CN108462481B - A proportional LMP filtering method based on parameter adjustment under μ-law function - Google Patents

Abstract

The invention discloses a proportional LMP filtering method based on parameter adjustment under μ-law function. Desired output signal; Multiply the input signal of the adaptive filter by the real-time weight vector of the filter to obtain the actual output signal; Difference between the expected output signal and the real-time output signal to obtain the signal error, calculate the cost function; Introduce μ law Under the function, the diagonal matrix of the parameters is adjusted according to the system sparsity, and the weight vector is adjusted; the adjusted weight vector is used as the new real-time weight vector of the filter. The invention enables the adaptive filter to maintain a good convergence speed and filtering accuracy in a system with a relatively large sparsity, and also maintain a good convergence speed and filtering accuracy in a system with a relatively small sparsity, thereby improving the adaptive filtering. adaptability of the device to the environment.

Description

A proportional LMP filtering method based on parameter adjustment under μ-law function

technical field

The invention relates to the technical field of digital signal processing, in particular to a proportional LMP filtering method based on parameter adjustment under a μ-law function.

Background technique

An adaptive filter is a filter that tracks the time-varying characteristics of the signal by changing the parameters of the traditional filter through an adaptive algorithm. The traditional filter needs to know the channel structure, but in practice many channels are unknown, while the adaptive filter needs to know the channel structure. The filter can adaptively find the optimal filter parameters in an iterative manner according to the statistical characteristics of the signal or noise without knowing the system structure. This characteristic makes the adaptive filter in the field of communication echo cancellation, channel equalization , filtering and inverse filtering, system identification, noise elimination, etc. have been widely used.

In recent years, with the development of informatization and modern digital technology, the requirements for signal feature extraction and noise elimination of unknown channels in many fields have become stronger and stronger, and it is necessary to be able to process signals in real time. The LMP algorithm is an adaptive processing algorithm that can filter, smooth, and predict signals. The LMP algorithm takes the p-th power of the absolute value of the error signal as the cost function, and uses the gradient descent method to obtain the weight update formula.

In sparse system identification, the length of the adaptive filter will increase exponentially, which not only reduces the convergence speed of the algorithm, but also reduces the filtering accuracy. However, in this large number of adaptive filter coefficients, only a few coefficients have significant values, and most of the rest are zero or very small numbers, so it is necessary to adopt some method to alleviate the adaptive filter in this kind of performance degradation in the case. In 2000, Donald L.Duttweiler proposed the coefficient scale adaptive algorithm. Coefficient proportional adaptation refers to the introduction of a step size control matrix, so that the step size parameter at the current moment is proportional to the absolute value of the filter coefficient at the current moment. In this way, a larger filter coefficient can obtain a larger step size parameter , smaller filter coefficients obtain smaller step size parameters, thus improving the convergence speed of the algorithm. The proportional LMP algorithm introduces a step size control matrix on the basis of the LMP algorithm, so that different coefficients can be properly adjusted by different step size parameters, which effectively improves the convergence speed of the algorithm. However, the proportional LMP algorithm is proposed for the impulse response with a large degree of sparsity. When the system sparsity decreases, the convergence speed of the proportional LMP algorithm will deteriorate sharply, even slower than the LMP algorithm.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, provide a proportional LMP filtering method based on parameter adjustment under the μ-law function, introduce a diagonal matrix that adjusts parameters with the system sparsity under the μ-law function, and combine the cost function to adjust the self- The weight vector of the adaptive filter is adjusted, so that the adaptive filter can not only maintain a good convergence speed and filtering accuracy in a system with large sparsity, but also maintain a good convergence speed and filtering accuracy in a system with small sparsity. The filtering accuracy improves the adaptability of the adaptive filter to the environment.

The object of the present invention is to be achieved through the following technical solutions: a proportional LMP filtering method based on parameter adjustment under a μ-law function, comprising the following steps:

相乘，再加上噪声信号v(n)，得到期望输出信号d(n)：S1. Combine the input signal of the adaptive filter x(n)=[x(n), x(n-1),...,x(n-L+1)] ^T with the weight vector of the filter expected value

Multiply and add the noise signal v(n) to get the desired output signal d(n):

d(n)=w ^*T x(n)+v(n);

In the formula, L represents the channel length;

S2. Combine the input signal of the adaptive filter x(n)=[x(n), x(n-1),...,x(n-L+1)] ^T with the real-time weight vector of the filter w(n)=[w ₁ (n),w ₂ (n),...,w _L (n)] Multiply by ^T to get the actual output signal y(n):

y(n)= ^wT (n)x(n);

S3. Make the difference between the expected output signal d(n) and the real-time output signal y(n) to obtain the signal error e(n):

e(n)=d(n)-y(n);

S4. Calculate the cost function of the LMP algorithm according to the signal error e(n):

J _LMP (n)=|e(n)| ^p ;

S5. Introduce the diagonal matrix G(n)=diag(g ₁ (n),g ₂ (n),...,g _L (n)) that adjusts the parameters with the system sparsity under the μ-law function, and combine the cost The function J _LMP (n) adjusts the weight vector w(n);

S6. Use the adjusted weight vector as a new real-time weight vector of the filter, repeat steps S1 to S5, and iteratively update the weight vector of the adaptive filter in each filtering process.

Wherein, the step S5 includes the following sub-steps:

Introduce a diagonal matrix G(n)=diag(g ₁ (n),g ₂ (n),...,g _L (n)) that adjusts parameters with the system sparsity under the μ-law function, where the diagonal matrix G The step factor g _i (n) in (n) is:

The diagonal matrix G(n) is combined with the cost function J _LMP (n) to adjust the weight vector w(n). The adjusted weight vector is:

In the formula, Q(n)=|e(n)| ^p-1 sgn(e(n))x(n), ηp is the global step size parameter.

The beneficial effects of the present invention are as follows: the present invention introduces a diagonal matrix for adjusting parameters with the system sparsity under the μ-law function, and adjusts the weight vector of the adaptive filter in combination with the cost function, so that the adaptive filter can It can maintain a good convergence speed and filtering accuracy in a system with a large degree of sparseness, and can also maintain a good convergence speed and filtering accuracy in a system with a small sparse degree, which improves the adaptability of the adaptive filter to the environment.

Description of drawings

Fig. 1 is the system principle block diagram of the present invention;

FIG. 2 is a schematic diagram of a proportional LMP filtering model corresponding to the method of the present invention.

Detailed ways

The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following.

As shown in Figure 1, a proportional LMP filtering method based on parameter adjustment under μ-law function includes the following steps:

相乘，再加上噪声信号v(n)，得到期望输出信号d(n)：S1. Combine the input signal of the adaptive filter x(n)=[x(n), x(n-1),...,x(n-L+1)] ^T with the weight vector of the filter expected value

Multiply and add the noise signal v(n) to get the desired output signal d(n):

d(n)=w ^*T x(n)+v(n);

In the formula, L represents the channel length;

S2. Combine the input signal of the adaptive filter x(n)=[x(n), x(n-1),...,x(n-L+1)] ^T with the real-time weight vector of the filter w(n)=[w ₁ (n),w ₂ (n),...,w _L (n)] Multiply by ^T to get the actual output signal y(n):

y(n)= ^wT (n)x(n);

S3. Make the difference between the expected output signal d(n) and the real-time output signal y(n) to obtain the signal error e(n):

e(n)=d(n)-y(n);

S4. Calculate the cost function of the LMP algorithm according to the signal error e(n):

J _LMP (n)=|e(n)| ^p ;

S5. Introduce the diagonal matrix G(n)=diag(g ₁ (n),g ₂ (n),...,g _L (n)) that adjusts the parameters with the system sparsity under the μ-law function, and combine the cost The function J _LMP (n) adjusts the weight vector w(n);

S6. Use the adjusted weight vector as a new real-time weight vector of the filter, repeat steps S1 to S5, and iteratively update the weight vector of the adaptive filter in each filtering process.

Wherein, the step S5 includes the following sub-steps:

Introduce a diagonal matrix G(n)=diag(g ₁ (n),g ₂ (n),...,g _L (n)) that adjusts parameters with the system sparsity under the μ-law function, where the diagonal matrix G The step factor g _i (n) in (n) is:

μ represents an objective convergence criterion, which is generally a positive number.

The diagonal matrix G(n) is combined with the cost function J _LMP (n) to adjust the weight vector w(n). The adjusted weight vector is:

In the formula, Q(n)=|e(n)| ^p-1 sgn(e(n))x(n), ηp is the global step size parameter.

As shown in Figure 2, which is a schematic diagram of the proportional LMP filtering model corresponding to the method of the present invention, first calculate the error between the expected output signal and the real-time output signal, and then design the cost function of the filtering algorithm under the minimum mean square p-norm criterion: J _LMP (n)=|e(n)| ^p , and then introduce the diagonal matrix G(n)=diag(g ₁ (n),g ₂ (n),...,g _L (n)) combined cost The function J _LMP (n) adjusts the weight vector w(n);

In the existing proportional LMP algorithm, the step factor g _i (n) in the diagonal matrix G(n) is:

γ(n)=max{φ,w ₁ (n),...,|w _L (n)|};

和φ是正常数因子，目的是为了防止滤波器系数过小而使算法停滞；χ_i(n)表示在n时刻第l个滤波器系数绝对值和

中最大的一个；in

and φ is a constant factor, the purpose is to prevent the filter coefficient from being too small to make the algorithm stagnate; χ _i (n) represents the absolute value of the lth filter coefficient at time n and the sum of

the largest of the

However, the proportional LMP algorithm is proposed for impulse responses with a relatively large degree of sparseness. However, the convergence speed of the proportional LMP algorithm is even slower than that of the LMP algorithm when dealing with impulse responses with a relatively small degree of sparseness. To solve this problem, replace the step factor g _i (n) in the diagonal matrix G(n) with:

Where -1≤β<1, g _i (n) plays a role of adjusting the algorithm according to the sparsity. By adjusting β, the algorithm can be switched between the LMP algorithm and the proportional LMP algorithm. The specific performance is: when β is closer to -1, the algorithm is closer to the LMP algorithm, so it is suitable for non-sparse systems; when β is close to 1, the algorithm is closer to the proportional LMP algorithm, so it is suitable for sparse systems. When β is larger, the algorithm is more suitable for the case of large sparsity, and the smaller β is, the more suitable the algorithm is for the algorithm with small sparsity.

In order to better measure the sparsity, the μ-law function is introduced in the present invention, and the μ-law function can be described as:

F( _wi (n))=log(1+μ| _wi (n)|);

中的|w_i(n)|、|w_j(n)|带入，即可得到对角矩阵G(n)中的最终的步长因子：μ represents an objective convergence criterion, generally a positive number, and the description result of the μ-law function is used as a formula

Bring |w _i (n)| and |w _j (n)| into the diagonal matrix G(n) to get the final step factor in the diagonal matrix G(n):

Using the matrix G(n) corresponding to the step size factor and the cost function to adjust the weight vector of the adaptive filter, the adaptive filter can show good performance for both sparse and non-sparse impulse responses. Good characteristics, specifically, it can not only maintain a good convergence speed and filtering accuracy in a system with large sparsity, but also maintain a good convergence speed and filtering accuracy in a system with small sparsity, which improves the adaptive filtering. adaptability of the device to the environment.

Claims (1)

1. A proportional LMP filtering method based on parameter adjustment under a mu-law function is characterized in that: the method comprises the following steps:

s1, an input signal x (n) = [ x (n), x (n-1),. ], x (n-L + 1) of the adaptive filter] ^T And the expected value of the weight vector of the filter

Multiplying, and adding the noise signal v (n) to obtain the desired output signal d (n):

d(n)＝w ^*T x(n)+v(n)；

wherein, L represents the channel length;

s2, an input signal x (n) = [ x (n), x (n-1),.., x (n-L + 1) of the adaptive filter] ^T With the filter real-time weight vector w (n) = [ w = ₁ (n),w ₂ (n),…,w _L (n)] ^T Multiplying to obtain an actual output signal y (n):

y(n)＝w ^T (n)x(n)；

s3, subtracting the expected output signal d (n) from the real-time output signal y (n) to obtain a signal error e (n):

e(n)＝d(n)-y(n)；

s4, calculating a cost function of the LMP algorithm according to the signal error e (n):

J _LMP (n)＝|e(n) | ^p ；

s5, introducing a diagonal matrix G (n) = diag (G) of parameters adjusted along with system sparsity under the mu-law function ₁ (n),g ₂ (n),…,g _L (n)), and incorporating a cost function J _LMP (n) for the weight directionAdjusting the amount w (n);

wherein the step factor G in the diagonal matrix G (n) _i (n) is:

wherein beta is more than or equal to-1 and less than 1; mu represents a convergence standard, and a normal number is taken;

the diagonal matrix G (n) is compared with a cost function J _LMP (n) combining, adjusting the weight vector w (n), wherein the adjusted weight vector is as follows:

wherein Q (n) = | e (n) <withoutcircuit defects ^p-1 sgn (e (n)) x (n), η p is a global step size parameter;

and S6, taking the adjusted weight vector as a new real-time weight vector of the filter, repeating the steps S1-S5, and carrying out iterative updating on the weight vector of the self-adaptive filter in each filtering process.

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