A Sparse Constraint Total Minimum Logarithmic Hyperbolic Cosine Adaptive Filter

Abstract

The present invention discloses a sparse-constrained total least log hyperbolic cosine adaptive filter, belonging to the field of digital filter design. This adaptive filter is established by linear constraint conditions and the log hyperbolic cosine function, and at the same time, an l1 norm penalty term is added to the cost function, and the total least squares method is introduced. By adding the l1 norm penalty, the problem of performance degradation of the algorithm in the case of unknown system sparsity is solved. The l1 norm-based constrained total least log hyperbolic cosine adaptive filter disclosed by the present invention can be applied to the identification of sparse systems and can also be used in adaptive beamforming to reduce energy consumption.

Description

Technical Field

[0001] The present invention discloses an adaptive filter, and specifically discloses a sparse constraint total least log hyperbolic cosine adaptive filter, belonging to the field of digital filter design. Background Art

[0002] System identification is an important branch of adaptive signal processing. Many traditional problems such as adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation, and active noise control can be attributed to system identification problems. In many application scenarios, most of the unknown systems are sparse systems, that is, most of the elements in the coefficient vector of the unknown system are zero or close to zero. The sparse system identification problem is often involved in theoretical and engineering practices and is one of the current research hotspots. Current research shows that using the low-order norm regularization or proportional update of the weight vector can effectively improve the convergence speed of the adaptive filter.

[0003] In addition, in the real physical world, many fields require the system to satisfy both linear constraints and sparsity conditions at the same time. For example, in the beamforming technology commonly used in the Global Navigation Satellite System (GNSS), due to the limitations of the power supply system, in order to reduce the system power consumption and extend the standby time, a sparse antenna array is sometimes adopted. Andrade et al. proposed an l 1 -norm constrained normalized LMS adaptive algorithm [de Andrade J F, de Campos M L R, Apolinário J A. An l 1 -constrained normalized LMS algorithm and its application to thinned adaptive antenna arrays [C] / / 2013 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2013: 3806 - 3810]. This algorithm combines low-order norm constraints and linear constraints, but it performs poorly in the presence of noise in the input signal. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a sparse constraint total least log hyperbolic cosine adaptive filter (l 1 -CLTL). This filter adds an l 1 -norm constraint penalty term to the cost function of the CLTL adaptive filtering algorithm, thereby improving its identification ability for sparse systems.

[0005] To implement the above solution, the present invention aims to: propose an l 1 -CLTL filter, which is used to better simulate the characteristics of a system simultaneously subjected to linear and sparse constraints when the input signal and the output signal are contaminated by noise.

[0006] The l 1 -CLTL filter updates the coefficient vector including the following steps:

[0007] 1) Calculate the error signal e using the input signal at time n and the desired signal n , that is where is the input signal contaminated by noise u n , is the desired signal contaminated by noise v n , x n = [x n , x n-1 ,... x n-M+1 T is the input vector composed of the first M sample values {x n , x n-1 ,... x n-M+1} of the input signal, w n = [w 0,n , w 1,n ,... w M-1,n T is the coefficient vector composed of M tap coefficients of the adaptive filter, and T represents the transpose operation;

[0008] 2) The modified augmented weight vector n can be calculated from the coefficient vector w where is the variance ratio between the output noise v n and the input noise u n sequences;

[0009] 3) Calculate the intermediate variable g using the input vector n the error signal e , the parameter λ and the augmented weight vector according to the calculation formula LTL (w n ), where tanh(·) represents the hyperbolic tangent operator;

[0010] 4) Calculate the intermediate variable 1 from the l norm error and α = sgn(w n )​​T Psgn(w n ), where P = I L -C(C T C) -1 C T ;

[0011] 5) Update the coefficient vector of the adaptive filter using the calculation formula , where μ is the step size, q = C(C T C) -1 f, C and f are the linear constraint matrix and vector.

[0012] Preferably, in the step 4), calculate the l norm error according to the calculation formula 1 where t = ||w || is the given positive sparsity parameter, t o = sgn(w n ) n w T is an intermediate variable, sgn(·) represents the sign operator, w n = R o C(C -1 R T R - 1 C) -1 f, and R is the autocorrelation matrix of the input signal.

[0013] Advantageous Effects

[0014] Compared with the existing technology, the l 1 -CLTL filter proposed in this application converges faster in a sparse system, has better robustness, and can still exhibit good performance when both the input signal and the output signal are corrupted by noise. Description of the Drawings

[0015] The present invention will be further described below in conjunction with the drawings and embodiments:

[0016] Figure 1 is the structural schematic diagram of the sparse constraint total least log hyperbolic cosine adaptive filter according to the embodiment of the present invention;

[0017] Figure 2 is the comparison of the normalized mean square error of the adaptive filter according to the embodiment of the present invention in the embodiment.

[0018] Figure 3 is the comparison of the beam pattern of the adaptive filter according to the embodiment of the present invention in the embodiment.

[0019] Figure 4Schematic diagram of the enabling situation of the adaptive filter in the embodiment of the present invention in a sparse uniform linear array in the embodiment. Detailed implementation manners

[0020] Embodiment

[0021] The l 1 -CLTL filter proposed in this application, its working process:

[0022] First, combine the minimum logarithmic hyperbolic cosine function and the l 1 norm constraint penalty term, and introduce linear constraints and total least squares method to update the unknown system coefficient vector, and use the Lagrange multiplier method to calculate the update formula of the adaptive filter coefficients proposed in the implementation manner of this application.

[0023] This embodiment uses the method of computer experiments to verify the performance of the l 1 -CLTL filter. In the experiment, the l 1 -CLTL filter disclosed in the present invention is used to identify the unknown system in an environment where the input and output signals are corrupted by noise. The unknown system used in the experiment is a sparse system, and its performance is compared with the performance of the CLMS, CLL, CLTL, and l 1 -CLMS adaptive filtering algorithms. And use the l 1 -CLTL filter disclosed in the present invention to implement the beamforming problem.

[0024] The l 1 -CLTL adaptive filter disclosed in the implementation manner of this application performs system identification including the following steps:

[0025] 1) Calculate the error signal e through the input signal at time n and the desired signal n , that is where is the input signal contaminated by noise u n , is the desired signal contaminated by noise v n , x n = [x n , x n-1 ,... x n-M+1 T is the input vector composed of the first M sample values {x n , x n-1 ,... x n-M+1} of the input signal, w n = [w 0,n , w 1,n ,... w M-1,n T ​​is the coefficient vector composed of M tap coefficients of the adaptive filter, and T represents the transpose operation;

[0026] 2) From the coefficient vector w n the modified augmented weight vector can be calculated as where is the output noise v n and the variance ratio between the input noise u n sequences. According to the calculation formula calculate l 1 norm error where t = ||w o || is the given positive sparsity parameter, t n = sgn(w n ) T w n is an intermediate variable, sgn(·) represents the sign operator, and w o = R -1 C(C T R -1 C) -1 f, and R is the autocorrelation matrix of the input signal;

[0027] 3) From the input vector the error signal e n , the parameter λ, and the augmented weight vector calculate the intermediate variable g (w n ) according to the calculation formula LTL , where tanh(·) represents the hyperbolic tangent operator;

[0028] 4) From the l 1 norm error calculate the intermediate variables and α = sgn(w n ) T Psgn(w n ) where P = I L - C(C T C) -1 C T ;

[0029] 5) Update the coefficient vector of the adaptive filter using the calculation formula , where μ is the step size, q = C(C T C) -1 f, and C and f are the linear constraint matrix and vector.

[0030] In the experiment, Gaussian - Bernoulli noise is used to simulate non - Gaussian heavy - tailed noise, and it is (1 - φ n )A n + φ nB n is composed, where A n and B n are Gaussian noise processes with variances of and respectively. φ n is a Bernoulli process, and P[φ n = 1] = P r , P[φ n = 0] = 1 - P r .

[0031] In the sparse system identification experiment, the input signal is a white signal with a variance of . The normalized mean square deviation (NMSD) is used as a measure of the algorithm performance, that is, NMSD = 10log(||w n - w|| 2 / ||w opt || 2 ), with the unit of dB, where log represents taking the logarithm, w opt is the optimal weight vector, and are 0.3 and 10 respectively, and P r = 0.02. Figure 2 The NMSD curves obtained from the simulation in

[0032] are all obtained by averaging 1000 independent iterations. and are 0.8 and 100 respectively, and P r = 0.05. The constraint matrix C and the response vector f are such that the output of the array gets a unit response in the direction of the useful signal.

[0033] It can be seen from Figure 2 that the l 1 - CLTL filter of the embodiment of the present application has good robustness, has the fastest convergence speed and the lowest steady-state misadjustment in sparse system identification, and still has good performance in an environment where both the input signal and the output signal are corrupted by noise.

[0034] According to Figure 3 's beam pattern, it can be seen that the l 1 - CLTL adaptive filtering algorithm suppresses the interference signal at a more accurate angle. Figure 4 shows the distribution of the enabled array elements for the sparse linear array. A unit linear array composed of 21 array elements, only 11 of which are enabled, confirms that the l 1- CLTL can generate sparse solutions, so some array elements can be turned off to reduce power consumption in applications such as adaptive antenna arrays.

[0035] From the experimental results, it can be seen that the l disclosed in the present invention 1 - The CLTL adaptive filter has strong anti-impulse interference ability and sparse system identification ability, and can still maintain good performance when both the input signal and the output signal are corrupted by noise.

[0036] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable those who are familiar with this technology to understand the content of the present invention and implement it accordingly, and cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit and essence of the present invention should be covered within the protection scope of the present invention.

Claims

1. A sparse-constrained total least log-cosh adaptive filter, Characterized in that, The steps for updating the coefficient vector of the adaptive filter are as follows: 1) Calculate the error signal e using the input signal at time n n and the desired signal , i.e., where n is the input signal contaminated by noise u and n is the desired signal contaminated by noise v n , x n = [x n-1 , x n-M+1 T is the input vector composed of the first M samples {x n , x n-1 ,... x n-M+1} of the input signal, and w n = [w 0,n , w 1,n ,... w M-1,n T is the coefficient vector composed of the M tap coefficients of the adaptive filter, and T represents the transpose operation;​​ 2) Augmented weight vector is calculated from coefficient vector w n ​ 3) From the input vector error signal e n , the adjustment parameter λ of the lncosh function, and the augmented weight vector and according to the calculation formula calculate the intermediate variable g LTL (w n ), where tanh(·) represents the hyperbolic tangent operator; 4) From l 1 Norm error Calculate the intermediate variable r n and α, α = sgn(w n ) T Psgn(w n )), where P = I L -C(C T C) -1 C T ; 5) Use the calculation formula to update the coefficient vector of the adaptive filter, where μ is the step size, q = C(C T C) -1 f, C and f are the linear constraint matrix and vector.

2. The adaptive filter according to claim 1, Characterized in that, In step 4), according to the calculation formula calculate l 1 norm error where t = ||w o || is a given positive sparsity parameter, t n = sgn(w n ) T w n is an intermediate variable, sgn(·) represents the sign-taking operator, w o = R -1 C(C T R -1 C) -1 f, and R is the autocorrelation matrix of the input signal.

3. The adaptive filter according to claim 1, Characterized in that, In step 2), where β is the variance ratio n between the output noise v n and the input noise u sequences.

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