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http://dx.doi.org/10.3837/tiis.2018.06.007

Performance Evaluation of Lower Complexity Hybrid-Fix-and-Round-LLL Algorithm for MIMO System  

Lv, Huazhang (5G Innovation Center, Network Technology Research Institute of China Unicom)
Publication Information
KSII Transactions on Internet and Information Systems (TIIS) / v.12, no.6, 2018 , pp. 2554-2580 More about this Journal
Abstract
Lenstra-Lenstra-$Lov{\acute{a}}sz$ (LLL) is an effective receiving algorithm for Multiple-Input-Multiple-Output (MIMO) systems, which is believed can achieve full diversity in MIMO detection of fading channels. However, the LLL algorithm features polynomial complexity and shows poor performance in terms of convergence. The reduction of algorithmic complexity and the acceleration of convergence are key problems in optimizing the LLL algorithm. In this paper, a variant of the LLL algorithm, the Hybrid-Fix-and-Round LLL algorithm, which combines both fix and round measurements in the size reduction procedure, is proposed. By utilizing fix operation, the algorithmic procedure is altered and the size reduction procedure is skipped by the hybrid algorithm with significantly higher probability. As a consequence, the simulation results reveal that the Hybrid-Fix-and-Round-LLL algorithm carries a faster rate of convergence compared to the original LLL algorithm, and its algorithmic complexity is at most one order lower than original LLL algorithm in real field. Comparing to other families of LLL algorithm, Hybrid-Fix-and-Round-LLL algorithm can make a better compromise in performance and algorithmic complexity.
Keywords
LLL algorithm; lattice reduction; algorithmic complexity; size reduction; MIMO system;
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1 W. H. Mow, "Maximum likelihood sequence estimation from the lattice viewpoint," IEEE Trans. Inf. Theory, vol. 40, pp. 1591-1600, Sept. 1994.   DOI
2 E. Viterbo and J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. Inf. Theory, vol. 45, pp. 1639-1642, July 1999.   DOI
3 H. Yao and G. W. Wornell, "Lattice-reduction-aided detectors for MIMO communication systems," in Proc. of Globecom'02, Taipei, China, pp. 17-21, Nov. 2002.
4 L. Babai, "On Lovasz's lattice reduction and the nearest lattice point problem," Combinatorica, vol. 6, pp. 1-13, 1986.   DOI
5 Lenstra AK, Lenstra HW, Lovasz L Factoring polynomials with rational coefficients. Math Ann 261, pp. 515-534, 1982.   DOI
6 C. Ling, "Towards characterizing the performance of approximate lattice decoding in MIMO communications," in Proc. of International Symposium on Turbo Codes, Munich, Germany, Apr. 3-7, 2006.
7 Cong Ling, "On the Proximity Factors of Lattice Reduction-Aided Decoding," IEEE Trans. Signal Processing, vol.59 no.6, pp. 2795-2808, June 2011.
8 M. Taherzadeh, A. Mobasher, and A. K. Khandani, "LLL lattice-basis reduction achieves the maximum diversity in MIMO systems," in Proc. of IEEE Int. Symp. Inf. Theory (ISIT), Adelaide, Australia, 2005.
9 C. Ling and N. Howgrave-Graham, "Effective LLL reduction for lattice decoding," in Proc. of IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
10 C. Ling. H. Mow, and N. Howgrave-Graham, "Variants of the LLL algorithm in digital communications: Complexity analysis and fixed complexity implementation," Mathematics, 2010,
11 Wen Zhang, Sanzheng Qiao, and Yimin Wei. HKZ and Minkowski, "A Diagonal Reduction Algorithms for MIMO Detection," IEEE Transactions on Signal Processing, vol. 60, No. 11, 2012.
12 Gan YH, Ling C, Mow WH, "Complex lattice reduction algorithm for low-complexity full-diversity MIMO detection," IEEE Trans Signal Process, vol. 57, pp. 2701-2710, 2009.   DOI
13 Ma X, Zhang W, "Performance analysis for MIMO systems with lattice-reduction aided linear equalization," IEEE Trans Communication, vol. 56, pp. 309-318, 2008.   DOI
14 Jinming Wen, Xiao-Wen Chang, "A Greedy Selection-Based Approach for Fixed-Complexity LLL Reduction," IEEE Communication Letters, Vol.21, No.9, pp.1965-1968, Sep.2017.   DOI
15 M. S. H. Vetter, V. Ponnampalamand and P. Hoeher, "Fixed complexity LLL algorithm," IEEE Trans. Signal Process, vol. 57, no. 4, pp. 1634 -1637, Apr. 2009.   DOI
16 Cong Ling, Wai Ho Mow, "Reduced and Fixed-Complexity Variants of the LLL Algorithm for Communications," IEEE Trans. Communications, vol.61 no.3, pp 1040-1050, March 2013.
17 K. Zhao, Y. Li, H. Jiang, and S. Du, "A low complexity fast lattice reduction algorithm for MIMO detection," in Proc. of IEEE Int. Symp. Personal, Indoor, Mobile Radio Commun. (PIMRC), Sydney, Australia, Sep. 2012, pp. 1612-1616.
18 Qingsong.Wen, and Xiaoli Ma, "Efficient Greedy LLL Algorithm for Lattice Decoding," IEEE Transactions on Wireless Communications, vol.15,No.5, pp.3560-3572, May.2016.   DOI
19 Wei Wang, Meixia Hu, Yongzhao Li, Hailin Zhang, Zan Li, "Computationally efficient fixed complexity LLL algorithm for lattice-reduction-aided multiple-input-multiple-output precoding," IET Communications, vol.10, No. 17, pp.2328-2335, July.2016.   DOI
20 Dirk Wubben, Dominik Seethaler, Joakim Jalden, Gerald Matz, "Lattice Reduction," IEEE Trans. Signal Processing Magazine, vol.28 issue.3, pp 70-91, April 2011.   DOI
21 L.Bai and J.Choi, "Low-Complexity-MIMO Detection. Springer Science Business Media," LLC 2012.
22 Murray R. Bremner, "Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications," CRC Press, LLC, 2012.