Abstract
Minimization of the Euclidean distance between output distribution and Dirac delta functions as a performance criterion is known to match the distribution of system output with delta functions. In the analysis of the algorithm developed based on that criterion and recursive gradient estimation, it is revealed in this paper that the minimization process of the cost function has two gradients with different functions; one that forces spreading of output samples and the other one that compels output samples to move close to symbol points. For investigation the two functions, each gradient is controlled separately through individual normalization of each gradient with their related input. From the analysis and experimental results, it is verified that one gradient is associated with the role of accelerating initial convergence speed by spreading output samples and the other gradient is related with lowering the minimum mean squared error (MSE) by pulling error samples close together.
Highlights
IntroductionAdaptive signal processing is carried out by minimizing or maximizing an appropriate performance criterion for adjusting weights of algorithms designed based on that criterion [1]
Adaptive signal processing is carried out by minimizing or maximizing an appropriate performance criterion for adjusting weights of algorithms designed based on that criterion [1].The mean squared error (MSE) criterion that measures the average of the squares of the error signal is widely employed in the Gaussian noise environment
For finite impulse response (FIR) adaptive filter structures in impulsive noise environments, Euclidian distance (ED) between the output distribution and a set of Dirac delta functions has been used as an efficient performance criterion taking advantage of the outlier-cutting effect of Gaussian kernel for output pairs and symbol-output pairs [7]
Summary
Adaptive signal processing is carried out by minimizing or maximizing an appropriate performance criterion for adjusting weights of algorithms designed based on that criterion [1]. For finite impulse response (FIR) adaptive filter structures in impulsive noise environments, ED between the output distribution and a set of Dirac delta functions has been used as an efficient performance criterion taking advantage of the outlier-cutting effect of Gaussian kernel for output pairs and symbol-output pairs [7]. In this approach with output distribution and delta functions, minimization of the ED (MED) leads to adaptive algorithms that adjust weights so as for the output distribution to be formed into the shape of delta functions located at each symbol point, that is, output samples concentrate on symbol points. Through simulation in multipath channel equalization under impulsive noise, their roles of managing sample pairs are verified, and it is shown that the proposed method of controlling each component through power normalization increases convergence speed and lowers steady state MSE significantly in multipath and impulsive noise environment
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