LORD(Layered Orthogonal Lattice Detector) 以及球狀解碼(Sphere Decoding) 都可以達到相當於ML(Maximum Likelihood)的效能, 但是各自有缺點, LORD在傳送天線為三根以上的時候, 當我們傳送64-QAM 的信號, 效能想達到ML , 此時, 搜尋的複雜度高於212 , 我們知道這在硬體實踐上是相當困難的。於是, 我們考慮使用球狀解碼, 但是球狀解碼的搜尋半徑, 往往影響到搜尋的複雜度, 所以選擇球狀解碼的搜尋半徑大小成為搜尋複雜度的關鍵, 因此本篇論文將結合LORD 以及球狀解碼來降低搜尋的複雜
度。

It is know that the LORD (Layered Orthogonal Lattice Detector) and the sphere
decoding achieve performance equaling that of ML. However, both detectors have
different disadvantage. When the transmit antenna number is greater than three
antennas, it is difficult to apply the LORD. Therefore, we consider using the sphere
decoding together with the LORD. The complexity of the sphere decoding highly
depends on the initial radius. In this thesis, we intend to reduce the sphere decoding
complexity by using LORD.

摘要 i
Abstract ii
目錄 ii
圖次 iv
表次 v
1 緒論 1
2 多重輸入多重輸出技術的系統架構 2
2.1 接收信號. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 QR分解. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 預先處理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 解調 9
3.1 ML解調. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 LORD解調. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
3.2.1 傳送以及接收天線各為2根的LORD 解調. . . . . . . 10
3.2.2 傳送以及接收天線各為2根以上的LORD 解調. . . 12
3.2.3 LLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 球狀解碼 16
4.1 搜尋半徑. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 搜尋方式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.1 例子. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.3 LLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 結合球狀解碼與正交格子層搜尋 25
5.1 搜尋的半徑. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 模擬結果與分析 27
7 結論 35
參考文獻 36
附錄 37

[1] M. Siti and M. Fitz, “Layered orthogonal lattice detector for two transmit antenna
communications,” Arxiv preprint cs/0508064, 2005.
[2] A. Chan and I. Lee, “A new reduced-complexity sphere decoder for multiple
antenna systems,” in Communications, 2002. ICC 2002. IEEE International
Conference on, vol. 1. IEEE, 2002, pp. 460–464.
[3] M. Siti and M. Fitz, “On reduced complexity soft-output mimo ml detection,”
Arxiv preprint cs/0603096, 2006.
[4] C. Studer, A. Burg, and H. Bolcskei, “Soft-output sphere decoding: Algorithms
and vlsi implementation,” Selected Areas in Communications, IEEE Journal on,
vol. 26, no. 2, pp. 290–300, 2008.
[5] B. Hassibi and H. Vikalo, “On the sphere-decoding algorithm i. expected complexity,”
Signal Processing, IEEE Transactions on, vol. 53, no. 8, pp. 2806–2818,
2005.
[6] M. Yee, “Max-log-map sphere decoder,” in Acoustics, Speech, and Signal Pro-
cessing, 2005. Proceedings.(ICASSP'05). IEEE International Conference on,
vol. 3. IEEE, 2005, pp. iii–1013.
[7] E. Zimmermann, W. Rave, and G. Fettweis, “On the complexity of sphere decoding,”
in Proc. International Symp. on Wireless Pers. Multimedia Commun.,
Abano Terme, Italy. Citeseer, 2004.
36