Joint channel and data estimation method based on deconvolution

Abstract

The invention discloses a joint channel and data estimation method based on deconvolution. The joint channel and data estimation method comprises the following steps: S1, acquiring channel and data signal initial estimation of a multiple-input-multiple-output system through a signal pre-estimation module; s2, based on channel and data signal initial estimation, obtaining initial estimation of channel and data signal distribution through a priori pre-estimation module; and S3, carrying out iteration precision processing on the initial estimation of the channel and the data signal through a priori adaptive optimization module, dynamically updating the distribution of the channel and the data signal in each iteration process by utilizing a deconvolution method, updating posteriori distribution by utilizing a Bayesian principle according to the updated distribution, and carrying out iteration until a convergence condition or a stop condition is reached. According to the method disclosed by the invention, the problem of missing channel and data distribution in joint channel and data estimation is solved by utilizing deconvolution.

Description

Technical Field

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

[0002] In order to improve data transmission rate and signal quality, modern wireless communication systems use Massive Multiple Input Multiple Output (MIMO) technology to enhance system performance by deploying a large number of antennas. However, this also brings challenges to 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 method will transfer the channel estimation error to the data estimation, affecting the accuracy.

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

[0004] In order to efficiently realize the joint estimation in JCD, the bilinear generalized approximate message passing algorithm (Bi-GAMP) is adopted. The application of the bilinear generalized approximate message passing algorithm in the joint channel and data estimation can be called the bilinear generalized approximate message passing joint estimation method (Bi-GAMP-JCD). The Bi-GAMP algorithm estimates the channel and data simultaneously through Bayesian inference and iterative message passing, gradually weakens the noise, and achieves high-precision signal recovery.

[0005] However, existing methods rely on known prior distributions of channels and data or their functional forms. In the iterative process, this prior information is used to guide the channel matrix H and data symbols 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 be difficult to converge effectively or even unable to continue iterating, because the lack of accurate prior information will lead to error accumulation in the estimation process, seriously affecting the final estimation accuracy. In actual wireless communication systems, the accurate prior distribution of channels and data is often difficult to obtain, which makes these methods challenging 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 work well under low signal-to-noise ratio conditions; MMSE estimation can achieve optimal estimation performance when prior information is known, but its implementation requires 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] In order to solve the above problems, the present invention proposes a joint channel and data estimation method based on deconvolution, which can adaptively learn the channel and data signal prior distribution 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 solution of the present invention is 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 estimation of the signal, an initial estimation of the channel and the signal prior distribution is obtained through the prior pre-estimation module;

[0011] S3: The initial estimates of the channel and data signal 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 updated based on the updated distribution using the Bayesian principle, and the iteration is continued until convergence or stopping conditions are reached.

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

[0013]

[0014] represents the user's transmission signal matrix; is the channel matrix; is a function with zero mean and variance Additive Gaussian white noise; is the normalization factor, the purpose of which 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 Select from K constellation point sets Ω, and each signal is selected from K discrete constellation points with equal probability. In 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:

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

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

[0018] In the model, the H channel matrix has missing 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 is a linear minimum mean square error estimator (LMMSE), which obtains the initial estimation of the channel information and the data signal by minimizing the mean square value of the estimation error. During initialization, the system first estimates the channel using the pilot signal through the signal pre-estimation module to obtain preliminary information about the channel. Then, the initial channel estimation result is combined with the received data signal, and the signal pre-estimation module is used to perform an initial estimation of the data signal to obtain the initial estimation of the transmitted signal.

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

[0021] A) Channel estimation stage: The system first transmits a known pilot signal X p The receiving end uses the pilot signal and the receiving signal Y 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 into the formula to reflect the influence of N transmitting antennas in the system. Since the channel and noise of the system will be amplified as the number of antennas increases, N is multiplied to ensure that the noise adjustment in the channel estimation process matches the number of transmitting antennas, thereby maintaining the numerical stability of the matrix operation and the accuracy of the estimation;

[0025] B) 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, and the specific process is as follows:

[0029] A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector Treat the imaginary and real parts separately and find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define appropriate step sizes in these two intervals according to the equidistant division method A series of discrete points are generated in a fixed step size within a specified interval. The intervals between these points are uniform. Starting from the minimum value, the fixed interval value is gradually increased until the maximum value is reached or extended a little further. 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 piecewise 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]

[0035] 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;

[0036] B) When we process channel information, we extract local information by integrating the function within each interval; for the channel The weighted processing in the kth interval can be expressed as:

[0037]

[0038] Equivalent to a continuous probability density function Integrate over the kth interval to obtain the probability mass within the interval;

[0039] Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as:

[0040]

[0041] because exist The integral result is equal to the integral within this interval.

[0042] 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;

[0043] For data signals, local information in each interval can also be extracted:

[0044]

[0045] Using indicator functions It can be expressed as:

[0046]

[0047] Therefore, the probability density function of the data signal is is converted into a more discrete probability mass function f s ;

[0048] C) Construct a count vector, set Falling The sample count is That is set up Falling The sample count is Right now c represents count; therefore, the count vector can be expressed as:

[0049]

[0050] Where T represents transpose;

[0051] D) Build a multinomial distribution model, count vector Its total count and count vector in K categories The total count in S categories satisfies:

[0052]

[0053] After the prior pre-estimation module, the initial estimates of the channel prior distribution and the data signal prior distribution are expressed as:

[0054]

[0055] Among them, the count vector Obey a parameter (MN, f H ) is a multinomial distribution, where f H is the probability distribution of the channel in each discrete interval; the count vector Subject to a parameter The multi-top distribution of It is the probability distribution of the data signal in each discrete interval.

[0056] Preferably, in step S3, the initial estimates obtained by S1 and S2 are first input into the Bi-GAMP-JCD embedded in the priori adaptive optimization module, and the initial estimate of the channel and data signal distribution of S2 is used in the first iteration; then the channel and data signal distribution are dynamically updated by iteratively refining the priori adaptive optimization module, and iterate until convergence or stopping conditions are reached. The specific process is:

[0057] A) Definition The posterior distributions of are:

[0058] B) Initialization: V H (1) = 1 M×N , t = 0;

[0059] C) Initialize V x (1) V H (1) and 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:

[0060] V p (t) = v H (t)|X p | 2 ;

[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]

[0067] D) Continuously iteratively update the channel and data signal distribution until convergence or stopping conditions;

[0068] Among them, V p , V z , V s , V r , V q , are the 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, is the matrix The transpose of the square of each element, Yes Seek 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 for P(X d |Y) probability distribution to find the mean, It means that the pair is proportional to P(X d |Y)’s probability distribution finds the variance; is the mean of the probability distribution of P(H|Y), It means to find 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.

[0069] Preferably, the a priori adaptive optimization module in step S3 uses a deconvolution method to estimate the a priori distribution of the channel and data signal;

[0070] For channel information, during the Bi-GAMP-JCD iteration process, there is a likelihood function It means that under the given channel h, about the intermediate variable The likelihood of is an intermediate variable, a variable matrix Elements in

[0071] 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:

[0072] 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 trial number of MN (i.e. )Multinomial distribution, expressed as:

[0073]

[0074] B) Construct the transfer matrix P∈R J×R , where the j-th row and r-th column element p jr ,Right now When hour, is equal to its observed value q j probability;

[0075] C) Prior Adaptive Optimization Module Let g(θ) be an exponential family model defined on the space τ, expressed as follows using a discrete formula:

[0076] g(α)=e Qα-1ψ(α) ;

[0077] 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, and also the dimension of the unknown vector α;

[0078] In summary, the discrete form of the convolution formula can be expressed as:

[0079] Therefore, the joint probability mass function of the multinomial distribution is:

[0080] Then there is The multinomial log-likelihood function with respect to α is:

[0081] The constant is is a constant with respect to α;

[0082] Maximum likelihood estimate of α L can be solved numerically α Get, and substitute it back Get an estimate of the channel prior distribution

[0083] D) The real and imaginary parts after deconvolution are recombined to obtain the final channel information in complex form;

[0084] Similarly for data signals, during the Bi-GAMP-JCD iteration process, there is a likelihood function It means that under the given channel h, about the intermediate variable The likelihood is that here is an intermediate variable, a variable matrix Elements in

[0085] Therefore, the convolution expression is: The real and imaginary parts of the complex signal are treated as two independent signals for deconvolution to obtain an estimate of the prior distribution of the data signal.

[0086] Preferably, in step S3, the prior adaptive optimization module is embedded in Bi-GAMP-JCD, and Bi-GAMP-JCD and the prior adaptive optimization module interact with each other, and finally continuously update the prior distribution of the channel and data signal by continuously exchanging information. The likelihood function in Bi-GAMP-JCD updates the prior distribution estimate of the channel and data signal through deconvolution, and then uses the prior distribution estimate of the channel and data signal to perform Bayesian theorem inference to obtain the posterior distribution:

[0087]

[0088] 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.

[0089] In the above technical scheme, 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-GAMP-JCD, and the likelihood function in the Bi-GAMP-JCD updates the prior distribution of the channel and data signals through a deconvolution method; the Bi-GAMP-JCD and the prior adaptive optimization module continuously exchange information through an iterative process, update the prior and posterior distributions in each iteration, and gradually converge to more accurate prior and posterior distributions.

[0090] Deconvolution-based joint channel and data estimation method, in scenarios where both the channel and data signals and their prior distributions are unknown or missing:

[0091] A signal pre-estimation module, used to obtain channel information and initial estimation of data signals of a MIMO system;

[0092] A priori pre-estimation module, used for extracting an initial estimate of a priori distribution of channel information and signal based on the channel information and signal initial estimate;

[0093] 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 using the Bayesian principle according to the updated distribution until the preset iteration termination condition is met.

[0094] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0095] The present invention proposes a joint channel and data estimation method based on deconvolution, which is suitable for scenarios where channel and data signals and their prior distributions are unknown or missing. The method embeds a priori adaptive optimization module into a Bi-GAMP-JCD framework, and uses deconvolution technology to dynamically update the prior distribution according to the likelihood function in Bi-GAMP-JCD, thereby solving the problem that the prior distributions of the channel and data signals need to be known and fixed in the traditional method, so that the system can adaptively adjust the prior distributions of the channel and data signals according to actual data, thereby enhancing flexibility and adaptability. Bi-GAMP-JCD and the priori adaptive optimization module iteratively exchange information to gradually update the prior distributions of the channel and data signals, thereby maintaining good performance in large-scale high-dimensional systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0097] Figure 2 It is a structural schematic diagram of the method of the present invention.

[0098] Figure 3 A schematic diagram of the performance comparison of the known channel prior distribution Bi-GAMP-JCD and the unknown channel prior distribution EB-Bi-GAMP-JCD under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12dB provided in the embodiment.

[0099] Figure 4 The embodiment provides a schematic diagram of the comparison between the iteratively refined channel prior distribution of the present invention and the real channel prior distribution under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12dB.

[0100] Figure 5 A schematic diagram of the performance comparison of the known data signal prior distribution Bi-GAMP-JCD and the data signal prior distribution EB-Bi-GAMP-JCD under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12dB provided in the embodiment.

[0101] Figure 6 The schematic diagram of the recovery of the data signal prior distribution after iterative refinement of the present invention under the conditions of M=200, N=50, L1=50, L2=450, and signal-to-noise ratio=12dB provided in the embodiment. DETAILED DESCRIPTION

[0102] To facilitate understanding of the present invention, the technical solution of the present invention is 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.

[0103] 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.

[0104] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0105] It is hereby declared that the content described in the present invention is different from the patent named "An Iterative Signal Detection Method and System for a Priori Missing Scenario", 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 for a priori missing scenario 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 distribution 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 patent application scenario of an iterative signal detection method and system for a priori missing scenario is only the recovery signal when the prior data signal is unknown.

[0106] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0107] The overall process of this program refers to Figure 1 The overall structure of this scheme refers to Figure 2 .

[0108] Implementation Case 1

[0109] This embodiment provides a joint channel and data estimation method based on deconvolution, such as Figure 2 As shown, the steps include:

[0110] S1: Obtain channel information and initial signal estimation of the MIMO system through the signal pre-estimation module;

[0111] 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 a priori pre-estimation module;

[0112] S3: Iterate and refine the initial estimates of the channel and data signal through the prior adaptive optimization module; use the deconvolution method to dynamically update the channel and data signal distribution during each iteration, and use the Bayesian principle to update the posterior distribution based on the updated distribution, and iterate until convergence or stopping conditions.

[0113] Example 2

[0114] Based on Example 1, this example further discloses the following contents:

[0115] In the traditional Bi-GAMP algorithm, the prior distribution of the channel and data signal is required to be known, while some existing Bi-GAMP variants assume that the functional form of the prior distribution of the channel and data signal 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 iterated directly; now the prior adaptive module is embedded in Bi-GAMP-JCD, so that when the prior functional form is unknown, the prior distribution can be adaptively estimated through deconvolution, and it can also be adaptively adjusted according to different scenarios and channel conditions.

[0116] 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.

[0117] In step S1, the system first uses a pilot signal X p Perform channel estimation.

[0118] Specifically, the transmitting end sends the pilot signal matrix X p , the receiving end receives the corresponding pilot reception 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 get the initial estimate of the channel, the expression is:

[0119]

[0120] in, 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.

[0121] The system uses the channel matrix estimated by the pilot signal Combined with the received data signal matrix Y d , the transmitted data signal is estimated. At this time, the receiving end uses the channel estimation result And the data signal matrix Y d , the signal pre-estimation module is used again to process the received data signal to obtain the initial estimate of the data signal, which is expressed as:

[0122]

[0123] in, Represents the channel matrix Take the conjugate transposed matrix.

[0124] Using channel estimation Estimating the data signal actually compensates for the impact of the channel.

[0125] 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, and the specific process is as follows:

[0126] A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector Treat the imaginary and real parts separately and find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define appropriate step sizes in these two intervals according to the equidistant 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. Starting from the minimum value, the fixed interval value is gradually increased until the maximum value is reached or extended a little further. The expression is:

[0127]

[0128] 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 piecewise 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.

[0129] For the channel discrete point set and The corresponding scaling indicator function is defined as:

[0130]

[0131] 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;

[0132] B) When we process channel information, we extract local information by integrating the function within each interval; for the channel The weighted processing in the kth interval can be expressed as:

[0133]

[0134] Equivalent to a continuous probability density function Integrate over the kth interval to obtain the probability mass within the interval;

[0135] Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as:

[0136]

[0137] because exist The integral result is equal to the integral within this interval.

[0138] 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;

[0139] For data signals, local information in each interval can also be extracted:

[0140]

[0141] Using indicator functions It can be expressed as:

[0142]

[0143] Therefore, the probability density function of the data signal is is converted into a more discrete probability mass function f s ;

[0144] C) Construct a count vector, set 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:

[0145]

[0146] Where T represents transpose;

[0147] D) Build a multinomial distribution model, count vector Its total count and count vector in K categories The total count in S categories satisfies:

[0148]

[0149] After the prior pre-estimation module, the initial estimates of the channel prior distribution and the data signal prior distribution are expressed as:

[0150]

[0151] Among them, the count vector Subject to a parameter (MN,f H ) is a multinomial distribution, where f H is the probability distribution of the channel in each discrete interval; the count vector Subject to a parameter A multinomial distribution, where It is the probability distribution of the data signal in each discrete interval.

[0152] The value obtained from 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 in the first iteration of the Bi-GAMP-JCD algorithm;

[0153] The prior adaptive optimization module is embedded in Bi-GAMP-JCD, and 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;

[0154] For channel information, during the Bi-GAMP-JCD iteration process, there is a likelihood function It means that under the given channel h, about the intermediate variable The likelihood of can be equivalent to the expression:

[0155]

[0156] 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:

[0157] When performing deconvolution, in order to simplify the deconvolution operation, first Rearranging the matrix into a column vector gives The real and imaginary parts of the complex signal are treated as two independent signals. The specific process is as follows:

[0158] A) Given a fixed step-size channel value space τ = {θ1,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:

[0159]

[0160] B) Construct the transfer matrix P∈R J×R , where the j-th row and r-th column element p jr ,Right now When hour, Equal to its measured value q j probability;

[0161] C) Prior Adaptive Optimization Module Let g(θ) be an exponential family model defined on the space τ, expressed as follows using a discrete formula:

[0162]

[0163] 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, and also the dimension of the unknown vector α;

[0164] In summary, the discrete form of the convolution formula can be expressed as: f q (α) = Pg(α);

[0165] Therefore, the joint probability mass function of the multinomial distribution is:

[0166]

[0167] Then there is The multinomial log-likelihood function with respect to α is:

[0168]

[0169] The constant is is a constant with respect to α;

[0170] The following score function calculation for α:

[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 it back 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 a 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: The real and imaginary parts of the complex signal are treated as two independent signals for deconvolution, and the prior distribution of the data signal is estimated.

[0179] Preferably, in step S3, the prior adaptive optimization module is embedded in the Bi-GAMP-JCD algorithm; this module interacts with the Bi-GAMP-JCD, and dynamically adjusts and updates the prior distribution of the channel and data signal by continuously exchanging information, so that it is closer to the actual signal characteristics; in the Bi-GAMP-JCD, the obtained likelihood function is used to update the prior distribution estimation of the channel and data signal through a deconvolution operation; then, the updated prior distribution is used to infer through the Bayesian 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 input obtained by S1 and S2 is 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 adopted in the first iteration; then, through deconvolution, the channel and data signal prior distribution 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 iteration 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] V p (t) = v H (t)|X p | 2 ;

[0187]

[0188] if t>1then

[0189]

[0190] else

[0191]

[0192] end if

[0193]

[0194] Among them, V p , V z , V s , V r , V q , are the 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, is the matrix The transpose of the square of each element, Yes Seek 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 for P(X d |Y) probability distribution to find the mean, It means that the pair is proportional to P(X d |Y)’s probability distribution finds the variance; is the mean of the probability distribution of P(H|Y), It means to find 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.

[0195] 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:

[0196] like Figure 3As shown in the figure, the performance comparison of Bi-GAMP-JCD with known channel prior distribution and EB-Bi-GAMP-JCD with unknown channel prior distribution shows that the EB-Bi-GAMP-JCD algorithm shows good convergence in the iterative process, and its mean square error (MSE) gradually decreases and tends to be stable as the number of iterations increases. This means that even in the case of unknown prior distribution, the EB-Bi-GAMP-JCD algorithm can achieve performance close to that of known priors.

[0197] like Figure 4 As shown in the figure, the effect of comparing the iteratively refined channel prior distribution with 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 iteratively refined 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.

[0198] like Figure 5 As shown in the figure, the performance comparison of Bi-GAMP-JCD with known data signal prior distribution and EB-Bi-GAMP-JCD with known data signal prior distribution shows that the two are very close in performance. This shows that even without relying on known data signal prior distribution, the EB-Bi-GAMP-JCD algorithm can gradually optimize the prior distribution through iteration and achieve performance close to that of the Bi-GAMP-JCD algorithm.

[0199] like Figure 6 As shown in the figure, the effect of recovering the prior distribution of the data signal after iterative refinement is respectively the real part and the 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.

[0200] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0201] The embodiments of the present invention are only used as a clear explanation of the principles of the invention and should not be regarded as limiting the specific implementation methods of the invention. For ordinary technicians in the field, other different forms of changes or modifications can be made on the basis of the above description. It is not necessary and impossible to list all the implementation methods here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in 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 method comprises the following steps: S1: obtaining an initial estimation of a channel and a data signal of a multiple-input multiple-output system through a signal pre-estimation module; S2: Based on the initial estimation of the channel and the data signal, an initial estimation of the prior distribution of the channel and the data signal is obtained through a priori pre-estimation module; S3: The initial estimation of the channel and data signal is iteratively refined through the prior adaptive optimization module. The channel and data signal distribution is dynamically updated in each iteration using the deconvolution method. The posterior distribution is updated based on the updated distribution using the Bayesian principle. The iteration is continued until convergence or stopping conditions are reached.

2. The deconvolution-based joint channel and data estimation method according to claim 1, characterized in that: In the scenario described in step S1 where the prior distribution of the channel and data is unknown or missing, the multi-input multi-output system model is specifically: represents the user's transmission signal matrix; is the channel matrix; is a function with zero mean and variance Additive Gaussian white noise, 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 method affects the prior probability distribution of the signal. In K-order quadrature amplitude modulation, each symbol x nl Select from K constellation point sets Ω, each signal is selected from K discrete constellation points with equal probability; in 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 H channel matrix has missing channel information between the transmit and receive antennas and X d The data signal and its distribution are unknown.

3. The deconvolution-based joint channel and data estimation method according to claim 1, characterized in that: The signal pre-estimation module in step S1 obtains the initial estimation of the channel information and the 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 stage: The system first transmits a known pilot signal X p The receiving end uses the pilot signal and the receiving signal Y 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; N is introduced in the formula to reflect the influence of N transmit antennas in the system; since the channel and noise of the system will be amplified as the number of antennas increases, multiply by N to ensure 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; B) Signal estimation stage: Combined with the initial channel estimation results and the received data signal Y d , the data signal is initially restored 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.

4. The deconvolution-based joint channel and data estimation method according to claim 3, characterized in that: 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 based on the initial estimate using the equidistant division method to calculate the frequency; the specific steps are as follows: A) For channel and data signals, the matrix Rearrange to a column vector Pair Vector Treat the imaginary and real parts separately and find The minimum value in and maximum value turn up The minimum value in and maximum value As their respective intervals, define appropriate step sizes in these two intervals according to the equidistant 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. Starting from the minimum value, the fixed interval value is gradually increased until the maximum value is reached or extended a little further. The expression is: 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 piecewise 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. For the channel discrete point set and The corresponding scaling indicator function is defined as: 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; B) When we process channel information, we extract local information by integrating the function within each interval; for the channel The weighted processing in the kth interval can be expressed as: This is equivalent to converting the continuous probability density function Integrate over the kth interval to obtain the probability mass within the interval; Indicator function Ensuring that the integral is performed only within the specified interval can be expressed as: because exist The integral result is equal to the integral within this interval. 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; For data signals, local information in each interval can also be extracted: Using indicator functions It can be expressed as: Therefore, the probability density function of the data signal is is converted into a more discrete probability mass function f s ; C) Construct a count vector, set 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 in K categories The total count in 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 ) is a multinomial distribution, where f H is the probability distribution of the channel in each discrete interval; the count vector Subject to a parameter A multinomial distribution of It is the probability distribution of the data signal in each discrete interval.

5. The deconvolution-based joint channel and data estimation method according to claim 4, characterized in that: 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 dynamically updated by iterative refinement through the prior adaptive optimization module, and the iteration is performed until convergence or stopping conditions are reached. The specific process is as follows: A) Definition The posterior distributions of are: B) Initialization: V H (1) = 1 M×N , t = 0; C) Initialize V x (1) V H (1) and 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: V p (t)=v H (t)|X p | 2 ; 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: D) Continuously iteratively update the channel and data signal distribution until convergence or stopping conditions; Among them, V p , V z , V s , V r , V q , are the 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, is the matrix The transpose of the square of each element, Yes Seek 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 for P(X d |Y) probability distribution to find the mean, It means that the pair is proportional to P(X d |Y)’s probability distribution finds the variance; is the mean of the probability distribution of P(H|Y), It means to find 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.

6. The deconvolution-based joint channel and data estimation method according to claim 5, characterized in that: 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, during the Bi-GAMP-JCD iteration process, there is a likelihood function It means that under the given channel h, about the intermediate variable The likelihood of is an intermediate variable, a variable matrix Elements in 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: 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 trial number of MN (i.e. )Multinomial distribution, expressed as: B) Construct the transfer matrix P∈R J×R , where the j-th row and r-th column element p jr ,Right now When hour, is 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, 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, and also the dimension of the unknown vector α; In summary, the discrete form of the convolution formula can be expressed as: Therefore, the joint probability mass function of the multinomial distribution is: Then there is The multinomial log-likelihood function with respect to α is: The constant is is a constant with respect to α; Maximum likelihood estimate of α Solve L numerically α Available Substitute back Get 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 It means that under the given channel h, about the intermediate variable The likelihood of is an intermediate variable, a variable matrix Elements in So the convolution expression is: The real and imaginary parts of the complex signal are treated as two independent signals for deconvolution to obtain an estimate of the prior distribution of the data signal.

7. The deconvolution-based joint channel and data estimation method according to claim 6, characterized in that: In step S3, the prior adaptive optimization module is embedded in Bi-GAMP-JCD. Bi-GAMP-JCD 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 signal. The likelihood function in Bi-GAMP-JCD updates the prior distribution estimate of the channel and data signal through deconvolution, and then uses the prior distribution estimate of the channel and data signal to perform Bayesian theorem inference to obtain the posterior distribution: 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.

8. An iterative signal detection system in a priori missing scenario, 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, used to obtain channel information and initial estimation of data signals of a MIMO system; A priori pre-estimation module, used for extracting an initial estimate of a priori distribution of channel information and signal based on the channel information and signal initial estimate; 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 using the Bayesian principle according to the updated distribution until the preset iteration termination condition is met.

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