CN110034747B

CN110034747B - Robust complex scale symbol adaptive filter

Info

Publication number: CN110034747B
Application number: CN201910259804.6A
Authority: CN
Inventors: 倪锦根; 吴一凡
Original assignee: Suzhou University
Current assignee: Suzhou University
Priority date: 2019-04-02
Filing date: 2019-04-02
Publication date: 2023-02-03
Anticipated expiration: 2039-04-02
Also published as: CN110034747A

Abstract

The invention discloses a robust complex scale symbol adaptive filter, and belongs to the field of digital filter design. The filter adopts a symbol operation and proportion self-adaptive method to enhance the anti-impulse noise interference capability and accelerate the convergence speed. The filter can be applied to instruments and communication equipment which are interfered by noise in an electronic and communication system and have sparse estimation systems.

Description

Robust complex scale symbol adaptive filter

Technical Field

The invention discloses a robust complex scale symbol self-adaptive filter, and belongs to the field of digital filter design.

Background

Complex adaptive filters have been widely used in recent years because the amount of information that complex numbers can carry exceeds real numbers. Commonly used complex adaptive filters are complex least mean square filter (abbreviated as CLMS filter), complex normalized least mean square filter (abbreviated as CNLMS filter), etc. since these two filters are low in computational complexity and easy to implement. In some special circumstances, the output signal of an unknown system may be disturbed by impulse noise. Because the two filters adopt the minimum mean square error criterion, the pulse noise resistance is poor, namely the robustness is not strong.

System identification is an important branch of adaptive signal processing, and many problems of traditional adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation, active noise control and the like can be summarized as system identification problems. In some applications, most elements in the coefficient vector of an unknown system are zero or near zero, and such systems are generally referred to as sparse systems. Sparse system identification problems often involve theoretical and engineering practices, such as zero attraction theory and the application of proportional adaptive strategies in satellite transmission channels as well as echo cancellation channels. Duttweiler D L proposes a proportional normalized least mean square filter (abbreviated as PNLMS filter) [ Proportate normalized least mean square adaptation in echo cancellers, IEEE Transactions on spech and Audio Processing,2000,8 (5): 508-518]. However, the filter can only be used in the real number domain, and cannot be used for complex sparse system identification.

Therefore, to estimate a complex sparse system in an impulse interference environment, a robust sparse adaptive filter needs to be designed.

Disclosure of Invention

In order to solve the above problems, the present invention discloses a robust complex scale symbol adaptive filter (abbreviated as RCPSA filter). The RCPSA filter adopts an anti-impulse interference method and a proportional adaptive strategy to update the weight vector of the filter. The updating weight vector of the RCPSA filter mainly comprises the following steps:

1) By input signal x at n times _n And a desired signal d _n Calculating an error signal e _n I.e. by

Wherein x is _n ＝[x _n ,x _n-1 ,...x _n-L+1 ] ^T Representing the first L samples x of the input signal _n ,x _n-1 ,...x _n-L+1 Is formed of an input vector, w _n ＝[w _0,n ,w _2,n ,...w _L-1,n ] ^T The weight vector is formed by L weights of the adaptive filter, T represents transposition operation, and H represents conjugate transposition operation.

2) From an input vector x _n Conjugation of error signal

Modulus e (n) of the error signal and a complex scaling matrix G _n-1 Calculating the intermediate vector updated by the weight vector

Wherein: delta is a small normal number to avoid zero denominator in the iteration, which in a typical environment ranges from 10 ^-4 ,10 ^-1 ](ii) a The complex scale matrix is denoted G _n-1 ＝diag{g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Denotes the element g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Write into a diagonal matrix, taking the diagonal elements of the matrix as

||w _n-1 || ₁ Representing the coefficient vector l to the adaptive filter ₁ Norm, parameter alpha is in the range of-1, 1) for balancing between sparse and non-sparse systems, and parameter epsilon is a small normal number for avoidingThe denominator is zero in the iteration-free process, and the value range is [10 ] ^-6 ,10 ^-3 ]。

3) By iterative formula w _n ＝w _n-1 +μG _n-1 f _n Updating weight vector of the adaptive filter, wherein mu represents the step length of the filter and the value range is [0.0001,0.05 ]]。

In the above step 2), if the matrix G is _n-1 Taking the identity matrix as the basis matrix, the RCPSA filter degenerates to a robust complex symbol adaptive filter (abbreviated as RCSA filter).

Advantageous effects

Compared with the existing symbol adaptive filter scheme, the adaptive filter disclosed by the invention has stronger robustness and can accelerate the convergence speed of the identification of the complex sparse system.

Drawings

The invention is further described with reference to the following figures and examples:

FIG. 1 is a block diagram of a robust complex scale symbol adaptive filter architecture;

fig. 2 is a comparison of mean square deviation curves of the adaptive filter under the action of a round gaussian white signal.

FIG. 3 is a comparison of the mean square deviation curves of the adaptive filter under the action of the round Gaussian colored signal.

Detailed Description

Examples

The principle of the technical scheme of the invention is as follows:

firstly, expanding a cost function of the established normalized symbol adaptive filter into a complex domain and correcting, then solving the gradient of the corrected cost function, taking the gradient as an intermediate vector for reducing the pulse interference sensitivity, and then introducing a complex proportion matrix into a fastest descent method to obtain a weight vector updating formula of the adaptive filter disclosed by the application.

The embodiment of the invention adopts a computer experiment method to verify the performance of the RCPSA filter. The RCPSA filter disclosed by the invention is used for identifying an unknown complex sparse system in an impulse noise interference environment, and the performance of the RCPSA filter is compared with the performance of a complex normalized least mean square adaptive filter (abbreviated as a CNLMS filter) and an RCSA filter.

In order to make the experimental result more general, the round Gaussian white signal and the round Gaussian colored signal are selected to be respectively subjected to the experiment, and the variance of the round Gaussian white signal

Variance of round Gaussian colored signal

Wherein, the round Gaussian colored signal is generated by an AR (1) model, and the transfer function is F (z) = 1/(1-0.5 z) ^-1 ). In the experiment, mean Square Deviation (MSD) was used as a measure of algorithm performance, which is defined as

In dB, where wo represents the unknown system to be identified,

express vector w _n -w ^o L of ₂ The square of the norm, log denotes the common logarithm. The simulated MSD curves in the figure are obtained by averaging 100 independent experiments.

Pulse signal v used in the experiment _n Comprises a zero mean, a variance of

White gaussian noise gamma of _n And an impulse noise z _n I.e. v _n ＝γ _n +z _n . Impulse noise z _n Generated by the Bernoulli Gaussian process, i.e. z _n ＝ξ _n ψ _n Wherein xi is _n Is a Bernoulli process, and P [ delta ] _n ＝1]＝0.01，P[δ _n ＝0]＝0.99，ψ _n White gaussian noise with zero mean.

The method for identifying the unknown complex sparse system by the RCPSA adaptive filter comprises the following steps:

2) From an input vector x _n Conjugation of error signals

In this example, δ is taken to be 0.025. In other embodiments, the delta value lies in the interval [10 ] ^-4 ,10 ^-1 ]Internal; the complex scale matrix is denoted G _n-1 ＝diag{g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Indicates to put the element g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Write into a diagonal matrix, taking the diagonal elements of the matrix as

ε is used to avoid zero denominator in the iteration, and ε is taken to be 0.0001 in this example. In other embodiments, the value of ε is located at [10 ] ^-6 ,10 ^-3 ]And (4) the following steps.

3) By iterative formula w _n ＝w _n-1 +0.01G _n-1 f _n And updating the formula.

As can be seen from fig. 2 and 3, the RCPSA filter disclosed by the present invention has good impulse noise resistance under both sparse conditions and non-sparse conditions, and has the fastest convergence rate when estimating a complex sparse system compared with an RCSA that does not adopt a scaling strategy.

The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered in the protection scope of the present invention.

Claims

1. A robust complex scale sign adaptive filter characterized by: in the complex domain, the adaptive filter updates its weight vector based on a proportional-adaptive strategy;

the weight vector updating comprises the following steps:

Wherein x is _n ＝[x _n ,x _n-1 ,...x _n-L+1 ] ^T Representing the first L samples x of the input signal _n ,x _n-1 ,...x _n-L+1 Formed of input vectors, w _n ＝[w _0,n ,w _2,n ,...w _L-1,n ] ^T The weight vector is formed by L weights of the adaptive filter, T represents transposition operation, and H represents conjugate transposition operation;

2) From an input vector x _n Conjugation of error signal

Modulo e (n) of the error signal and a complex scaling matrix G _n-1 Calculating the intermediate vector updated by the weight vector

Wherein: delta is a small normal number, which is used to avoid the occurrence of zero denominator in the iteration, and the value range is [10 ] ^-4 ,10 ^-1 ](ii) a The complex scale matrix is denoted G _n-1 ＝diag{g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Indicates to put the element g _0,n-1 ,g _1,n-1 ...,g _L-1,n-1 Write into a diagonal matrix, taking the diagonal elements of the matrix as

||w _n-1 || ₁ Expressing the coefficient vector l to the adaptive filter ₁ Norm with parameter alpha in the range of-1, 1) for balancing between sparse and non-sparse systems, and parameter epsilon, a very small normal number for avoiding denominator zero in the iterative process, with a value in the range of [10 ] ^-6 ,10 ^-3 ]；