隨著近代通訊系統的演進，大量的資料在傳輸的過程中被要求迅速且可靠地傳送，多重輸入多重輸出系統因此成為無線通訊發展的主流趨勢，因為它能更有效增加頻譜使用效率並大幅提升通訊吞吐量，但也因此增加接收端偵測器的複雜度。球體解碼演算法的提出雖然能有效得到最大概似解，但是偏高的複雜度使得它仍持續待改善。
在本論文中，我們利用差分度量結合梯度搜尋於多重輸入多重輸出系統建立一套偵測器演算法。首先，我們定義差分度量並推導出不同階層的差分度量之遞迴關係式，接著配合指示函數則能用以確認一些初始數列的位元是否符合最大概似解；藉由多個初始序列的平行搜尋方法不僅能避免高階數的搜尋，還能提升表現效能，隨後以不同階數的搜尋與初始序列的多寡進行模擬，得出結論確認此套演算法能在效能與複雜度之間取得平衡，並說明了此套演算法主要受搜尋階數的影響，最後應用前述方法設計出改良的平行搜尋偵測器並在4×4的多天線系統進行模擬與比較。

With the development of modern communications, large amounts of data are to be transferred rapidly and reliably. Therefore, the multiple-input multiple output (MIMO) system has become the mainstream of wireless communications because the MIMO system can make full use of spectrum efficiently and increase the transmission throughput. As a result, the design of low-complexity detection has become a significant issue. Although the sphere decoding (SD) algorithm is an efficient approach to obtain the optimum maximum likelihood (ML) detection, it still has high complexity, especially at high signal-to-noise ratio (SNR). In this thesis, we propose an efficient detection algorithm for the MIMO system associated with differential metrics and gradient search. First, we define the differential metrics and derive the recursive calculation of differential metrics of different orders for gradient search. Then, we apply the indicative functions to determine some possible ML bits of the initial sequence. By simulation, we observe the performance of search of different orders and initial sequences. We conclude that the maximum order of search dominates the performance. We also compare the parallel search with the proposed modified parallel search that uses diverse initial sequences, and the latter can not only avoid the complexity of high-order search but also improve the performance.

[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. 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.
[3]. L. G. Barbero and J. S. Thompson, “Fixing the complexity of the sphere decoder for MIMO detection,” IEEE Trans. Wireless Commun., vol. 7, no. 7, pp. 2131-2142, June 2008.
[4]. G. D. Golden, C. J. Foschini, R. A. Valenzuela, and P. W. 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]. R. F. H. Fischer 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]. M.-X. Chang and W.-Y. Chang, “Efficient maximum likelihood detection for the MIMO system based on differential metrics,” in Proc. IEEE WCNC 2015, pp. 603-608, Mar. 2015.
[11]. M.-X. Chang and W.-Y. Chang, “Efficient detection for MIMO systems based on gradient search,” IEEE Trans. Veh. Technol., vol. 65, no, 12, pp. 10057-10063, Dec. 2016.
[12]. M.-X. Chang and W.-Y, Chang, “Maximum likelihood detection for MIMO systems based on differential metrics,” IEEE Trans. Signal Process., vol. 65, no. 14, pp. 3718-3732, Jul. 2017.