A power line channel estimation method, a power line communication receiving device and a medium

Abstract

The application discloses a power line channel estimation method, device and medium, and the method comprises the following steps: S1, a Vandermonde structure manifold matrix containing multipath delay information is constructed; S2, based on the Vandermonde structure manifold matrix, a super-complete manifold matrix containing all potential delay point positions is constructed, and a channel estimation problem is converted into a sparse representation problem; S3, an unconstrained optimization objective function is constructed; S4, singular value decomposition is performed on received OFDM pilot signal data of multiple time periods, a signal subspace is extracted, and compression and noise suppression of sampling data are realized; S5, the data compressed through step S4 is substituted into the optimization objective function constructed in step S3 to obtain high-precision multipath delay estimation; and S6, based on the multipath delay estimation, a complete power line channel response is reconstructed, and high-resolution and high-robustness channel estimation results are obtained in a power line channel environment with high noise and strong multipath interference at a relatively low calculation complexity.

Description

Technical Field

[0001] This invention relates to the field of power line communication technology, and in particular to a method for high-precision and robust power line channel estimation in orthogonal frequency division multiplexing (OFDM) systems using sparse representation theory and second-order cone programming optimization algorithm, as well as the device and storage medium for implementing the method. Background Technology

[0002] Power line communication (PLC) utilizes existing power line networks for data transmission, offering the advantage of eliminating the need for rewiring and making it a key technology for building smart grids and the Internet of Things (IoT). However, the power line channel environment is exceptionally complex; the diversity of loads and the irregularity of line topology lead to severe signal reflection and refraction, resulting in significant multipath effects and frequency-selective fading. Orthogonal frequency division multiplexing (OFDM) technology, due to its high spectral efficiency and multipath resistance, is widely used in PLC systems to overcome these challenges. However, the performance of OFDM systems is highly dependent on the receiver's accurate estimation of channel state information (CSI).

[0003] Traditional channel estimation methods, such as least squares (LS) and linear minimum mean square error (LMMSE) estimation, have limited accuracy in high-noise, high-interference environments like PLCs. While MUSIC-type algorithms based on subspace decomposition can improve resolution, their performance heavily depends on the signal-to-noise ratio and the number of samples, and they require some prior channel information (such as the number of multipath paths), making them insufficiently robust in practical PLC environments. Furthermore, many existing high-resolution algorithms have extremely high computational complexity, making it difficult to meet the real-time requirements of PLC devices.

[0004] Therefore, there is an urgent need in this field for a power line channel estimation method that can balance high estimation accuracy, strong robustness, and low computational complexity. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problem of how to achieve high-resolution, high-robustness and computationally efficient estimation of power line channel multipath parameters without relying on precise initial values. The invention proposes a power line channel estimation method, a power line communication receiving device and a medium.

[0006] The technical problem of this invention is solved by the following technical solution: In a first aspect, the present invention provides a power line channel estimation method, comprising the following steps: S1. The frequency domain channel model of the power line channel is transformed into the time domain impulse response model. The equal arithmetic characteristics between the subcarrier frequencies of the orthogonal frequency division multiplexing (OFDM) system are used to construct a Vandermonde structure manifold matrix containing multipath delay information. S2. Based on the Vandermonde structure manifold matrix, construct an overcomplete manifold matrix containing all potential delay point locations, transforming the channel estimation problem into a sparse representation problem, where non-zero values ​​exist only at the actual multipath delay locations. S3. Construct an unconstrained optimization objective function with the Frobenius norm distance between the observed data and the estimated data as the fidelity term and the L1 norm of the estimated signal as the sparsity penalty term. S4. Perform singular value decomposition on the received OFDM pilot signal data from multiple time periods, extract the signal subspace, and achieve compression and noise suppression of the sampled data; S5. Substitute the data compressed in step S4 into the optimization objective function constructed in step S3, and transform the optimization problem into a second-order cone programming form. Use a convex optimization algorithm to solve it to obtain a high-precision multipath delay estimate. S6. Based on the multipath delay estimation, the complete power line channel response is reconstructed.

[0007] In some embodiments, the following technical features are also included: In step S1, the time-domain impulse response model Represented as: ; in, This represents the weight factor of the l-th path. The delay of the l-th path, Let be the transmission distance of the l-th path, and v be the speed of electromagnetic wave propagation in the copper conductor. , Let represent the Dirac impulse function, and t represent the time variable.

[0008] In some embodiments, the Vandermonde structure manifold matrix described in step S1 Represented as: ; in, , Let Vandermonde structure manifold represent the delay information corresponding to the l-th path.

[0009] In some embodiments, the overcomplete manifold matrix described in step S2 Represented as: ; in, Indicates vector Diagonalize the grid points to represent all time delay locations of interest. , Denotes an overcomplete set matrix. This indicates that its value is not zero only when the delay points of L paths exist; otherwise, it is all zero.

[0010] In some embodiments, the objective function in step S3 is expressed as: ; Where min represents the minimum value. Denotes the square of the F-norm. Represents the 0 norm, This represents the energy of the noise, and 'st' indicates that the constraint is true; at this time... The dimension is ,in This represents the Gaussian white noise matrix, where M represents the number of samples, and the OFDM symbols of the N pilots acquired at the power line receiver. .

[0011] In some embodiments, performing singular value decomposition on the received signal data in step S4 specifically involves: decomposing the received signal matrix... Y The singular value decomposition is performed as follows: ;in, U Describes a left singular vector matrix. V Describes a right singular vector matrix. Indicates conjugate transpose; Due to the properties of singular value decomposition, the received signal matrix Y is decomposed into a signal subspace and a noise subspace, and then the following processing is performed: ; Therefore, there is ; in, This represents the received data after singular value decomposition. Represents the data compression matrix. This represents the data matrix after singular value decomposition of the received signal matrix in an OFDM system. and Definition and similar.

[0012] In some embodiments, the convex optimization algorithm in step S5 includes the interior point method, which transforms the optimization problem into a second-order cone programming form, specifically including the following steps: S51. After reducing the dimensionality of the received signal matrix, the second-order cone optimization problem is defined as follows: ; in Let represent a linear objective function, x represent the variable to be optimized, and T represent the transpose. Let A and c represent the linear constraint inequality, and b and d represent constant terms. This represents a linear constraint equation, where g is a constant term; S52. Using auxiliary variables p and q, and by transferring the nonlinear part to the constraints, the objective function represented by the Lagrange multiplier method is rewritten in the following form: ; in, Represents the regularization parameter. Represents a vectorized operator. Represents the square of the 2-norm. It is a column vector. Represents a column vector consisting of 1s; S53. The multipath delay information of the power line channel can be obtained by solving the second-order cone optimization function. After obtaining the actual delay, it is necessary to further solve for the weighting factor of each path. The received signal is then processed as follows: ; in Represents the Kronecker product. This represents the Khatri-Rao product.

[0013] In some embodiments, reconstructing the complete power line channel response in step S6 specifically includes the following steps: The weight factors are solved using the orthogonal basis matching algorithm, and the specific steps are as follows: Due to pilot signal Given prior knowledge that the time delay information has been estimated, a dictionary of orthogonal basis matching is constructed. ,in This represents the channel delay response constructed from the estimated delay information, and is therefore expressed as... Using the basis from the dictionary as the objective function, we obtain an estimate of the weight factor for the l-th path through matching. This enables closed-loop reconfiguration of the power line channel.

[0014] In a second aspect, the present invention provides a power line communication receiving device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the above-described method.

[0016] The beneficial effects of this invention compared to the prior art include: The proposed power line channel estimation method transforms the channel estimation problem into an optimization problem within a sparse representation framework. It cleverly relaxes the non-convex L0 norm problem into an L1 norm problem, further transforming it into a second-order cone programming problem that can be efficiently solved using convex optimization algorithms. This combination of technical features synergistically achieves the top-level benefit of obtaining high-resolution, highly robust channel estimation results with relatively low computational complexity in high-noise, high-multipath interference power line channel environments. Specifically: 1) The Vandermonde manifold and overcomplete dictionary constructed using the arithmetic progression characteristics of OFDM subcarriers are used to discretize the continuous time delay parameter estimation, laying the foundation for sparse representation and initially improving the potential of parameter estimation. 2) Using the L1 norm as a sparsity penalty term ensures the sparsity of the solution while avoiding the non-convex problem of the L0 norm, thus enhancing the feasibility of the algorithm. 3) Singular value decomposition is performed on the received data matrix to effectively extract the signal subspace and suppress the noise subspace. This intermediate effect not only compresses the data dimension and reduces the computational load of subsequent optimization, but also significantly improves the robustness to noise. 4) The optimization problem is finally transformed into a second-order cone programming form and solved using the interior point method. This technique ensures that the algorithm can reliably converge to the global optimum and has high solution efficiency. It does not rely on precise initial value settings, further enhancing the robustness and practicality of the algorithm.

[0017] These intermediate effects progress step by step, work together, and ultimately achieve the aforementioned beneficial top-level effect.

[0018] In addition, some embodiments also have the following beneficial effects: By employing the time-domain impulse response model and Vandermonde manifold defined in step S1, the multipath characteristics of the power line channel can be characterized more accurately, providing an accurate mathematical model for subsequent sparse representation.

[0019] By employing the overcomplete manifold matrix constructed in step S2, all potential time delay points can be included in the estimation range, ensuring that no real multipath components are missed and improving the completeness of the estimation.

[0020] By employing the objective function constructed in step S3 with the L1 norm as the penalty term, the convexity of the optimization problem can be maintained while ensuring the sparsity of the estimation, thus creating conditions for efficient solution.

[0021] By employing singular value decomposition on the received signal data in step S4, the signal and noise can be effectively distinguished, data compression and noise reduction can be achieved, the scale of subsequent optimization problems can be reduced, and the estimation accuracy can be improved.

[0022] By adopting the technique of transforming the optimization problem into a second-order cone programming problem in step S5 and solving it using the interior point method, the global optimal solution can be obtained efficiently and reliably, avoiding the risk of getting trapped in local optima and improving the quality of the solution and the stability of the algorithm.

[0023] By using the orthogonal basis matching algorithm to reconstruct the channel response in step S6, the complex gain of each path can be estimated quickly and accurately after knowing the time delay information, thus completing the full reconstruction of the channel.

[0024] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0025] Figure 1 This is a flowchart of the power line channel estimation method in an embodiment of the present invention.

[0026] Figure 2 This is another flowchart of the power line channel estimation method in this embodiment of the invention.

[0027] Figure 3 This is a simulation diagram of the time delay information estimation in an embodiment of the present invention.

[0028] Figure 4 This is a comparison diagram of the power line channel estimated by the method in this embodiment of the invention and the actual power line channel. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0030] Implementation concept: The core of this invention lies in leveraging the inherent sparsity of power line channel response to transform channel estimation into a sparse recovery problem by constructing an overcomplete dictionary. To overcome the challenges of L0 norm optimization, L1 norm convex relaxation is employed, and a corresponding optimization objective function is constructed. To further improve the algorithm's robustness under low signal-to-noise ratios and reduce computational complexity, singular value decomposition is introduced for data preprocessing. Finally, the optimization problem is reconstructed into a second-order cone programming form and solved using a convex optimization algorithm, thereby achieving high-precision, low-complexity channel estimation.

[0031] Example 1: This embodiment proposes a power line channel estimation method based on Second-Order Cone Programming (SOCP). This method utilizes the arithmetic progression characteristics of subcarriers in an OFDM system to construct manifold samples (the manifold refers to the Vandermonde-style vector data formed by the frequency points of each subcarrier in the OFDM system) to form an overcomplete basis. Based on this, an L1-norm-based penalty term is applied to enhance the sparsity of the channel response. Furthermore, Singular Value Decomposition (SVD) of the data matrix is ​​introduced to compress the sample data across multiple time periods, reducing computational complexity. Finally, the sparse optimization problem is placed within the framework of second-order cone programming and solved using a convex optimization algorithm, further reducing the computational complexity of the proposed method to achieve efficient estimation of the power line channel. Specifically, as... Figure 1 As shown, the method includes the following steps: S1. Transform the frequency domain channel model of the power line channel into a time domain impulse response model. Utilize the equal arithmetic characteristics between the subcarrier frequencies of the OFDM (orthogonal frequency division multiplexing) system to construct a Vandermonde structure manifold matrix containing multipath delay information.

[0032] S2. Based on the Vandermonde structure manifold matrix, construct an overcomplete manifold matrix containing all potential delay point locations, transforming the channel estimation problem into a sparse representation problem, where non-zero values ​​exist only at the actual multipath delay locations.

[0033] S3. Construct an unconstrained optimization objective function with the Frobenius norm distance between the observed and estimated data as the fidelity term and the L1 norm of the estimated signal as the sparsity penalty term. This step transforms the above-mentioned sparsity problem into an optimization problem based on the L0 norm. However, the L0 norm is a non-convex optimization problem, which needs to be further transformed into an L1 norm problem to achieve convex relaxation. Then, the deviation between the observed matrix and the ideal multipath delay received signal matrix is ​​measured by the Frobenius norm (F norm), thereby using the Lagrange multiplier method to construct the unconstrained optimization problem.

[0034] S4. Perform singular value decomposition on the received OFDM pilot signal data from multiple time periods to extract the signal subspace, thereby compressing the sampled data and suppressing noise. This step uses singular value decomposition to compress the multidimensional time-sampled data, extract principal component data and remove noise data, and reduces the computational complexity of the algorithm.

[0035] S5. Substitute the data compressed in step S4 into the optimization objective function constructed in step S3, and transform the optimization problem into a second-order cone programming problem. Use a convex optimization algorithm to solve this problem to obtain a high-precision multipath delay estimate. This step further reduces computational complexity by transforming the problem into a second-order cone programming problem and using an efficient convex optimization algorithm to quickly solve this nonlinear optimization problem. S6. Based on the multipath delay estimation, reconstruct the complete power line channel response. This step then uses the obtained multipath delay to complete the closed-loop reconstruction of the channel response.

[0036] In step S1, the frequency domain channel model of the power line channel is transformed into a time domain impulse response model. Utilizing the arithmetic progression characteristic between the frequencies of each subcarrier in OFDM, the multipath delay is constructed as a manifold matrix in Vandermonde form. Specifically, S11, Frequency Domain Channel Model of Power Line Channel as follows: in Let represent the weight factor of the l-th path, and ; v is the speed at which electromagnetic waves propagate in a copper conductor, typically 1000 m / s. m / s; Let be the transmission distance of the l-th path; This is the coefficient of the exponential term in the decay function, typically between 0.5 and 1; and The attenuation coefficient; This represents the summation symbol; Indicates the natural index; Pi; At this point, the time-domain impulse response of the power line channel... It can be represented as follows: in This represents the weight factor of the l-th path. The delay of the l-th path, Let represent the Dirac impulse function, and t represent the time variable; S12. In an OFDM system, the OFDM modulated signal after adding a cyclic prefix. It can be represented as follows: in This represents the nth OFDM symbol being transmitted, and K represents the number of subcarriers used in one OFDM symbol; Indicates the duration of an OFDM symbol. Indicates the frequency difference between subcarriers; The duration of the loop prefix, and by default. Greater than the maximum multipath delay time; Therefore, in an OFDM system, the received signal of the power line channel... It can be represented as follows: in This represents independent and identically distributed additive white Gaussian noise; Therefore, after matched filtering, the k-th subchannel in the OFDM system under the power line channel can be obtained. as follows: At this point, the Vandermonde structure manifold of the time delay information corresponding to the l-th path. The definition is as follows: in The transpose symbol is used; then the manifold matrix of all L multipaths is... It is expressed as follows: in ; Therefore, the channel composed of all sub-channels in the OFDM system It is expressed as follows: in Indicates vector Diagonalize the elements; S13. OFDM symbols of N pilot signals acquired at the power line receiver. It is represented as follows, in, This represents the channel matrix containing L path delay information; This indicates the pilot signal transmitted by the transmitter, and This represents the transmitted signals on each of the L paths; The Gaussian white noise matrix is ​​represented by the following expression: distributed.

[0037] Furthermore, in step S2, combining the framework of step S1, and utilizing the formal manifold matrix structure characteristics of the Vandermonde matrix, a manifold matrix of the overcomplete set is constructed, specifically as follows: S21. To formulate this problem as a sparse representation problem, this embodiment introduces an overcomplete representation based on all possible source locations. Let the grid point locations of all interested time delay locations be denoted as . The grid range should cover the maximum possible delay spread of the power line channel, typically from 0 to a few microseconds. The grid spacing can be determined based on the required delay resolution Δτ (Δτ = 1 / (2*Bandwidth)), where Bandwidth refers to the width of the frequency range (Hz). The number of potential delay point locations is usually much larger than the number of actual delay points, and may even exceed the number of subcarriers K in an OFDM system. Therefore, a supercomplete set matrix is ​​constructed using the potential delay point locations, whose columns consist of manifold vectors corresponding to each potential delay point location, as follows: Note that at this time... It is known and does not depend on the actual location of the delay point; Therefore, the overcomplete channel matrix formed by all sub-channels in the OFDM system It is expressed as follows: in, Indicates vector Diagonalization, that is, dividing a matrix by its diagonal elements. The elements in the array are composed of 0, and all other elements are 0. This indicates that its value is non-zero only when the delay points of L paths exist; otherwise, it is all zero. Furthermore, in step S3, combining the overcomplete set form from step S2, the unconstrained optimization problem is constructed, specifically as follows: S31. In fact, this overcomplete representation allows this embodiment to transform the parameter estimation problem into a sparse spectrum estimation problem. Similar to many nonparametric source localization techniques, this method uses signal energy to determine the estimated value of the true time delay location, ideally exhibiting a dominant peak at the true time delay location. In this parameter estimation problem, assuming a small number of true time delays is a prerequisite for ensuring sparsity, i.e., only a few non-zero elements; then, regularization can be used to balance the fidelity and sparsity of the data, thereby solving the inverse problem. The objective function of this problem is as follows: in Denotes the square of the F-norm. Represents the 0 norm, This represents the energy of the noise; st This indicates that the constraint is "as is". The dimension is , where M represents the number of samples; However, the 0-norm is a non-convex function and cannot be solved efficiently. Therefore, the 0-norm needs to be relaxed to the 1-norm, thus transforming the original constrained optimization problem into the following form: in This represents the L1 norm. Furthermore, according to the Lagrange multiplier method, this constrained problem can be equivalently written as the following unconstrained optimization problem: in This represents the regularization parameter; this form is a typical unconstrained optimization problem based on L1 norm regularization, which adjusts... To balance the fitting error with the sparsity of the solution.

[0038] Furthermore, in step S4, combining the optimization model from step S3, the multidimensional time-sampled data is compressed using the singular value decomposition method. Specifically, S41. Suppose there exists a received signal matrix Y, then the singular value decomposition of Y is as follows: in, U Describes a left singular vector matrix. V Describes a right singular vector matrix. Indicates conjugate transpose; Due to the properties of singular value decomposition, the received signal matrix Y is decomposed into a signal subspace and a noise subspace, and then the following processing is performed: Therefore, in, This represents the received data after singular value decomposition. Represents the data compression matrix. =[I,0], where I is the identity matrix with dimension L*L, and 0 is the zero matrix with dimension L*(KL); This represents the data matrix after singular value decomposition of the received signal matrix in an OFDM system. and Definition and similar; Furthermore, in step S5, the convex optimization algorithm is preferably the interior-point method. Combined with the singular value decomposition method used in step S4 to compress the multidimensional time-sampled data, the problem is transformed into a second-order cone programming problem. The efficient interior-point method is then used to quickly solve this nonlinear optimization problem. Specifically, S51. First, after reducing the dimensionality of the received signal matrix, the second-order cone optimization problem is defined as follows: in Let represent a linear objective function, x represent the variable to be optimized, and T represent the transpose. Let represent the i-th linear constraint inequality, where A and c represent the coefficient matrices of the linear inequality, and b and d are constant terms. This represents a linear constraint equation, where g is a constant term; S52. To linearize the objective function represented by the Lagrange multiplier method, auxiliary variables p and q are used, and the nonlinear part is transferred to the constraints. The objective function represented by the Lagrange multiplier method is rewritten in the following form: in, Represents the regularization parameter. Represents a vectorized operator. Represents the square of the 2-norm. It is a column vector. Represents a column vector consisting of 1s; S53. Next, the multipath delay information of the power line channel can be obtained by solving the second-order cone optimization function. After obtaining the actual delay, the weighting factor of each path needs to be further solved. The received signal is then processed as follows: in Represents the Kronecker product; This represents the Khatri-Rao product.

[0039] Next, in step 6, the weighting factors can be solved using the orthogonal basis matching algorithm, as follows: (Due to the pilot signal...) Given prior knowledge that the time delay information has been estimated, a dictionary of orthogonal basis matching can be directly constructed. ,in This represents the channel delay response constructed from the estimated delay information. Therefore, it is... Using the basis in the dictionary as the objective function, we can obtain an estimate of the weight factor of the l-th path through matching. .

[0040] Example 2: This embodiment provides a power line channel estimation method based on second-order cone programming, such as... Figure 2 As shown, it includes the following steps: S1. The frequency domain channel model of the power line channel is transformed into the time domain impulse response model. The multipath delay parameter is modeled as a manifold matrix in the form of a Vandermonde matrix by utilizing the equal arithmetic characteristics between the frequencies of each subcarrier in OFDM. S2. Using the formal manifold matrix structure properties of the Vandermonde matrix, construct the manifold matrix of the overcomplete set. Since only the signal corresponding to the multipath delay in the overcomplete set has a non-zero value, it has sparsity (sparseness means that in the dataset, only a small number of elements have non-zero values, while the majority of the other elements have zero values). S3. Construct the above-mentioned sparsity problem based on The optimization problem of norms, but Norm is a non-convex optimization problem, which needs to be further transformed into The norm problem is to achieve convex relaxation (convex relaxation refers to relaxing the constraints of the original non-convex problem and transforming it into a convex problem, so that the new feasible solution range includes all the solutions of the original problem, making it easier to solve). Then, the deviation between the observation matrix and the ideal multipath delay received signal matrix is ​​measured by the Frobenius norm of the observation matrix and the ideal multipath delay received signal matrix, thereby using the Lagrange multiplier method to construct the unconstrained optimization problem. S4. Using the singular value decomposition method, multidimensional time-sampled data is compressed to extract principal component data (principal component data refers to the signal part that constitutes the received data and does not contain noise) and remove noise data, thereby reducing the computational complexity of the algorithm. S5. To further reduce computational complexity, the problem was transformed into a second-order cone programming problem. The efficient interior-point method was used to quickly solve the nonlinear optimization problem. Then, the multipath delay was obtained to complete the closed-loop reconstruction of the channel response. The power line channel estimation method based on second-order cone programming, in step S1, transforms the frequency domain channel model of the power line channel into a time domain impulse response model. Utilizing the arithmetic progression characteristic between the frequencies of each subcarrier in OFDM, the multipath delay is constructed as a manifold matrix in Vandermonde form. Specifically, S11, Frequency Domain Channel Model of Power Line Channel as follows: in Let represent the weight factor of the l-th path, and ; v is the speed at which electromagnetic waves propagate in a copper conductor, typically 1000 m / s. m / s; Let be the transmission distance of the l-th path; This is the coefficient of the exponential term in the decay function, typically between 0.5 and 1; and This is the attenuation coefficient, typically taking values ​​of 0 and 7.8*10^-10; This represents the summation symbol; Indicates the natural index; Pi; At this point, the time-domain impulse response of the power line channel... It can be represented as follows: in This represents the weight factor of the l-th path. The delay of the l-th path, Represents the Dirac impulse function; S12. In an OFDM system, the OFDM modulated signal after adding a cyclic prefix. It can be represented as follows: in This represents the nth OFDM symbol being transmitted, and K represents the number of subcarriers used in one OFDM symbol; Indicates the duration of an OFDM symbol. Indicates the frequency difference between subcarriers; The duration of the loop prefix, and by default. Greater than the maximum multipath delay time; Therefore, in an OFDM system, the received signal of the power line channel... It can be represented as follows: in This represents independent and identically distributed additive white Gaussian noise; Therefore, after matched filtering, the k-th subchannel in the OFDM system under the power line channel can be obtained. as follows: At this point, the Vandermonde structure manifold of the time delay information corresponding to the l-th path. The definition is as follows: in The transpose symbol is used; then the manifold matrix of all L multipaths is... It is expressed as follows: in ; Therefore, the channel composed of all sub-channels in the OFDM system It is expressed as follows: in Indicates vector Diagonalize the elements; S13. OFDM symbols of N pilot signals acquired at the power line receiver. It is represented as follows, in, This represents the channel matrix containing L path delay information; This indicates the pilot signal transmitted by the transmitter, and This represents the transmitted signals on each of the L paths; The Gaussian white noise matrix is ​​represented by the following expression: distributed.

[0041] Furthermore, in step S2, combining the framework of step S1, and utilizing the formal manifold matrix structure characteristics of the Vandermonde matrix, a manifold matrix of the overcomplete set is constructed, specifically as follows: S21. To formulate this problem as a sparse representation problem, this embodiment introduces an overcomplete representation based on all possible time delay locations. Let the grid point positions where all time delay locations of interest are located be denoted as . The locations are selected at equal intervals between (0, ½Ts). The number of potential delay points is usually much larger than the number of actual delay points, and may even exceed the number of subcarriers K in an OFDM system. Therefore, a supercomplete set matrix is ​​constructed using the potential delay point locations, whose columns consist of manifold vectors corresponding to each potential delay point location, as follows: Note that at this time... It is known and does not depend on the actual location of the delay point; Therefore, the overcomplete channel matrix formed by all sub-channels in the OFDM system It is expressed as follows: in This indicates that its value is non-zero only when the delay points of L paths exist; otherwise, it is all zero. Furthermore, in step S3, combining the overcomplete set form from step S2, the unconstrained optimization problem is constructed, specifically as follows: S31. In fact, this overcomplete representation allows this embodiment to transform the parameter estimation problem into a sparse spectrum estimation problem. Similar to many nonparametric source localization techniques, this method uses signal energy to determine the estimated value of the true time delay location, ideally exhibiting a dominant peak at the true time delay location. In this parameter estimation problem, assuming a small number of true time delays is a prerequisite for ensuring sparsity, i.e., only a few non-zero elements; then, regularization can be used to balance the fidelity and sparsity of the data, thereby solving the inverse problem. The objective function of this problem is as follows: in This represents the square of the F-norm (Frobenius norm). Represents the 0 norm, This represents the energy of the noise; at this time The dimension is , where M represents the number of samples; However, the L0 norm is a non-convex function and cannot be solved efficiently. Therefore, the L0 norm needs to be relaxed to the L1 norm, resulting in the following form: in Represents the 1-norm; Further, according to the Lagrange multiplier method, it can be written in the following form: in Let represent the regularization parameter. Given that the noise distribution type is known or can be modeled, the spatial spectrum S(λ) of the regularization parameter can be constructed. Select this parameter, where It expresses expectation.

[0042] Furthermore, in step S4, combining the optimization model from step S3, the multidimensional time-sampled data is compressed using the singular value decomposition method. At high signal-to-noise ratios, this can be determined by the difference between the singular values ​​of the signal and the noise, a very common method. At low signal-to-noise ratios, the number of multipath paths needs to be known. Specifically, S41. Suppose there exists a received signal matrix Y, then the singular value decomposition of Y is as follows: in Indicates conjugate transpose; Due to the properties of singular value decomposition, the received signal matrix Y is decomposed into a signal subspace and a noise subspace, and then the following processing is performed: Therefore, in This represents the data matrix after singular value decomposition of the received signal matrix in an OFDM system. and Definition and similar; Furthermore, in step S5, combining the singular value decomposition method used in step S4 to compress the multidimensional time-sampled data, the problem is transformed into a second-order cone programming problem. The efficient interior point method (IPM) is then used to quickly solve this nonlinear optimization problem, specifically CVX. S51. After reducing the dimensionality of the received signal matrix, the second-order cone optimization problem is defined as follows: in Represents a linear objective function. Let represent the constraint inequality of the i-th linear equation. Represents a linear constraint equation; First, to linearize the objective function represented by the Lagrange multiplier method, auxiliary variables p and q are used, and the nonlinear part is transferred to the constraints. The objective function represented by the Lagrange multiplier method is rewritten in the following form: in Represents a vectorized operator. Represents the square of the 2-norm. It is a column vector. Represents a column vector consisting of 1s; S52. Next, the multipath delay information of the power line channel can be obtained by solving the second-order cone optimization function. Figure 3 This shows a comparison of the multipath delay spectra of the method in this embodiment and the traditional MUSIC method, such as... Figure 3 As shown, the attenuation value at the non-target delay position of the traditional MUSIC algorithm is -40dB, while the attenuation value of the L1-SVD algorithm can reach below -100dB, demonstrating the noise suppression capability of the proposed method. At the same time, it can be seen from the figure that the peak value of the proposed method is sharper, thus the estimation of the peak point is more accurate and the precision is higher.

[0043] After obtaining the actual time delay, it is necessary to further solve for the weighting factors of each path. Therefore, the received signal is processed as follows: in This represents the Kronecker product. This represents the Khatri-Rao product (Khatri–Rao product). Next, the weighting factors can be solved using the Orthogonal Matching Pursuit (OMP) algorithm, as follows: (Due to the pilot signal...) Given prior knowledge that the time delay information has been estimated, a dictionary of orthogonal basis matching can be directly constructed. ,in This represents the channel delay response constructed from the estimated delay information. Therefore, it is... Using the basis in the dictionary as the objective function, we can obtain an estimate of the weight factor of the l-th path through matching. This enables closed-loop reconfiguration of the power line channel.

[0044] Experimental Example The power line channel estimation method based on second-order cone programming proposed in this embodiment of the invention is verified by simulation experiments as follows.

[0045] Simulation scenario and parameter settings: Consider setting the frequency range of the orthogonal frequency division multiplexing (OFDM) system to 0~12MHz, and the number of subcarriers K = 64. It should be noted that in a power line OFDM system, the total number of available subcarriers is typically 512; here, K = 64 indicates that only the initial 64 consecutive subcarriers are used for pilot data transmission. The number of multipath paths is considered to be L = 2, and the attenuation factor... , , Delay , It is any complex number modulo between 0.5 and 1, and In this simulation, the time delay is set to The number of orthogonal frequency division multiplexing symbols occupied by the pilot is set in accordance with the typical setting adopted in the current State Grid physical layer protocol, i.e., N = 13; the simulation uses snr=20dB.

[0046] The comparison results between the channel frequency response estimated by the method in this embodiment and the actual channel frequency response are as follows: Figure 4 As shown. From Figure 4 It can be observed that the channel attenuation curve fitted by the proposed method has a high degree of fit in the low-frequency part, such as below 4MHz, and is close to the real channel attenuation curve. It can also reflect a certain degree of channel attenuation change after 4MHz.

[0047] Experimental verification has shown that the embodiments of the present invention have the following advantages: To address the sparsity characteristics of power line channels, a channel estimation formula based on a sparse representation framework is proposed. This method first employs Singular Value Decomposition (SVD) based on subspaces for multi-sampled data to achieve effective noise suppression and data dimensionality reduction. Then, it utilizes an efficient optimization algorithm based on second-order cone programming (BCP) to solve for time delay information. Compared with traditional methods, particularly the MUSIC method, this invention offers the following advantages: improved channel delay resolution, no reliance on precise initial value settings, and significantly enhanced robustness to noise and limited sample sizes. This invention, through SVD decomposition, compresses the data volume and reduces the impact of noise, thereby improving channel delay resolution and enhancing the robustness of the proposed algorithm. Furthermore, by placing the L1 norm optimization problem within the framework of BCP optimization, the global optimum can be obtained without relying on precise initial value settings.

[0048] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A power line channel estimation method, characterized in that, Includes the following steps: S1. The frequency domain channel model of the power line channel is transformed into the time domain impulse response model. The equal arithmetic characteristics between the subcarrier frequencies of the orthogonal frequency division multiplexing (OFDM) system are used to construct a Vandermonde structure manifold matrix containing multipath delay information. S2. Based on the Vandermonde structure manifold matrix, construct an overcomplete manifold matrix containing all potential delay point locations, transforming the channel estimation problem into a sparse representation problem, where non-zero values ​​exist only at the actual multipath delay locations. S3. Construct an unconstrained optimization objective function with the Frobenius norm distance between the observed data and the estimated data as the fidelity term and the L1 norm of the estimated signal as the sparsity penalty term. S4. Perform singular value decomposition on the received OFDM pilot signal data from multiple time periods, extract the signal subspace, and achieve compression and noise suppression of the sampled data; S5. Substitute the data compressed in step S4 into the optimization objective function constructed in step S3, and transform the optimization problem into a second-order cone programming form. Use a convex optimization algorithm to solve it to obtain a high-precision multipath delay estimate. S6. Based on the multipath delay estimation, the complete power line channel response is reconstructed.

2. The method as described in claim 1, characterized in that, The time-domain impulse response model described in step S1 Represented as: ； in, Indicates the first l The weighting factor of each path, For the first l The delay of the path, Let be the transmission distance of the l-th path, and v be the speed of electromagnetic wave propagation in the copper conductor. , Let represent the Dirac impulse function, and t represent the time variable.

3. The method as described in claim 2, characterized in that, The Vandermonde structure manifold matrix described in step S1 Represented as: ； in, , Indicates the first l The Vandermonde structure manifold for the time delay information corresponding to each path.

4. The method as described in claim 3, characterized in that, The overcomplete manifold matrix described in step S2 Represented as: ； in, Indicates vector Diagonalize the grid points to represent all time delay locations of interest. , Denotes an overcomplete set matrix. This indicates that its value is not zero only when the delay points of L paths exist; otherwise, it is all zero.

5. The method as described in claim 4, characterized in that, The objective function described in step S3 is expressed as: ； Where min represents the minimum value. Denotes the square of the F-norm. Represents the 0 norm, Represents the energy of noise. st This indicates that "the constraint is"; at this time The dimension is ,in Represents the Gaussian white noise matrix. M This represents the number of samplings, specifically the N pilot OFDM symbols acquired at the power line receiver. .

6. The method as described in claim 5, characterized in that, In step S4, the singular value decomposition of the received signal data specifically involves: decomposing the received signal matrix... Y The singular value decomposition is performed as follows: ;in, U Describes a left singular vector matrix. V Describes a right singular vector matrix. Indicates conjugate transpose; Due to the properties of singular value decomposition, the received signal matrix Y is decomposed into a signal subspace and a noise subspace, and then the following processing is performed: ， Therefore, there is ， in, This represents the received data after singular value decomposition. Represents the data compression matrix. This represents the data matrix after singular value decomposition of the received signal matrix in an OFDM system. and Definition and similar.

7. The method as described in claim 6, characterized in that, The convex optimization algorithm in step S5 includes the interior point method, which transforms the optimization problem into a second-order cone programming form, specifically including the following steps: S51. After reducing the dimensionality of the received signal matrix, the second-order cone optimization problem is defined as follows: ； in Let represent a linear objective function, x represent the variable to be optimized, and T represent the transpose. Indicates the first i There are three linear constraint inequalities, where A and c represent coefficient matrices, and b and d are constant terms. The constraint equation represents linearity, where g is a constant term; S52, Using Auxiliary Variables p and q Furthermore, by transferring the nonlinear part to the constraints, the objective function represented by the Lagrange multiplier method is rewritten in the following form: ； in, Represents the regularization parameter. Represents a vectorized operator. Represents the square of the 2-norm. It is a column vector. Represents a column vector consisting of 1s; S53. The multipath delay information of the power line channel can be obtained by solving the second-order cone optimization function. After obtaining the actual delay, it is necessary to further solve for the weighting factor of each path. The received signal is then processed as follows: ； in Represents the Kronecker product. This represents the Khatri-Rao product.

8. The method as described in claim 7, characterized in that, The reconstruction of the complete power line channel response in step S6 specifically includes the following steps: The weight factors are solved using the orthogonal basis matching algorithm, and the specific steps are as follows: Due to pilot signal Given prior knowledge that the time delay information has been estimated, a dictionary of orthogonal basis matching is constructed. ,in This represents the channel delay response constructed from the estimated delay information, and is therefore expressed as... As the objective function, matching is performed using the base in the dictionary to obtain the first... l Estimates of the weighting factor for strip diameter This enables closed-loop reconfiguration of the power line channel.

9. A power line communication receiving device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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