Abstract
Under the condition that the step size is less than one, a statistical tracking behavior analysis for the affine projection algorithm based on direction error is discussed. When the unknown true weight vector is modeled by the stochastic walk model, the mean weight error is derived under the four assumptions based on the deterministic recursive equation. Furthermore, the statistical tracking behavior of the steady state is analyzed for the affine projection algorithm based on direction error. Simulation analysis is shown to suppniort the mathematical results.
Highlights
Since the normalized least mean square Wen algorithm is computational simplicity, this algorithm is widely put into use by the adaptation algorithm
Based on the idea that the successive vectors of the input signal are orthogonal with each other, the best improvement convergence will be obtained; the normalized least mean square based on orthogonal correction factors (NLMS-OCF) was shown in [3]
Since the weights update direction and the direction that is caused by the adaptive error are not the same for the PAP algorithm, an affine projection (AP) algorithm based on direction error (AP-DE) was given to resolve the nonconformity problem [6]
Summary
Since the normalized least mean square Wen algorithm is computational simplicity, this algorithm is widely put into use by the adaptation algorithm. Fast AP algorithms have been given as well [7] These algorithms, including the AP, PAP, and NLMS-OCF, can be considered a class of the AP algorithms, which updates the adaptive weights according to the multiple vectors of the input signal. Based on the assumption that the input signal is the identically and independent distributed form, the statistical analysis of the class of the AP algorithms was shown, in which the mean weight error (MWE) and the mean-square error (MSE) were shown to study the convergence behavior for the NLMS-OCF algorithm [12, 13]. In the adaptive direction of the weight update, when we set each weight error to be zero, the optimal step size for the PAP algorithm was given; using this model, the MWE and MSE were derived based on the deterministic recursive equations [15]. The simulation analysis is given to show the proposed statistical tracking behavior
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