A method for impulse noise downlink wave frequency offset and sparse channel joint estimation

Abstract

The application discloses a kind of impulse noise download wave frequency deviation and sparse channel joint estimation method, comprising: impulse noise is modeled as mixed Gaussian distribution;Iterative exchange external information between minimum mean square error module and sparse bayesian learning module;The mixed coefficient and variance parameter of mixed Gaussian noise are iteratively updated using expectation maximization algorithm;Type II maximum likelihood estimation is used and combined with Newton method to realize the fine estimation of carrier frequency offset, while using sparse bayesian learning framework to estimate channel and estimate the precision parameter of each tap of channel to promote channel sparsity.The application innovatively constructs the three-layer iterative architecture including MMSE module, SBL module and CFO compensation module.Through the exchange of external information between modules, the joint processing of channel impulse response estimation, noise parameter optimization and frequency offset correction is realized, and the system robustness in complex interference environment is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication channel estimation, specifically a method for jointly estimating impulse noise download wave frequency offset and sparse channel. Background Technology

[0002] The impact of impulse noise and CFO on underwater acoustic communication systems is multifaceted. They not only individually degrade communication quality but can also produce synergistic effects, leading to channel estimation failure and severely impacting the reliability of the communication system. Specific impacts are as follows:

[0003] (1) Signal quality degradation: Impulse noise, as a sudden high-energy interference in underwater acoustic signals, will cause a sharp drop in the instantaneous signal-to-noise ratio of the received signal. At the same time, the CFO caused by the relative motion between the transmitter and receiver will lead to a frequency domain shift in the received signal. The superposition effect of these two interferences further deteriorates the quality of the received signal. Underwater acoustic communication systems rely on the receiver to accurately detect the signal and determine the symbol. The occurrence of impulse noise will directly cause the demodulator to generate continuous bit errors at the corresponding moment, while the phase rotation and frequency shift caused by CFO will exacerbate this bit error effect and seriously affect the reliability of data transmission. When the intensity of impulse noise is high or the frequency of occurrence is high, the superimposed effect of CFO will make it more difficult for the receiver to correctly recover the original information, resulting in more serious data errors and loss.

[0004] (2) Decreased channel estimation accuracy: Impulse noise violates the assumption of Gaussian noise in traditional estimation algorithms, causing significant deviations in channel estimation results based on least squares or least mean square error. CFO introduces additional phase noise and frequency offset disturbances, further distorting the estimation results of the channel impulse response. Since channel state information is the basis for subsequent equalization and decoding, the reduced estimation accuracy caused by these two types of interference will seriously affect the receiver's signal processing capability, further deteriorating information transmission and equalization performance. In environments with severe impulse noise or rapidly changing channels, the superimposed effect of CFO will make channel estimation more difficult to converge, severely restricting system reliability.

[0005] To address the aforementioned problems, this invention proposes a joint optimization scheme: First, the impulse noise is modeled as a mixture of Gaussian distributions, and the original non-Gaussian noise model is transformed into a conditional Gaussian model by introducing latent variables; simultaneously, a statistical model of the CFO parameters is established. Based on the design concepts of message passing and modularity, joint optimization is achieved through iterative exchange of external information between the noise processing module, the CFO estimation module, and the channel estimation module. This method can not only adaptively update the parameters of the mixture of Gaussian noise but also synchronously estimate and compensate for the influence of residual CFO, effectively suppressing the dual interference of impulse noise and CFO on the channel estimation accuracy, and significantly improving the reliability of underwater acoustic communication systems in complex environments. Summary of the Invention

[0006] The purpose of this invention is to provide a joint estimation method for impulse noise download wave frequency offset and sparse channel to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A joint estimation method for impulse noise-based carrier frequency offset and sparse channel is proposed, which performs robust channel estimation under the interference of impulse noise and carrier frequency offset. Specifically:

[0009] Step 1: Model the impulse noise as a mixture of Gaussian distributions. By introducing latent variables, the original mixture of Gaussian noise model is transformed into a conditional Gaussian model, and the mathematical relationship between the observed signal, channel parameters, noise signal and carrier frequency offset is established.

[0010] Step 2: Based on the design concept of message passing and modularization, external information is iteratively exchanged between the minimum mean square error module responsible for noise processing and the sparse Bayesian learning module based on channel estimation, so as to achieve joint optimization of channel estimation, carrier frequency offset and noise processing.

[0011] Step 3: Within the minimum mean square error module, the expectation-maximization algorithm is used to iteratively update the mixing coefficients and variance parameters of the Gaussian mixture noise, thereby achieving adaptive estimation of the noise parameters.

[0012] Step 4: Within the sparse Bayesian learning module, Type II maximum likelihood estimation combined with Newton's method is used to achieve a fine estimation of carrier frequency offset. At the same time, the sparse Bayesian learning framework is used to perform channel estimation and estimate the accuracy parameters of each channel tap to promote channel sparsity.

[0013] Furthermore, the introduction of latent variables transforms the original Gaussian mixture noise model into a conditional Gaussian model, specifically as follows:

[0014] Step 1.1: Establish a linear model of the observed signal. The received signal is represented as the observation matrix multiplied by the channel tap vector to be estimated, plus mixed Gaussian noise. The observation matrix is ​​in Toeplitz form composed of pilot symbols.

[0015] Step 1.2: Model the mixed Gaussian noise as a mixture of two Gaussian components. The probability density function of each element of the noise vector is the weighted sum of the background noise Gaussian component and the impulse noise Gaussian component, with the weights being the mixing coefficients.

[0016] Step 1.3 introduces a binary latent variable to indicate the noise source of each sampling point. When the latent variable takes the first value, it means that the sampling point is only affected by background noise, and its noise follows a Gaussian distribution with a mean of zero and a variance equal to the variance of the background noise. When the latent variable takes the second value, it means that the sampling point is affected by impulse noise, and its noise follows a Gaussian distribution with a mean of zero and a variance equal to the variance of the impulse noise. This transforms the non-Gaussian noise into a joint Gaussian model with the latent variable as a condition.

[0017] Furthermore, based on the message passing and modular design principles, external information is iteratively exchanged between the minimum mean square error module responsible for noise processing and the sparse Bayesian learning module for channel estimation, specifically as follows:

[0018] Step 2.1: In the minimum mean square error module, the mixed posterior mean and variance of the latent variables are calculated using prior information and the received signal. The extrinsic information is extracted through the expectation propagation rule and transmitted to the sparse Bayesian learning module.

[0019] Step 2.2: In the sparse Bayesian learning module, combined with the external information transmitted by the minimum mean square error module, sparse Bayesian learning is used to estimate the carrier frequency offset and the channel, and the external information is transmitted back.

[0020] Step 2.3: Repeat steps 2.1 to 2.2 until the preset number of iterations or convergence condition is reached.

[0021] Furthermore, step 2.1 specifically includes:

[0022] Step 2.1.1: Initialize external information by setting the pseudo-observations and their variances passed from the sparse Bayesian learning module to the minimum mean square error module, and initializing them to a weak information state.

[0023] Step 2.1.2: In the minimum mean square error module, based on the current received signal and input external information, calculate the posterior mean and posterior variance of the latent variables under the conditions of taking the first and second values, respectively.

[0024] Step 2.1.3: Calculate the posterior probability of the latent variables;

[0025] Step 2.1.4: Based on the law of total probability, calculate the mean and variance of the mixed posterior distribution using the results of steps 2.1.2 and 2.1.3;

[0026] Step 2.1.5: Extract extrinsic information using the expectation propagation rule, and output extrinsic information containing pseudo-observations and variance from the minimum mean square error module to the sparse Bayesian learning module.

[0027] Furthermore, step 2.2 specifically includes:

[0028] Step 2.2.1: In the sparse Bayesian learning module, based on the received extrinsic information, channel and carrier frequency offset estimation is performed using the sparse Bayesian learning framework to obtain the carrier frequency offset estimate and the posterior variance and posterior mean of the channel taps.

[0029] Step 2.2.2: Calculate the pseudo-observation posterior and its variance corresponding to the carrier frequency offset and channel estimation, and extract the extrinsic information to be sent back to the minimum mean square error module.

[0030] Further, step 3 includes:

[0031] Step 3.1: Based on the current observation signal and the external information input of the sparse Bayesian learning module, calculate the posterior of the pseudo-observation using the conditional Gaussian model established in Step 1;

[0032] Step 3.2: The parameters of the Gaussian mixture noise are iteratively updated using the expectation-maximization algorithm. In each iteration, the sufficient statistics of each Gaussian component are calculated based on the posterior probability of the latent variables, and the mixing coefficient, background noise variance, and impulse noise variance are updated. The mixing coefficient is taken as the average of the posterior probabilities of the latent variables, and the background noise variance and impulse noise variance are taken as the weighted average of the squares of the noise under the background component and the impulse component, respectively. This allows the estimated noise distribution to gradually approach the true distribution, enabling the algorithm to adapt to unknown noise environments.

[0033] Furthermore, the precise estimation of carrier frequency offset using Type II maximum likelihood estimation combined with Newton's method is specifically as follows:

[0034] Step 4.1: Based on the external information input of the minimum mean square error module, establish the Type II maximum likelihood estimation problem;

[0035] Step 4.2: Divide the frequency domain into grids to obtain a coarse estimate of the carrier frequency offset;

[0036] Step 4.3: Use Newton's method to perform a fine estimation of the carrier frequency offset.

[0037] Furthermore, the channel estimation using the sparse Bayesian learning framework specifically includes: calculating the posterior mean and posterior variance of each channel tap, determining the posterior second moment of each channel tap based on the sum of the squared modulus of the posterior mean and the posterior variance, and updating the accuracy parameters corresponding to each channel tap according to the posterior second moment.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] 1) This invention presents a joint estimation method for impulse noise download wave frequency offset and sparse channel, revealing the generation mechanism and statistical characteristics of mixed Gaussian noise in underwater acoustic communication, and elucidating the impact mechanism of CFO interference on channel estimation. This method not only analyzes the superposition process of background noise and impulse noise and its non-Gaussian properties, but also quantifies the degrading effect of Doppler frequency offset caused by relative motion between the transmitter and receiver on system performance, providing theoretical guidance for engineering practice in complex underwater acoustic environments.

[0040] 2) This method, by introducing a latent variable system, transforms the non-Gaussian noise model into a conditional Gaussian model while establishing the mathematical relationship between the CFO parameters and the received signal. This joint modeling strategy is not only applicable to parameter estimation under impulse noise environments, but also provides a general framework design approach for non-ideal communication systems with simultaneous frequency offset interference.

[0041] 3) Based on message passing and modular design principles, this method innovatively constructs a three-layer iterative architecture comprising an MMSE module, an SBL module, and a CFO compensation module. Through external information exchange between modules, joint processing of channel impulse response estimation, noise parameter optimization, and frequency offset correction is achieved, significantly improving the system robustness under complex interference environments.

[0042] 4) This method extends the traditional EM algorithm by simultaneously updating the Gaussian mixture noise parameters in the MMSE module and performing CFO maximum likelihood estimation in the SBL module. This parameter adaptation mechanism enables the algorithm to simultaneously track dynamic noise distribution and time-varying frequency offset, eliminating the reliance on prior knowledge of noise statistical characteristics and frequency offset range.

[0043] 5) The pulse noise download wave frequency offset and sparse channel joint estimation method of the present invention can effectively suppress the influence of mixed Gaussian noise on the channel estimation accuracy and improve the reliability and stability of underwater acoustic communication system in pulse noise environment. Attached Figure Description

[0044] Figure 1 This is a flowchart of the present invention.

[0045] Figure 2 These are the time-domain waveforms and probability distribution fitting plots of mixed Gaussian noise, where (a) is the time-domain waveform of the mixed Gaussian noise sequence, and (b) is the distribution histogram and probability density function fitting curve of the mixed Gaussian noise sample.

[0046] Figure 3This is a diagram of the joint estimation module structure for carrier frequency offset and sparse channel and the iterative interaction module for external information of the present invention. Module A is a sparse Bayesian learning module, and module B is a minimum mean square error module. The minimum mean square error module performs noise processing on the received signal based on a Gaussian mixture noise model, and the sparse Bayesian learning module performs channel estimation based on an observation model that includes carrier frequency offset. The two modules achieve joint iterative estimation of noise parameters, carrier frequency offset, and sparse channel by exchanging the mean and variance of external information.

[0047] Figure 4 This is the convergence curve of the iterative estimation of the mixed Gaussian noise parameters and carrier frequency offset parameters in this invention, where (a) is the background noise variance. The estimated convergence curve, (b) is the impulse noise variance. (c) is the estimated convergence curve of the mixing coefficient ρ, and (d) is the estimated convergence curve of the carrier frequency offset parameter ω.

[0048] Figure 5 This is the convergence curve of the normalized mean square error of the channel estimation in this invention.

[0049] Figure 6 This is a diagram showing the channel estimation results of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention provides a method for jointly estimating impulse noise download wave frequency offset and sparse channel, such as... Figure 1As shown, robust channel estimation is performed under the interference of impulse noise and carrier frequency offset (CFO). First, the impulse noise is modeled as a Gaussian mixture distribution. By introducing latent variables, the original Gaussian mixture noise model is transformed into a conditional Gaussian model, establishing the mathematical relationship between the observed signal, channel parameters, noise signal, and CFO. Then, based on the message passing and modular design principles, external information is iteratively exchanged between the minimum mean square error (MMSE) module responsible for noise processing and the sparse Bayesian learning (SBL) module based on channel estimation, achieving joint optimization of channel estimation, CFO, and noise processing. Within the MMSE module, the expectation-maximization algorithm (EM algorithm) is used to iteratively update the mixing coefficients and variance parameters of the Gaussian mixture noise, achieving adaptive estimation of the noise parameters. Within the SBL module, Type II maximum likelihood estimation combined with Newton's method is used to achieve a fine estimation of CFO. Simultaneously, the SBL framework is used for channel estimation, estimating the accuracy parameters of each channel tap to promote channel sparsity.

[0052] Impulse noise is characterized by sparsity, non-Gaussianity, and parameter uncertainty. Sparsity manifests in its sparse occurrence in the time domain, meaning that most sampling times are only affected by background noise, with only a small number of sampling points experiencing strong impulse interference. Non-Gaussianity is reflected in the heavy-tailed nature of its probability density function, making it impossible to accurately model using a single Gaussian distribution; a mixture of multiple Gaussian components is required. Parameter uncertainty arises because the probability of impulse noise occurrence and its power level are usually unknown and time-varying, necessitating online estimation to adapt to the actual channel environment. Figure 2 As shown in (a), the horizontal axis represents the sampling points, the vertical axis represents the noise amplitude, the blue curve represents the mixed Gaussian noise sequence, and the red circles represent the locations of impulse noise and their corresponding amplitudes. Figure 2 As shown in (a), the noise amplitude at most sampling points fluctuates slightly around zero, with only a few sampling points exhibiting sudden noise with larger amplitudes, indicating that the mixed Gaussian noise is sparse and impulsive in the time domain. Figure 2 As shown in Figure (b), the horizontal axis represents the noise amplitude, the vertical axis represents the probability density, the gray histogram represents the empirical distribution of the Gaussian mixture noise samples, and the red curve represents the fitted probability density function obtained using the Gaussian mixture model. Figure 2 As shown in (b), the probability distribution of the noise sample has a high peak value near zero and exhibits a long tail characteristic in the region far from zero, indicating that the noise distribution is non-Gaussian and heavy-tailed. The fitting curve of the Gaussian mixture model has a similar trend to the empirical distribution of the noise sample, indicating that it is reasonable to use the Gaussian mixture model to characterize the statistical characteristics of the noise.

[0053] Mixed Gaussian noise (GMG) is a model of background noise and sudden impulse interference experienced by a communication receiver in a real-world operating environment. Background noise has stable power, while impulse noise is characterized by random occurrence, large amplitude, and short duration. The superposition of these two noises forms a non-Gaussian mixed distribution. CFO interference is the Doppler effect caused by the relative movement of the transmitting and receiving ends, resulting in frequency expansion or contraction of the received signal. Although the receiver compensates for the Doppler shift through resampling, residual CFO still exists.

[0054] Constructing the joint estimation method for impulse noise download wave frequency offset and sparse channel of the present invention requires introducing latent variables to transform the original mixed Gaussian noise model into a conditional Gaussian model, including the following steps:

[0055] Step 1 involves modeling the impulse noise as a Gaussian mixture distribution. By introducing latent variables, the original Gaussian mixture noise model is transformed into a conditional Gaussian model, establishing the mathematical relationship between the observed signal, channel parameters, noise signal, and carrier frequency offset. Specifically, this includes:

[0056] Step 1.1: Establish a linear model of the observed signal. The received signal can be represented as:

[0057] (1)

[0058] Among them, the observation vector It is an M-dimensional complex vector. , Let be the phase rotation matrix caused by CFO, M be the number of sampling points of the observed signal, m be the sampling point index, diag(·) be the diag function, e be the natural constant, and ω be the carrier frequency offset parameter. Let L be the channel impulse response to be estimated. The Toeplitz observation matrix is ​​composed of pilot symbols. It is a mixed Gaussian noise vector.

[0059] Step 1.2: Model the mixed Gaussian noise as a mixture of two Gaussian components, where the m-th element of the noise vector is w. m The probability density function p(w) m )for:

[0060] (2)

[0061] in, The mixing coefficient represents the probability of impulse noise occurring. For the background noise variance, The variance of impulse noise. For w m Follows a mean of 0 and a variance of The probability density function of the complex Gaussian distribution.

[0062] Step 1.3, introduce a binary latent variable s m ∈ {0,1} indicates the noise source for each sampling point, i.e., when s m =0 indicates background noise, which follows a variance of . Gaussian distribution; when s m =1 indicates impulse noise, which follows a variance of . The Gaussian distribution is thus used to transform non-Gaussian noise into a joint Gaussian model conditional on latent variables.

[0063] (3)

[0064] Step 2, based on the design principles of messaging and modularity, such as Figure 3 As shown, external information is iteratively exchanged between the minimum mean square error module responsible for noise processing and the sparse Bayesian learning module based on channel estimation, achieving joint optimization of channel estimation, carrier frequency offset, and noise processing. This includes the following steps:

[0065] Step 2.1 involves calculating the mixed posterior mean and variance of the latent variables using prior information and the received signal in the minimum mean square error module, and then extracting extrinsic information through the expectation propagation rule and transmitting it to the sparse Bayesian learning module. Specifically, this includes:

[0066] Step 2.1.1: Initialize extrinsic information and set the pseudo-observations passed from the sparse Bayesian learning module to the minimum mean square error module. and its variance It is initialized to a weak information state.

[0067] Step 2.1.2, in the minimum mean square error module, based on the current received signal Calculate the latent variable s based on the input external information. m =0 and when s m Posterior mean and posterior variance under the condition that =1:

[0068] (4)

[0069] Among them, y m For the m-th received signal, and These are the latent variables s m posterior mean and posterior variance when = 0 and These are the latent variables s m The posterior mean and posterior variance when =1.

[0070] Step 2.1.3: Calculate the posterior probability of the latent variable, i.e., the probability λ of the m-th sampling point being affected by impulse interference. m:

[0071] (5)

[0072] Where exp(·) is the exp function.

[0073] Step 2.1.4: Calculate the mean of the mixed posterior distribution based on the law of total probability. and variance :

[0074] (6)

[0075] Step 2.1.5: Extract extrinsic information using the expectation propagation rule, and output spurious observations from the minimum mean square error module to the sparse Bayesian learning module. and variance External information:

[0076] (7)

[0077] Step 2.2: In the sparse Bayesian learning module, combining the extrinsic information transmitted by the minimum mean square error module, sparse Bayesian learning is used to estimate the carrier frequency offset and channel, and the extrinsic information is then fed back. Specifically, this includes:

[0078] Step 2.2.1, in the sparse Bayesian learning module, based on the received extrinsic information... and The corresponding column vectors are: and Channel estimation is performed using a sparse Bayesian learning framework to obtain its posterior covariance matrix. and posterior mean :

[0079] (8)

[0080] in,(·) H The conjugate transpose operator is used for column vectors. α represents the precision parameters of each tap in the channel. l For the first The precision parameters of each channel tap are iteratively updated to improve channel sparsity. Channel estimates. for:

[0081] (9)

[0082] Step 2.2.2: Calculate the pseudo-observation posterior and its variance corresponding to the carrier frequency offset and channel estimation, and extract the extrinsic information to be fed back to the minimum mean square error module.

[0083] (10)

[0084] in, and These are the posterior matrix and posterior variance of the pseudo-observations, and their m-th elements are respectively and , and These are the external mean and external variance passed to the MMSE module. -1 It takes the reciprocal of each element of the vector. Both division and multiplication are element-wise operations.

[0085] Step 2.3: Repeat steps 2.1 to 2.2 until the preset number of iterations or convergence condition is reached.

[0086] Step 3: Within the minimum mean square error module, the expectation-maximization algorithm is used to iteratively update the mixing coefficients and variance parameters of the Gaussian mixture noise, achieving adaptive estimation of the noise parameters. This includes the following steps:

[0087] Step 3.1, based on the current observed signal External information input The posterior distribution of the pseudo-observations is calculated using formulas (4)-(6). .

[0088] Step 3.2: Iteratively update the parameters of the Gaussian mixture noise using the Expectation-Maximization algorithm. In each iteration, the parameters are updated based on the posterior probability. Calculate the sufficient statistics for each Gaussian component, and update the mixing coefficients and background noise variance. and impulse noise variance ,Right now:

[0089] (11)

[0090] in, The posterior mean of the background component, For the posterior variance of the background component, The posterior mean of the impulse component, The posterior variance under the impulse component is used to gradually approximate the true noise distribution, enabling the algorithm to adapt to unknown noise environments.

[0091] Step 4: Within the sparse Bayesian learning module, Type II maximum likelihood estimation combined with Newton's method is used to achieve a fine estimation of the carrier frequency offset. Simultaneously, a sparse Bayesian learning framework is employed for channel estimation, estimating the accuracy parameters of each channel tap to promote channel sparsity. This includes the following steps:

[0092] Step 4.1, based on the external information input by the minimum mean square error module Input, the Type II maximum likelihood estimation problem is:

[0093] (12)

[0094] in, , , , , This is an estimated value for the carrier frequency offset parameter ω. It is an optimization operator that finds ω that minimizes the subsequent objective function. The objective function g(ω) with respect to ω is defined as follows: .

[0095] Step 4.2: Divide the frequency domain Ω into a grid to obtain a coarse estimate of the carrier frequency offset. ,Right now

[0096] (13)

[0097] in, This means searching for the carrier frequency offset parameter ω in the candidate carrier frequency offset set (search grid) Ω that minimizes the objective function g(ω).

[0098] Step 4.3: Use the coarse estimate as the initial value for Newton's iteration, that is, let... The CFO parameters are iteratively updated using the first and second derivatives of g(ω) obtained through Newton's method, i.e.:

[0099] (14)

[0100] Where t is the number of Newton iterations. and These are the first and second derivatives of the objective function, respectively. Iteration stops when the difference between the estimated carrier frequency offsets obtained from two consecutive iterations is less than a preset threshold, or when the preset maximum number of iterations is reached, and the final iteration result is used as a refined estimate of the CFO. During the differentiation process, Treat it as a constant, that is Therefore, the first derivative is:

[0101] (15)

[0102] The second derivative is:

[0103]

[0104] Where R{·} denotes the real part operation, (·) H For the conjugate transpose operator

[0105] Sparse Bayesian learning framework for estimating the channel number The accuracy parameter α of each tap l The updated formula is:

[0106] (17)

[0107] Where a and b are hyperparameters that control the prior distribution of channel sparsity, μ l For the channel estimate of the l-th tap, Σ ll It is the l-th diagonal element of its posterior variance.

[0108] The aforementioned Type II maximum likelihood estimation refers to treating channel coefficients as random latent variables and using their posterior mean and posterior covariance to characterize the channel estimation results and their uncertainties. Given current extrinsic information and noise variance, a marginal likelihood function is constructed regarding the CFO parameter ω. By maximizing this marginal likelihood function, the negative logarithmic marginal likelihood objective function, ignoring constant terms independent of ω, is equivalently minimized. The estimated CFO parameters are obtained. The first term is a residual term weighted by the covariance matrix, used to characterize the degree of matching between the observed and reconstructed signals under the current CFO parameters; the second term is the logarithmic determinant of the covariance matrix, used to characterize the impact of channel estimation uncertainty on the marginal likelihood. Compared to directly fitting the channel coefficients as determinants, Type II maximum likelihood estimation incorporates the uncertainty of the channel coefficients into the CFO estimation process, which is beneficial for improving the robustness of CFO estimation under impulse noise environments.

[0109] The Newton method described above is a method for iteratively finding a local optimum using the first and second derivatives of the objective function. This invention first divides the search grid within a preset carrier frequency offset search range, and obtains a coarse estimate of the CFO by comparing the objective function values ​​corresponding to each candidate CFO. Then, the coarse estimate is used as the initial value for the Newton iteration, and the formula is updated according to the Newton method. The CFO parameters are updated iteratively, where t is the number of Newton iterations. and These are the first and second derivatives of the objective function, respectively. Iteration stops when the difference between the estimated carrier frequency offset values ​​obtained from two consecutive iterations is less than a preset threshold, or when the preset maximum number of iterations is reached, and the final iteration result is used as a refined estimate of the CFO.

[0110] This invention employs a CFO estimation method combining frequency domain grid search and Newton's method. The frequency domain grid search determines a coarse estimate of the CFO within a preset search range, providing initial values ​​for Newton's iteration. Newton's method utilizes local first- and second-order information from the Type II negative logarithmic marginal likelihood objective function to continuously optimize the carrier frequency offset near the coarse estimate, thereby obtaining a refined estimate. This approach reduces the sensitivity of Newton's iteration to initial values ​​and avoids the increased computational load that would result from simply improving estimation accuracy through a denser search grid.

[0111] Set the simulation environment parameters as follows: mixing coefficient ρ = 0.2, background noise variance... The variance of impulse noise is 0.1. The value is 5, and ω is 2π×10. -4 ,like Figure 4 As shown, the impulse noise and CFO parameters estimated by this invention converge after approximately 10 iterations. The convergence result is: the estimated variance of the background noise. The relative error is 0.026; the estimated variance of impulse noise is... The relative error is 0.1312; the estimated mixing coefficient is... The relative error is 0.0215, achieving self-adaptation to unknown noise environments. Among these, Figure 4 In the middle (a), the mixing coefficient is... The convergence curve, Figure 4 (b) represents the variance of the background noise. The convergence curve, Figure 4 (c) represents the variance of the impulse noise. The convergence curve, Figure 4 In the curve (d), ω converges. Figure 4 As can be seen from (a) to (d), the estimated values ​​of background noise variance, impulse noise variance, mixing coefficient and carrier frequency offset parameter can all stabilize after a finite number of iterations, indicating that the present invention can perform joint iterative estimation of noise statistical parameters and carrier frequency offset parameters under the joint interference of mixed Gaussian noise and carrier frequency offset.

[0112] like Figure 5 As shown, the proposed method for joint estimation of impulse noise download wave frequency offset and sparse channel in the above-mentioned impulse noise environment can achieve convergence of the normalized mean square error of channel estimation after about 10 iterations, and finally converge to -24.5323 dB.

[0113] like Figure 6As shown, the proposed method for joint estimation of impulse noise download wave frequency offset and sparse channel is compared with the traditional orthogonal matching pursuit method. Ultimately, the normalized mean square error of the channel estimation value of the traditional method is -6.0602 dB, while the normalized mean square error of the channel estimation value of the present invention is -24.5323 dB, which is an improvement of 18.4721 dB, significantly improving the performance of channel estimation under impulse noise environment.

[0114] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for jointly estimating impulse noise download wave frequency offset and sparse channel, characterized in that, Robust channel estimation is performed under interference from impulse noise and carrier frequency offset, specifically as follows: Step 1: Model the impulse noise as a mixture of Gaussian distributions. By introducing latent variables, the original mixture of Gaussian noise model is transformed into a conditional Gaussian model, and the mathematical relationship between the observed signal, channel parameters, noise signal and carrier frequency offset is established. Step 2: Based on the design concepts of message passing and modularization, external information is iteratively exchanged between the minimum mean square error module responsible for noise processing and the sparse Bayesian learning module based on channel estimation, so as to achieve joint optimization of channel estimation, carrier frequency offset and noise processing. Step 3: Within the minimum mean square error module, the expectation-maximization algorithm is used to iteratively update the mixing coefficients and variance parameters of the Gaussian mixture noise, thereby achieving adaptive estimation of the noise parameters. Step 4: Within the sparse Bayesian learning module, Type II maximum likelihood estimation combined with Newton's method is used to achieve a fine estimation of carrier frequency offset. At the same time, the sparse Bayesian learning framework is used to perform channel estimation and estimate the accuracy parameters of each channel tap to promote channel sparsity.

2. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 1, characterized in that, The introduction of latent variables transforms the original Gaussian mixture noise model into a conditional Gaussian model, specifically as follows: Step 1.1: Establish a linear model of the observed signal. The received signal is represented as the observation matrix multiplied by the channel tap vector to be estimated, plus mixed Gaussian noise. The observation matrix is ​​in Toeplitz form composed of pilot symbols. Step 1.2: Model the mixed Gaussian noise as a mixture of two Gaussian components. The probability density function of each element of the noise vector is the weighted sum of the background noise Gaussian component and the impulse noise Gaussian component, with the weights being the mixing coefficients. Step 1.3 introduces a binary latent variable to indicate the noise source of each sampling point. When the latent variable takes the first value, it means that the sampling point is only affected by background noise, and its noise follows a Gaussian distribution with a mean of zero and a variance equal to the variance of the background noise. When the latent variable takes the second value, it means that the sampling point is affected by impulse noise, and its noise follows a Gaussian distribution with a mean of zero and a variance equal to the variance of the impulse noise. This transforms the non-Gaussian noise into a joint Gaussian model conditioned by the latent variable.

3. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 1, characterized in that, The design concept based on message passing and modularity involves iteratively exchanging external information between the minimum mean square error module responsible for noise processing and the sparse Bayesian learning module for channel estimation. Step 2.1: In the minimum mean square error module, the mixed posterior mean and variance of the latent variables are calculated using prior information and the received signal. The extrinsic information is extracted through the expectation propagation rule and transmitted to the sparse Bayesian learning module. Step 2.2: In the sparse Bayesian learning module, combined with the external information transmitted by the minimum mean square error module, sparse Bayesian learning is used to estimate the carrier frequency offset and the channel, and the external information is transmitted back. Step 2.3: Repeat steps 2.1 to 2.2 until the preset number of iterations or convergence condition is reached.

4. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 3, characterized in that, Step 2.1 specifically refers to: Step 2.1.1: Initialize external information by setting the pseudo-observations and their variances passed from the sparse Bayesian learning module to the minimum mean square error module, and initializing them to a weak information state. Step 2.1.2: In the minimum mean square error module, based on the current received signal and input external information, calculate the posterior mean and posterior variance of the latent variables under the conditions of taking the first and second values, respectively. Step 2.1.3: Calculate the posterior probability of the latent variables; Step 2.1.4: Based on the law of total probability, calculate the mean and variance of the mixed posterior distribution using the results of steps 2.1.2 and 2.1.3; Step 2.1.5: Extract extrinsic information using the expectation propagation rule, and output extrinsic information containing pseudo-observations and variance from the minimum mean square error module to the sparse Bayesian learning module.

5. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 3, characterized in that, Step 2.2 specifically refers to: Step 2.2.1: In the sparse Bayesian learning module, based on the received extrinsic information, channel and carrier frequency offset estimation is performed using the sparse Bayesian learning framework to obtain the carrier frequency offset estimate and the posterior variance and posterior mean of the channel taps. Step 2.2.2: Calculate the pseudo-observation posterior and its variance corresponding to the carrier frequency offset and channel estimation, and extract the extrinsic information to be sent back to the minimum mean square error module.

6. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 1, characterized in that, Step 3 includes: Step 3.1: Based on the current observation signal and the external information input of the sparse Bayesian learning module, calculate the posterior of the pseudo-observation using the conditional Gaussian model established in Step 1; Step 3.2: The parameters of the Gaussian mixture noise are iteratively updated using the expectation-maximization algorithm. In each iteration, the sufficient statistics of each Gaussian component are calculated based on the posterior probability of the latent variables, and the mixing coefficient, background noise variance, and impulse noise variance are updated. The mixing coefficient is taken as the average of the posterior probabilities of the latent variables, and the background noise variance and impulse noise variance are taken as the weighted average of the squares of the noise under the background component and the impulse component, respectively. This allows the estimated noise distribution to gradually approach the true distribution, enabling the algorithm to adapt to unknown noise environments.

7. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 1, characterized in that, The method of using Type II maximum likelihood estimation combined with Newton's method to achieve fine estimation of carrier frequency offset is as follows: Step 4.1: Based on the external information input of the minimum mean square error module, establish the Type II maximum likelihood estimation problem; Step 4.2: Divide the frequency domain into grids to obtain a coarse estimate of the carrier frequency offset; Step 4.3: Use Newton's method to perform a fine estimation of the carrier frequency offset.

8. The method for jointly estimating impulse noise download wave frequency offset and sparse channel according to claim 1, characterized in that, The channel estimation using the sparse Bayesian learning framework specifically includes: calculating the posterior mean and posterior variance of each channel tap; determining the posterior second moment of each channel tap based on the sum of the squared modulus of the posterior mean and the posterior variance; and updating the accuracy parameters corresponding to each channel tap based on the posterior second moment.

Images