Abstract
Abstract This paper extends the recently introduced variable step-size (VSS) approach to the family of adaptive filter algorithms. This method uses prior knowledge of the channel impulse response statistic. Accordingly, optimal step-size vector is obtained by minimizing the mean-square deviation (MSD). The presented algorithms are the VSS affine projection algorithm (VSS-APA), the VSS selective partial update NLMS (VSS-SPU-NLMS), the VSS-SPU-APA, and the VSS selective regressor APA (VSS-SR-APA). In VSS-SPU adaptive algorithms the filter coefficients are partially updated which reduce the computational complexity. In VSS-SR-APA, the optimal selection of input regressors is performed during the adaptation. The presented algorithms have good convergence speed, low steady state mean square error (MSE), and low computational complexity features. We demonstrate the good performance of the proposed algorithms through several simulations in system identification scenario.
Highlights
Adaptive filtering has been, and still is, an area of active research that plays an active role in an ever increasing number of applications, such as noise cancellation, channel estimation, channel equalization and acoustic echo cancellation [1,2]
We extend the approach in [21] to the Affine projection algorithm (APA), selective partial update (SPU)-NLMS, Selective Partial Update APA (SPU-APA), and selective regressors (SR)-APA and four novel variable step-size (VSS) adaptive filter algorithms are established
Variable Step-Size Selective Partial Update AP algorithm using statistics of channel response The filter coefficients in VSS-SPU-APA are updated by wF(n + 1) = wF(n) + UF(n)XF(n) XTF (n)XF(n) −1e(n) (75) Approximating e(n) with e (n) ≈ XTF (n) hF − wF(n) + v(n) ≈ −XTF (n)wF(n) + v(n) (76) and substituting (76) into (75), we obtain
Summary
Still is, an area of active research that plays an active role in an ever increasing number of applications, such as noise cancellation, channel estimation, channel equalization and acoustic echo cancellation [1,2]. A number of adaptive filtering structures, based on affine subspace projections [3,4], data reusing adaptive algorithms [5,6], block adaptive filters [2] and multi rate techniques [7,8] have been proposed in the literatures In all these algorithms, the selected fixed step-size can change the convergence and the steady-state mean square error (MSE). The step-size vector with different values for each filter coefficient was used In this approach, based on prior knowledge of the channel impulse response statistics, the optimal step-size vector is obtained by minimizing the mean-square deviation (MSD) between the optimal and estimated filter coefficients. Another feature which is important in adaptive filter algorithms is computational complexity. |.| norm of a scalar ||.||2 squared Euclidean norm of a vector (.)T transpose of a vector or a matrix tr(.) trace of a matrix E[.] expectation operator
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