在多天線廣播系統中使用固定複雜度之晶格縮減方法於TH預編碼器

Fixed Complexity Lattice-Reduction-Aided Tomlinson-Harashima Precoding for MIMO Broadcast Channels

楊明哲(Ming-Che Yang)

指導教授 ： 吳仁銘

國立清華大學/電機資訊學院/電機工程學系/碩士(2010年)

https://doi.org/10.6843/NTHU.2010.00553

摘要

這篇論文提出一個固定複雜度的晶格縮減方法運用於多天線廣播系統的TH預編碼器[1]中。晶格縮減方法運用於TH預編碼器中能達到最大多樣性秩序。但晶格縮減演算法的複雜度非固定，不適合用於硬體實現。在固定複雜度的晶格縮減演算法中，我們考慮固定複雜度的LLL-deep演算法[2]用於TH預編碼器中。固定複雜度的LLL-deep演算法在原始基底做SQR排序和長度減縮。然而我們發現在排序TH預編碼器中，在對偶基底做SQR排序會比在原始基底做SQR排序有更好的效能。所以這篇論文提出一個修改版本的固定複雜度LLL-deep演算法，是在對偶基底做SQR排序和長度減縮，不同於原本固定複雜度LLL-deep在原始基底做SQR排序和長度減縮。另外，因為複雜度是固定的，所以適合做硬體的實現。模擬結果顯示在固定複雜度的晶格縮減方法中，對於固定數目的長度減縮次數，本篇論文提出的方法和固定複雜度的LLL[3]演算法以及固定複雜度的LLL-deep演算法比起來會有較低的錯誤率。LLL[4]的平均長度減縮次數為21，在4-正交幅度調變、四發四收通道中，固定長度減縮次數為24，效能能逼近LLL。在16-正交幅度調變、四發四收通道中，固定長度減縮次數為18，效能能逼近LLL。而且有幾乎和LLL演算法一樣的錯誤率和多樣性秩序。

關鍵字

晶格減縮 ； TH預編碼 ； 固定複雜度

並列摘要

In this thesis, a fixed complexity lattice reduction algorithm with the Tomlinson-Harashima precoding (THP) [1] is proposed for MIMO broadcast channels. Fixed complexity LLL algorithm in deep insertion (LLL-deep) [2] do sorted-QR (SQR) ordering and size reduction on the primal basis. However, we observe that doing SQR ordering on the dual basis is better than doing SQR ordering on the primal basis in ordering THP. So we proposed a modified version of fixed complexity LLL-deep algorithm that do SQR ordering and size reduction on the dual basis, which is different from fixed complexity LLL-deep that do SQR ordering and size reduction on the primal basis. Also, the complexity of proposed algorithm is fixed, which is more sutiable for hardware implementation. Simulation results show that for a fixed number of reduction stages, the performance of proposed lattice reduction algorithm is better than the fixed LLL algorithm [3] and fixed complexity LLL-deep algorithm in THP, and has nearly the same performance and diversity order as LLL [4].

並列關鍵字

lattice reduction ； Tomlinson-Harashima precoding ； THP ； fixed complexity

參考文獻

[2] C. Ling and W. H. Mow, "A unified view of sorting in lattice reduction: From v-blast to lll and beyond," in IEEE ITW 2009. Information Theory Workshop, 2009., oct. 2009, pp. 529-533.

[3] H. Vetter, V. Ponnampalam, M. Sandell, and P. Hoeher, "Fixed complexity lll algorithm," IEEE Transactions on Signal Processing, vol. 57, no. 4, pp. 1634-1637, april 2009.

[4] A. K. Lenstra, H. W. L. Jr., and L. Lovasz, "Factoring polynomials with rational coefficients," Mathematische Annalen, vol. 261, pp. 515 - 534, 1982.

[5] E. Telatar, "Capacity of multi-antenna gaussian channels," European Transactions on Telecommunications, vol. 10, no. 6, pp. 585-595, 1999.

[6] G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Technical Journal, vol. 1, no. 2, pp. 41-59, 1996.