近年來，無線通訊的蓬勃發展中，多輸入多輸出系統(MIMO)已成為獨一無二的關鍵技術，使用多輸入多輸出系統不但可以增加傳輸率(transmission rate)和傳送距離，還能增加吞吐量(throughput)，因此此系統受到廣大學者的研究及應用。目前也有許多的解調技術被提出，例如ZF解調、MMSE解調，以及本論文提到的球狀解碼等等都是多輸入多輸出系統中的重要解調方法。
然而，ZF解調跟MMSE解調雖然可以降低複雜度，但是錯誤率(BER)也會比最大概似偵測法(MLD)還高。而球狀解碼可以有效地降低複雜度，也可以把錯誤率維持在與MLD差不多。而這篇論文則是在以球狀解碼的最佳優先搜尋為基礎的情況下，使用差分度量結合梯度搜尋建立一套有效的偵測演算法，並且與使用球狀解碼計算出來的初始序列做結合，在不同階數的梯度搜尋下試著得到接近MLD的錯誤率表現。

In recent years, Multiple-Input and Multiple-Output(MIMO)has become a unique key technology in the booming development of wireless communication. The use of MIMO not only increases transmission rate and transmission distance, but also increases throughput, so this system has been widely studied and applied. Many demodulation techniques have been proposed, such as ZF detection, MMSE detection, and the sphere decoding mentioned in this paper, which are all important detection methods in the MIMO systems.
However, ZF detection and MMSE detection can reduce the complexity, but the bit error rate(BER) is higher than that of the maximum likelihood detection (MLD). Sphere decoding can effectively reduce the complexity and keep the BER similar to MLD. In this paper, an effective detection algorithm is proposed based on the best-first search of sphere decoding, using the differential metric combined with the gradient search, and combined with the initial sequence computed by sphere decoding to obtain BER close to MLD at different orders of gradient search.

[1] B. Hassibi and H. Vikalo. “On the sphere-decoding algorithm i. expected complexity.” IEEE Trans. Signal Process., 53:2806-2818, 2005.

[2] R. Hunger, “Floating Point Operations in Matrix-Vector Calculus,” Ph.D. dissertation, Munich Univ. Technol., Inst. Circuit Theory Signal Process., Munich, Germany, 2005.

[3] Ming-Xian Chang and Wang-Yueh Chang. “Maximum-Likelihood Detection for MIMO Systems Based on Differential Metrics.” IEEE Trans. on Signal Processing, pp.3718~3712, 2017.

[4] Ming-Xian Chang and Wang-Yueh Chang. “Efficient Detection for MIMO Systems Based on Gradient Search.” IEEE Trans. on Vehicular Technology, pp.10057~10063, 2016.

[5] Ming-Xian Chang and Wang-Yueh Chang, “Efficient maximum likelihood detection for the MIMO system based on differential metrics,” in Proc. IEEE WCNC 2015, pp. 603-608, Mar. 2015.

[6] Pei-Hua Wu and Ming-Xian Chang. “Detection of mimo systems based on dynamic search for high-order modulations.” In 2019 90th Vehicular Technology Conference(VTC2019-Fall),pages 1-5, 2019.

[7] H. E1 Gamal M. O. Damen and G. Caire. “On maximum-likelihood detection and the search for the closest lattice point.” IEEE Trans. Inf. Theory, 49:2389-2402, 2003.

[8] W. Zhao and G. Giannakis, “Sphere decoding algorithms with improved radius search,” IEEE Trans. Commun., vol. 53, no. 7, pp. 1104–1109, July 2005