滤波器的参数设置和信噪比强弱会影响变阶数自适应最小均方(least mean square, LMS) 算法的性能，在噪声环境未知的情况下，变阶数LMS 的稳态性能是衡量滤波器好坏的重要指标. 在分析凸组合分数阶变阶数LMS 自适应滤波算法稳态性能的基础上，提出一种变宽度凸组合变阶数自适应滤波算法. 理论分析和仿真结果表
明，在噪声环境未知情况下，所提算法相比于凸组合分数阶变阶数自适应滤波算法和变误差宽度的分数阶变阶数自适应滤波算法而言，有更好的环境自适应能力、更快的收敛速度和更好的阶数稳定性，具有实用性.
In digital filters, the parameter setting and SNR affect performance of the variable order least mean square (LMS) algorithm, especially in a variable noise environment. Stable performance of variable order LMS is an important factor in the evaluation of filters. This paper analyzes stability of convex combined variable tap-length LMS. According to the variable error width, convex combination of adaptive filters for variable fractional tap-length LMS algorithm based on variable width is proposed. Theoretical analysis and simulation results show that, in a variable noise environment, the proposed algorithm can better suit the environment and converge faster, and is more stable in tap-length, as compared to other techniques including convex combination of adaptive filters for variable fractional tap-length LMS algorithm and adaptive filters for a variable tap-length LMS algorithm based on variable error width.
[1] RIERA-PALOU F, NORAS J M, CRUICKSHANK D G M. Linear equalizers with dynamic and automatic length selection [J]. Electronics Letters, 2001, 37(25): 1553-1554.
[2] YUAN T G, KUN T, HUI J C. LMS algorithm with gradient descent filter length [J]. IEEE Signal Processing Letters, 2004, 11(3): 305-307.
[3] GONG Y, COWAN C F N. An LMS style variable tap-length algorithm for structure adaptation [J]. IEEE Trans Signal Processing, 2005, 53(7): 2400-2407.
[4] ZHANG Yonggang, CHAMBERS J A. Convex combination of adaptive filters for variable tap-length LMS algorithm [J]. IEEE Signal Processing Letters, 2007, 13(10): 628-631.
[5] KOZAT S S, ERDOGAN A T, SINGER A C, SAYED A H. Steady-State MSE performance analysis of mixture approaches to adaptive filtering [J]. IEEE Transactions on Signal Processing, 2010, 58(8): 4050-4063.
[6] 张勇刚, 李宁, 郝燕玲. 改进的变阶数LMS自适应滤波算法[J]. 哈尔滨工程大学学报, 2010, 31(3): 350-354.
ZHANG Yonggang, LI Ning, HAO Yanling. Analysis of an improved variable order least mean square algorithm [J]. Journal of Harbin Engineering University. 2010, 31(3): 350-354. (in Chinese)
[7] ARENAS-GARCIA J, FIGUEIRAS-VIDAL A R, SAYED A H. Mean-square performance of a convex combination of two adaptive filters [J]. IEEE Transactions on Signal Processing, 2006, 54(3): 1078-1090.
[8] PAPOULIS E V, STATHAKI T. A normalized robust mixed norm adaptive algorithm for system identification [J]. IEEE Signal Processing, 2004, 1(11): 56-59.
[9] ARENAS-GARCIA J, GOMEZ-VERDEJO V, FIGUEIRAS- VIDAL A R. New algorithms for improved adaptive convex combination of LMS transversal filters [J]. IEEE Trans. Instrum. Meas., 2005, 54(6): 2239-2249.
[10] ZHANG Yonggang, LI Ning, CHAMBERS J A, SAYED A H. Steady-state performance analysis of a variable tap-length LMS algorithm [J]. IEEE Transactions on Signal Processing. 2008, 56(2): 839-845.
