Robust frequency domain distributed channel estimation method based on censored regression model

Abstract

The invention discloses a robust frequency domain distributed channel estimation method based on a censored regression model. The method mainly comprises the following steps: A, collecting sample signals of node censored data in a distributed network; b, establishing a corrected sample signal deletion model; c, obtaining a frequency domain input signal # imgabs0 # D, and obtaining an output gi (k) through an overlapping storage method; e, updating parameters # imgabs1 # F by a stochastic gradient method, and obtaining an output hi (k) by an overlapping storage method; g, acquiring an error # imgabs2 # H, and establishing a cost function f (ei (k)) based on an asymmetric entropy criterion; i, updating the parameter sigma i (k) by a stochastic gradient method; j, performing frequency domain updating on the intermediate estimation vector # imgabs3 #; k, combining the neighbor nodes to obtain updated channel parameter estimation; and L, iterating, and repeating the steps from A to K until the end of distributed adaptive channel estimation. The method provided by the invention can overcome the adverse effect of data deletion of nodes in the distributed network, and has more efficient and robust distributed channel estimation capability.

Description

Technical Field

[0001] The invention belongs to the technical field of digital signal processing, and in particular relates to a robust frequency domain distributed channel estimation method based on a censored regression model. Background Art

[0002] In the field of digital signal processing, adaptive system identification involves accurate estimation of system parameters, which is an important prerequisite for system analysis and improving system performance. The core of the adaptive method is that it can dynamically adjust the parameters of the system model according to the changes in input and output signals to ensure that the model can accurately reflect the state changes of the system. In this process, the adaptive filtering method needs to be based on optimization criteria to achieve accurate estimation of system parameters.

[0003] The distributed channel estimation problem is one of the important applications in the fields of communications and networks. A major challenge facing channel estimation based on distributed signal processing technology is how to deal with and process the uncertainty noise in the signal. These noises may be caused by a variety of factors, including environmental interference and equipment noise, which interfere with the true characteristics of the channel and make the system identification process more complicated. In order to solve this problem, adaptive channel estimation methods usually integrate noise suppression and signal smoothing techniques to enhance the accuracy and robustness of identification.

[0004] In the channel estimation problem, the situation where some measurement values ​​are not accurately obtained due to the influence of the saturation characteristics of the actual physical sensor equipment is called measurement censoring. Measurement censoring has a significant impact on the performance of the adaptive method. It reduces the amount of data available for estimation and analysis, resulting in inaccurate channel estimation of the traditional distributed least mean-square method (DLMS) or causing significant performance degradation. Therefore, the distributed channel estimation method needs to have the ability to handle measurement censoring, alleviate the impact of measurement censoring on the adaptive signal processing results, and ensure the accuracy and reliability of signal estimation. Reference 1 "Liu Z, Li C, Liu Y. Distributed censored regression overnetworks[J]. IEEE Transactions on Signal Processing, 2015, 63(20): 5437-5449." proposes a distributed least mean square method based on a censored regression model. This method can perform distributed learning on the system parameters to be identified under the censored regression model. However, as the dimension of channel parameters increases, the computational complexity increases, the amount of calculation increases, and the method is not robust to non-Gaussian noise interference. It is necessary to further improve the performance of the distributed channel estimation method. Summary of the invention

[0005] The purpose of the present invention is to provide a robust frequency domain distributed channel estimation method based on a censored regression model, which can effectively compensate for the estimation deviation caused by the censored information, and is combined with the maximum asymmetric entropy criterion to be applied to the frequency domain distributed adaptive filter. It has the robustness of compensating for the measurement censored data and resisting non-Gaussian interference, and has high computational efficiency and better distributed channel estimation performance.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: using the censored regression model to correct the distortion of the system output signal caused by measurement censoring, reducing the sensitivity of the learning process to large deviation values ​​through the maximum asymmetric entropy criterion, performing frequency domain calculations on linear convolution and linear correlation operations in the time domain through overlapping and stored fast Fourier transform, and performing accurate and efficient distributed channel estimation in the frequency domain;

[0007] The steps of this method are as follows:

[0008] A. Censored Regression Model

[0009] Establish a distributed network consisting of a group of N nodes, and for each node in the network, use the M-dimensional input signal u at the current time n i (n)=[u i (n),u i (n-1),...,u i (n-M+1)] T ,i=1,2,...,N, the actual M-dimensional channel parameter is w o =[w1,w2,...,w M ] T , the complete system measurement information is The background noise η i (n) has a mean of 0 and a variance of Gaussian white noise, υ i (n) is non-Gaussian noise with mean 0;

[0010] Considering the censoring characteristics of actual physical sensors, the measured sample signal

[0011] B. Correction of sample selection bias

[0012] The data loss caused by physical sensors leads to sample selection bias, which needs to be corrected and the vector parameters are selected.

[0013] According to the censored regression model, the corrected sample signal model is obtained as follows:

[0014]

[0015] where φ(·) represents the standard normal cumulative distribution function, represents the standard normal distribution probability density function;

[0016] C. Establish frequency domain input signal vector

[0017] In the kth data block, the input signal is cached to generate an input signal vector u of length M i (k)=[u i (kM+1),u i (kM+2),…,u i (kM+M)] T , where the data block length is the same as the tap delay length;

[0018] From the previous data block u i (k-1) and the current data block u i (k) Combination, frequency domain operation on the combined vector Where FFT stands for Fast Fourier Transform, represents the index in the frequency domain;

[0019] D. Get the output of the linear convolution operation

[0020] According to overlapping storage, using the frequency domain input signal vector and 2M-dimensional vector where q i (k) is the vector parameter q i The M-dimensional output vector g is obtained by inverse fast Fourier transform IFFT operation. i (k):

[0021] Take the last M elements, where represents the Hadamard product;

[0022] E. Vector parameters Frequency domain update of

[0023] Introducing indicator variable c i (n), satisfying the condition And get the M-dimensional data block c i (k) = [c i (kM+1),c i (kM+2),…,c i (kM+M)] T ;

[0024] Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the following frequency domain signal vector;

[0025]

[0026] According to the overlapping storage method, the output of the linear correlation operation is obtained:

[0027] Take the first M elements, where conj(·) represents the complex conjugation operation;

[0028] By using the stochastic gradient method, we get the parameter vector The frequency domain update criterion of is:

[0029]

[0030] in is the step size parameter;

[0031] F. Get the output of the linear convolution operation

[0032] According to overlapping storage, using the frequency domain input signal vector and a 2M-dimensional estimation vector The M-dimensional output vector h is obtained by IFFT operation i (k):

[0033] Take the last M elements;

[0034] G. Calculation of error vector

[0035] Using the frequency domain input signal vector and 2M-dimensional frequency domain parameter vector where w i (k) is the channel parameter w o The M-dimensional output vector y is obtained by IFFT operation. i (k):

[0036] Take the last M elements;

[0037] By i (n) Get the M-dimensional data block d i (k) = [d i (kM+1),d i (kM+2),...,d i (kM+M)] T , and get the error vector:

[0038]

[0039] where σ i (k) is σ i estimates;

[0040] H. Establishing a robust cost function

[0041] The cost function is established based on the asymmetric entropy criterion:

[0042]

[0043] The parameters

[0044] At the moment n=kM+j,j=1,2,…,M, the partial derivative of the cost function on the error signal is obtained:

[0045]

[0046] Note that the data block f(e i (k)) = [f(e i (kM+1)),f(e i (kM+2)),...,f(e i (kM+M))] T ;

[0047] I. Parameter σ i (k) Updates

[0048] By using the stochastic gradient method, we get the parameter σ i (k) Updates:

[0049]

[0050] in is the step size parameter;

[0051] J. Intermediate estimation vector Frequency domain update of

[0052] Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the frequency domain signal vector:

[0053]

[0054] According to the overlapping storage method, the linear correlation operation is calculated in the frequency domain to obtain an M-dimensional gradient vector:

[0055] Take the first M elements;

[0056] By using the stochastic gradient method, the frequency domain update rule of the intermediate estimation vector is obtained as follows:

[0057]

[0058] where μ i is the step size parameter;

[0059] K, the combination between neighbor nodes to obtain the updated channel parameter estimate

[0060]

[0061] Where N i is the set of neighbor nodes of node i in the distributed network, node l is the neighbor of node i, and the combination coefficient a l,i Following Metropolis rules:

[0062]

[0063] L. Iteration: repeat steps A to K until the distributed adaptive channel estimation is completed.

[0064] The beneficial effects of the present invention are:

[0065] The present invention overcomes the influence of incomplete observation of system output signals caused by actual sensor deletion characteristics, can correct the distortion of system output signals caused by measurement deletion, and is applied to frequency domain distributed adaptive channel estimation based on asymmetric entropy criterion. This method has the robustness against non-Gaussian noise interference, and calculates linear convolution and linear correlation operations through overlapping storage fast Fourier transform, which significantly reduces the computational complexity. It further improves the performance of distributed channel estimation under sensor measurement deletion conditions, and has more efficient and robust adaptive channel parameter estimation capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a topological diagram of a distributed network in an embodiment of the present invention;

[0067] Figure 2 It is a network mean square deviation curve diagram of the method of the present invention, the method of document 1 and the traditional DLMS method in Experiment 1 when the channel model is a set of randomly generated parameters;

[0068] Figure 3 It is a network channel parameter diagram whose channel model complies with the ITU-T G.168 standard;

[0069] Figure 4 It is a network mean square deviation curve diagram of the method of the present invention, the method of document 1 and the traditional DLMS method in Experiment 2 when the channel model conforms to the network channel parameters of the ITU-T G.168 standard. DETAILED DESCRIPTION

[0070] Example:

[0071] The specific steps of the robust frequency domain distributed channel estimation method based on the censored regression model in this embodiment are as follows:

[0072] A. Censored Regression Model

[0073] Establish a distributed network consisting of a group of N nodes, and for each node in the network, use the M-dimensional input signal u at the current time n i (n)=[u i (n),u i (n-1),...,u i (n-M+1)] T ,i=1,2,...,N, the actual M-dimensional channel parameter is w o =[w1,w2,...,w M ] T , the complete system measurement information is The background noise η i (n) has a mean of 0 and a variance of Gaussian white noise, υ i (n) is non-Gaussian noise with mean 0;

[0074] Considering the censoring characteristics of actual physical sensors, the measured sample signal

[0075] B. Correction of sample selection bias

[0076] The data loss caused by physical sensors leads to sample selection bias, which needs to be corrected and the vector parameters are selected.

[0077] According to the censored regression model, the corrected sample signal model is obtained as follows:

[0078]

[0079] where φ(·) represents the standard normal cumulative distribution function, represents the standard normal distribution probability density function;

[0080] C. Establish frequency domain input signal vector

[0081] In the kth data block, the input signal is cached to generate an input signal vector u of length M i (k)=[u i (kM+1),u i (kM+2),...,u i (kM+M)] T , where the data block length is the same as the tap delay length;

[0082] From the previous data block u i (k-1) and the current data block u i (k) Combination, frequency domain operation on the combined vector Where FFT stands for Fast Fourier Transform, represents the index in the frequency domain;

[0083] D. Get the output of the linear convolution operation

[0084] According to overlapping storage, using the frequency domain input signal vector and 2M-dimensional vector where q i (k) is the vector parameter q i The M-dimensional output vector g is obtained by inverse fast Fourier transform IFFT operation. i (k):

[0085] Take the last M elements, where represents the Hadamard product;

[0086] E. Vector parameters Frequency domain update of

[0087] Introducing indicator variable c i (n), satisfying the condition And get the M-dimensional data block c i (k) = [c i (kM+1),c i (kM+2),...,c i (kM+M)] T ;

[0088] Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the following frequency domain signal vector;

[0089]

[0090] According to the overlapping storage method, the output of the linear correlation operation is obtained:

[0091] Take the first M elements, where conj(·) represents the complex conjugation operation;

[0092] By using the stochastic gradient method, we get the parameter vector The frequency domain update criterion of is:

[0093]

[0094] in is the step size parameter;

[0095] F. Get the output of the linear convolution operation

[0096] According to overlapping storage, using the frequency domain input signal vector and a 2M-dimensional estimation vector The M-dimensional output vector h is obtained by IFFT operation i (k):

[0097] Take the last M elements;

[0098] G. Calculation of error vector

[0099] Using the frequency domain input signal vector and 2M-dimensional frequency domain parameter vector where w i (k) is the channel parameter w o The M-dimensional output vector y is obtained by IFFT operation. i (k):

[0100] Take the last M elements;

[0101] By i (n) Get the M-dimensional data block d i (k) = [d i (kM+1),d i (kM+2),...,d i (kM+M)] T , and get the error vector:

[0102]

[0103] where σ i (k) is σ i estimates;

[0104] H. Establishing a robust cost function

[0105] The cost function is established based on the asymmetric entropy criterion:

[0106]

[0107] The parameters

[0108] At the moment n=kM+j,j=1,2,…,M, the partial derivative of the cost function on the error signal is obtained:

[0109]

[0110] Note that the data block f(e i (k)) = [f(e i (kM+1)),f(e i (kM+2)),…,f(e i (kM+M))] T ;

[0111] I. Parameter σ i (k) Updates

[0112] By using the stochastic gradient method, we get the parameter σ i (k) Updates:

[0113]

[0114] in is the step size parameter;

[0115] J. Intermediate estimation vector Frequency domain update of

[0116] Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the frequency domain signal vector:

[0117]

[0118] According to the overlapping storage method, the linear correlation operation is calculated in the frequency domain to obtain an M-dimensional gradient vector:

[0119] Take the first M elements;

[0120] By using the stochastic gradient method, the frequency domain update rule of the intermediate estimation vector is obtained as follows:

[0121]

[0122] where μ i is the step size parameter;

[0123] K, the combination between neighbor nodes to obtain the updated channel parameter estimate

[0124]

[0125] Where N i is the set of neighbor nodes of node i in the distributed network, node l is the neighbor of node i, and the combination coefficient a l,i Following Metropolis rules:

[0126]

[0127] L. Iteration: repeat steps A to K until the distributed adaptive channel estimation is completed.

[0128] Numerical simulation experiment:

[0129] In order to verify the effectiveness of the present invention, numerical simulation experiments were conducted and compared with the existing document 1 method and the traditional DLMS method.

[0130] In numerical simulation, the topology of the distributed network is as follows: Figure 1 As shown, there are 10 nodes in total. The channel model of Experiment 1 is a set of randomly generated parameters of length 8. The system input is a first-order autoregressive signal sequence with a correlation coefficient of 0.6. Gaussian white noise with a signal-to-noise ratio of 30dB is selected as the background noise, and F-distributed noise with a probability density distribution of F(40,3) is added. The measurement sensor equipment presents the characteristics of missing data.

[0131] The parameter values ​​of the method of the present invention in Experiment 1 are: μ i =0.035, The step size parameter of the method in Reference 1 is: i =0.008; the step size parameter of the traditional DLMS method is: μ i =0.004.

[0132] In distributed channel estimation experiments, the network mean square deviation is generally used as an evaluation indicator of the estimation effect. After 100 independent tests, the faster the network mean square deviation curve converges and the lower the steady-state value, the better the distributed channel estimation performance.

[0133] Figure 2 This is the network mean square deviation curve of the method of the present invention, the method of reference 1 and the traditional DLMS method in Experiment 1. Figure 2 It can be seen that the method in document 1 and the traditional DLMS method are not robust to non-Gaussian noise interference because they use mean square error as the cost function, and the network mean square deviation curve diverges. The method of the present invention can converge well and has a good distributed channel estimation effect.

[0134] The channel model of Experiment 2 is 128 in length and complies with the network channel parameters of the ITU-T G.168 standard. Its amplitude is as follows: Figure 3 The system input and noise interference conditions are the same as those in Experiment 1, and the measurement sensor equipment presents the characteristics of missing data.

[0135] The parameter values ​​of the method of the present invention in Experiment 2 are: μ i =0.003, λ i =1; the step size parameter of the method in reference 1 is: μ i =0.002; the step size parameter of the traditional DLMS method is: μ i =0.004.

[0136] Figure 4 This is the network mean square deviation curve of the method of the present invention, the method of reference 1 and the traditional DLMS method in Experiment 2. Figure 4It can be seen that under the interference of F-distributed noise, the method in document 1 and the traditional DLMS method fail, and the method of the present invention has good convergence performance, high computational efficiency, and excellent distributed channel parameter estimation effect.

Claims

1. A robust frequency domain distributed channel estimation method based on a censored regression model, the steps of which are: A. Censored Regression Model Establish a distributed network consisting of a group of N nodes, and for each node in the network, use the M-dimensional input signal u at the current time n i (n)=[u i (n),u i (n-1),…,u i (n-M+1)] T ,i=1,2,...,N, the actual M-dimensional channel parameter is w o =[w1,w2,...,w M ] T , the complete system measurement information is The background noise η i (n) has a mean of 0 and a variance of Gaussian white noise, υ i (n) is non-Gaussian noise with mean 0; Considering the censoring characteristics of actual physical sensors, the measured sample signal B. Correction of sample selection bias The data loss caused by physical sensors leads to sample selection bias, which needs to be corrected and the vector parameters are selected. According to the censored regression model, the corrected sample signal model is obtained as follows: where φ(·) represents the standard normal cumulative distribution function, represents the standard normal distribution probability density function; C. Establish frequency domain input signal vector In the kth data block, the input signal is cached to generate an input signal vector u of length M i (k)=[u i (kM+1),u i (kM+2),...,u i (kM+M)] T , where the data block length is the same as the tap delay length; From the previous data block u i (k-1) and the current data block u i (k) Combination, frequency domain operation on the combined vector Where FFT stands for Fast Fourier Transform, represents the index in the frequency domain; D. Get the output of the linear convolution operation According to overlapping storage, using the frequency domain input signal vector and 2M-dimensional vector where q i (k) is the vector parameter q i The M-dimensional output vector g is obtained by inverse fast Fourier transform IFFT operation. i (k): Take the last M elements, where represents the Hadamard product; E. Vector parameters Frequency domain update of Introducing indicator variable c i (n), satisfying the condition And get the M-dimensional data block c i (k) = [c i (kM+1),c i (kM+2),...,c i (kM+M)] T ; Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the following frequency domain signal vector; According to the overlapping storage method, the output of the linear correlation operation is obtained: Take the first M elements, where conj(·) represents the complex conjugation operation; By using the stochastic gradient method, we get the parameter vector The frequency domain update criterion of is: in is the step size parameter; F. Get the output of the linear convolution operation According to overlapping storage, using the frequency domain input signal vector and a 2M-dimensional estimation vector The M-dimensional output vector h is obtained by IFFT operation i (k): Take the last M elements; G. Calculation of error vector Using the frequency domain input signal vector and 2M-dimensional frequency domain parameter vector where w i (k) is the channel parameter w o The M-dimensional output vector y is obtained by IFFT operation. i (k): Take the last M elements; By i (n) Get the M-dimensional data block d i (k) = [d i (kM+1),d i (kM+2),...,d i (kM+M)] T , and get the error vector: where σ i (k) is σ i estimates; H. Establishing a robust cost function The cost function is established based on the asymmetric entropy criterion: The parameters At the moment n=kM+j,j=1,2,...,M, the partial derivative of the cost function with respect to the error signal is obtained: Note that the data block f(e i (k)) = [f(e i (kM+1)),f(e i (kM+2)),…,f(e i (kM+M))] T ; I. Parameter σ i (k) Updates By using the stochastic gradient method, we get the parameter σ i (k) Updates: in is the step size parameter; J. Intermediate estimation vector Frequency domain update of Perform FFT operation on the 2M-dimensional signal after zero padding to obtain the frequency domain signal vector: According to the overlapping storage method, the linear correlation operation is calculated in the frequency domain to obtain an M-dimensional gradient vector: Take the first M elements; By using the stochastic gradient method, the frequency domain update rule of the intermediate estimation vector is obtained as follows: where μ i is the step size parameter; K, the combination between neighbor nodes to obtain the updated channel parameter estimate Where N i is the set of neighbor nodes of node i in the distributed network, node l is the neighbor of node i, and the combination coefficient a l,i Following Metropolis rules: L. Iteration: repeat steps A to K until the distributed adaptive channel estimation is completed.

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