Markov chain Monte Carlo-based sparse Bayesian parameter estimation method

Abstract

The invention discloses a sparse Bayesian parameter estimation method based on a Markov chain Monte Carlo (MCMC). The sparse Bayesian parameter estimation method is suitable for super-resolution target number detection and high-precision target parameter estimation in a communication perception integration (ISAC) scene. The method comprises the following steps: a base station transmits an orthogonal frequency division multiplexing (OFDM) signal and receives a target reflection echo; performing frequency domain transformation on the echo signal and constructing a high-dimensional observation vector; target parameters are modeled as random variables including path complex gain, time delay, Doppler frequency shift and angle, and a learnable parameterized sensing matrix is constructed; the sparse Bayesian framework is combined with MCMC sampling, the parameters are iteratively updated through random small-batch gradient optimization and the Metropolis-Hastings criterion, and finally the estimation result of the target parameters is output. According to the method, the precision limitation of a traditional gridding method is broken through, super-resolution parameter estimation is achieved, meanwhile, the calculation complexity and the storage overhead are remarkably reduced, and the method is suitable for the high-precision sensing requirement in a 6G communication system.

Description

Technical Field

[0001] The present invention relates to a sparse Bayesian parameter estimation method based on Markov chain Monte Carlo, and belongs to the field of integrated communication and sensing in wireless communication technology. Background Art

[0002] With the highly convergent development of communication systems and radar systems in terms of hardware facilities, application frequency bands, underlying technologies, etc., integrated sensing and communications (ISAC) has become one of the key technologies for the development of the sixth-generation mobile communication system (6G). In the communication-centric ISAC architecture, the most widely concerned is to reuse orthogonal frequency division multiplexing (OFDM) communication signals in a multiple input multiple output (MIMO) system for target sensing, providing high-resolution target detection and high accuracy in three-dimensional parameter estimation of range-velocity-angle while ensuring communication performance. However, traditional sensing methods, such as the fast Fourier transform (FFT), are often designed for radar systems and face significant challenges in the MIMO-OFDM scenario: firstly, it is difficult to directly adapt to the requirements of joint target detection and multi-dimensional parameter estimation of communication signals; secondly, the sensing accuracy is limited by the time-frequency domain sampling rate and cannot break through the Rayleigh limit to achieve super-resolution detection. Therefore, in the MIMO-OFDM system, how to achieve high-performance target sensing tasks under low-complexity constraints has become the core issue in the design of ISAC receivers.

[0003] Compressed Sensing (CS) technology can theoretically achieve target detection and three-dimensional parameter estimation simultaneously by exploiting the sparsity of target parameters and combining a sensing matrix adapted to the parameter space. However, its actual resolution and estimation accuracy are closely related to the scale of the sensing matrix. In a high-dimensional parameter space, a large-scale sensing matrix needs to be constructed, resulting in an exponential increase in computational complexity and storage overhead, severely restricting real-time requirements. Sparse Bayesian Learning (SBL), as a Bayesian inference method under the CS framework, assigns the target parameters as random variables with a sparse prior, providing a more flexible algorithm design idea. However, existing SBL-based algorithms such as variational inference and expectation maximization algorithms not only have their estimation accuracy and resolution limited by the grid division accuracy of the sensing matrix, but also involve complex operations such as matrix inversion and integration in the algorithms themselves, with high computational costs. Markov Chain Monte Carlo (MCMC) technology also starts from Bayes' theorem and approximates the target distribution by designing an appropriate proposal distribution and using random sampling. Under the condition of sufficient computing resources, it can provide a low-complexity inference method. However, MCMC has the problem of low search efficiency, and its convergence speed slows down as the exploration space increases, hindering its application in high-dimensional parameter spaces.

[0004] Therefore, how to organically combine SBL and MCMC methods, design and construct a joint optimization framework with both super-resolution detection and gridless precision estimation, and at the same time overcome the problems of high computational complexity, large storage overhead, low computational efficiency, and poor generalization in existing technologies has become the key challenge to break through the performance boundary of the ISAC system. Summary of the Invention

[0005] Technical Problem: In view of the above deficiencies in the prior art, the present invention provides a method for parameter estimation of a target using Markov Chain Monte Carlo sparse Bayesian. By constructing a sparse Bayesian framework with a parameterizable and learnable sensing matrix, the detection of the number of targets and the distance-velocity-angle parameters are uniformly modeled as random variables, and using the Markov Chain Monte Carlo method, combined with random mini-batch gradient information and the Adam optimizer, super-resolution detection results and estimation accuracy approaching the Cramer-Rao Lower Bound (CRLB) are achieved with relatively low computational complexity and storage overhead.

[0006] Technical Solution: A sparse Bayesian parameter estimation method based on Markov Chain Monte Carlo provided by the present invention includes the following steps:

[0007] S1. The base station transmits an OFDM communication signal through a uniform linear array antenna and receives the echo signal reflected by the target.

[0008] S2. Down-convert and perform fast Fourier transform on the echo signal to generate a frequency-domain signal matrix, and stack it into a high-dimensional observation vector according to the subcarrier and symbol dimensions;

[0009] S3. Model the target parameters as random variables, including path complex gain, delay, Doppler frequency shift, and angle. The path complex gain is used as the sparsifying variable, and a learnable parameterized sensing matrix is constructed, whose column vectors are continuously generated by delay-Doppler-angle parameters; select appropriate priors for the parameters and form a joint posterior probability distribution;

[0010] S4. Initialize the parameter vector to be estimated, and set the sampling iteration number t = 1;

[0011] S5. Calculate the posterior distribution of the parameter vector to be estimated using the observed values of the received signals in a random mini-batch. According to the gradient information of the posterior distribution, combine the Adam optimizer and random walk noise to calculate the proposed parameter vector of the parameter vector to be estimated; execute the Metropolis-Hastings algorithm to accept or reject the sample; set the sampling iteration variable t = t + 1;

[0012] S6. Determine whether t reaches the maximum iteration number N max , if not, jump to step S5 to continue sampling; if so, give the parameter estimation result.

[0013] Preferably, step S2 specifically includes: down-converting the received signal to the baseband, obtaining the frequency-domain form of the received signal through fast Fourier transform, and stacking the frequency-domain received signals along the subcarrier dimension and the OFDM symbol dimension.

[0014] Preferably, the construction of the learnable parameterized sensing matrix in step S3 includes the following steps:

[0015] Step S3.1: Model the delay, Doppler frequency shift, and angle parameters as random variables with truncated Gaussian distributions to limit the physical value ranges of the parameters;

[0016] Step S3.2: Dynamically generate the column vectors of the sensing matrix based on the random variable parameters established in step 3.1, where each column vector corresponds to a set of continuous delay-Doppler-angle parameter combinations;

[0017] Step S3.3: Apply a hierarchical Gaussian sparse prior to the path complex gain, and control the sparsity degree of the effective column vectors in the sensing matrix constructed in step 3.2 by adjusting the hyperparameters of the prior distribution.

[0018] Preferably, the generation of the proposed parameter vector in step S5 includes the following steps:

[0019] Step S511: Randomly select a small batch of samples from the received signal observations, and calculate the logarithmic posterior distribution of the current parameter vector based on the learnable parameterized sensing matrix and the prior of the parameter to be estimated set;

[0020] Step S512: Calculate the gradient of the logarithmic posterior distribution obtained in Step S511, and extract the parameter update direction information;

[0021] Step S513: Input the gradient information obtained in Step S512 into the Adam optimizer for first-order moment and second-order moment estimation, and inject random walk noise with a preset variance at the same time;

[0022] Step S514: According to the optimization result output in Step S513, generate a candidate parameter vector as the proposed parameter vector in combination with a dynamically decaying learning rate.

[0023] Preferably, the steps of accepting or rejecting samples in the Metropolis-Hastings algorithm executed in Step S5 specifically include:

[0024] Step S521: Based on the generated proposed parameter vector, calculate the ratio of its posterior probability to the current parameter vector;

[0025] Step S522: Determine the sample acceptance probability according to the probability ratio obtained in Step S521, where the acceptance probability takes the minimum value of the ratio and 1;

[0026] Step S523: Generate a random number uniformly distributed in the interval (0, 1), and compare it with the acceptance probability calculated in Step S522:

[0027] If the random number is less than the acceptance probability, use the proposed parameter vector as the next iteration sample;

[0028] Otherwise, retain the current parameter vector as the next iteration sample.

[0029] Preferably, the output of the parameter estimation result in Step S6 includes the following steps:

[0030] Step S6.1: After completing the preset number of MCMC sampling iterations, screen out the sample sequence collected in the stationary state;

[0031] Step S6.2: Calculate the statistical mean of each parameter for the sample sequence obtained in Step S6.1 as the final estimated values of the target distance, speed, and angle;

[0032] Step S6.3: Based on the sparse variable amplitude distribution in the estimation result of Step S6.2:

[0033] Identify significant non-zero terms through a preset amplitude threshold to determine the number of detected targets;

[0034] Extract the combinations of time delay, Doppler frequency shift, and angle parameters corresponding to each non-zero term;

[0035] Step S6.4: Match and verify the parameter combinations parsed in step S6.3 with the statistical estimation results in step S6.2, and output a complete set of estimated target parameters.

[0036] Preferably, the method is applicable to the communication and sensing integration scenario of the MIMO-OFDM system, and realizes the detection of the number of targets and the joint estimation of the distance, speed, and angle of the targets.

[0037] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention effectively combines sparse Bayesian learning and the MCMC method, significantly improves the sensing performance in the ISAC system while ensuring the communication performance, and achieves multiple breakthroughs in terms of computational complexity, estimation accuracy, and practicality. Specifically, in the SBL framework, a dynamically generated learnable parameterized sensing matrix is used to replace the fixed large-scale dictionary, and the time delay, Doppler frequency shift, and angle are modeled as continuous random variables, breaking through the discrete grid division limit, achieving gridless parameter estimation accuracy and super-resolution beyond the Rayleigh limit, while reducing the computational and storage requirements brought by the large-scale sensing matrix; for the high-dimensional parameter estimation problem brought by the learnable parameterized sensing matrix, an MCMC algorithm that fuses random mini-batch gradient information and the Adam optimizer is used to avoid the high-dimensional matrix inversion operation in traditional sparse Bayesian learning while significantly improving the computational efficiency, introducing an annealing factor and an adaptive step size decay mechanism to enhance the robustness of the algorithm under different signal-to-noise ratios, and achieving super-resolution detection results and estimation accuracy approaching the Cramer-Rao lower bound with low computational complexity and storage overhead. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of an embodiment of the present invention;

[0040] Figure 2 is a schematic diagram of the system model of an embodiment of the present invention;

[0041] Figure 3 is the change of the detection probability of different numbers of targets with the signal-to-noise ratio (SNR) in an embodiment of the present invention;

[0042] Figure 4 is a comparison diagram of the parameter estimation accuracy of an embodiment of the present invention with traditional compressive sensing algorithms NOMP and OMP and the Cramer-Rao lower bound with the change of the signal-to-noise ratio SNR, where 4.1 is the distance parameter estimation performance, 4.2 is the speed parameter estimation performance, and 4.3 is the angle parameter estimation performance. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0044] Consider a downlink ISAC scenario of a single base station in a millimeter-wave (mmWave) MIMO communication system, as Figure 2 shown. In this embodiment, the base station transmits OFDM signals to communicate with U single-antenna users and is reflected by L moving targets. The base station is equipped with two uniformly linear arrays (ULAs) with N antennas placed in parallel as the transmitting antenna and the echo receiving antenna respectively. The spacing between the two ULAs is 5λ to 10λ to prevent self-interference between the transmitted and received signals. The antenna spacing of each ULA where λ represents the wavelength. The carrier frequency of the OFDM signal is f c , and the subcarrier spacing is Δf. M and K are the number of subcarriers and the number of symbols of OFDM respectively. The total symbol period of OFDM is T s = T d + T cp , where represents the data period, represents the cyclic prefix period. Then the form of the noise-free echo signal received by the base station can be expressed as:

[0045]

[0046] where, b l represents the path complex gain, τ l represents the delay of the l-th target, f D,l represents the Doppler frequency shift of the l-th target, θ AOA,l and θ AOD,l represent the transmission angle and the arrival angle of the l-th target. Since the target distance is much larger than the transceiver antenna spacing in normal cases, it can be considered that the transmission angle θ AOA,l is equivalent to the reception angle θ AOD,l , denoted as θ l , a(·) is the steering vector, defined as x m,k is the transmitted signal, and rect(·) represents the rectangular window function.

[0047] As Figure 1 shown, the embodiment of the present invention provides a sparse Bayesian parameter estimation method based on Markov chain Monte Carlo, which specifically includes the following steps:

[0048] S1. The base station transmits OFDM communication signals through the uniformly linear array antenna and receives the echo signals reflected by the targets;

[0049] S2. Perform down-conversion and fast Fourier transform on the echo signal to generate a frequency-domain signal matrix, and stack it into a high-dimensional observation vector according to the sub-carrier and symbol dimensions. The specific steps are as follows:

[0050] S201. Down-convert the received signal to the baseband. The expression of the frequency-domain received signal obtained by fast Fourier transform is:

[0051]

[0052] where y m,k is the frequency-domain received signal at the m-th sub-carrier and the k-th OFDM symbol. L represents the number of targets, b l represents the path complex gain, τ l represents the delay of the l-th target, Δf represents the sub-carrier spacing, f D,l represents the Doppler frequency shift of the l-th target, T s represents the symbol period, θ l represents the angle between the l-th target and the normal direction of the base station antenna, a(·) is the steering vector, (·) H represents the conjugate transpose of the matrix, x m,k is the transmitted signal, z m,k is the additive complex Gaussian white noise, which follows the CN(0,σ 2 ) distribution, and σ 2 is the noise variance.

[0053] S202. Stack the received signals along the sub-carrier and OFDM symbol dimensions, and transform the echo signal into where d l =vec([c 1,1,l ,...,c M,1,l ,...,c M,K,l T ). Using this step to match the echo signal with the compressive sensing model is beneficial to constructing a learnable parameterized sensing matrix.

[0054] S3. Model the target parameters as random variables, including path complex gain, delay, Doppler frequency shift, and angle. The path complex gain is used as the sparsifying variable, and a learnable parameterized sensing matrix is constructed, whose column vectors are continuously generated by the delay-Doppler-angle parameters. Select appropriate priors for the parameters and form a joint posterior probability distribution;

[0055] Furthermore, the parameters to be estimated for the l-th target are the path complex gain b l , the delay τ l , the Doppler frequency shift f D,l , and the angle θ l , and model them as random variables; ​

[0056] Taking the path complex gain as the sparsifying variable, with Q >> L as the length of this variable; using the time delay, Doppler shift, and angle variables of length Q as the parameters for each column of the learnable dictionary, a sparse signal reconstruction problem model is constructed, and the specific expression is:

[0057] y = Db + z

[0058] where D = [d1(τ1, f D,1 , θ1), d2(τ2, f D,2 , θ2),..., d Q (τ Q , f D,Q , θ Q )] is a learnable sensing matrix with parameters to be estimated, and each column has the same form as d l in step S202; the prior of the time delay, Doppler shift, and angle is selected as a truncated Gaussian distribution within the detection range; is the sparsifying variable, and the prior is selected as a hierarchical Gaussian sparse prior, and the specific expression is:

[0059]

[0060] where ρ q is the reciprocal of the variance of each path complex gain estimator, and is a random variable that controls the sparsity degree of b. Its prior is set as κ and ξ are hyperparameters; stacking all the parameters to be estimated gives the parameter vector to be estimated η = [b, ρ, τ, f D , θ] T , and MCMC will sample from the posterior distribution of this parameter vector to be estimated and generate an estimated value using the sample mean.

[0061] S4. Initialize the parameter vector to be estimated, and set the sampling iteration number t = 1;

[0062] S5. Calculate the posterior distribution of the parameter vector to be estimated using the observed values of the received signals in random mini - batches, and calculate the proposed parameter vector of the parameter vector to be estimated using its gradient information, including the Adam optimizer and random walk noise; perform the MH acceptance step to obtain the sample for the next sampling step; set the sampling iteration variable t = t + 1;

[0063] The calculation of the proposed vector specifically includes:

[0064] S511. Randomly select a mini - batch of samples of size S to calculate the likelihood probability, combine the prior distribution selected for the parameters to be estimated, and calculate the log - posterior using Bayes' theorem. The expression is:

[0065]

[0066] Among them, the likelihood distribution follows a complex Gaussian distribution with a mean of Db and a variance of σ 2 ;

[0067] S512. According to the gradient of the log posterior distribution γ is the annealing factor;

[0068] S513. Perform the gradient ascent process of the log posterior distribution, introduce the Adam optimizer to accelerate convergence, and add random perturbation noise. The expression for the proposed parameter vector is:

[0069]

[0070] where, ò t is the learning rate, which decreases as the number of samples t increases; ε is a hyperparameter to prevent overflow; n is the perturbation noise, which follows a Gaussian distribution with a mean of 0 and a variance of 2ò t ; and are the momentum term and variance term of the gradient respectively, and the expressions are:

[0071]

[0072] where, β1 and β2 are decay factors.

[0073] The MH acceptance step specifically includes:

[0074] S521. Use the proposed parameter vector η' at the sampling iteration time t obtained in step S513 as the candidate sample;

[0075] S522. Calculate the acceptance probability α of the candidate sample according to the Metropolis-Hastings criterion. The expression is:

[0076]

[0077] where, min represents taking the minimum value, p(η'|y) is the posterior probability of the proposed parameter vector η';

[0078] S523. Take a random number τ uniformly distributed between (0,1), and judge whether α is less than τ. If not, let the sample η at the next sampling time t+1 = η'; if so, discard the candidate sample η', and let the sample η at the next sampling time t+1 = η t , where η t is the sample of the current sampling iteration.

[0079] S6. Judge whether t reaches the maximum number of iterations N max , if not, jump to step S5 to continue sampling; if so, give the parameter estimation result. After the algorithm ends, use the obtained Nmax Take one sample as the sample sequence, and collect N burnin samples that transfer to the steady state after N sample iterations, and calculate the mean value of N sample samples as the estimation result of the parameter η; The number of significant non-zero terms in is the number of moving targets, and the corresponding are the time delay, Doppler frequency and the angle between the target and the normal direction of the base station antenna, which can be obtained through and to calculate the distance and speed of the target, which directly corresponds to the departure angle (angle of arrival) of the target.

[0080] To enable those skilled in the art to better understand the solution of the present invention, the following presents a comparison of the results of the parameter estimation method and the comparison method based on Markov chain Monte Carlo - sparse Bayesian in this embodiment.

[0081] The considered simulation scenario is described as follows:

[0082] Consider a base station with a uniform linear array having N = 8 antennas, the number of subcarriers M = 128 for the transmitted OFDM signal, the number of symbols K = 14, the carrier frequency = 30 GHz, and the subcarrier spacing is 100 MHz. Randomly generate moving targets within the simulation scenario range, the number of targets does not exceed 5, the range of the target position from the base station is [0, 500] m, the range of the target speed is [-30, 30] m / s, the range of the angle between the target position and the normal direction of the base station antenna is [-80, 80]°, and the amplitude of the path complex gain is where σ RCS is the radar reflection coefficient, set to 1, and the phase is randomly generated from [0, 2π].

[0083] Consider the hyperparameters are selected as:

[0084] The sparsification dimension Q is set to 10, meeting the requirement of being much larger than L; the random sample batch size S = 128, the temperature factor, and the two decay factors β1 and β2 of the Adam optimizer are set to 0.9 and 0.999 respectively, and ε is set to 10 -8 , ò t The initial value of the learning rate is 0.15, and it decreases by 0.001 with each step increase. The total number of samples N max is 4.5×10 4 , where N burnin is 4×10 4 , N sample is 5000.

[0085] Figure 3 Shows the detection probability P for different numbers of targetscd Variation with the signal-to-noise ratio (SNR). The present invention determines the number of detected targets by calculating the number of significant non-zero elements in the sparse vector b. An appropriate threshold σ th = 0.9 is selected according to experience. When the magnitude of the path complex gain b l of the l-th target exceeds this threshold, the target is considered to exist. Only when all targets are accurately identified in a multi-target scenario is it considered a successful detection. The experimental results are based on 100 Monte Carlo trials. The results show that for SNR values higher than 10 dB, P cd can almost approach 100% for different numbers of targets. In a single-target scenario, even when the SNR is -15 dB, there is still a 60% probability of successful detection. Although P cd decreases due to false alarms or missed detections as the number of targets increases, in a scenario with a relatively large number of targets (such as three targets), the probability of successful detection can still reach 55% when the SNR is -5 dB.

[0086] Figure 4 Shows the comparison of the root mean square error (RMSE) of parameter estimation between the present invention and the comparative method in the simulation scenario, as well as the Cramér-Rao bound (CRLB), which is the theoretical lower bound of the parameter estimation accuracy. Figure 4In 4.1, 4.2, and 4.3, the estimation results of distance, speed, and angle are shown respectively. The comparison methods include the NOMP algorithm in the literature "Newtonized Orthogonal Matching Pursuit: Frequency Estimation Over the Continuum," in IEEE Transactions on Signal Processing, vol. 64, no. 19, pp. 5066 - 5081, Oct. 1, 2016 and the OMP algorithm in "Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition," in Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 1993. Experiments show that: for this method, at a signal - to - noise ratio (SNR) of 10 dB, the root - mean - square errors (RMSEs) of distance, speed, and angle estimation reach 0.12 m, 0.08 m / s, and 0.03° respectively, and when the SNR is 0 dB, it achieves performance gains of 30 dB, 20 dB, and 20 dB compared with the NOMP method. The square root of the Cramér - Rao lower bound (s - CRLB) defines the lower bound of the RMSE of any unbiased estimator and provides a theoretical limit for the estimation accuracy in a noisy environment. The present invention has a deviation of less than 1.8 dB from the theoretical lower limit of the s - CRLB when the SNR is higher than 10 dB, demonstrating near - optimal performance. In contrast, both NOMP and OMP have a significant gap with the s - CRLB, especially at low SNR. Although NOMP introduces Newtonian iteration optimization, its RMSE still deviates from the s - CRLB by more than 12 dB at - 10 dB. The OMP method shows an exponential performance degradation, confirming the inherent defect of traditional greedy algorithms being sensitive to noise, while the method provided by the present invention has noise robustness.

[0087] The above - described is only a preferred embodiment of the present invention in conjunction with the accompanying drawings, and it cannot be used to limit the scope of rights covered by the present invention. It should be understood that any equivalent changes made without departing from the spirit of the present invention fall within the protection scope covered by the claims of the present invention.

Claims

1. A sparse Bayesian parameter estimation method based on Markov chain Monte Carlo, characterized in that, The method includes the following steps: S1. The base station transmits OFDM communication signals through a uniform linear array antenna and receives the echo signals reflected by the target. S2. Down-convert and perform fast Fourier transform on the echo signals to generate a frequency-domain signal matrix, which is stacked into a high-dimensional observation vector according to subcarrier and symbol dimensions. S3. Model the target parameters as random variables, including path complex gain, time delay, Doppler frequency shift, and angle. The path complex gain is used as the sparsifying variable, and a learnable parameterized sensing matrix is constructed, whose column vectors are continuously generated by time delay-Doppler-angle parameters. Select appropriate priors for the parameters and form a joint posterior probability distribution. S4. Initialize the parameter vector to be estimated and set the sampling iteration number t = 1. S5. Calculate the posterior distribution of the parameter vector to be estimated using the observed values of randomly selected small batches of received signals. According to the gradient information of the posterior distribution, combine the Adam optimizer and random walk noise to calculate the proposed parameter vector of the parameter vector to be estimated. Execute the Metropolis-Hastings algorithm to accept or reject the sample. Set the sampling iteration variable t = t + 1. S6. Determine whether t has reached the maximum number of iterations N max If not, jump to step S5 to continue sampling; if so, give the parameter estimation result.

2. The sparse Bayesian parameter estimation method based on Markov chain Monte Carlo according to claim 1, wherein Step S2 specifically includes: Down-convert the received signal to the baseband, obtain the frequency-domain form of the received signal through fast Fourier transform, and stack the frequency-domain received signals along the subcarrier dimension and the OFDM symbol dimension.

3. The sparse Bayesian parameter estimation method based on Markov chain Monte Carlo according to claim 1, wherein The construction of the learnable parameterized sensing matrix in step S3 includes the following steps: Step S3.1: Model the time delay, Doppler frequency shift, and angle parameters as random variables with truncated Gaussian distributions to limit the physical value ranges of the parameters. Step S3.2: Dynamically generate the column vectors of the sensing matrix based on the random variable parameters established in step 3.1, where each column vector corresponds to a set of continuous time delay-Doppler-angle parameter combinations. Step S3.3: Apply a hierarchical Gaussian sparse prior to the path complex gain and control the sparsity degree of the effective column vectors in the sensing matrix constructed in step 3.2 by adjusting the hyperparameters of the prior distribution.

4. The sparse Bayesian parameter estimation method based on Markov chain Monte Carlo according to claim 1, wherein The generation of the proposed parameter vector in step S5 includes the following steps: Step S511: Randomly select a small batch of samples from the observed values of the received signals, and calculate the log posterior distribution of the current parameter vector based on the learnable parameterized sensing matrix and the set prior of the parameter to be estimated. Step S512: Calculate the gradient of the log posterior distribution obtained in step S511 and extract the parameter update direction information. Step S513: Input the gradient information obtained in step S512 into the Adam optimizer for first-order and second-order moment estimation, and inject random walk noise with a preset variance at the same time. Step S514: According to the optimization result output in step S513, generate a candidate parameter vector as the proposed parameter vector in combination with a dynamically decaying learning rate.

5. The method for sparse Bayesian parameter estimation based on Markov chain Monte Carlo according to claim 1 or 4, characterized in that The steps of accepting or rejecting samples in the Metropolis-Hastings algorithm executed in step S5 specifically include: Step S521: Calculate the posterior probability ratio between the generated proposed parameter vector and the current parameter vector. Step S522: Determine the sample acceptance probability according to the probability ratio obtained in step S521, where the acceptance probability takes the minimum value of the ratio and 1. Step S523: Generate a random number uniformly distributed in the interval (0, 1), and compare it with the acceptance probability calculated in Step S522: If the random number is less than the acceptance probability, use the proposed parameter vector as the next iteration sample; Otherwise, retain the current parameter vector as the next iteration sample.

6. The sparse Bayesian parameter estimation method based on Markov chain Monte Carlo according to claim 1, wherein The output of the parameter estimation result in Step S6 includes the following steps: Step S6.1: After completing the MCMC sampling iteration for a preset number of times, screen out the sample sequence collected in the steady state; Step S6.2: Calculate the statistical mean of each parameter for the sample sequence obtained in Step S6.1 as the final estimated values of the target distance, speed, and angle; Step S6.3: Based on the sparsified variable amplitude distribution in the estimation result of Step S6.2: Identify significant non-zero terms through a preset amplitude threshold to determine the number of detected targets; Extract the time delay, Doppler frequency shift, and angle parameter combinations corresponding to each non-zero term; Step S6.4: Match and verify the parameter combinations parsed in Step S6.3 with the statistical estimation result in Step S6.2, and output the complete set of target parameter estimations.

7. The sparse Bayesian parameter estimation method based on Markov chain Monte Carlo according to any one of claims 1-6, characterized in that, The method is applicable to the integrated communication and sensing scenario of the MIMO-OFDM system, and realizes the detection of the number of targets and the joint estimation of the distance, speed, and angle of the targets.

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