An acoustic echo cancellation method based on nonlinear filtering

Abstract

The application discloses an acoustic echo cancellation method based on nonlinear filtering, and steps are as follows: step 1, signal acquisition and adaptive Hammerstein filter model construction; step 2, solution of a target function is calculated; step 3, setting adaptive Hammerstein filter parameter initial value; step 4, updating parameters; step 5, echo signal cancellation; step 6, iteration until the end of conversation. The application considers different echo environments, uses an adaptive algorithm to estimate the parameters of the system, has a faster convergence speed, can adjust the filter parameters under different echo environments, makes the filter quickly obtain a better filtering effect, and adapts to an environment with higher real-time requirement; the application uses Euclidean projection to update the adaptive filter parameters, can effectively eliminate the echo in a communication system, and has a better echo cancellation effect.

Description

Technical Field

[0001] This invention relates to the field of adaptive echo cancellation, specifically an acoustic echo cancellation method based on nonlinear filtering. Background Technology

[0002] In recent years, with the widespread use of communication equipment, users have occasionally heard their own voices during calls. This phenomenon is called echo. The presence of echoes seriously affects call quality and may even cause calls to be interrupted. Therefore, it is necessary to use effective methods for acoustic echo cancellation to improve call quality. Adaptive echo cancellation is currently the most widely used echo cancellation method. It uses an adaptive filtering algorithm to adjust the filter coefficients, estimating an approximate echo signal to simulate the actual echo signal. Then, it subtracts the simulated echo signal from the acquired mixed signal, thereby achieving the purpose of echo cancellation. Traditional echo cancellation methods either approximate the echo path as a linear environment, resulting in poor echo cancellation performance in complex environments, or the filter coefficients converge slowly, making them unable to cope with rapidly changing echo environments. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an acoustic echo cancellation method based on nonlinear filtering.

[0004] An acoustic echo cancellation method based on nonlinear filtering, comprising the following steps:

[0005] Step 1: Signal acquisition and adaptive Hammerstein filter model construction;

[0006] Step 2: Calculate the solution to the objective function;

[0007] Step 3: Set the initial values ​​for the adaptive Hammerstein filter parameters.

[0008] Step 4: Update parameters;

[0009] Step 5: Echo cancellation;

[0010] Step 6: Iterate until the call ends.

[0011] Furthermore, step 1 is detailed as follows:

[0012] The remote signal is sampled to obtain the remote signal sample value at the current sampling time n. The far-end signal is broadcast on the loudspeaker and a microphone signal d(n) is generated by the loudspeaker-microphone system LEMS. The microphone signal d(n) consists of an echo signal y(n) and other near-end signals v(n), where v(n) represents the near-end speech in the intercom situation. The Hammerstein model is used to model the LEMS. The far-end sampled signal x(n) is used as the input of the adaptive Hammerstein filter. The echo signal estimate at the current time n is obtained through the filter.

[0013] The adaptive Hammerstein filter model consists of two subsystems: a memoryless polynomial and a finite impulse response. The input to the memoryless polynomial subsystem is... The relationship between the output s(n) and the output s(n) is as follows:

[0014]

[0015] In the formula The sampled value of the far-end signal at sampling time n The column vectors formed by these vectors are all of dimension L. a The column vector, with the superscript T indicating transpose.

[0016] The relationship between the input s(n) and the output y(n) of the finite impulse response subsystem is as follows:

[0017]

[0018] In the formula: X(n-1)=[x(n-1),···,x(nL b )], h(n)=vec([x(n),X(n-1)]), in For a dimension L b A column vector, X(n-1) is a vector of dimension L a ×L b The matrix vec(A) represents the process of straightening the columns of an m×n matrix A in order to form an m×n column vector.

[0019] Furthermore, step 2 is detailed below:

[0020] 2-1. Solve for the parameters of the adaptive Hammerstein filter model, representing it as a non-convex optimization problem, and define the objective function. In the formula, γ (0 < γ ≤ 1) is the forgetting factor. This is to ensure that the model parameters are within the non-convex feasible region. The solution is then projected onto the feasible region S during the solution process, which is equivalent to solving for the objective function: θ∈S. The solution to this problem is found using the ADMM (Alternating Direction Multiplier Method) algorithm, with the following augmented Lagrangian function defined:

[0021]

[0022] In the formula, the penalty term ρ>0, let And when hour otherwise To avoid excessive computational complexity due to too many iterations, the ADMM algorithm iterative process, i.e., the adaptive and projection process, is performed only once at each time step.

[0023]

[0024]

[0025]

[0026] Where P S (θ(n)+η(n-1)) represents the Euclidean projection of the vector (θ(n)+η(n-1)) onto the nonconvex feasible region S.

[0027] 2-2. Solve the objective function using the ADMM algorithm, transforming the objective function into the following form:

[0028]

[0029] Find:

[0030] θ(n)=R -1 (n)p(n), where R(n)=H(n)+ρI, the superscript -1 denotes the inverse matrix, I is the identity matrix with the same dimension as matrix H(n), and H(n) is the autocorrelation function matrix of the input signal. s(n) is the cross-correlation function vector of the input signal.

[0031] Define the following two matrices and Right now:

[0032]

[0033] above e j (j=1,2,…) is a unit column vector where the j-th element is 1 and the rest are 0, ξ=ρ(1-γ), χ j (n)(j=1,2,…,L) represents the j-th element of the column vector χ(n). L = L a +L b .

[0034] From the above formula, we can deduce that Further deductions can be made Using the matrix inversion lemma, we can obtain:

[0035]

[0036] In the formula, the gain vector Update item From the above formula, we can derive:

[0037]

[0038] The solution process for the objective function obtained from the above formula is as follows: First, we obtain the result from the above formula. Then obtain the results sequentially. at last Therefore, the solution θ(n) of the objective function can be obtained.

[0039] 2-3. Based on the Euclidean distance minimization criterion, find the Euclidean projection of vector θ(n) + η(n-1) onto the nonconvex set S, such that the vectors on the feasible region S are... To minimize the Euclidean distance between the vector θ(n) + η(n-1), we need to solve the following expression:

[0040]

[0041] In the formula: ω(n)=θ(n)+η(n-1),

[0042] Solving the above equation, we get the solution... The Euclidean distance is minimized at time, where

[0043] Θ(n) = [ω1(n), Θ2(n)],

[0044]

[0045] Q(n)=Θ(n)Θ T (n)

[0046] In this result, unless the largest eigenvalue of Q(n) is 1, the solution may become unstable after multiple iterations. Therefore, we need to introduce... Replace Q(n), where λ max Let Q(n) be the largest eigenvalue. The closed-form solution for minimizing the projected filter parameters is calculated as follows:

[0047]

[0048]

[0049]

[0050] In the formula Let represent the Kronecker product, and let vector u(n) be the eigenvector corresponding to the largest eigenvalue of matrix Q(n).

[0051] Furthermore, step 3 is as follows: Set the initial values ​​required for the Hammerstein filter parameter estimation process.

[0052] Furthermore, step 4 is detailed below:

[0053] Update the vector sequentially using the method proposed in step 2. The updated objective function solution θ(n) is obtained.

[0054] Furthermore, step 5 is as follows: using the updated filter parameters θ(n) from step 4, the estimated echo signal at the current time n is obtained. Then subtract the estimated echo signal at this moment from the microphone signal d(n) at the current moment. Receive signal

[0055] Furthermore, step 6 is as follows: Let n = n + 1, and repeat steps 4 to 6 until the call ends.

[0056] The present invention has the following beneficial effects:

[0057] 1. This invention takes into account different echo environments and uses an adaptive algorithm to estimate system parameters. It has a fast convergence speed and can quickly adjust filter parameters under different echo environments, enabling the filter to quickly obtain better filtering effects and adapt to environments with high real-time requirements.

[0058] 2. This invention uses Euclidean projection to update the adaptive filter parameters, which can effectively eliminate echo in the communication system and has a good echo cancellation effect. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the specific process of the acoustic echo cancellation method based on nonlinear filtering according to the present invention.

[0060] Figure 2 This is a model diagram of an acoustic echo cancellation system in a nonlinear environment.

[0061] Figure 3 A diagram illustrating the filter parameter update process. Detailed Implementation

[0062] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only for illustration and explanation of the present invention, but are not intended to limit the present invention.

[0063] In actual phone calls, the presence of echo can severely impact call quality and may even cause the call to be interrupted. Traditional echo cancellation methods either approximate the echo path as a linear environment, resulting in poor echo cancellation performance in complex environments, or use filter coefficients with slow convergence, failing to cope with rapidly changing echo environments. This invention describes the basic filtering problem as a recursive least squares optimization problem with a nonconvex feasible region constraint, and proposes an acoustic echo cancellation method based on nonlinear filtering. The method obtains filter parameter estimates through two iterative steps: adaptive filtering and Euclidean projection. It considers the convergence speed and accuracy of parameter estimation in nonlinear environments, achieving better echo cancellation performance.

[0064] See details Figure 1 This invention provides an acoustic echo cancellation method based on nonlinear filtering, the steps of which are as follows:

[0065] An acoustic echo cancellation method based on nonlinear filtering, comprising the following steps:

[0066] Step 1: Signal acquisition and adaptive Hammerstein filter model construction;

[0067] The remote signal is sampled to obtain the remote signal sample value at the current sampling time n. The far-end signal is broadcast through a loudspeaker, generating a microphone signal d(n) via a loudspeaker-microphone system (LEMS). The microphone signal d(n) consists of an echo signal y(n) and other near-end signals v(n), where v(n) represents the near-end speech in a two-way communication scenario. A Hammerstein model is used to model the LEMS. The far-end sampled signal x(n) serves as the input to an adaptive Hammerstein filter. The filter yields an estimate of the echo signal at the current time n. The acoustic echo cancellation system model in a nonlinear environment is as follows: Figure 2 As shown.

[0068] The adaptive Hammerstein filter model consists of two subsystems: a memoryless polynomial and a finite impulse response. The input to the memoryless polynomial subsystem is... The relationship between the output s(n) and the output s(n) is as follows:

[0069]

[0070] In the formula The sampled value of the far-end signal at sampling time n The column vectors formed by these vectors are all of dimension L. a The column vector, with the superscript T indicating transpose.

[0071] The relationship between the input s(n) and the output y(n) of the finite impulse response subsystem is as follows:

[0072]

[0073] In the formula: X(n-1)=[x(n-1),···,x(nL b )], h(n)=vec([x(n),X(n-1)]), in For a dimension L b A column vector, X(n-1) is a vector of dimension L a ×L b The matrix vec(A) represents the process of straightening the columns of an m×n matrix A in order to form an m×n column vector.

[0074] Step 2: Calculate the solution to the objective function;

[0075] 2-1. Solve for the parameters of the adaptive Hammerstein filter model, representing it as a non-convex optimization problem, and define the objective function. In the formula, γ (0 < γ ≤ 1) is the forgetting factor. This is to ensure that the model parameters are within the non-convex feasible region. The solution is then projected onto the feasible region S during the solution process, which is equivalent to solving for the objective function: θ∈S. The solution to this problem is found using the ADMM (Alternating Direction Multiplier Method) algorithm, with the following augmented Lagrangian function defined:

[0076]

[0077] In the formula, the penalty term ρ>0, let And when hour otherwise To avoid excessive computational complexity due to too many iterations, the ADMM algorithm iterative process, i.e., the adaptive and projection process, is performed only once at each time step.

[0078]

[0079]

[0080]

[0081] Where P S(θ(n)+η(n-1)) represents the Euclidean projection of the vector (θ(n)+η(n-1)) onto the nonconvex feasible region S.

[0082] 2-2. Solve the objective function using the ADMM algorithm, transforming the objective function into the following form:

[0083]

[0084] Find:

[0085] θ(n)=R -1 (n)p(n), where R(n)=H(n)+ρI, the superscript -1 denotes the inverse matrix, I is the identity matrix with the same dimension as matrix H(n), and H(n) is the autocorrelation function matrix of the input signal. s(n) is the cross-correlation function vector of the input signal.

[0086] Define the following two matrices and Right now:

[0087]

[0088] above e j (j=1,2,…) is a unit column vector where the j-th element is 1 and the rest are 0, ξ=ρ(1-γ), χ j (n)(j=1,2,…,L) represents the j-th element of the column vector χ(n). L = L a +L b .

[0089] From the above formula, we can deduce that Further deductions can be made Using the matrix inversion lemma, we can obtain:

[0090]

[0091] In the formula, the gain vector Update item From the above formula, we can derive:

[0092]

[0093] The solution process for the objective function obtained from the above formula is as follows: First, we obtain the result from the above formula. Then obtain the results sequentially. at last Therefore, the solution θ(n) of the objective function is obtained, and the solution process is as follows: Figure 3 As shown.

[0094] 2-3. Based on the Euclidean distance minimization criterion, find the Euclidean projection of vector θ(n) + η(n-1) onto the nonconvex set S, such that the vectors on the feasible region S are... To minimize the Euclidean distance between the vector θ(n) + η(n-1), we need to solve the following expression:

[0095]

[0096] In the formula: ω(n)=θ(n)+η(n-1),

[0097] Solving the above equation, we get the solution... The Euclidean distance is minimized at time, where

[0098] Θ(n) = [ω1(n), Θ2(n)],

[0099]

[0100] Q(n)=Θ(n)Θ T (n)

[0101] In this result, unless the largest eigenvalue of Q(n) is 1, the solution may become unstable after multiple iterations. Therefore, we need to introduce... Replace Q(n), where λ max Let Q(n) be the largest eigenvalue. The closed-form solution for minimizing the projected filter parameters is calculated as follows:

[0102]

[0103]

[0104]

[0105] In the formula Let represent the Kronecker product, and let vector u(n) be the eigenvector corresponding to the largest eigenvalue of matrix Q(n).

[0106] Step 3: Set the initial values ​​for the adaptive Hammerstein filter parameters.

[0107] Setting initial values ​​required for the Hammerstein filter parameter estimation process. η(0).

[0108] Step 4: Update parameters;

[0109] Update the vector sequentially using the method proposed in step 2. The updated objective function solution θ(n) is obtained.

[0110] Step 5: Echo cancellation;

[0111] Using the updated filter parameters θ(n) from step 4, the estimated echo signal at the current time n is obtained. Then subtract the estimated echo signal at this moment from the microphone signal d(n) at the current moment. Receive signal

[0112] Step 6: Iterate until the call ends;

[0113] Let n = n+1, and repeat steps 4 to 6 until the call ends.

[0114] This invention addresses the impact of echoes generated by communication systems on communication quality. It proposes a nonlinear filtering echo cancellation method, utilizing far-end signals and microphone signals to design and train an adaptive Hammerstein filter. The filtering problem is transformed into a recursive least-squares optimization problem with a non-convex feasible region constraint. The alternating direction multiplier method is used to solve the non-convex optimization problem. System parameters are progressively solved through ridge regression and Euclidean distance minimization, enabling the system to better simulate actual echo signals and effectively eliminate echoes.

[0115] It should be understood that the above description of the preferred embodiments is quite detailed and should not be construed as a limitation on the scope of protection of this invention. Any substitutions or modifications made by those skilled in the art under the guidance of this invention without departing from the scope of protection of the claims of this invention shall fall within the scope of protection of this invention. The scope of protection of this invention shall be determined by the appended claims.

Claims

1. An acoustic echo cancellation method based on nonlinear filtering, characterized in that, The steps are as follows: Step 1: Signal acquisition and adaptive Hammerstein filter model construction; Step 2: Calculate the solution to the objective function; Step 3: Set the initial values ​​for the adaptive Hammerstein filter parameters; Step 4: Update parameters; Step 5: Echo cancellation; Step 6: Iterate until the call ends; Step 1 is as follows: The remote signal is sampled to obtain the remote signal sample value at the current sampling time n. The far-end signal is broadcast on the loudspeaker and a microphone signal d(n) is generated by the loudspeaker-microphone system LEMS. The microphone signal d(n) consists of an echo signal y(n) and other near-end signals v(n), where v(n) represents the near-end speech in the intercom situation. The Hammerstein model is used to model the LEMS. The far-end sampled signal x(n) is used as the input of the adaptive Hammerstein filter. The echo signal estimate at the current time n is obtained through the filter. The adaptive Hammerstein filter model consists of two subsystems: a memoryless polynomial and a finite impulse response. The input to the memoryless polynomial subsystem is... The relationship between the output s(n) and the output s(n) is as follows: In the formula The sampled value of the far-end signal at sampling time n The column vectors formed by these vectors are all of dimension L. a The column vector, where the superscript T indicates transpose; The relationship between the input s(n) and the output y(n) of the finite impulse response subsystem is as follows: In the formula: X(n-1)=[x(n-1),…,x(nL b )], h(n)=vec([x(n),X(n-1)]), in For a dimension L b The column vector X(n-1) is a vector of dimension L. a ×L b The matrix vec(A) represents the process of straightening the columns of an m×n matrix A in order to form an m×n column vector. Step 2 is as follows: 2-1. Solve for the parameters of the adaptive Hammerstein filter model, representing it as a non-convex optimization problem, and define the objective function. In the formula, γ (0 < γ ≤ 1) is the forgetting factor; to ensure that the model parameters are within the non-convex feasible region The solution is then projected onto the feasible region S during the solution process, which is equivalent to solving for the objective function: θ∈S; Solve this problem using the ADMM algorithm, defining the following augmented Lagrangian function: In the formula, the penalty term ρ>0, let And when hour otherwise To avoid excessive computational complexity due to too many iterations, the ADMM algorithm iterative process, i.e., the adaptive and projection process, is performed only once at each time step. Where P S (θ(n)+η(n-1)) denotes the Euclidean projection of vector (θ(n)+η(n-1)) onto a nonconvex feasible region S; 2-2. Solve the objective function using the ADMM algorithm, transforming the objective function into the following form: Find: θ(n)=R -1 (n)p(n), where R(n)=H(n)+ρI, the superscript -1 denotes the inverse matrix, I is the identity matrix with the same dimension as matrix H(n), and H(n) is the autocorrelation function matrix of the input signal. s(n) is the cross-correlation function vector of the input signal. Define the following two matrices and Right now: above e j (j=1,2,…) is a unit column vector where the j-th element is 1 and the rest are 0, ξ=ρ(1-γ), χ j (n)(j=1,2,…,L) represents the j-th element of the column vector χ(n). L = L a +L b ; From the above formula, we can deduce that Further deductions can be made Using the matrix inversion lemma, we can obtain: In the formula, the gain vector Update item From the above formula, we can derive: The solution process for the objective function obtained from the above formula is as follows: First, we obtain the result from the above formula. Then obtain the results sequentially. at last Therefore, the solution θ(n) of the objective function can be obtained; 2-3. Based on the Euclidean distance minimization criterion, find the Euclidean projection of vector θ(n) + η(n-1) onto the nonconvex set S, such that the vectors on the feasible region S are... To minimize the Euclidean distance between the vector θ(n) + η(n-1), we need to solve the following expression: In the formula: ω(n)=θ(n)+η(n-1), Solving the above equation, we get the solution... The Euclidean distance is minimized at time, where Θ(n) = [ω1(n), Θ2(n)], Q(n)=Θ(n)Θ T (n) In this result, unless the largest eigenvalue of Q(n) is 1, the solution may become unstable after multiple iterations. Therefore, we need to introduce... Replace Q(n), where λ max Let Q(n) be the largest eigenvalue. The closed-form solution for minimizing the projected filter parameters is calculated as follows: In the formula Let represent the Kronecker product, and let vector u(n) be the eigenvector corresponding to the largest eigenvalue of matrix Q(n).

2. The acoustic echo cancellation method based on nonlinear filtering according to claim 1, characterized in that, Step 3 is as follows: Set the initial values ​​required for the Hammerstein filter parameter estimation process. η(0).

3. The acoustic echo cancellation method based on nonlinear filtering according to claim 2, characterized in that, Step 4 is as follows: Update the vector sequentially using the method proposed in step 2. The updated objective function solution θ(n) is obtained.

4. The acoustic echo cancellation method based on nonlinear filtering according to claim 3, characterized in that, Step 5 is as follows: Using the updated filter parameters θ(n) from step 4, the estimated echo signal at the current time n is obtained. Then subtract the estimated echo signal at this moment from the microphone signal d(n) at the current moment. Receive signal 5. The acoustic echo cancellation method based on nonlinear filtering according to claim 4, characterized in that, Step 6 is as follows: Let n = n + 1, and repeat steps 4 to 6 until the call ends.

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