A signal recovery method integrating noise detection and prior estimation

Abstract

The present invention provides a signal recovery method integrating noise detection and prior estimation, which includes: based on the observed signal and the channel matrix, obtaining a pre-estimation of the original signal by using a zero interference equalization module; iteratively optimizing the estimated value of the signal by using an adaptive signal processing module; based on the pre-estimation of the original signal and the information extracted from the noise observation of the original signal generated by the adaptive signal processing module, obtaining a pre-estimation of the signal distribution through a semi-parametric Bayesian module, and updating the estimation of the original signal distribution in each iteration process of the adaptive signal processing module; updating the estimated value of the noise variance through an iterative noise estimation module, and updating it in each iteration process of the adaptive signal processing module. The present invention overcomes the difficulty that inaccurate signal recovery is caused by noise fluctuations brought about by environmental factors, and can accurately recover the signal even when the prior information of the original signal is missing.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to a signal recovery method integrating noise detection and prior estimation Background Art

[0002] In modern wireless communication systems, signal recovery and estimation are one of the key technologies to ensure communication quality. Especially in the case of large multi-path fading, noise variation, and channel uncertainty, how to accurately recover the original signal has become a challenging problem

[0003] Specifically, consider a linear observation model, where the received signal is obtained by linearly transforming the original signal through a known channel matrix and then adding noise. In this model, the noise is assumed to be zero-mean Gaussian noise, but its variance is unknown and may vary in different environments. More complexly, the prior distribution of the signal is usually unavailable because signals in wireless communication may be affected by various factors such as user behavior and channel changes. Therefore, the signal recovery method must operate under the conditions of lacking prior information of the signal and uncertain noise characteristics, avoiding relying on any assumptions about the signal distribution and effectively handling the uncertainty of the noise

[0004] The above research problem is contrasted and distinguished from the existing three types of signal recovery problems as follows

[0005] Problem of unknown prior information: In such problems, it is assumed that the prior distribution of the signal can be reasonably modeled in some way. The main challenges lie in how to efficiently utilize the known prior information and how to achieve optimal recovery when the signal and noise distributions are known. The scenario studied in the present invention requires the algorithm to not only handle the uncertainty of the signal but also cope with the challenge of uncertain noise variance

[0006] Problems of unknown prior information and noise distribution: In this problem, both the prior distribution of the signal and the distribution of the noise are unknown. In practical applications, due to various influences such as environmental factors, device errors, and system dynamics, the characteristics of the signal and the statistical characteristics of the noise may not be accurately predicted. Such problems usually require complex statistical inference and adaptive algorithms to estimate the distributions of the signal and the noise. The main difficulty in the problem studied in the present invention is that the variance of the noise is unknown and variable, which is different from the situation where the noise distribution is completely unknown

[0007] Problems of unknown prior information and channel distribution in bilinear problems: Bilinear problems usually occur in communication scenarios such as multi-input multi-output (MIMO) systems, where the interaction between the signal and the channel is non-linear. In such problems, signal recovery not only needs to consider noise interference but also deal with the complex non-linear relationship between the signal and the channel

[0008] Existing signal recovery methods can be roughly divided into three categories: traditional estimation methods, maximum likelihood estimation (MLE), and Bayesian estimation methods. Traditional estimation methods such as the least squares (LS) method have the advantage of simple calculation and do not require prior distribution information. However, the limitation of this method is that it ignores the influence of noise and has poor robustness to noise. Especially in a high-noise environment, the LS estimate is easily severely interfered by noise, resulting in inaccurate estimation results. Maximum likelihood estimation (MLE) can maximize the likelihood function of the observed data without prior information to perform signal recovery. Although this method has strong estimation ability, as the data dimension increases, the computational complexity grows exponentially. Especially in the case of large-scale data sets, the computational cost of MLE is extremely high and it is difficult to apply to practical scenarios. Bayesian estimation methods can provide more accurate results for signal recovery by combining prior knowledge and observed data. When the prior distribution is known, the Bayesian method can use the statistical characteristics of the signal for inference and has strong robustness. However, in actual wireless communication scenarios, the prior distribution of the signal is usually not accurately obtained, and the change of noise is also an issue that cannot be ignored, which challenges the effectiveness of the Bayesian method in such cases.

[0009] To address the problem of unknown noise variance, the prior art has proposed a latent variable maximization algorithm, which is applicable to cases where the determined distribution contains latent variables or incomplete data. In this situation, although the latent variables cannot be directly observed, they have an important impact on the observed data. It becomes difficult to directly use maximum likelihood estimation (MLE) to estimate the model parameters, and the latent variable maximization algorithm solves the original problem by iteratively optimizing the parameters and decomposing it into two steps: updating the latent variable distribution and updating the parameters, so as to gradually approach the maximum likelihood estimate of the parameters. The noise during transmission is usually assumed to follow a Gaussian distribution. In this case, the latent variable maximization algorithm can effectively estimate the unknown noise variance and shows good performance in this context, being able to provide relatively accurate estimates. However, the latent variable maximization algorithm also has limitations, that is, it depends on specific distribution assumptions and is difficult to extend to estimate more complex or a wide range of signal distributions. In contrast, the semi-parametric model combines the advantages of parametric and non-parametric methods. When facing an unknown distribution form, it can estimate some parameters to adapt to classical scenarios such as heavier-tailed distributions, noise, and outliers. Compared with the latent variable maximization algorithm, the semi-parametric model can handle different data distributions more flexibly while maintaining high efficiency and has a wider application range.

[0010] In summary, in the face of complex channel conditions and unknown prior signal distributions, how to design a robust signal detection and recovery method that can effectively cope with noise fluctuations and handle the uncertainty of prior signal knowledge remains an urgent problem in the current wireless communication field. Summary of the Invention

[0011] To overcome the difficulty that the Bayesian algorithm cannot be carried out due to the unknown form of the prior signal distribution and the unknown noise level, the present invention provides a signal recovery method integrating noise detection and prior estimation, which can estimate a wide range of prior distributions through data features and partial parameter modeling forms, and at the same time estimate the noise level.

[0012] To achieve the object of the present invention, the present invention is implemented by adopting the following technical solutions:

[0013] A signal recovery method integrating noise detection and prior estimation, comprising the following steps:

[0014] S1: Based on the observed signal and the channel matrix, use the zero-forcing equalization module to obtain a pre-estimation of the original signal;

[0015] S2: Use the adaptive signal processing module to iteratively optimize the estimated value of the signal;

[0016] S3: Based on the pre-estimation of the original signal and the information extracted from the noise observation of the original signal generated by the adaptive signal processing module, obtain a pre-estimation of the signal distribution through the semi-parametric Bayesian module, and update the estimation of the original signal distribution in each iteration process of the adaptive signal processing module;

[0017] S4: Update the estimated value of the noise variance through the iterative noise estimation module, and update it in each iteration process of the adaptive signal processing module.

[0018] In the signal recovery method integrating noise detection and prior estimation, the mathematical model of the wireless communication system is:

[0019] y = Ax + n;

[0020] where x ∈ C N×1 represents the original signal, A ∈ C M×N represents the channel matrix, n ∈ C M×1 represents additive white Gaussian noise with unknown noise variance, y ∈ C M×1 represents the system observed signal, and both M and N are positive integers.

[0021] Preferably, in step S1, a zero-forcing equalizer is used to obtain a pre-estimation of the original signal. By filtering the received observation signal, interference and multipath effects are eliminated, so as to obtain a preset of the original signal and transmit it to the adaptive signal processing module as an initialization drive. The expression is:

[0022]

[0023] Wherein, represents the initial estimate of the original signal obtained by using the zero-forcing equalizer, and A * represents the conjugate transpose of the channel matrix A.

[0024] Furthermore, the adaptive signal processing module in step S2 approximately calculates the posterior distribution of the signal. In each iteration step, each component of the signal receives information from adjacent components and uses this information to update the current estimate of the signal, alternately updating the estimate value and variance of the original signal, and finally gradually approaching the true original signal; in each round of iteration, the message is updated through the current estimate value until convergence or the set number of iterations is reached;

[0025] The relationship between y Y |Z(y m |z m ) is modeled by the transition probability p m and The approximate true marginal posterior distribution p(z |y) of z m is used, and the approximate true marginal posterior distribution of x m is approximated by Specifically: n The true marginal posterior distribution of x

[0026]

[0027] Where represents an intermediate variable, represents the estimated value of z m , represents the estimated variance of z m , y m represents the m-th element of the observation signal y, z m represents the product of the m-th row of the channel matrix A and the original signal x, represents the estimated posterior variance of the original signal x, represents the estimated value of the original signal x, represents the estimated variance of the noise; combined with the above intermediate variables, the approximate true marginal posterior distribution of x is approximated by n The specific iterative formula is:

[0028]

[0029] where is an intermediate variable, and can be regarded as the observed value of the Gaussian noise observation of the original signal x n and the noise variance, that is, Using this key information, the estimated distribution of x can be obtained by combining the semi-parametric Bayesian module and the estimated value, specifically:

[0030]

[0031]

[0032] where and are the estimated values of the original signal x and the variance generated by the iterative process of the adaptive signal processing module. t represents the number of iterations. The subscripts m and n represent the m-th and n-th elements in the corresponding vectors respectively. A mn represents the element in the m-th row and n-th column of the channel matrix A, is the estimate of the original signal distribution p(x), represents the semi-parametric Bayesian module;

[0033] and represent z m 's approximate posterior distribution 's mean and variance, represents the variance of the additive zero-mean Gaussian noise n estimated in the (t + 1)-th iteration, which is determined by the distribution of the noise.

[0034] Preferably, the adaptive Bayesian module in step S3 is a data-driven distribution modeling method, which combines the pre-estimation of the original signal and the information extracted from the noise observation data of the original signal generated by the adaptive signal processing module and the parameter modeling method to construct the estimate of the unknown prior distribution p(x) Specifically:

[0035] A: Set the equidistant discrete sampling space Ω of the original signal x, specifically:

[0036] Ω = (x (1) , x (2) , …, x (L) );

[0037] where x (1)∈R is the minimum sampling value of the original signal x in the sampling space Ω, and the interval between each sampling point in the sampling space Ω is a fixed value Δx;

[0038] Under this setting, the probability distribution p(x) of the original signal x can be approximated by a discrete vector p i (i = 1, 2…, L) represents the probability value of the original signal sampled at x (i) and satisfies

[0039] Similarly, set the equidistant discrete sampling space of the intermediate variable as Specifically:

[0040]

[0041] where r (1) is in the sampling space The minimum sampling value, and the interval between each sampling point in the sampling space is a fixed value Δr, and the specific setting range should be slightly larger than the range of ;

[0042] B: Further, in the process of the adaptive Bayesian method, there is a marginal density function where is a Gaussian distribution with zero mean and variance For the discrete sampling space, this marginal density function can be expressed in vector form where is a k×L transition probability matrix, and the vector U = (u1, u2,..., u K ) is obtained, and u k (k = 1, 2,..., K) represents the marginal probability value at r (k) ;

[0043] Count all the intermediate variables according to the sampling space, and obtain the frequency R = (R1, R2,..., R K ) at each sampling point, where R k is falling within the interval and is a sufficient statistic of and follows a multinomial distribution with K outcomes, N draws, and probability vector U

[0044] Preferably, by means of parametric modeling, the estimated prior distribution is modeled as B is a structural matrix of L×p, composed of natural spline functions. represents the l-th row of the B matrix, and α is a p×1 vector of unknown parameters. Thus, the marginal density function U can also be approximated as a discrete probability distribution.

[0045] C: Its estimated value is obtained by the maximum likelihood method. Then the estimated value of the prior distribution obtained by the adaptive Bayesian module can be expressed as Specifically:

[0046] Take the logarithm of the probability distribution of the frequency cumulative vector R. The expression is:

[0047]

[0048] The score function of the parameter vector α can be expressed as The result of the maximum likelihood estimation It can be set that Solve to obtain, and then obtain the final estimated value of the prior distribution

[0049] Preferably, in the iterative noise estimation module in step S4, the maximum latent variable maximization algorithm is used to increase the lower bound of the likelihood function ln p(y;σ) iteratively in each iteration, so that the likelihood function can converge to a local maximum or an extreme point, thereby updating the estimation of the variance of the Gaussian noise. Specifically:

[0050] Initialize the variance of the Gaussian noise where SNR 0 is the signal-to-noise ratio for initialization. In the case of unknown noise variance, to avoid the algorithm falling into a local optimal solution, increase the lower bound of ln p(y;σ) in each iteration:

[0051]

[0052] where is the m-th element of the product Ax of the channel matrix A and the original signal x. To obtain It is necessary to take the derivative of the above formula and set it equal to zero to obtain the iterative formula for the specific Gaussian noise variance:

[0053]

[0054] In the above technical solution, the zero-interference equalization module filters the received observation signal to obtain a pre-estimation of the original signal, and transmits the pre-estimation value to the adaptive processing module as the initial driving parameter; in the first iteration, the semi-parametric Bayesian module uses the intermediate variable as the distribution feature of the data statistics of the original signal, and combines parametric modeling to obtain the initial estimation of the original signal distribution; the iterative noise estimation module finds the solution of the maximum likelihood estimation of the parameter in the statistical model as the estimation of the noise variance; the semi-parametric Bayesian module and the iterative noise estimation module are embedded in the adaptive signal processing module, and the distribution of the original signal and the estimation of the noise variance are iteratively updated until the algorithm converges to the optimal solution, and finally the estimated original signal is obtained.

[0055] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0056] The zero-interference equalization module used in the present invention as the initial drive of the adaptive processing module can provide appropriate initialization parameters, improve the stability and convergence speed of the algorithm; the semi-parametric Bayesian module estimates the true distribution through data statistics and parametric modeling in the case of missing the original signal distribution information, which is more accurate than the method that does not require the prior distribution; at the same time, the latent variable maximization algorithm can dynamically detect the fluctuating noise level caused by environmental factors, and improve the stability of the signal detection system. Description of the Drawings

[0057] Figure 1 The flowchart of a signal recovery method integrating noise detection and prior estimation provided for Embodiment 1;

[0058] Figure 2 For Embodiment 2, with the parameters N = 512, modulation mode QAM, M = 1024, and SNR = 10 dB, the distribution of the original signal x estimated by the semi-parametric Bayesian module

[0059] Figure 3 For Embodiment 2, with the parameters N = 512, modulation mode QAM, M = 1024, and SNR = 10 dB, the performance comparison diagram of the least squares method LS without prior distribution, the method proposed by the present invention, and only using the zero-interference equalization module and the adaptive Bayesian module when the prior distribution is known and the noise variance is also known. Detailed Embodiments

[0060] To enable those skilled in the art to better understand the solution of this application, the following will clearly and completely describe the technical solution in the embodiments of this application in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without creative efforts shall fall within the scope of protection of this application.

[0061] The accompanying drawings are only for illustrative purposes and cannot be regarded as a limitation of this patent; for better illustration of the embodiments, some components may be omitted, enlarged or reduced, which does not represent the size of the actual product.

[0062] For those skilled in the art, it is understandable that some well-known structures and their descriptions in the accompanying drawings may be omitted.

[0063] The following further describes the technical solution of the present invention in conjunction with the accompanying drawings and embodiments.

[0064] Embodiment 1

[0065] As Figure 1 shown, the present invention provides a signal recovery method integrating noise detection and prior estimation. Refer to Figure 1 , which includes the following steps:

[0066] S1: Based on the observed signal and the channel matrix, use the zero interference equalization module to obtain a pre-estimation of the original signal;

[0067] S2: Use the adaptive signal processing module to iteratively optimize the estimated value of the signal;

[0068] S3: Based on the pre-estimation of the original signal and the information extracted from the noise observation data of the original signal generated by the adaptive signal processing module, obtain a pre-estimation of the signal distribution through the semi-parametric Bayesian module, and update the estimation of the original signal distribution in each iteration process of the adaptive signal processing module;

[0069] S4: Update the estimated value of the noise variance through the iterative noise estimation module and update it in each iteration process of the adaptive signal processing module.

[0070] Embodiment 2

[0071] On the basis of Embodiment 1, this embodiment further discloses the following content:

[0072] Specifically, the mathematical model of the wireless communication system is:

[0073] y = Ax + w;

[0074] The mathematical model shows that the original signal \(x\) is sent from the transmitting end and, after passing through a channel with additive white Gaussian noise \(w\), the signal \(y\) is received at the receiving end, where \(x\in\mathbb{C}\). N×1 represents the original signal, \(A\in\mathbb{C}\). M×N represents the channel matrix, \(w\in\mathbb{C}\). M×1 represents additive zero-mean Gaussian noise with unknown noise variance, \(y\in\mathbb{C}\). M×1 represents the system observation signal, and both \(M\) and \(N\) are positive integers.

[0075] Preferably, in step S1, a zero-forcing equalizer is used to obtain a pre-estimate of the original signal. By filtering the received observation signal, interference and multipath effects are eliminated, thereby obtaining a pre-set of the original signal and passing it into the adaptive signal processing module as an initialization drive. The expression is:

[0076]

[0077] where represents the initial estimate of the original signal obtained using a zero-forcing equalizer, \(A\) * represents the conjugate transpose of the channel matrix \(A\).

[0078] Furthermore, the adaptive signal processing module in step S2 approximately calculates the posterior distribution of the signal. In each iteration step, each component of the signal receives information from adjacent components and uses this information to update the current estimate of the signal, alternately updating the estimate of the original signal and its variance, and finally gradually approaching the true original signal; in each round of iteration, the message is updated using the current estimate until convergence or the set number of iterations is reached;

[0079] Model the relationship between \(y\) Y |Z(y m |z m ) using the transition probability \(p\) m and approximate the true marginal posterior distribution \(p(z\) |y) of \(z\) m using m and approximate the true marginal posterior distribution of \(x\) using n . The specific iteration formula is:

[0080]

[0081] where represents an intermediate variable, represents the estimate of \(z\) m , represents the estimated variance of \(z\) m , \(y\) mDenotes the m-th element of the observed signal y, z m Denotes the m-th row of the channel matrix A The product with the original signal x, Denotes the estimated posterior variance of the original signal x, Denotes the estimated value of the original signal x, Denotes the estimated variance of the noise; combined with the above intermediate variables using To approximate x n The true marginal posterior distribution of, the specific iteration formula is:

[0082]

[0083] Where Is an intermediate variable, And Can be regarded as the observed value and noise variance of the Gaussian noise observation of the original signal x n That is, Using this key information, the estimated distribution of x can be estimated by combining the semi-parametric Bayesian module And the estimated value, specifically:

[0084]

[0085]

[0086] Where And Are the estimated values of the estimated value and variance of the original signal x generated by the iteration of the adaptive signal processing module, t represents the number of iterations, the subscripts m and n respectively represent the m-th and n-th elements in the corresponding vector, A mn Denotes the element in the m-th row and n-th column of the channel matrix A, Is the estimate of the original signal distribution p(x), Denotes the semi-parametric Bayesian module;

[0087] And Denotes z m The approximate posterior distribution of The mean and variance of, Denotes the variance of the additive zero-mean Gaussian noise n estimated in the (t + 1)-th iteration, Determined by the distribution of the noise, in the scenario described in this embodiment, it is a Gaussian distribution Obtained:

[0088]

[0089] Preferably, the semi-parametric Bayesian module in step S3 is a data-driven distribution modeling method that combines pre-estimation of the original signal, information extracted from the noise observation data of the original signal generated by the adaptive signal processing module, and parametric modeling methods to construct an estimate of the unknown prior distribution p(x). Specifically:

[0090] A: Set an equidistant discrete sampling space Ω for the original signal x, specifically:

[0091] Ω = (x (1) , x (2) , …, x (L) );

[0092] where x (1) ∈R is the minimum sampling value of the original signal x in the sampling space Ω, the interval between each sampling point in the sampling space Ω is a fixed value Δx. In this embodiment, the range of the original signal x can be limited to [-3, 3], and Δx is taken as 0.01, obtaining Ω = (-3, -2.99, …, 2.99, 3);

[0093] Under this setting, the probability distribution p(x) of the original signal x can be represented by a discrete vector p i (i = 1, 2 …, L) represents the probability value of the original signal sampled at x (i) , and satisfies

[0094] Similarly, set the equidistant discrete sampling space of the intermediate variable as Specifically:

[0095]

[0096] where r (1) is in the sampling space the minimum sampling value, the interval between each sampling point in the sampling space is a fixed value Δr. Similarly, the range of can be set to [-3, 3], and the interval is equally divided into (K + 1) small intervals, and the interval length is

[0097] B: Further, in the process of the adaptive Bayesian method, there is a marginal density function where is a Gaussian distribution with zero mean and variance . For the discrete sampling space, this marginal density function can be expressed in vector form where is a k×L transition probability matrix, and a vector U = (u1, u2,..., u K ) is obtained, where u k (k = 1, 2,..., K) represents the marginal probability value at r (k) ;

[0098] All intermediate variables are counted according to the sampling space, and the frequency R = (R1, R2,..., R K ) at each sampling point is obtained, where R k is the number falling within the interval [r (k) , r (k) + Δr], and it is a sufficient statistic of , and follows a multinomial distribution with K outcomes, N draws, and probability vector U

[0099] Preferably, through parametric modeling, the estimated prior distribution is modeled as B is an L×p structure matrix composed of natural spline functions, represents the l-th row of the B matrix, α is a p×1 unknown parameter vector, and thus the marginal density function U can also be approximated as a discrete probability distribution

[0100] C: Its estimated value is obtained by the maximum likelihood method Then the estimation of the prior distribution obtained by the adaptive Bayesian module can be expressed as Specifically:

[0101] Taking the logarithm of the probability distribution of the frequency cumulative vector R, the expression is:

[0102]

[0103] The score function of the parameter vector α can be expressed as The result of the maximum likelihood estimation can set to be solved, and then the final estimation of the prior distribution is obtained

[0104] Preferably, the maximum latent variable maximization algorithm in step S4 increases the lower bound of the likelihood function ln p(y; σ) in each iteration through an iterative method, so that the likelihood function can converge to a local maximum or extreme point, thereby updating the estimation of the variance of the Gaussian noise Specifically:

[0105] Initializing the variance of the Gaussian noise where SNR0 is the signal-to-noise ratio for initialization, and in the experiment, it is appropriate to take SNR 0 = 10. In the case of unknown noise variance, to avoid the algorithm falling into a local optimal solution, the lower bound of ln p(y; σ) is increased in each iteration:

[0106]

[0107] where is the m-th element of the product Ax of the channel matrix A and the original signal x. To obtain it is necessary to take the derivative of the above formula and set it equal to zero to obtain the iterative formula for the specific Gaussian noise variance:

[0108]

[0109] In summary, the zero interference equalization module filters the received observation signal to obtain a pre-estimation of the original signal, and transmits the pre-estimation value to the adaptive processing module as the initial driving parameter; in the first iteration, the semi-parametric Bayesian module uses the intermediate variable as the distribution feature of the data statistics of the original signal, and combines parameter modeling to obtain the initial estimation of the original signal distribution; the iterative noise estimation module finds the solution of the maximum likelihood estimation of the parameter in the statistical model as the estimation of the noise variance; the semi-parametric Bayesian module and the iterative noise estimation module are embedded in the adaptive signal processing module, and the distribution of the original signal and the estimation of the noise variance are iteratively updated until the algorithm converges to the optimal solution, and finally the estimation of the original signal x is obtained The estimated distribution of the original signal and the variance estimation of the original signal x.

[0110] The zero interference equalization module used in this embodiment as the initial drive of the adaptive processing module can provide appropriate initialization parameters, improve the stability and convergence speed of the algorithm; the semi-parametric Bayesian module estimates the true distribution through data statistics and parameter modeling in the case of missing original signal distribution information, which is more accurate than the method that does not require prior distribution; at the same time, the hidden variable maximization algorithm can dynamically detect the fluctuating noise level caused by inter-cell interference, improving the stability of the signal detection system.

[0111] Embodiment 3:

[0112] This embodiment adopts the following signal and channel configurations and parameter settings to verify the feasibility and effectiveness of the present invention. The dimension of the system is set to the dimension N = 512 of the original signal x, the modulation method of the original signal x is 16-QAM, the dimension M = 1024 of the observation signal y, the channel matrix A is a 1024×512 complex matrix, and each element A mn obeys an independent and identical complex Gaussian distribution The additive Gaussian noise w is a 1024×1 complex vector and follows a complex Gaussian distribution The signal-to-noise ratio SNR is 10 dB. The performance evaluation metric for the simulation is the mean square error (MSE) of the signal x, which describes the estimated original signal The normalized error between the estimated original signal and the actual original signal. The smaller the mean square error, the better the performance. The MSE is defined as

[0113] Figure 2 Denotes the estimate of the distribution of the original signal x obtained by the final semi-parametric Bayesian module after multiple iterations It can be clearly judged that The modulation method of

[0114] Figure 3 Respectively show the performance of the least squares method LS without prior distribution, the method proposed in the present invention, and the case where the prior distribution is known and the noise variance is also known, only using the zero interference equalization module and the adaptive Bayesian module; the least squares method can obtain the estimated value without iteration, but the performance is very unsatisfactory; the MSE of the EM-semi-parametric-adaptive Bayesian method proposed in the present invention and the case where the prior distribution is known and the noise variance is also known, only using the zero interference equalization module and the adaptive Bayesian module both finally converge. The performance of the present invention is very close to the theoretical upper limit of the latter, meeting the theoretical expectations

Claims

1. A signal recovery method integrating noise detection and prior estimation, characterized in that, It includes the following steps: S1: Based on the observation signal and the channel matrix, use the zero-forcing equalization module to obtain a pre-estimated value of the original signal; S2: Use the adaptive signal processing module to iteratively optimize the pre-estimated value of the original signal; S3: Based on the pre-estimated value of the original signal and the information on the Gaussian noise observation of the original signal extracted from the adaptive signal processing module, obtain a pre-estimation of the signal distribution through the semi-parametric Bayesian module, and update the estimation of the original signal distribution during each iteration of the adaptive signal processing module; S4: Update the estimated value of the noise variance through the iterative noise estimation module, and update the estimated value of the noise variance during each iteration of the adaptive signal processing module; The specific steps for the zero-forcing equalization module to obtain the pre-estimated value of the original signal include: The feature of step S1 is that by filtering the received observation signal to eliminate interference and multipath effects, the pre-set of the original signal is obtained and passed into the adaptive signal processing module as the initialization drive. The expression is: Among them, represents the initial estimated value of the original signal obtained by using the zero-forcing equalization module, A * represents the conjugate transpose of the channel matrix A, and y represents the system observation signal; The feature of step S2 is that the adaptive signal processing module approximately calculates the posterior distribution of the signal. In each iteration step, each component of the signal receives information from adjacent components and uses this information to update the current signal estimation. The estimated value and variance of the original signal are alternately updated, and finally gradually approach the true original signal; in each round of iteration, the message is updated through the current estimated value until convergence or the set number of iterations is reached; Through the transition probability p Y|Z (y m |z m ) to model the relationship between y m and , and use to approximate the marginal posterior distribution p(z m |y) of the true z m Specifically: Among them represents an intermediate variable, represents the estimated value of z m ; represents the estimated variance of z m , y m represents the m-th element of the observed signal y, z m represents the m-th row of the channel matrix A multiplied by the original signal x, represents the estimated posterior variance of the original signal x, represents the estimated value of the original signal x, represents the estimated variance of the noise; combined with the above intermediate variable using to approximate the true marginal posterior distribution of x n , and the specific iteration formula is as follows: wherein is an intermediate variable, and are regarded as the observed values and noise variances of the Gaussian noise observation of the original signal x n , that is Using this key information, the estimated distribution and the estimated value of x are obtained by combining the semi-parametric Bayesian module estimation, specifically: Among them and are the estimated values of the original signal x and the variance iteratively generated by the adaptive signal processing module. t represents the number of iterations. The subscripts m and n respectively represent the m-th and n-th elements in the corresponding vectors. A mn represents the element in the m-th row and n-th column of the channel matrix A, is the estimate of the original signal distribution p(x), represents the semi-parametric Bayesian module; and represent the approximate posterior distribution of z m with mean and variance , and represents the variance of the additive zero-mean Gaussian noise n estimated at the (t + 1)-th iteration, which is determined by the distribution of the noise; The feature of step S3 is that the adaptive Bayesian module uses data-driven modeling distribution, combines the information extracted from the data and the parameter modeling method to construct an estimate of the unknown prior distribution p(x). Specifically: A: Set the equidistant discrete sampling space Ω of the original signal x, specifically: Ω = (x(1), x(2), …, x(L)); where x (1) ∈R is the minimum sampling value of the original signal x in the sampling space Ω, and the interval between each sampling point in the sampling space Ω is a fixed value Δx; In this setting, the probability distribution p(x) of the original signal x is represented by a discrete vector to denote, p i (i = 1, 2…, L) represents the probability value of the original signal sampled at x ( i ) and satisfies Similarly, set an intermediate variable The equidistant discrete sampling space of Specifically: where r (1) is the minimum sampling value in the sampling space T, and the interval between each sampling point in the sampling space T is a fixed value Δr. The specific setting range should be 1 time larger than the range of ; The adaptive Bayesian module is a data-driven distribution modeling method that combines the information extracted from the data and the parametric modeling method to construct an estimate of the unknown prior distribution p(x). Specifically: B: Further, there is a marginal density function in the process of the adaptive Bayesian method where is a Gaussian distribution with zero mean and variance . For a discrete sampling space, this marginal density function is expressed in vector form where is a k×L transition probability matrix, and the vector U = (u1, u2,..., u K ) is obtained, and u k (k = 1, 2,..., K) represents the marginal probability value at r ( k ) . All intermediate variables are counted according to the sampling space to obtain the frequency R=(R1, R2,..., R K ), where R k is the number falling within the interval and is a sufficient statistic, following a multinomial distribution with K outcomes, N draws, and probability vector U By means of parametric modeling, the estimated prior distribution is modeled as B is an L×p structural matrix composed of natural spline functions, represents the l-th row of the B matrix, α is a p×1 vector of unknown parameters, and thus the marginal density function U is approximated as a discrete probability distribution C: Its estimated value is obtained by the maximum likelihood method Then the adaptive Bayesian module obtains the estimated representation of the prior distribution as Specifically: Take the logarithm of the probability distribution of the frequency cumulative vector R. The expression is: The scoring function of the parameter vector α is expressed as The result of the maximum likelihood estimation Let Solve to obtain, and then obtain the estimation of the final prior distribution The feature of step S4 is that, by using the latent variable maximization algorithm, the lower bound of the likelihood function lnp(y;σ) is increased in each iteration through an iterative method, so that the likelihood function can converge to a local maximum or an extreme point, and thereby the estimation of the variance of the Gaussian noise is updated. Specifically: Initialize the variance of Gaussian noise where SNR 0 is the signal-to-noise ratio for initialization. In the case of unknown noise variance, to avoid the algorithm falling into a local optimal solution, the lower bound of ln p(y; σ) is increased at each iteration: where is the m-th element of the product Ax of the channel matrix A and the original signal x. To obtain it is necessary to take the derivative of the above equation and set it equal to zero to obtain an iterative formula for the specific Gaussian noise variance:

2. In the signal recovery method integrating noise detection and prior estimation according to claim 1, it is characterized in that The mathematical model of the wireless communication system is: y = Ax + n; where \(x\in\mathbb{C}\) N×1 represents the original signal, \(A\in\mathbb{C}\) M×N represents the channel matrix, \(n\in\mathbb{C}\) M×1 represents additive white Gaussian noise with unknown noise variance, \(y\in\mathbb{C}\) M×1 represents the system observation signal, and both \(M\) and \(N\) are positive integers; The zero-forcing equalization module obtains the pre-estimated value of the original signal and passes it into the adaptive signal processing module for initialization. The adaptive signal processing module combines the semi-parametric Bayesian module and the iterative noise estimation module to iteratively optimize the estimated values of the distribution and noise variance of the original signal, and finally outputs the estimated value of the original signal and the estimated value of the prior distribution.

3. A signal recovery method integrating noise detection and prior estimation, according to claim 1 or 2, characterized in that The method is implemented through the following modules: Zero-forcing equalization module, used to obtain the pre-estimated value of the original signal; Adaptive signal processing module, combined with the semi-parametric Bayesian module and the iterative noise estimation module, used to iteratively estimate the pre-estimated value of the original signal; Semi-parametric Bayesian module, used to analyze the intermediate variable data of each iteration of the adaptive signal processing module, so as to establish an estimation of the prior distribution; Iterative noise estimation module, configured to update and output the estimated value of the noise variance during each iteration period of the adaptive signal processing module.

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