量。所以，找出快速且有效率地偵測器用在高速率的多輸入多輸出系統是非常重要的問題。球體解碼演算法雖然提供一個有效率的方法來得到最大概似解，但它的複雜度依然太高尤其是在低訊號雜訊比時。
在本篇論文中，我們介紹一個利用差分度量低複雜度的偵測演算法用於多天線多輸出系統。一開始我們會先介紹基本不同階數的差分度量和推導出的遞迴關係。之後我們也會介紹有用的工具，像是指示函式能用來確認一些初始數列的位元是否為最大概似解。藉由多個初始點的平行搜尋方法我們可以避免高階數的搜尋，這些工具都可以有效的降低複雜度。在第四章的最後，我們會應用這些方法在能量停止機制演算法上作為我們所提出的演算法並且比較4X4的天線系統和8X8的天線系統的表現與複雜度。

In recent years, with the increasing demand on transferring large amounts of data rapidly and reliably, the multiple-input multiple-output (MIMO) system has become more attractive in modern wireless communications. The MIMO system can provide efficient use of spectrum and achieves high throughput. Therefore, the study on finding fast and efficient detector for high-rate MIMO transmission is an important issue in wireless communications. The sphere decoding (SD) algorithm is an efficient approach to obtain the optimal maximum-likelihood (ML) detection. However, the SD algorithm is of much high complexity, especially at lower signal-to-noise ratio (SNR).
In this thesis, we first study on low-complexity detection algorithms for the MIMO system based on differential metrics. First, we introduce the differential metrics of different orders and the recursive relations. Then we apply the indicative functions, which can be used to determine some ML bits of the initial sequence. By parallel search with different initial sequences, we can avoid the complexity of high-order search. These approaches can used to efficiently reduce the complexity in the MIMO detection. In the proposed algorithm, we apply stop condition and indicative functions in the detection of the MIMO system. The simulation results validate our study and algorithm.

[1]. D. Gesbert, M. Shafi, D.-S. Shiu, and P. J. Smith, “From theory to practice: an overview of MIMO space-time coded wireless systems,” IEEE J. Sel. Areas Commun., vol. 21, pp. 281-302, Apr. 2003.
[2]. M. O. Damen, H. E. Gamal, and G. Caire, “On maximum-likelihood detection and the search for the closest lattice point,” IEEE Trans. Inf. Theory, vol. 49, pp. 2389-2402, Oct. 2003.
[3]. L. G. Barbero, J. S. Thompson, S. Wilson, and P. Borjesson, “OFDM channel estimation by singular value decomposition,” IEEE Trans. Wireless Commun., vol. 7, pp. 2131-2142, June 2008.
[4]. G. Golden, C. Foschini, R. Valenzuela, and P. Wolniansky, “Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture,” IEEE Electron. Lett., vol. 35, no. 1, pp. 14-16, Jan. 1999.
[5]. C. Zheng, X. Chu, J. McAllister, and R. Woods, “Real-valued fixed-complexity sphere decoder for high dimensional QAM-MIMO systems,” IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4493-4499, Sept. 2011.
[6]. T. H. Kim, “Low-complexity sorted QR decomposition for MIMO systems based on pairwise column symmetrization,” IEEE Trans. Wireless Commun., vol. 13, no 3, pp. 1388-1396, Mar. 2014.
[7]. J. C. Braz and R. S. Neto, “Low-complexity sphere decoding detector for generalized spatial modulation systems,” IEEE Commun. Lett., vol. 18, no. 6, pp. 949-952, Apr. 2014.
[8]. J. Benesty, Y. Huang, and J. Chen, “A fast recursive algorithm for optimum sequential signal detection in a BLAST system,” IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1722-1730, July 2003.
[9]. F. Fisher and C. Windpassinger, “Real versus complex-valued equalization in V-BLAST systems,” IEEE Electron. Lett., vol. 39, no. 5, pp. 470-471, Mar. 2003.
[10]. CHANG, Ming-Xian, CHANG, Wang-Yueh, Efficient maximum likelihood detection for the MIMO system based on differential metrics. In: 2015 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2015. p. 603-608.