A Joint Channel and Data Estimation Method Based on Deconvolution

Abstract

The present invention discloses a joint channel and data estimation method based on deconvolution, comprising: S1: obtaining an initial estimate of the channel and data signals of a multi-input multi-output system through a signal pre-estimation module; S2: obtaining an initial estimate of the channel and data signal distribution through a priori pre-estimation module based on the initial estimate of the channel and data signals; S3: iteratively refining the initial estimate of the channel and data signals through a priori adaptive optimization module, dynamically updating the channel and data signal distribution during each iteration using a deconvolution method, and updating the posterior distribution based on the updated distribution using the Bayesian principle, and iterating until convergence or a stopping condition is met. The present invention uses deconvolution to solve the problem of missing channel and data distribution in joint channel and data estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and more particularly, relates to a deconvolution-based joint channel and data estimation method. Background Art

[0002] To improve data rates and signal quality, modern wireless communication systems employ massive multiple-input, multiple-output (MIMO) technology, enhancing system performance by deploying a large number of antennas. However, this also presents challenges in channel estimation and data detection. Traditional methods use pilot signals for step-by-step estimation, first estimating the channel matrix and then recovering the data symbols. However, this approach propagates channel estimation errors into the data estimation, affecting accuracy.

[0003] The Joint Channel and Data Estimation (JCD) method provides a more tightly coupled estimation strategy. In the JCD framework, the base station no longer estimates the channel separately and then recovers the data. Instead, it uses Bayesian inference to directly use the received signal and known pilot information to simultaneously estimate the channel matrix H and the data symbol X. d , which avoids the problem of error transmission in traditional step-by-step estimation and thus improves the accuracy of the overall estimation.

[0004] To efficiently implement joint estimation in JCD, the bilinear generalized approximate message passing (Bi-GAMP) algorithm is employed. Applying Bi-GAMP to joint channel and data estimation is known as the Bi-GAMP-JCD method. The Bi-GAMP algorithm uses Bayesian inference and iterative message passing to simultaneously estimate the channel and data, gradually attenuating noise and achieving high-precision signal recovery.

[0005] However, existing methods rely on the known prior distribution of the channel and data or their functional forms. In the iterative process, this prior information is used to guide the channel matrix H and the data symbol X dThe estimation of the prior distribution helps the algorithm gradually approach the optimal solution. However, when the prior distribution is unknown or inaccurate, the iterative process of Bi-GAMP-JCD may have difficulty converging effectively or even be unable to continue iterating. This is because the lack of accurate prior information will lead to error accumulation during the estimation process, seriously affecting the final estimation accuracy. In actual wireless communication systems, the precise prior distribution of channels and data is often difficult to obtain, which makes these methods challenging to use in practical applications and limits their applicability. In comparison, traditional channel estimation methods, such as least squares (LS) estimation and minimum mean square error (MMSE) estimation, each have their own limitations. Although the LS estimation method is simple and does not require prior information, it does not perform well in low signal-to-noise ratio conditions. MMSE estimation can achieve optimal estimation performance when prior information is known, but its implementation requires an accurate prior probability distribution and has high computational complexity. Although the Expectation Maximization (EM) method is a classic method for solving the problem of latent variable estimation, it requires knowing the form of the prior distribution function of the latent variable. If this form is unknown, the E-step and M-step of the EM algorithm will be seriously affected, making it difficult for the algorithm to converge or converge to a suboptimal solution. Summary of the Invention

[0006] To solve the above problems, the present invention proposes a joint channel and data estimation method based on deconvolution, which can adaptively learn the prior distribution of channel and data signals from data in scenarios where the channel and data signals and their prior distributions are unknown or missing.

[0007] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0008] A joint channel and data estimation method based on deconvolution comprises the following steps:

[0009] S1: Obtain channel information and initial signal estimation of the MIMO system through the signal pre-estimation module;

[0010] S2: Based on the channel information and the initial signal estimate, the initial estimate of the channel and signal prior distribution is obtained through the prior pre-estimation module;

[0011] S3: The initial estimates of the channel and data signals are iteratively refined through the prior adaptive optimization module. The channel and data signal distributions are dynamically updated during each iteration using the deconvolution method. The posterior distribution is then updated based on the updated distribution using the Bayesian principle. The iteration continues until convergence or a stopping condition is reached.

[0012] Preferably, in the scenario where the prior distribution of the channel and the data is unknown or missing in step S1, the multi-input multi-output system model is specifically:

[0013]

[0014] represents the user's transmitted signal matrix; is the channel matrix; is a function with zero mean and variance Additive Gaussian white noise; It is the normalization factor, whose purpose is to normalize the energy of the channel matrix H and the transmit signal matrix X;

[0015] In the MIMO model, the transmit signal matrix X is generated by modulation, and the modulation method affects the prior probability distribution of the signal. In K-order quadrature amplitude modulation, each symbol x nl Each signal is selected from a set of K constellation points Ω with equal probability. During the symbol time, the transmitted signal matrix X contains L symbols, of which the first L1 symbols are pilot symbols used for channel estimation, and the remaining L2 = L-L1 symbols are used for data transmission. The signal is divided into blocks as follows:

[0016] X=[X p ,X d ],in

[0017] Y=[Y p ,Y d ],in

[0018] In the model, the H channel matrix lacks channel information between the transmit and receive antennas and X d The data signal and its distribution are unknown.

[0019] Preferably, in step S1, the signal pre-estimation module adopts a linear minimum mean square error (LMMSE) estimation method for the initial estimation of the channel and the data signal. Although the present invention assumes that the channel matrix H and the data signal X d The prior probability distribution of is unknown or missing, but the transmitted signal matrix X in this method contains a part of the pre-set known pilot sequence X p , which corresponds to the received signal Y at the receiving end p It can be directly observed. Therefore, LMMSE estimation can be done based on X without presetting H or Xd probability distribution function. p 、Y p and noise variance, and an effective initial estimation of the channel is performed by minimizing the mean square error criterion.

[0020] Specifically, the signal pre-estimation module is divided into two main stages:

[0021] A) Channel estimation phase: The system first transmits a known pilot signal X p , the receiving end receives the signal Y through the pilot signal p With the help of the signal pre-estimation module, the channel matrix is initially estimated

[0022]

[0023] in, represents pseudo-inverse, ⊙ represents Hadamard product, represents noise variance, I N represents the N×N identity matrix, Represents the pilot matrix X p Take the conjugate transposed matrix;

[0024] N is introduced in the formula to reflect the influence of N transmit antennas in the system. Since the system channel and noise will be amplified as the number of antennas increases, multiplying by N ensures that the noise adjustment in the channel estimation process matches the number of transmit antennas, thereby maintaining the numerical stability of the matrix operation and the accuracy of the estimation.

[0025] B) Data signal estimation stage: Combined with the initial channel estimation results and the received data signal Y d , preliminarily recovering the data signal through the signal pre-estimation module to obtain an initial estimate of the data signal;

[0026]

[0027] in, Represents the channel matrix Take the conjugate transposed matrix.

[0028] Preferably, in step S2, the a priori pre-estimation module provides an initial estimate for the a priori distribution of the channel and the data signal by using the equidistant division method to calculate the frequency based on the initial estimate of the signal pre-estimation module. The specific process is as follows:

[0029] A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector The imaginary and real parts are processed separately to find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define the appropriate step size in these two intervals according to the equal distance division method In a specified interval, a series of discrete points are generated with a fixed step size. The intervals between these points are uniform. The expression is:

[0030]

[0031] If the discrete point set The length is K, discrete point set The length is S, and the above expression can be written as: In this discrete point set and We define a scaled indicator function for each discrete point. The role of these indicator functions is to perform segmentation processing on specific local intervals, ensuring that the function value is only calculated within these local intervals, and the function value outside the interval is zero.

[0032] For the channel discrete point set and The corresponding scaling indicator function is defined as:

[0033]

[0034] The role of the indicator function: a) perform segmentation processing on each local interval and ensure that the function value outside the interval is zero; b) indicate the scaling factor in the function and Ensures the normalization of processing results in each interval;

[0035] B) When we process channel information, we extract local information by integrating the function within each interval; for channel The weighted processing in the kth interval can be expressed as:

[0036]

[0037] Equivalent to a continuous probability density function Integrate over the kth interval to obtain the probability mass within the interval;

[0038] Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as:

[0039]

[0040] because exist The integral result is equal to the integral within the interval.

[0041] Therefore, the continuous channel probability density function is converted into a discrete probability mass function fk , which simplifies the calculation process and allows us to use discrete methods for subsequent processing and estimation;

[0042] For data signals, local information in each interval can also be extracted:

[0043]

[0044] Using indicator functions It can be expressed as:

[0045]

[0046] Therefore, the probability density function of the data signal is is converted into a more discrete probability mass function f s ;

[0047] C) Construct a counting vector, let Falling The sample count is Right now set up Falling The sample count is Right now c represents count; therefore, the count vector can be expressed as:

[0048]

[0049] Where T represents transpose;

[0050] D) Build a multinomial distribution model, count vector Its total count and count vector in K categories The total count of S categories satisfies:

[0051]

[0052] After the prior pre-estimation module, the initial estimates of the channel prior distribution and the data signal prior distribution are expressed as:

[0053]

[0054] Among them, the count vector Obey a parameter (MN,f H ) multinomial distribution, where f H is the probability distribution of the channel in each discrete interval; the count vector Obey a parameter A multinomial distribution where It is the probability distribution of the data signal in each discrete interval.

[0055] Preferably, in step S3, the initial estimates obtained by S1 and S2 are first input into the Bi-GAMP-JCD embedded in the prior adaptive optimization module, and the initial estimates of the channel and data signal distribution of S2 are used in the first iteration; then the channel and data signal distribution are iteratively refined and dynamically updated through the prior adaptive optimization module, and the iteration is performed until convergence or stopping conditions are reached. The specific process is as follows:

[0056] A) Definition The posterior distributions of are:

[0057] B) Initialization: V H(1)=1 M×N , t=0;

[0058] C) Initialize V x (1) V H (1) and obtained in S1 The initial estimate is substituted into the iterative formula of Bi-GAMP-JCD for denoising, and then deconvolution is performed. The iterative formula is:

[0059] V p (t) = v H (t)|X p | 2 ;

[0060]

[0061]

[0062] V q (t)=[V s (t)[|X p | 2 ,|X d | 2 ] * ] -1 ;

[0063]

[0064] The first iteration prior distribution uses the initial distribution of the channel and data signal obtained in S2 The second iteration begins with the a priori adaptive optimization module to accurately process the channel and data signal distribution. Then execute:

[0065]

[0066] D) Continuously refine and iterate the channel and data signal distribution until convergence or stopping conditions are reached;

[0067] Among them, V p 、 V z 、 V s 、 V r 、 V q 、 are all intermediate variable matrices of the Bi-GAMP-JCD iterative process, t is the number of iterations, represents a matrix whose elements are all 1, represents a matrix with all elements equal to 0; Y is the received signal matrix, represents the noise variance of the channel, t is the number of iterations, Yes The square of the modulus, It is a matrix The transpose of the square of each element, Yes Find the inverse, A matrix whose elements are all zero; Prior_AOM indicates that the prior adaptive optimization module updates the channel and data signal distribution through deconvolution; is P(X d |Y) probability distribution to find the mean, Indicates that the pair is proportional to P(X d Find the variance of the probability distribution of |Y); is the mean of the probability distribution of P(H|Y), Indicates the variance of the probability distribution proportional to P(H|Y); / is the division operation, represents matrix dot division, ⊙ represents Hadamard product, * represents conjugate transpose, and h' and x' represent integral variables.

[0068] Preferably, the prior adaptive optimization module in step S3 uses a deconvolution method to estimate the prior distribution of the channel and data signal;

[0069] For channel information, in the Bi-GAM P-JCD iterative process, there is a likelihood function Indicates that under a given channel h, the intermediate variable Likelihood; here is an intermediate variable, a variable matrix Elements in

[0070] Therefore, the convolution expression is: During deconvolution, the real and imaginary parts of the complex signal are treated as two independent signals. The specific process is:

[0071] A) Given a fixed step-size channel value space τ = {θ1,θ2,...,θ r ,...,θ R};right Rearrange the matrix into a column vector Find the minimum value q min and the maximum value q max In this interval, the equal distance division method is used with a fixed step size of Δq to divide the small intervals and obtain the observation space The count vector is: Count Vector The probability vector on J categories is f q , following a number of trials MN (i.e. )Multinomial distribution, expressed as:

[0072]

[0073] B) Construct the transfer matrix P∈R J×R , where the element p in row j and column r is jr ,Right now When hour, Equal to its observed value q j probability;

[0074] C) Prior Adaptive Optimization Module Let g(θ) be an exponential family model defined on the space τ, and expressed using the discrete formula:

[0075] g(α)=e Qα-1ψ(α) ;

[0076] in, ψ(α) represents the normalization factor, 1 is a vector of all 1s of length K, Q∈R K×ν is the structure matrix, is the i-th row vector of Q, which is represented by the natural spline basis function Generate, ν is the degree of freedom, which is also the dimension of the unknown vector α;

[0077] In summary, the discrete form of the convolution formula can be expressed as:

[0078] Therefore, the joint probability mass function of the multinomial distribution is:

[0079] Then there is The polynomial log-likelihood function with respect to α:

[0080] Where constant is is a constant about α;

[0081] Maximum likelihood estimate of α L can be solved numerically α Get, and substitute Get an estimate of the channel prior distribution

[0082] D) The real and imaginary parts after deconvolution are recombined to obtain the final channel information in complex form;

[0083] Similarly for data signals, during the Bi-GAMP-JCD iteration process, there is a likelihood function Indicates that under a given channel h, the intermediate variable Likely, here is an intermediate variable, a variable matrix Elements in

[0084] Therefore, the convolution expression is: Deconvolve the real and imaginary parts of the complex signal as two independent signals to obtain an estimate of the prior distribution of the data signal.

[0085] Preferably, in step S3, the prior adaptive optimization module is embedded in the Bi-GAMP-JCD. The Bi-GAMP-JCD and the prior adaptive optimization module interact with each other, and by continuously exchanging information, the prior distribution of the channel and data signal is continuously updated. The likelihood function in the Bi-GAMP-JCD is deconvolved to update the prior distribution estimate of the channel and data signal, and then the prior distribution estimate of the channel and data signal is used to perform Bayesian inference to obtain the posterior distribution:

[0086]

[0087] Among them, x' d and h' random variables, and is for all possible x' d or h', these are normalization factors that ensure that the probability density function of the posterior distribution integrates to 1 over its domain.

[0088] In the above technical solution, in a scenario where the channel and data signals and their prior distributions are unknown or missing, the signal pre-estimation module and the prior pre-estimation module provide initial estimates and initial distribution estimates for the channel and data signals; the prior adaptive optimization module is embedded in the Bi-GAM P-JCD, and the likelihood function in the Bi-GAM P-JCD updates the prior distributions of the channel and data signals through a deconvolution method; the Bi-GAM P-JCD and the prior adaptive optimization module continuously exchange information through an iterative process, updating the prior and posterior distributions in each iteration, and gradually converging to more accurate prior and posterior distributions.

[0089] Deconvolution-based joint channel and data estimation method, in scenarios where the channel and data signals and their prior distributions are unknown or missing:

[0090] A signal pre-estimation module is used to obtain channel information and initial estimation of data signals of a MIMO system;

[0091] an a priori pre-estimation module, configured to extract an initial estimate of a priori distribution of the channel information and the signal based on the channel information and the initial signal estimate;

[0092] The Bi-GAMP-JCD embedded in the prior adaptive optimization module is used to iteratively refine the initial estimates of the prior distribution of the channel and data signals, and update the posterior distribution based on the updated distribution using the Bayesian principle until the preset iteration termination condition is met.

[0093] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0094] The present invention proposes a deconvolution-based joint channel and data estimation method, which is suitable for scenarios where the channel and data signals and their prior distributions are unknown or missing. The method embeds a prior adaptive optimization module into the Bi-GAM P-JCD framework and uses deconvolution technology to dynamically update the prior distribution according to the likelihood function in the Bi-GAM P-JCD. This solves the problem of traditional methods requiring the prior distributions of the channel and data signals to be known and fixed, enabling the system to adaptively adjust the prior distributions of the channel and data signals according to actual data, thereby enhancing flexibility and adaptability. The Bi-GAM P-JCD and the prior adaptive optimization module iteratively exchange information to gradually update the prior distributions of the channel and data signals, and can maintain good performance in large-scale high-dimensional systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 Schematic diagram of the method of the present invention.

[0096] Figure 2 Schematic diagram of the structure of the method of the present invention.

[0097] Figure 3 This is a schematic diagram of the performance comparison between the known channel prior distribution Bi-GAM P-JCD and the unknown channel prior distribution EB-Bi-GAM P-JCD under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12d B provided in the embodiment.

[0098] Figure 4 This is a schematic diagram of the comparison between the iteratively refined channel prior distribution and the true channel prior distribution under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12d B provided in the embodiment.

[0099] Figure 5 Schematic diagram of performance comparison between Bi-GAM P-JCD and EB-Bi-GAM P-JCD prior distributions of known data signals under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio (SNR)=12d B provided in the embodiment.

[0100] Figure 6 This is a schematic diagram of recovering the data signal prior distribution after iterative refinement according to the present invention under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12d B provided in an embodiment. DETAILED DESCRIPTION

[0101] To facilitate understanding of the present invention, the technical solution of the present invention will be described in more detail below with reference to the accompanying drawings. The present invention is not limited to the embodiments and can be implemented in various forms.

[0102] The drawings are for illustrative purposes only and are not to be construed as limitations of this patent; certain components may be omitted, enlarged, or reduced in size to better illustrate the embodiments and do not represent the dimensions of the actual product.

[0103] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0104] It is hereby declared that the content of the present invention is different from the patent entitled "A method and system for iterative signal detection in a scenario with missing priors", and is improved on the basis of the patent. The main differences are: a) The multi-input multi-output model of the present invention is more complex, which is a MIMO signal transmission of multiple time slices or multiple symbols, in which the transmit and receive signals are in matrix form, and it is a bilinear multi-input multi-output model, while the patent for an iterative signal detection method and system in a scenario with missing priors uses a linear model, in which the transmit and receive signals are in vector form. b) The application scenarios are different. The present invention is aimed at complex scenarios where the prior distributions of channel information and data signals are unknown, and the receiving end needs to perform joint channel and data estimation at the same time, while the application scenario of the patent for an iterative signal detection method and system in a scenario with missing priors is only the recovery signal when the prior data signal is unknown.

[0105] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0106] The overall process of this program refers to Figure 1 The overall structure of this program refers to Figure 2 .

[0107] Implementation Case 1

[0108] This embodiment provides a joint channel and data estimation method based on deconvolution, such as Figure 2 As shown, the steps include:

[0109] S1: Obtain channel information and initial signal estimation of the MIMO system through the signal pre-estimation module;

[0110] S2: Based on the initial estimation of the channel and data signal, an initial estimation of the channel and data signal distribution is obtained through the prior pre-estimation module;

[0111] S3: Iterate and refine the initial estimates of the channel and data signals through the prior adaptive optimization module; use the deconvolution method to dynamically update the channel and data signal distributions during each iteration, and use the Bayesian principle to update the posterior distribution based on the updated distribution, iterating until convergence or stopping conditions are reached.

[0112] Example 2

[0113] Based on Example 1, this example further discloses the following contents:

[0114] The traditional Bi-GAMP algorithm requires that the prior distributions of the channel and data signals be known. Some existing Bi-GAMP variants assume that the functional form of the prior distributions of the channel and data signals is known, and only the parameters need to be solved. However, when the functional form of the prior distribution is unknown, the Bi-GAMP algorithm cannot be directly iterated. Now, the prior adaptive module is embedded in Bi-GAMP-JCD, so that even when the prior functional form is unknown, the prior distribution can be adaptively estimated through deconvolution, and adaptive adjustment can be made according to different scenarios and channel conditions.

[0115] Before extracting the initial estimates of the channel and data signal, it is necessary to model the MIMO system: Get the pilot signal matrix Pilot received signal matrix Data receiving signal matrix Channel noise is a function with zero mean and variance Additive white Gaussian noise.

[0116] In step S1, the system first uses the pilot signal X p Perform channel pre-estimation.

[0117] Specifically, the transmitting end sends the pilot signal matrix X p The receiving end receives the corresponding pilot signal matrix Y p During the transmission process, the signal passes through the channel H and is affected by the noise W. The receiving end uses the known pilot signal X p and the received pilot signal Y p , use the signal pre-estimation module to estimate the channel and obtain the initial estimate of the channel, which is expressed as:

[0118]

[0119] Among them, Denotes the channel matrix X p Take the conjugate transposed matrix, represents the noise variance of the channel, I N Represents the N×N identity matrix.

[0120] The system uses the channel matrix estimated by the pilot signal Combined with the received data signal matrix Y d , estimate the transmitted data signal. At this time, the receiving end uses the channel estimation result And the data signal matrix Y d , again use the signal pre-estimation module to process the received data signal and obtain the initial estimate of the data signal, which is expressed as:

[0121]

[0122] in, Represents the channel matrix Take the conjugate transposed matrix.

[0123] Using channel estimation Estimating the data signal is actually compensating for the influence of the channel.

[0124] Preferably, in step S2, the a priori pre-estimation module provides an initial estimate for the a priori distribution of the channel and the data signal by using the equidistant division method to calculate the frequency based on the initial estimate of the signal pre-estimation module. The specific process is as follows:

[0125] A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector The imaginary and real parts are processed separately to find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define the appropriate step size in these two intervals according to the equal distance division method On this basis, a series of discrete point sets are generated in a specified interval with a fixed step size. The intervals between these points are uniform, and the expression is:

[0126]

[0127] If the discrete point set The length is K, discrete point set The length is S, and the above expression can be written as: In this discrete point set and We define a scaled indicator function for each discrete point. The role of these indicator functions is to perform segmentation processing on specific local intervals, ensuring that the function value is only calculated within these local intervals, and the function value outside the interval is zero.

[0128] For the channel discrete point set and The corresponding scaling indicator function is defined as:

[0129]

[0130] The role of the indicator function: a) perform segmentation processing on each local interval and ensure that the function value outside the interval is zero; b) indicate the scaling factor in the function and Ensures the normalization of processing results in each interval;

[0131] B) When we process channel information, we extract local information by integrating the function within each interval; for channel The weighted processing in the kth interval can be expressed as:

[0132]

[0133] Equivalent to a continuous probability density function Integrate over the kth interval to obtain the probability mass within the interval;

[0134] Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as:

[0135]

[0136] because exist The integral result is equal to the integral within the interval.

[0137] Therefore, the continuous channel probability density function is converted into a discrete probability mass function f k , which simplifies the calculation process and allows us to use discrete methods for subsequent processing and estimation;

[0138] For data signals, local information in each interval can also be extracted:

[0139]

[0140] Using indicator functions It can be expressed as:

[0141]

[0142] Therefore, the probability density function of the data signal is is converted into a more discrete probability mass function f s ;

[0143] C) Construct a counting vector, let Falling The sample count is Right now set up Falling The sample count is Right now c represents count; therefore, the count vector can be expressed as:

[0144]

[0145] Where T represents transpose;

[0146] D) Build a multinomial distribution model, count vector Its total count and count vector in K categories The total count of S categories satisfies:

[0147]

[0148] After the prior pre-estimation module, the initial estimates of the channel prior distribution and the data signal prior distribution are expressed as:

[0149]

[0150] Among them, the count vector Obey a parameter (MN,f H ) multinomial distribution, where f H is the probability distribution of the channel in each discrete interval; the count vector Obey a parameter A multinomial distribution where It is the probability distribution of the data signal in each discrete interval.

[0151] Obtained by S1 in step 3 and As the channel information and data signal initialization input of the Bi-GAMP-JCD algorithm, the f obtained by S2 H and As the initial prior distribution input of the channel and data signal for the first iteration of the Bi-GAMP-JCD algorithm;

[0152] The prior adaptive optimization module is embedded in Bi-GAMP-JCD. The prior adaptive optimization module deconvolves the likelihood functions of the channel and data signals of Bi-GAMP-JCD respectively to update the prior distribution of the channel and data signals;

[0153] For channel information, during the Bi-GAMP-JCD iteration process, there is a likelihood function Indicates that under a given channel h, the intermediate variable The likelihood of can be equivalent to the expression:

[0154]

[0155] Where ω is the mean of 0 and the variance is Gaussian random variables, H is a random variable that obeys the true distribution g(h); this process can be described as a convolution expression:

[0156] When performing deconvolution, in order to simplify the deconvolution operation, first Rearranging the matrix into column vectors gives When the real and imaginary parts of the complex signal are treated as two independent signals, the specific process is as follows:

[0157] A) Given a fixed step-size channel value space τ={τ1,θ2,...,θ r ,...,θ R};right Find the minimum and maximum values, use the equal distance division method in this interval, fix the step size to Δq, divide the small interval, and obtain the observation space set up Falling on q j and q j+1 The sample count between (Right now ), so the count vector is: Count Vector The probability vector on J categories is f q , which follows a number of trials MN (i.e. )Multinomial distribution, expressed as:

[0158]

[0159] B) Construct the transfer matrix P∈R J×R , where the element p in row j and column r is jr ,Right now When hour, Equal to its measured value q j probability;

[0160] C) Prior Adaptive Optimization Module Let g(θ) be an exponential family model defined on the space τ, and expressed using the discrete formula:

[0161] g(α)=e Qα - 1ψ(α) ;

[0162] in, ψ(α) represents the normalization factor ψ(α) represents the normalization factor, 1 is a vector of all 1s of length K, Q∈R K×ν is the structure matrix, is the i-th row vector of Q, which is represented by the natural spline basis function Generate, ν is the degree of freedom, which is also the dimension of the unknown vector α;

[0163] In summary, the discrete form of the convolution formula can be expressed as: f q (α) = Pg(α);

[0164] Therefore, the joint probability mass function of the multinomial distribution is:

[0165]

[0166] Then there is The polynomial log-likelihood function with respect to α:

[0167]

[0168] Where constant is is a constant about α;

[0169] The following score function calculation for α:

[0170]

[0171]

[0172] where D(g(α))=diag(g(α))-g(α)g(α) T , so we have:

[0173]

[0174] Maximum likelihood estimate of α L can be solved numerically α Get, and substitute Get an estimate of the channel prior distribution

[0175] D) Then, the Bayesian posterior distribution is calculated for the imaginary and real parts respectively, and finally the real and imaginary parts after deconvolution are recombined to obtain the final channel information in complex form;

[0176] Similarly for data signals, during the Bi-GAMP-JCD iteration process, there is a likelihood function Indicates that given data signal X d In the case of intermediate variables The likelihood of can be equivalent to the expression:

[0177]

[0178] The convolution expression is: Deconvolve the real and imaginary parts of the complex signal as two independent signals, and estimate the prior distribution of the data signal

[0179] Preferably, in step S3, a priori adaptive optimization module is embedded in the Bi-GAMP-JCD algorithm; this module interacts with the Bi-GAMP-JCD algorithm, and through continuous information exchange, dynamically adjusts and updates the prior distribution of the channel and data signal to make it closer to the actual signal characteristics; in the Bi-GAMP-JCD, the obtained likelihood function is used to update the prior distribution estimate of the channel and data signal through a deconvolution operation; then, the updated prior distribution is used to perform inference through Bayes' theorem to obtain the posterior distribution;

[0180]

[0181] Among them, x' d and h' random variables, and is for all possible x' d or h', these are normalization factors that ensure that the probability density function of the posterior distribution integrates to 1 over its domain.

[0182] Preferably, the initial estimation inputs obtained by S1 and S2 are embedded in the Bi-GAMP of the prior adaptive optimization module, and the initial estimation of the channel and data signal distribution of S2 is used in the first iteration; then, through deconvolution, the channel and data signal prior distributions are dynamically updated in each iteration, and the posterior distribution is updated using the Bayesian principle until the preset termination condition is met; the improved algorithm of the present invention is named EB-Bi-GAMP-JCD, and the iterative formula is as follows:

[0183] A) Definition:

[0184] B) Initialization: V H (1)=1 M×N , t=0;

[0185] C) Iteration (t=1:, T max )

[0186]

[0187] Among them, V p 、 V z 、 V s 、 V r 、 V q 、 are all intermediate variable matrices of the Bi-GAMP-JCD iterative process, represents a matrix whose elements are all 1, represents a matrix with all elements equal to 0; Y is the received signal matrix, represents the noise variance of the channel, t is the number of iterations, T max is the maximum number of iterations, Yes The square of the modulus, It is a matrix The transpose of the square of each element, Yes Find the inverse, A matrix whose elements are all zero; Prior_AOM indicates that the prior adaptive optimization module updates the channel and data signal distribution through deconvolution; is P(X d |Y) probability distribution to find the mean, Indicates that the pair is proportional to P(X d Find the variance of the probability distribution of |Y); is the mean of the probability distribution of P(H|Y), Indicates the variance of the probability distribution proportional to P(H|Y); / is the division operation, represents matrix dot division, ⊙ represents Hadamard product, * represents conjugate transpose, and h' and x' represent integral variables.

[0188] In a specific embodiment, the performance of the present invention for joint channel and data estimation under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12dB is as follows:

[0189] like Figure 3 Figure 2 shows a performance comparison of Bi-GAMP-JCD with a known channel prior distribution and EB-Bi-GAMP-JCD with an unknown channel prior distribution. The figure shows that the EB-Bi-GAMP-JCD algorithm exhibits good convergence during the iteration process, with its mean square error (MSE) decreasing and stabilizing as the number of iterations increases. This means that even with an unknown prior distribution, the EB-Bi-GAMP-JCD algorithm can achieve performance close to that of a known prior.

[0190] like Figure 4 As shown in the figure, the effect of comparing the iteratively refined channel prior distribution and the true channel prior distribution are respectively the real part and the imaginary part of the iteratively refined channel prior distribution. It can be seen from the figure that the channel prior distribution after iterative refinement by the EB-Bi-GAMP-JCD algorithm has a good fitting effect with the true channel prior distribution in both the real part and the imaginary part.

[0191] like Figure 5As shown in the figure, the performance comparison of Bi-GAMP-JCD with a known data signal prior distribution and EB-Bi-GAMP-JCD with a known data signal prior distribution shows that the two have very similar performance. This shows that even without relying on a known data signal prior distribution, the EB-Bi-GAMP-JCD algorithm can achieve performance close to that of the Bi-GAMP-JCD algorithm by iteratively optimizing the prior distribution.

[0192] like Figure 6 As shown in the figure, the effect of recovering the data signal prior distribution after iterative refinement is the real part and imaginary part of the final signal probability distribution. The probability distribution recovered by the algorithm clearly reflects the structural characteristics of the orthogonal amplitude modulation signal and can clearly determine the specific orthogonal amplitude modulation format.

[0193] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0194] The embodiments of the present invention are intended only to illustrate the principles of the invention and should not be construed as limiting the specific embodiments of the invention. A person skilled in the art would be able to make other variations or modifications based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the claims of the present invention.

Claims

1. A joint channel and data estimation method based on deconvolution, characterized in that The following steps are involved: S1: In a scenario where the prior distributions of the channel and data signals are unknown or missing, the signal pre-estimation module is used to obtain the initial estimates of the channel and data signals of the MIMO system; S2: Based on the initial estimation of the channel and data signal, obtain the initial estimation of the prior distribution of the channel and data signal through the prior pre-estimation module; S3: Iterate and refine the initial estimates of the channel and data signals through the prior adaptive optimization module. Use the deconvolution method to dynamically update the channel and data signal distributions during each iteration. Use the Bayesian principle to update the posterior distribution based on the updated distributions. Iterate until convergence or a stopping condition is reached. After the iteration is terminated, the channel matrix and data signal matrix obtained are the final channel and data signal estimation results. In the scenario where the prior distribution of channels and data is unknown or missing, the MIMO system model is specifically: represents the user's transmitted signal matrix; is the channel matrix; is a function with zero mean and variance Additive white Gaussian noise, M is the number of receiving antennas, N is the number of transmitting antennas, It is a normalization factor, the purpose of which is to normalize the energy of the channel matrix H and the transmit signal matrix X; In the MIMO model, the transmit signal matrix X is generated by modulation, and the modulation mode affects the prior probability distribution of the signal. In the K-order quadrature amplitude modulation, each symbol x nl Each signal is selected from a set of K constellation points Ω with equal probability. During the symbol time, the transmitted signal matrix X contains L symbols, of which the first L1 symbols are pilot symbols for channel estimation, and the remaining L2 = L-L1 symbols are used for data transmission. The signal is divided into blocks as follows: X=[X p ,X d ],in Y = [Y p , Y d , where In the model, the channel matrix H and the data signal X d The specific value at the receiving end is unknown, and its probability distribution is also unknown.

2. The deconvolution-based joint channel and data estimation method according to claim 1, wherein The signal pre-estimation module in step S1 obtains an initial estimate of the channel information and data signal by minimizing the mean square value of the estimation error; the signal pre-estimation module is divided into two main stages: A) Channel estimation phase: The system first transmits a known pilot signal X p , the receiving end receives the signal Y through the pilot signal p With the help of the signal pre-estimation module, the channel matrix is initially estimated for: in, represents pseudo-inverse, ⊙ represents Hadamard product, represents the noise variance, I N represents the N×N identity matrix, Represents the pilot matrix X p Take the conjugate transposed matrix; B) Data signal estimation stage: Combined with the initial channel estimation results and the received data signal Y d , the data signal is preliminarily recovered through the signal pre-estimation module, and the initial estimate of the data signal is obtained as: in, represents pseudo-inverse, ⊙ represents Hadamard product, represents the noise variance, I N represents the N×N identity matrix, Represents the channel matrix Take the conjugate transposed matrix.

3. The deconvolution-based joint channel and data estimation method according to claim 2, wherein: In step S2, the a priori pre-estimation module generates a discrete point set within the channel and data signal value interval based on the initial estimate using an equidistant partitioning method with a fixed step size, and counts the sample counts within each interval to provide an initial estimate of the a priori distribution of the channel and data signal. The specific steps are as follows: A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector The imaginary and real parts are processed separately to find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define the appropriate step size in these two intervals according to the equal distance division method On this basis, a series of discrete point sets are generated in a specified interval with a fixed step size. The intervals between these points are uniform, and the expression is: If the discrete point set The length is K, the discrete point set X d The length is S, and the above expression can be written as: In this discrete point set and X d On the channel, a scaled indicator function is defined for each discrete point; for the channel discrete point set and the data discrete point set X d , and its corresponding scaling indicator function is defined as: where k = 1, 2, ..., K; Where s=1,2,...,S; is a discrete point set The scaling indicator function of the kth interval of is a discrete point set X d The scaling indicator function of the sth interval; B) When processing channel information, local information is extracted by integrating the function within each interval; for the channel probability density function The weighted processing in the kth interval can be expressed as: The continuous probability density function is integrated within each partitioned interval to construct the corresponding discrete probability mass function. Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as: integral Time k =0; The interval outside is equivalent to the interval Integrate within, that is For data signals, local information in each interval can also be extracted: Using indicator functions It can be expressed as: C) Construct a counting vector, let Falling The sample count is Right now set up Falling The sample count is Right now c represents count; therefore, the count vector can be expressed as: Where T represents transpose; D) Build a multinomial distribution model, count vector Its total count and count vector X in K categories d c The total count of S categories satisfies: After the prior pre-estimation module, the initial estimates of the channel prior distribution and the data signal prior distribution are expressed as: Among them, the count vector Obey a parameter (MN,f H ) multinomial distribution, where f H Is the probability distribution of the channel in each discrete interval; the count vector X d c Obey a parameter A multinomial distribution, where It is the probability distribution of the data signal in each discrete interval.

4. The deconvolution-based joint channel and data estimation method according to claim 3, wherein: In step S3, the initial estimates obtained in steps S1 and S2 are first input into a bilinear generalized approximate message passing joint channel and data estimation algorithm embedded in a priori adaptive optimization module; The first iteration uses the initial estimation of the channel and data signal distribution in step S2, and then iterates and refines the channel and data signal distribution dynamically through the prior adaptive optimization module until convergence or stopping conditions are reached. The specific process is as follows: A) Definition The posterior distributions of are: B) Initialization: V x (1)=1 N×L2 、V H (1)=1 M×N , t=0; C) Initialize V x (1) V H (1) and obtained in S1 The initial estimate is substituted into the bilinear generalized approximate message passing joint channel and data estimation algorithm, and the iteration formula is: V p (t)=v H (t)|X p | 2 ; V q (t)=[V s (t)[|X p | 2 ,|X d | 2 ] * ] -1 ; Then obtain the prior distribution of the channel and data signal, where the first iteration prior distribution uses the initial distribution of the channel and data signal obtained in step S2 In subsequent iterations, deconvolution is performed and the channel and data signal distribution are precisely processed using the prior adaptive optimization module, i.e. Then find the posterior distribution P(X d |Y), P(H|Y0, and finally update the channel matrix and data signals Value: D) Continuously refine and iterate the channel and data signal distribution until convergence or stopping conditions are reached; Among them, V p 、 V z 、 V s 、 V r 、 V q 、 are the intermediate variable matrices of the iterative process of the bilinear generalized approximate message passing joint channel and data estimation algorithm, t is the number of iterations, represents a matrix whose elements are all 1, represents a matrix with all elements equal to 0; Y is the received signal matrix, represents the noise variance of the channel, t is the number of iterations, Yes The square of the modulus, It is a matrix The transpose of the square of each element, Yes Find the inverse, A matrix whose elements are all zero; Prior_AOM indicates that the prior adaptive optimization module updates the channel and data signal distribution through deconvolution; is P(X d |Y) probability distribution is the mean, which is the data signal Numerical value, Indicates that the pair is proportional to P(X d Find the variance of the probability distribution of |Y); It is to find the mean of the probability distribution of P(H|Y), which is the channel matrix Numerical value, Indicates the variance of the probability distribution proportional to P(H|Y); / is the division operation, represents matrix dot division, ⊙ represents Hadamard product, * represents conjugate transpose, h ' , x' represents the integral variable.

5. The deconvolution-based joint channel and data estimation method according to claim 4, wherein: The prior adaptive optimization module in step S3 uses a deconvolution method to estimate the prior distribution of the channel and data signal; For channel information, in the iterative process of the bilinear generalized approximate message passing joint channel and data estimation algorithm, there is a likelihood function Indicates that under a given channel h, the intermediate variable Likelihood; here is an intermediate variable, a variable matrix Elements in The convolution expression is: During deconvolution, the real and imaginary parts of the complex signal are treated as two independent signals. The specific process is: A) Given a fixed step-size channel value space τ = {θ1,θ2,...,θ r ,...,θ R };right Rearrange the matrix into a column vector Find the minimum value q min and the maximum value q max In this interval, the equal distance division method is used with a fixed step size of Δq to divide the small intervals and obtain the observation space q={q1,q2,...,q j ,...,q J }, the count vector is: Count vector q c The probability vector on J categories is f q , following a number of trials MN (i.e. )Multinomial distribution, expressed as: q c ~Mult J (MN,f q 0; B) Construct the transfer matrix P∈R J×R , where the element p in row j and column r is jr ,Right now When hour, Equal to its observed value q j probability; C) Prior Adaptive Optimization Module Let g(θ) be an exponential family model defined on the space τ, and use the discrete formula to express it as: g(a)=e Qα-1ψ(α) ; in, ψ(α) represents the normalization factor, which is a vector of all 1s of length K, Q∈R K×ν is the structure matrix, is the i-th row vector of Q, which is represented by the natural spline basis function ns(q c ,ν) is generated, ν is the degree of freedom and also the dimension of the unknown vector; In summary, the discrete form of the convolution formula can be expressed as: The joint probability mass function of the multinomial distribution is: Then there is The polynomial log-likelihood function with respect to α: Where constant is is a constant about α; Maximum likelihood estimate of α Solve L by numerical method α You can ask Substitute back Get the channel prior distribution estimate D) The real and imaginary parts after deconvolution are recombined to obtain the final channel information in complex form; Similarly for data signals, during the Bi-GAMP-JCD iteration process, there is a likelihood function Indicates that under a given channel h, the intermediate variable Likelihood; here is an intermediate variable, a variable matrix Elements in The convolution expression is: Deconvolve the real and imaginary parts of the complex signal as two independent signals to obtain an estimate of the prior distribution of the data signal.

6. The deconvolution-based joint channel and data estimation method according to claim 5, characterized in that In step S3, the prior adaptive optimization module is embedded in the bilinear generalized approximate message passing joint channel and data estimation algorithm. The bilinear generalized approximate message passing joint channel and data estimation algorithm and the prior adaptive optimization module interact with each other and continuously exchange information to continuously update the prior distribution of the channel and data signals. The likelihood function in the bilinear generalized approximate message passing joint channel and data estimation algorithm is deconvolved to update the prior distribution estimate of the channel and data signals. Then, the prior distribution estimate of the channel and data signals is used to perform Bayesian theorem inference to obtain the posterior distribution: Among them, x ' d and h ' As random variables, we perform integration operations separately, where ∫P Xd (Y|x ' d )P(x ' d )dx ' d For all possible values of x ' d Integrate, ∫P Xd (Y|h ' )P H (h ' )dh ' For all possible values of h ' Perform integration.

7. A joint channel and data estimation system based on deconvolution, the system being used to implement the steps of the method according to any one of claims 1 to 6, characterized in that: Use cases where the channel and data signal and their prior distributions are unknown or missing include: A signal pre-estimation module is used to obtain the channel information and initial estimation of the data signal of the MIMO system; A priori pre-estimation module, configured to extract an initial estimate of a priori distribution of the channel information and the signal based on the channel information and the initial signal estimate; The bilinear generalized approximate message passing joint channel and data estimation algorithm embedded in the prior adaptive optimization module is used to iteratively refine the initial estimate of the prior distribution of the channel and data signals, and update the posterior distribution based on the updated distribution using the Bayesian principle until the preset iteration termination condition is met. After the iteration terminates, the obtained channel matrix and data signal matrix are the final channel and data signal estimation results.

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