Signal recovery method integrating noise detection and prior estimation

Abstract

The invention provides a signal recovery method integrating noise detection and prior estimation, which comprises the following steps of: acquiring pre-estimation of an original signal by utilizing a zero interference equalization module based on an observation signal and a channel matrix; carrying out iterative optimization on the estimated value of the signal by utilizing a self-adaptive signal processing module; based on pre-estimation of the original signal and information extracted from noise observation of the original signal generated by the adaptive signal processing module, pre-estimation of signal distribution is obtained through a semi-parameter Bayesian module, and estimation of the original signal distribution is updated in each iteration process of the adaptive signal processing module; and the estimated value of the noise variance is updated through the iterative noise estimation module, and is updated in each iteration process of the adaptive signal processing module. According to the method, the difficulty of inaccurate signal recovery caused by noise fluctuation brought by environmental factors is overcome, and meanwhile, the signal can be accurately recovered when the prior information of the original signal is lacked.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a signal recovery method integrating noise detection and a priori estimation. Background Art

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

[0003] Specifically, consider a linear observation model in which the received signal is obtained by linearly transforming the original signal through a known channel matrix and then superimposing noise. In this model, the noise is assumed to be zero-mean Gaussian noise, but its variance is unknown and may change in different environments. To complicate matters further, the prior distribution of the signal is usually not available because the signal in wireless communications may be affected by many factors, such as user behavior, channel changes, etc. Therefore, the signal recovery method must be performed in the absence of prior information about the signal and under the condition of uncertain noise characteristics, avoiding relying on any assumptions about the signal distribution while effectively handling the uncertainty of the noise.

[0004] The above research problem is different from the existing three types of signal recovery problems in that:

[0005] Problems with unknown prior information: In this type of problem, the study assumes that the prior distribution of the signal can be reasonably modeled in some way. The main challenge is how to efficiently use the known prior information and how to achieve optimal recovery when the signal and noise distribution are known. The scenario studied in this paper requires the algorithm to not only deal with the uncertainty of the signal, but also to cope with the challenge of uncertainty in the noise variance;

[0006] Problems where both prior information and noise distribution are unknown: In this problem, both the prior distribution of the signal and the distribution of the noise are unknown. In practical applications, due to the influence of environmental factors, equipment errors, system dynamics and other factors, 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 distribution of the signal and noise. The difficulty of the problem studied in this invention lies mainly in the fact that the variance of the noise is unknown and changes, which is different from the situation where the noise distribution is completely unknown;

[0007] Prior information and unknown channel distribution in bilinear problems: Bilinear problems often occur in communication scenarios such as multiple-input multiple-output (MIMO) systems, where the interaction between signals and channels is nonlinear. In such problems, signal recovery not only needs to consider noise interference, but also needs to deal with the complex nonlinear relationship between signals and channels.

[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 being easy to calculate and not requiring 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 high-noise environments, LS estimation is easily seriously interfered by noise, resulting in inaccurate estimation results. Maximum Likelihood Estimation (MLE) can maximize the likelihood function of observed data without prior information to perform signal recovery. Although this method has strong estimation capabilities, the amount of calculation increases exponentially with the increase of data dimensions. Especially in the case of large-scale data sets, the computational overhead of MLE is extremely large and 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 variation of noise is also a problem that cannot be ignored, which challenges the effectiveness of the Bayesian method in such situations.

[0009] In order to solve the problem of unknown noise variance, the prior art proposes a latent variable maximization algorithm, which is applicable to the case where the determined distribution contains latent variables or incomplete data. In this case, although the latent variables cannot be directly observed, they have an important impact on the observed data. It becomes difficult to directly use the maximum likelihood estimation (MLE) to estimate the model parameters. The latent variable maximization algorithm optimizes the parameters iteratively and decomposes the original problem into two steps: updating the latent variable distribution and updating the parameters, thereby gradually approaching the maximum likelihood estimation of the parameters. The noise in the transmission process is usually assumed to follow a Gaussian distribution. In this case, the latent variable maximization algorithm can effectively estimate the unknown noise variance and show good performance in this scenario, which can provide a relatively accurate estimate. However, the latent variable maximization algorithm also has limitations, that is, it relies on specific distribution assumptions and is difficult to extend to estimate more complex or extensive types of signal distributions. In contrast, the semi-parametric model combines the advantages of parametric and non-parametric methods. When faced with unknown distribution forms, it can adapt to classic scenarios such as heavier tail distributions, noise and outliers by estimating some parameters. 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 range of applications.

[0010] In summary, when faced with complex channel conditions and unknown signal prior distribution, how to design a robust signal detection and recovery method that can effectively cope with noise fluctuations and handle the uncertainty of signal prior knowledge is still a problem that needs to be solved urgently in the current wireless communication field. Summary of the invention

[0011] In order to overcome the difficulty of Bayesian algorithm development caused by unknown signal prior distribution form and 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, and simultaneously estimate the noise level.

[0012] To achieve the purpose of the present invention, the present invention adopts the following technical solutions:

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

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

[0015] S2: Iteratively optimize the estimated value of the signal using an adaptive signal processing module;

[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, a pre-estimation of the signal distribution is obtained through the semi-parametric Bayesian module, and the estimation of the original signal distribution is updated in each iteration of the adaptive signal processing module;

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

[0018] In the signal recovery method integrating noise detection and a priori 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 zero-mean Gaussian noise with unknown noise variance, y∈C M×1 Represents the system observation signal, and M and N are both positive integers.

[0021] Preferably, in step S1, a zero interference equalizer is used to obtain a pre-estimation of the original signal, and the received observation signal is filtered to eliminate interference and multipath effects, thereby obtaining a preset of the original signal and transmitting it to the self-response signal processing module as an initialization drive, and the expression is:

[0022]

[0023] in, represents the initial estimate of the original signal obtained using the zero-interference equalizer, 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 the information to update the estimate of the current signal, alternately updating the estimate and variance of the original signal, and finally gradually approximating the true original signal; each round of iteration updates the message with the current estimate until convergence or the set number of iterations is reached;

[0025] Through the transition probability p Y|Z (y m |z m ) Modeling m and The relationship between Approximately true z m The marginal posterior distribution p(z m |y), use Approximate x n The true marginal posterior distribution of is:

[0026]

[0027] in represents the intermediate variable, Indicates z m The estimated value of Indicates z m The estimated variance y m represents the mth element of the observed signal y, z m represents the mth row of the channel matrix A The product of 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, Approximate x nThe true marginal posterior distribution of is, and the specific iteration formula is:

[0028]

[0029] in is the intermediate variable, and It can be regarded as the original signal x n The observed value and noise variance of the Gaussian noise observation are, that is, Using this key information, we can combine the semi-parametric Bayesian module to estimate the estimated distribution of x and estimated values, specifically:

[0030]

[0031] in and is the estimated value and variance of the original signal x generated by the adaptive signal processing module. t represents the number of iterations. The subscripts m and n represent the mth and nth elements in the corresponding vector, respectively. mn represents the element in the mth row and nth column of the channel matrix A, is an estimate of the original signal distribution p(x), represents a semiparametric Bayesian module;

[0032] and Indicates z m The approximate posterior distribution of The mean and variance of represents the variance of the additive zero-mean Gaussian noise n estimated at the t+1th iteration, Determined by the distribution of the noise.

[0033] Preferably, the adaptive Bayesian module in step S3 is a data-driven distribution modeling method, which combines 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 an estimate of the unknown prior distribution p(x). Specifically:

[0034] A: Set the equidistant discrete sampling space Ω of the original signal x, specifically:

[0035] Ω=(x (1) ,x (2) ,…,x (L) );

[0036] 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;

[0037] In this setting, the probability distribution p(x) of the original signal x can be expressed as a discrete vector To approximate, p i (i=1,2…,L) represents the original signal at x (i) The probability value of sampling at , and satisfy

[0038] Similarly, set the intermediate variables The equidistant discrete sampling space of Specifically:

[0039]

[0040] where r (1) for In the sampling space The minimum sampling value in the sampling space The interval between each sampling point is a fixed value Δr. The specific setting range should be The range is slightly larger;

[0041] B: Further, in the process of adaptive Bayesian method, there is a marginal density function in has a mean of zero and a variance of Gaussian distribution, for discrete sampling space, the edge density function can be expressed in vector form in is a k×L transition probability matrix, and we get the vector U=(u1,u2,...,u K ),u k (k=1,2,…,K) means that in r (k) The marginal probability value at ;

[0042] All intermediate variables According to the sampling space count, the frequency at each sampling point is obtained as R = (R1, R2, ..., R K ), where R k yes Falling in the range The number within and is A sufficient statistic for K results, N times of extraction, with a probability vector U multinomial distribution

[0043] Preferably, the prior distribution of the estimate is Modeled as B is an L×p structure matrix consisting of natural spline functions, represents the lth row of the B matrix, α is a p×1 unknown parameter vector, so the marginal density function U can also be approximated as a discrete probability distribution

[0044] C: Get its estimate through the maximum likelihood method Then the estimation of the prior distribution obtained by the adaptive Bayesian module can be expressed as Specifically:

[0045] Taking the logarithm of the probability distribution of the frequency cumulative vector R, the expression is:

[0046]

[0047] The score function of the parameter vector α can be expressed as Results of Maximum Likelihood Estimation Can make Solve and get the final estimate of the prior distribution

[0048] Preferably, the iterative noise estimation module in step S4 uses the maximum latent variable maximization algorithm to iteratively increase the lower bound of the likelihood function ln p(y; σ) in each iteration so that the likelihood function can converge to a local maximum or extreme point, thereby updating the estimate of the variance of the Gaussian noise. Specifically:

[0049] Initialize the variance of Gaussian noise Where SNR 0 is the signal-to-noise ratio used for initialization. In order to avoid the algorithm falling into a local optimal solution when the noise variance is unknown, the lower bound of ln p(y;σ) is increased in each iteration:

[0050]

[0051] in is the mth element of the product Ax of the channel matrix A and the original signal x. It is necessary to take the derivative of the above formula and equal it to zero to obtain the iterative formula of the specific Gaussian noise variance:

[0052]

[0053] In the above technical scheme, the zero-interference equalization module filters the received observation signal to obtain a pre-estimate of the original signal, and passes the pre-estimate 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 data statistics of the distribution characteristics of the original signal, and combines parameter modeling to obtain the initial estimate of the distribution of the original signal; the iterative noise estimation module finds the solution of the maximum likelihood estimate of the parameters in the statistical model as the estimate 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 estimate of the noise variance are iteratively updated until the algorithm converges to the optimal solution, and finally the estimated original signal is obtained.

[0054] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0055] The zero-interference equalization module used in the present invention serves as the initial driver of the adaptive processing module, which can provide appropriate initialization parameters and improve the stability and convergence speed of the algorithm. In the absence of original signal distribution information, the semi-parametric Bayesian module estimates the true distribution through data statistics and parameter modeling, which is more accurate than the method that does not require a priori distribution. At the same time, the latent variable maximization algorithm can dynamically detect the fluctuating noise level caused by environmental factors, thereby improving the stability of the signal detection system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flow chart of a signal recovery method integrating noise detection and a priori estimation provided in Example 1;

[0057] Figure 2 The distribution of the original signal x estimated by the semi-parametric Bayesian module under the settings of N=512, QAM, M=1024, and SNR=10dB described in Example 2 is

[0058] Figure 3 This is a performance comparison chart of the least squares method LS without prior distribution, the method proposed in the present invention, and the method using only the zero interference equalization module and the adaptive Bayesian module when the parameters N=512, modulation mode QAM, M=1024, and SNR=10dB are set as described in Example 2, and the prior distribution and noise variance are known. DETAILED DESCRIPTION

[0059] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this application.

[0060] The drawings are for illustrative purposes only and shall not be construed as limitations of this patent; certain components may be omitted, enlarged, or reduced in order to better illustrate the embodiments and do not represent the size of the actual product.

[0061] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0062] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0063] Example 1

[0064] like Figure 1 As shown, the present invention provides a signal recovery method integrating noise detection and a priori estimation, see Figure 1 , including the following steps:

[0065] S1: Based on the observed signal and the channel matrix, a zero-interference equalization module is used to obtain a pre-estimation of the original signal;

[0066] S2: Iteratively optimize the estimated value of the signal using an adaptive signal processing module;

[0067] 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, a pre-estimation of the signal distribution is obtained through the semi-parametric Bayesian module, and the estimation of the original signal distribution is updated in each iteration of the adaptive signal processing module;

[0068] S4: updating the estimated value of the noise variance through the iterative noise estimation module, and updating it in each iteration of the adaptive signal processing module.

[0069] Example 2

[0070] Based on Example 1, this example further discloses the following contents:

[0071] Specifically, the mathematical model of the wireless communication system is:

[0072] y = Ax + w;

[0073] This mathematical model indicates that the original signal x is sent from the transmitter, passes through a channel with additive white Gaussian noise w, and then receives the signal y at the receiver, where x∈C N×1 Represents the original signal, A∈C M×N represents the channel matrix, w∈C M×1 represents additive zero-mean Gaussian noise with unknown noise variance, y∈C M×1 Represents the system observation signal, and M and N are both positive integers.

[0074] Preferably, in step S1, a zero interference equalizer is used to obtain a pre-estimation of the original signal, and the received observation signal is filtered to eliminate interference and multipath effects, thereby obtaining a preset of the original signal and transmitting it to the self-response signal processing module as an initialization drive, and the expression is:

[0075]

[0076] in, represents the initial estimate of the original signal obtained using the zero-interference equalizer, A * represents the conjugate transpose of the channel matrix A.

[0077] 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 the information to update the estimate of the current signal, alternately updating the estimate and variance of the original signal, and finally gradually approximating the true original signal; each round of iteration updates the message with the current estimate until convergence or the set number of iterations is reached;

[0078] Through the transition probability p Y|Z (y m |z m ) Modeling m and The relationship between Approximately true z m The marginal posterior distribution p(z m |y), use Approximate x n The true marginal posterior distribution of is, and the specific iteration formula is:

[0079]

[0080] in represents the intermediate variable, Indicates z m The estimated value of Indicates z m The estimated variance, ym represents the mth element of the observed signal y, z m represents the mth row of the channel matrix A The product of 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, Approximate x n The true marginal posterior distribution of is, and the specific iteration formula is:

[0081]

[0082] in is the intermediate variable, and It can be regarded as the original signal x n The observed value and noise variance of the Gaussian noise observation are, that is, Using this key information, we can combine the semi-parametric Bayesian module to estimate the estimated distribution of x and estimated values, specifically:

[0083]

[0084] in and is the estimated value and variance of the original signal x generated by the adaptive signal processing module. t represents the number of iterations. The subscripts m and n represent the mth and nth elements in the corresponding vector, respectively. mn represents the element in the mth row and nth column of the channel matrix A, is an estimate of the original signal distribution p(x), represents a semiparametric Bayesian module;

[0085] and Indicates z m The approximate posterior distribution of The mean and variance of represents the variance of the additive zero-mean Gaussian noise n estimated at the t+1th iteration, Determined by the distribution of noise, in the scenario described in this embodiment, it is a Gaussian distribution get:

[0086]

[0087] Preferably, the semi-parametric Bayesian module in step S3 is a data-driven distribution modeling method, which combines 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 an estimate of the unknown prior distribution p(x). Specifically:

[0088] A: Set the equidistant discrete sampling space Ω of the original signal x, specifically:

[0089] Ω=(x (1) ,x (2) ,…,x (L) );

[0090] 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]. Δx is 0.01, and Ω = (-3, -2.99, ..., 2.99, 3) is obtained.

[0091] In this setting, the probability distribution p(x) of the original signal x can be expressed as a discrete vector To indicate that p i (i=1,2…,L) represents the original signal at x (i) The probability value of sampling at , and satisfy

[0092] Similarly, set the intermediate variables The equidistant discrete sampling space of Specifically:

[0093]

[0094] where r (1) for In the sampling space The minimum sampling value in the sampling space The interval between each sampling point is a fixed value Δr, which can also be set The range is [-3,3], and the interval is divided into (K+1) small intervals with equal interval length.

[0095] B: Further, in the process of adaptive Bayesian method, there is a marginal density function in has a mean of zero and a variance of Gaussian distribution, for discrete sampling space, the edge density function can be expressed in vector form in is a k×L transition probability matrix, and we get the vector U=(u1,u2,...,u K ),u k (k=1,2,…,K) means that in r (k) The marginal probability value at ;

[0096] All intermediate variables According to the sampling space count, the frequency at each sampling point is obtained as R = (R1, R2, ..., R K ), where R k yes Falling in the interval [r (k) ,r (k) +Δr], and is A sufficient statistic for K results, N times of extraction, with a probability vector U multinomial distribution

[0097] Preferably, the prior distribution of the estimate is Modeled as B is an L×p structure matrix consisting of natural spline functions, represents the lth row of the B matrix, α is a p×1 unknown parameter vector, so the marginal density function U can also be approximated as a discrete probability distribution

[0098] C: Get its estimate through the maximum likelihood method Then the estimation of the prior distribution obtained by the adaptive Bayesian module can be expressed as Specifically:

[0099] Taking the logarithm of the probability distribution of the frequency cumulative vector R, the expression is:

[0100]

[0101] The score function of the parameter vector α can be expressed as Results of Maximum Likelihood Estimation Can make Solve and get the final estimate of the prior distribution

[0102] 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 by an iterative method, so that the likelihood function can converge to a local maximum or extreme point, thereby updating the estimate of the variance of the Gaussian noise. Specifically:

[0103] Initialize the variance of Gaussian noise Where SNR 0is the signal-to-noise ratio used for initialization, and the experiment takes SNR 0 =10 is more appropriate. In the case of unknown noise variance, in order to avoid the algorithm falling into the local optimal solution, the lower bound of ln p(y;σ) is increased in each iteration:

[0104]

[0105] in is the mth element of the product Ax of the channel matrix A and the original signal x. It is necessary to take the derivative of the above formula and equal it to zero to obtain the iterative formula of the specific Gaussian noise variance:

[0106]

[0107] In summary, the zero-interference equalization module filters the received observation signal to obtain a pre-estimate of the original signal, and passes the pre-estimate 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 data to statistically analyze the distribution characteristics of the original signal, and combines parameter modeling to obtain an initial estimate of the distribution of the original signal; the iterative noise estimation module finds the solution of the maximum likelihood estimate of the parameters in the statistical model as an estimate 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 estimate of the noise variance are iteratively updated until the algorithm converges to the optimal solution, and finally an estimate of the original signal x is obtained. Estimated distribution of the original signal and an estimate of the variance of the original signal x.

[0108] The zero-interference equalization module used in this embodiment serves as the initial driver of the adaptive processing module, and can provide appropriate initialization parameters to improve the stability and convergence speed of the algorithm. In the absence of original signal distribution information, the semi-parametric Bayesian module estimates the true distribution through data statistics and parameter modeling, which is more accurate than the method that does not require a priori distribution. At the same time, the latent variable maximization algorithm can dynamically detect the fluctuating noise level caused by interference between cells, thereby improving the stability of the signal detection system.

[0109] Embodiment 3:

[0110] This embodiment adopts the following signal and channel configuration 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 mode of the original signal x is 16-QAM, the dimension M=1024 of the observed signal y, and the channel matrix A is a complex matrix of 1024×512. Each element A mn Follow independent and identical complex Gaussian distributions The additive Gaussian noise w is a complex vector of 1024×1 and follows a complex Gaussian distribution. The signal-to-noise ratio (SNR) is 10 dB. The performance evaluation index of the simulation is the mean square error (MSE) of the signal x, which describes the estimated original signal The normalized error between the actual original signal and the mean square error is smaller, indicating better performance. MSE is defined as

[0111] Figure 2 Represents 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 mode of the original signal x is consistent with the actual modulation mode;

[0112] Figure 3 The performances of the least squares method LS that does not require a priori distribution, the method proposed in the present invention, and the method using only the zero interference equalization module and the adaptive Bayesian module when the prior distribution and the noise variance are known are demonstrated respectively; the least squares method can obtain an estimate without iteration, but the performance is very unsatisfactory; the EM-semiparametric-adaptive Bayesian method proposed in the present invention and the MSE that uses only the zero interference equalization module and the adaptive Bayesian module when the prior distribution and the noise variance are known all eventually converge, and the performance of the present invention is very close to the theoretical upper limit of the latter, which is in line with theoretical expectations.

Claims

1. A signal recovery method integrating noise detection and a priori estimation, characterized in that: The following steps are involved: S1: Based on the observed signal and the channel matrix, a zero-interference equalization module is used to obtain a pre-estimation of the original signal; S2: Iteratively optimize the estimated value of the signal using an adaptive signal processing module; 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, a pre-estimation of the signal distribution is obtained through the semi-parametric Bayesian module, and the estimation of the original signal distribution is updated in each iteration of the adaptive signal processing module; S4: updating the estimated value of the noise variance by iterating the noise estimation module, and updating it in each iteration of the adaptive signal processing module.

2. The signal recovery method integrating noise detection and a priori estimation according to claim 1, characterized in that: The mathematical model of the wireless communication system is: y = Ax + n; where x∈C N×1 Represents the original signal, A∈C M×N represents the channel matrix, n∈C M×1 represents additive zero-mean Gaussian noise with unknown noise variance, y∈C M×1 Represents the system observation signal, M and N are both positive integers; The zero-interference equalization module obtains a pre-estimation of the original signal and passes it to 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 distribution of the original signal and the estimated value of the noise variance, and finally outputs the estimated value of the original signal and the estimate of the prior distribution.

3. According to the signal recovery method integrating noise detection and a priori estimation in claim 2, the zero interference equalizer obtains the original signal pre-estimation, characterized in that: By filtering the received observation signal to eliminate interference and multipath effects, the original signal is preset and passed to the self-response signal processing module as the initialization drive. The expression is: in, represents the initial estimate of the original signal obtained using the zero-interference equalizer, and A* represents the conjugate transpose of the channel matrix A.

4. The signal recovery method integrating noise detection and a priori estimation according to claim 3, characterized in that: The adaptive signal processing module calculates the posterior distribution of the signal approximately. In each iteration step, each component of the signal receives information from the adjacent components and uses this information to update the estimate of the current signal, alternately updating the estimate and variance of the original signal, and finally gradually approaching the true original signal; each round of iteration updates the message with the current estimate until convergence or the set number of iterations is reached; Through the transition probability p Y|Z (y m |z m ) Modeling ym and The relationship between Approximately true z m The marginal posterior distribution p(z m |y)Specifically: in represents the intermediate variable, Indicates z m The estimated value of Indicates z m The estimated variance, y m represents the mth element of the observed signal y, z m represents the mth row of the channel matrix A The product of 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 Approximate x n The true marginal posterior distribution of is, and the specific iteration formula is: in is the intermediate variable, and It can be regarded as the original signal x n The observed value and noise variance of the Gaussian noise observation are, that is, Using this key information, we can combine the semi-parametric Bayesian module to estimate the estimated distribution of x and estimated values, specifically: in and is the estimated value and variance of the original signal x generated by the adaptive signal processing module. t represents the number of iterations. The subscripts m and n represent the mth and nth elements in the corresponding vector, respectively. mn represents the element in the mth row and nth column of the channel matrix A, is an estimate of the original signal distribution p(x), represents a semiparametric Bayesian module; and Indicates z m The approximate posterior distribution of The mean and variance of represents the variance of the additive zero-mean Gaussian noise n estimated at the t+1th iteration, Determined by the distribution of the noise.

5. The signal recovery method integrating noise detection and a priori estimation according to claim 4, characterized in that: The Adaptive Bayesian module uses data-driven modeling distributions, combining information extracted from the data with parametric modeling methods 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 can be expressed as a discrete vector To indicate that p i (i=1, 2..., L) represents the original signal at x (i) The probability value of sampling at , and satisfy Similarly, set the intermediate variables The equidistant discrete sampling space of Specifically: where r (1) for In the sampling space The minimum sampling value in the sampling space The interval between each sampling point is a fixed value Δr. The specific setting range should be The range is slightly larger; The Adaptive Bayesian module is a data-driven distribution modeling method that combines information extracted from the data with parameter modeling methods to construct an estimate of the unknown prior distribution p(x) Specifically: B: Further, in the process of adaptive Bayesian method, there is a marginal density function in has a mean of zero and a variance of Gaussian distribution, for discrete sampling space, the edge density function can be expressed in vector form in is a k×L transition probability matrix, and we get the vector U=(u1, u2, ..., u K ),u k (k=1,2,...,K) represents the (k) The marginal probability value at ; All intermediate variables According to the sampling space counting, the frequency R at each sampling point is obtained as R = (R1, R2, ..., R K ), where R k yes Falling in the range The number within and is A sufficient statistic for K results, N times of extraction, with a probability vector U multinomial distribution Through the method of parametric modeling, the prior distribution of the estimation Modeled as B is an L×p structure matrix consisting of natural spline functions, represents the lth row of the B matrix, α is a p×1 unknown parameter vector, so the marginal density function U can also be approximated as a discrete probability distribution C: Get its estimate through the maximum likelihood method Then the estimation of the prior distribution obtained by the adaptive Bayesian module can be expressed as Specifically: Taking the logarithm of the probability distribution of the frequency cumulative vector R, the expression is: The score function of the parameter vector α can be expressed as Results of Maximum Likelihood Estimation Can make Solve and get the final estimate of the prior distribution 6. The signal recovery method integrating noise detection and a priori estimation according to claim 5, characterized in that: The hidden variable maximization algorithm is used to iteratively increase the lower bound of the likelihood function ln p(y; σ) in each iteration so that the likelihood function can converge to the local maximum or extreme point, thereby updating the estimate of the variance of the Gaussian noise. Specifically: Initialize the variance of Gaussian noise Where SNR 0 is the signal-to-noise ratio used for initialization. In order to avoid the algorithm falling into a local optimal solution when the noise variance is unknown, the lower bound of ln p(y;σ) is increased in each iteration: in is the mth element of the product Ax of the channel matrix A and the original signal x. It is necessary to take the derivative of the above formula and equal it to zero to obtain the iterative formula of the specific Gaussian noise variance:

7. A signal recovery method integrating noise detection and a priori estimation, characterized in that: The system comprises: A zero-interference equalization module for obtaining an estimate of the original signal; An adaptive signal processing module, combined with a semi-parametric Bayesian module and an iterative noise estimation module, is used to iteratively estimate the original signal; A semi-parametric Bayesian module is used to analyze the intermediate variable data of each iteration of the adaptive signal processing module to establish an estimate of the prior distribution; The iterative noise estimation module is used to estimate the variance of the noise in each iteration process of the adaptive signal processing module.

Images