外文资料翻译--基于lms算法的自适应组合滤波器(编辑修改稿)

外文资料翻译--基于lms算法的自适应组合滤波器(编辑修改稿)内容摘要：

rove the transient behavior of the algorithm. Note that the only unknown values in (6) are the variances. In our simulations we estimate 2q as in [4]:       kWkWm e di an iiq , (7) for k = 1, 2,... , L and 22 qZ   . The alternative way is to estimate 2n as:  Ti in eT 1 22 1 ， for x(i) = 0. （ 8） Expressions relating 2n and 2q in steady state, for different types of LMSbased algorithms, are known from literature. For the standard LMS algorithm in steady state, 2n and 2q are related 22 nq q  ,[3]. Note that any other estimation of 2q is valid for the proposed filter. Complexity of the CA depends on the constituent algorithms (Step 1), and on the decision algorithm (Step 3).Calculation of weighting coefficients for parallel algorithms does not increase the calculation time, since it is performed by a parallel hardware realization, thus increasing the hardware requirements. The variance estimations (Step 2), negligibly contribute to the increase of algorithm plexity, because they are performed at the very beginning of adaptation and they are using separate hardware realizations. Simple analysis shows that the CA increases the number of operations for, at most, N(L−1) additions and N(L−1) IF decisions, and needs some additional hardware with respect to the constituent algorithms. of bined adaptive filter Consider a system identification by the bination of two LMS algorithms with different steps. Here, the parameter q is μ ,.    10/, 21  qqQ . The unknown system has four timeinvariant coefficients,and the FIR filters are with N = 4. We give the average mean square deviation (AMSD) for both individual algorithms, as well as for their bination,Fig. 1(a). Results are obtained by averaging over 100 independent runs (the Monte Carlo method), with μ = . The reference dk is corrupted by a zeromean uncorrelated Gaussian noise with 2n = and SNR = 15 dB, and κ is . In the first 30 iterations the variance was estimated according to (7), and the CA picked the weighting coefficients calculated by the LMS with μ . As presented in Fig. 1(a), the CA first uses the LMS with μ and then, in the steady state, the LMS with μ /10. Note the region, between the 200th and 400th iteration,where the algorithm can take the LMS with either stepsize,in different realizations. Here, performance of the CA would be improved by increasing the number of parallel LMS algorithms with steps between these two also that, in steady state, the CA does not ideally pick up the LMS with smaller step. The reason is in the statistical nature of the approach. Combined adaptive filter achieves even better performance if the individual algorithms, instead of starting an iteration with the coefficient values taken from their previous iteration, take the ones chosen by the CA. Namely, if the CA chooses, in the kth iteration, the weighting coefficient vector PW ,then each individual algorithm calculates its weighting coefficients in the (k+1)th iteration according to:  kkpk XeEWW 21  (9) Fig. 1. Average MSD for considered algorithms. Fig. 2. Average MSD for considered algorithms. Fig. 1(b) shows this improvement, applied on the previous example. In order to clearly pare the obtained results,for each simulation we calculated the AMSD. For the first LMS (μ ) it was AMSD = , for the second LMS (μ /10) it was AMSD = , for the CA (CoLMS) it was AMSD = and for the CA with modification (9) it was AMSD = . 5. Simulation results The proposed bined adaptive filter with various types of LMSbased algorithms is implemented for stationary and nonstationary cases in a system identification of the bined filter is pared with the individual ones, that pose the particular bination. In all simulations presented here, the reference dk is corrupted by a zeromean uncorrelated Gaussian noise with n and SNR = 15 dB. Results are obtained by averaging over 100 independent runs, with N = 4, as in the previous section. (a) Time varying optimal weighting vector: The proposed idea may be applied to the SA algorithms in a nonstationary case. In the simulation, the bined filter is posed out of three SA adaptive filters with different steps, . Q = {μ , μ /2, μ /8}。 μ = . The optimal vectors is generated according to the presented model with Z ,and with κ = 2. In the first 30 iterations the variance。