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Complex affine projection adaptive signal processing method based on kernel function

An adaptive signal and affine projection technology, which is applied in the direction of adaptive network, impedance network, electrical components, etc., can solve the problems of algorithm instability and other problems, achieve ideal performance, good steady-state performance, and reduce the effect of offset error

Pending Publication Date: 2021-12-31
SOUTHWEST UNIV
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AI Technical Summary

Problems solved by technology

[0003] In the field of complex adaptive filtering, when the system is disturbed by impulse noise such as impulse noise, a series of algorithms of the existing affine projection family are not robust

Method used

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  • Complex affine projection adaptive signal processing method based on kernel function
  • Complex affine projection adaptive signal processing method based on kernel function
  • Complex affine projection adaptive signal processing method based on kernel function

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Experimental program
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Embodiment 1

[0075] Such as figure 1 As shown, Embodiment 1 of the present invention provides a complex affine projection adaptive signal processing method based on a kernel function, including the following steps:

[0076] S100: Initialize the number of iterations k=1; initialize the generalized linear model y(k)=w H x(k)+v H x * Standard weight vector of (k) and the conjugate weight vector are zero vectors, where m is the order of the filter, input signal vector for the current moment;

[0077] S200: Determine whether the number of iterations k is less than or equal to the projection order p, if so, enter step S300; otherwise, enter step S400;

[0078] S300: Set the input signal matrix at time k; calculate the error signal and the complex Gaussian kernel function according to the generalized linear model and the input signal matrix; set the identity matrix in the update formula to k order and update the weight vector; set k←k+1, and return to the step S200;

[0079] S400: Set ...

Embodiment 2

[0084] Embodiment 2 of the present invention provides a complex affine projection adaptive signal processing method based on a kernel function, comprising the following steps:

[0085] S110: Initialize the number of iterations k to be 1; initialize the generalized linear model y(k)=w H x(k)+v H x * Standard weight vector of (k) and the conjugate weight vector are zero vectors, where m is the order of the filter, input signal vector for the current moment;

[0086] S210: Determine whether the number of iterations k is less than or equal to the projection order p, if so, proceed to step S310; otherwise, proceed to step S410;

[0087] S310:

[0088] Construct the input signal matrix at the current time from the input signal vectors at the current time and the past time Calculate the error signal vector e(k)=d(k)- X T (k) w * And complex Gaussian kernel function vector κ(e(k))=exp(-|e(k)| 2 / 2σ 2 );

[0089] in, is the desired signal vector at discrete time k, ...

Embodiment 3

[0104] An embodiment of the present invention provides an adaptive signal processing method for complex affine projection with variable step size based on a kernel function, including the following steps:

[0105] S120: Initialize the number of iterations k=1; initialize the generalized linear model y(k)=w H x(k)+v H x * Standard weight vector of (k) and the conjugate weight vector are zero vectors, where m is the order of the filter, input signal vector for the current moment;

[0106] S220: Determine whether the number of iterations k is less than or equal to the projection order p, if so, enter step S320; otherwise, enter step S420;

[0107] S320:

[0108] Construct the input signal matrix at the current time from the input signal vectors at the current time and the past time Calculate the error signal vector e(k)=d(k)- X T (k) w * And complex Gaussian kernel function vector κ(e(k))=exp(-|e(k)| 2 / 2σ 2 );

[0109] in, is the desired signal vector at disc...

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Abstract

The invention discloses a complex affine projection adaptive signal processing method based on a kernel function, a complex Gaussian kernel function is applied to a generalized linear affine complex projection algorithm, and the robustness of an adaptive filtering system is improved by using the excellent performance of the Gaussian kernel function in a non-Gaussian environment, especially an impulse noise environment. When the number k of iterations is small, the unit matrix in the formula is updated to k order; when k is large, the unit matrix in the formula is updated to be p-order, and the accuracy of weight vector calculation is improved; and a variable step size method is used, so that the convergence speed is improved, and the offset error is reduced.

Description

technical field [0001] The invention relates to the field of adaptive signal processing, in particular to a kernel function-based complex affine projection adaptive signal processing method. Background technique [0002] Adaptive filtering algorithms are widely used in many fields, such as communication fields. The APA (affineprojection algorithms) algorithm is to orthogonally project the current weight coefficient vector onto the affine subspace defined by the projection order, and use the current and past input vectors to update the weight coefficient vector. Compared with traditional LMS and NLMS algorithms, especially for highly correlated input signals, APA converges faster. The APA algorithm is essentially a gradient descent algorithm. In order to reduce the computational complexity and improve the convergence speed, in recent years, researchers have proposed the augmented affine projection algorithm (augment APA, AAPA). As a general extension of APA, AAPA uses augme...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03H21/00
CPCH03H21/0043H03H2021/0054
Inventor 钱国兵尹涵刘君祝王世元邱晨
Owner SOUTHWEST UNIV
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