MLMS算法收敛条件和步长的选取

CONDITION FOR CONVERGENCE OF MLMS ALGORITHM AND CONVERGENCE STEPSIZE

利用有限方差估计的方法，对修正自适应均方误差（ＭＬＭＳ）算法进行了分析。从分析可以知道，ＭＬＭＳ算法收敛是受失调量Ｍ的影响的，算法收敛的必要条件是收敛门限其中，λ＿ｉ是信号特征值，λ＿ｍ＝ｍａｘλ＿ｉ．ｉ，ｊ∈｛１，２，…，Ｎ｝．步长μ与信号功率以ｔｒ（Ｒ）和失调量Ｍ有关，并且有μ＜μ￣＊，步长μ的选取满足下式的条件，即０＜μ＜Ｍ／ｔｒ（Ｒ），Ｍ＜１，计算机仿真结果与理论分析相吻合．

Using the method of the finite variance estimation,analyse MLMS algorithm。Theconvergence of the algorithm is interrelated with the misadjustinent M.The necessary condition forthe convergence is the convergent thresrold value μ￣*=1/λ_m, when λ≠λ_i(λ-signal eigenvalues,λ_m=maxλ_i,i=1,2,…,N),or μ￣*=1(N-1)λ,when λ=λ_i. The stride μ is relative to the totalprower tr(R)and the iT1isadjustment M of the signal,and μ<μ￣*·The selection of μ must meet thelatter formulas :0<μ<M/tr(R)and M<1.The results of the computer simulation accord withabove analysis.