球體解碼演算法能有效率地實作出高維度多重輸入多重輸出的最大概似解(ML)。在本篇論文中，我們比較了標準的球體解碼與使用差分量度的球體解碼，並且考慮在深度優先搜尋與寬度優先搜尋的條件。
使用差分量度的球體解碼能夠快速地縮小球體解碼的搜尋半徑，但我們需要多餘的事前運算才能夠使用差分量度縮小搜尋半徑。然而在非時變通道或是通道變化較慢的情況下，我們可以減少使用差分量度球體解碼的事前運算量。我們比較標準球體解碼與差分量度球體解碼的拜訪點數，再各自與寬度優先搜尋與深度優先搜尋做比較，最後得到深度優先搜尋為最少拜訪點數的搜尋方式。此外，我們限制了寬度優先搜尋所使用的記憶體大小，此方法下，較低訊雜比能夠降低所需要的拜訪點數，而且能夠接近絕對ML的錯誤率。

Sphere decoding algorithm can efficiently implement the maximum likelihood (ML) detection of the high-dimensional multiple-input multiple-output (MIMO) maximum likelihood (ML) system. In this thesis, we study the sphere decoding with standard and differential metrics. We consider both depth-first search and breadth-first search in the tree search of the sphere decoding.
The sphere decoding with differential metrics can update the radius more quickly. However, with the use of differential metric we need more calculations before the tree search. When the channel is time-invariant or slowly time-varying, we can reduce the advance calculations for the sphere decoding with differential metrics. We compare the visited nodes of the sphere decoding with standard and differential metrics, respectively, with depth-first search and breadth-first search. We find that the breadth-first search is the scheme attains fewer visited nodes. We also consider the scheme with limited memory for the breadth-first search, which attains close bit-error rate performance near the exact ML scheme with reduced visited nodes at lower signal-to-noise ratio (SNR).

[1]. G. J. Foschini and M. J. Gans. On limits of wireless communications in a fading environmentwhen using multiple antennas. Wirel. Pers. Commun., 6:311–335, 1998.
[2]. S.M. Alamouti. A simple transmit diversity technique for wireless communication. IEEE J. Select Areas Comm., 16:1451–1458, 1998.
[3]. S. Da-shan P.J. Smith D. Gesbert, M. Shafi and A. Naguib. From theory to practice: an overview of mimio space-time coded wireless systems. IEEE J. Select Areas Comm., 21:281–302, 2003.
[4]. Y. Huang J. Benesty and J. Chen. A fast recursive algorithm for optimum sequen- tial signal detection in blast system. IEEE Trans. Signal Process., 51:1722–1731, 2003.
[5]. H. El 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.
[6]. B. Hassibi and H. Vikalo. On the sphere-decoding algorithm i. expected complexity. IEEE Trans. Signal Process., 53:2806–2818, 2005.
[7]. E. Viterbo and J. Boutros. A universal lattice code decoder for fading channels. IEEE Trans. Inform. Theory, 45:1639–1642, 1999.
[8]. G. Rekaya and J. Belfiore. On the complexity of ml lattice decoders for decoding linear full rate space-time codes. In IEEE International Symposium on Information Theory, pages 206 – 206, 2003.
[9]. W. Zhao and G. Giannakis. Sphere decoding algorithms with improved radius search. IEEE Trans. Commun., 53:1104–1109, July 2005.