Iteration-based Variable Step-size LMS Algorithm and Its Performance Analysis
Liu Jian-cheng① Zhao Hong-zhi② Quan Hou-de① Tang You-xi②
①(Ordnance Engineering College of PLA, Shijiazhuang 050003, China) ②(National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu 611731, China)
针对固定步长LMS(Least Mean Square)算法(FXSSLMS)不能同时满足快速收敛和小稳态失调误差的问题，该文提出了迭代变步长LMS算法(IVSSLMS)。与已有的变步长LMS算法(VSSLMS)不同，该算法的步长因子不再是由输出误差信号控制，而是建立了与迭代时间的改进Logistic函数非线性关系，克服了定步长算法收敛慢及已有变步长算法抗噪声干扰能力差的问题。最后从理论上分析了算法的性能，给出了其参数取值方法。理论分析和仿真均表明，所提算法能够在快速收敛情况下获得小的稳态失调误差，在有色噪声干扰下稳态失调误差比已有算法降低了约7 dB。
The Iteration-based Variable Step-Size LMS (IVSSLMS) algorithm is proposed to overcome the compromise between the convergence speed and the steady-state misadjustment error, which can’not be handled in Fixed Step-Size LMS algorithm (FXSSLMS). This algorithm is different from other Variable Step-Size LMS (VSSLMS) algorithms, since its step-size is not controlled by the error signal but the iteration time. In the other words, a modified Logistic-function nonlinear relationship is constructed between the iteration time and the step-size to conquer the slow convergence speed of the FXSSLMS and interference of the current VSSLMS. Finally, the performance and parameters settings of the proposed algorithm are analyzed. The theoretical analysis and simulations verify that the proposed algorithm has not only faster convergence speed but also smaller misadjustment error. The misadjustment error of this algorithm, with color noise interfering, is 7 dB less than existing methods.
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