OFDM (Orthogonal Frequency Division Multiplexing) echo sensing method based on coarse grid block sparse prior sparse Bayesian learning

Abstract

The invention discloses an OFDM (Orthogonal Frequency Division Multiplexing) echo sensing method based on coarse grid block sparse prior sparse Bayesian learning, and relates to an OFDM echo sensing method. The invention aims to solve the problems that a standard SBL algorithm does not utilize all structure information in a signal in OFDM echo sensing and a large number of false peaks appear in global sensing. The method comprises the following steps: step 1, OFDM echo preprocessing; 2, initializing an iteration parameter and a hyper-parameter; step 3, estimating a posteriori mean value mu (i) and a posteriori variance sigma w (i); step 4, if or igt; if yes, iteration is stopped, and the step 6 is executed; otherwise, executing the step 5; 5, estimating a hyper-parameter sparse variable variance gamma (i) and an observation model variance sigma (i) by using coarse grid block sparse prior and an EM algorithm; and step 6, outputting a time delay Doppler domain sensing result. The invention belongs to the technical field of wireless communication and perception fusion.

Description

Technical Field

[0001] The present invention relates to an OFDM echo perception method, and belongs to the technical field of wireless communication and perception fusion. Background Art

[0002] With the rapid development of sixth-generation mobile communication systems, integrated perception and communication technologies have become a research hotspot. ISAC technology, by sharing spectrum, hardware, and signal processing platforms, achieves a deep fusion of perception and communication functions, promising broad application prospects in areas such as autonomous driving, smart cities, and intelligent transportation systems. Orthogonal frequency division multiplexing (OFDM), a core technology in 4G and 5G communication systems, has proven to be equally suitable for radar perception applications due to its robustness against multipath fading and improved spectrum efficiency. It can be used for perception tasks such as target detection, distance, and velocity estimation.

[0003] Delay-Doppler (DD) parameter estimation is a critical step in OFDM radar perception. Numerous algorithms have been proposed for DD parameter estimation, including traditional methods based on the two-dimensional Fourier transform (2D FFT), the Multiple Signal Classification (MUSIC) algorithm, the Orthogonal Matching Pursuit (OMP) algorithm, and the Sparse Bayesian Learning (SBL) algorithm. The 2D FFT method is simple to implement but is limited by Fourier resolution; the MUSIC algorithm is computationally complex and requires a known number of scattering points; and the OMP algorithm is computationally efficient but less accurate and also requires a known number of scattering points.

[0004] In contrast, the SBL algorithm, by introducing a sparse Bayesian framework, automatically determines model complexity and provides super-resolution parameter estimation, demonstrating superior performance in OFDM echo perception. However, the standard SBL algorithm fails to consider the internal structure of OFDM signals, fails to utilize all information, and fails to achieve optimal accuracy. Furthermore, it misinterprets noise as numerous false peaks. Summary of the Invention

[0005] In order to solve the problem that the standard SBL algorithm does not utilize all the internal structural information of the signal in OFDM echo perception and a large number of false peaks appear in global perception, the present invention proposes an OFDM echo perception method based on coarse grid block sparse prior sparse Bayesian learning.

[0006] The technical solution adopted by the present invention to solve the above problems is: the steps of the present invention include: Step 1: Preprocess the OFDM echo to obtain the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated. ,in , are the number of subcarriers and symbols of the OFDM signal respectively; Construct a sparse Bayesian compressed sensing model to determine the maximum number of delay and Doppler dimensions in a super-resolution fine grid and , both of which are and an integer multiple of ; Step 2: Initialize the iterative parameters used to control the SBL algorithm, including the maximum number of iterations and error tolerance ; Initialize the hyperparameters estimated by SBL, including the variance of sparse variables , observation model variance , intra-block variance , block sparse variance ; The number of iterations Set to 1; Step 3: Based on the initialized hyperparameters and , use the sparse Bayesian compressed sensing model constructed in step 1 to calculate the posterior mean and the posterior variance ; Step 4: If or Stop iteration and execute step 6; otherwise, execute step 5; Step 5: Based on the posterior mean obtained from the previous iteration and the posterior variance , combining coarse grid block sparse hyper prior with expectation maximization algorithm to estimate the variance of sparse variables of hyper parameters Variance of observed model , the number of iterations increases by one, and then execute step 3; Step 6: Rearrange into rows and columns , The matrix is ​​linearly transformed to obtain the delay-Doppler domain sensing result.

[0007] Furthermore, the OFDM echo preprocessing process in step 1 is as follows: Step 101: Receive The OFDM echo of the symbol duration is sampled and the cyclic prefix is ​​removed to obtain the baseband signal. ; Step 102: Rearrange into rows and columns , Matrix .right Fast Fourier transform of each column and point-by-point division of the communication modulation information matrix , the first Rank The elements in the column represent the OFDM signal The subcarrier in the The modulation information carried on the symbol is finally obtained, and the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated is obtained. ; Step 103: Vectorization, building a compressed sensing model, (1), In formula (1), yes The vectorization of is called the observation variable, is the dictionary matrix, its The columns are represented as: (2), In formula (2), represents the Kronecker product, is a sparse vector, It's noise. and are the maximum number of delay and Doppler dimensions in the super-resolution fine grid, respectively; Step 104: Construct a sparse Bayesian model. Assume Each element All have zero mean and variance Gaussian distribution, then the probability density function of the sparse vector can be described as: (3), In formula (3), Represents a sparse vector The variance of is a diagonal matrix, the first The elements are , the rest of the elements are 0; The SBL algorithm assumes that the observed variables conform to the Gaussian likelihood model: (4), In formula (4), represents the observed model variance.

[0008] Furthermore, the posterior mean in step 3 and the posterior variance The calculation process is: Combining formula (3) and formula (4) and using the Bayesian formula to obtain the posterior probability , and then get the posterior mean and the posterior variance The iterative expression is: (5), (6).

[0009] Furthermore, in step 5, the coarse grid block sparse hyper-prior is combined with the EM algorithm to estimate the variance of the hyper-parameter sparse variable Variance of observed model The process is: Step 501: Define a coarse grid hyper-prior; group the sparse variable elements that conform to the coarse grid distribution into a group, each group has a block sparse coefficient, and finally redefine the variance of each sparse variable element as follows: (7), In formula (7), represents the intra-block variance, It is Block sparse variance, It is The vector index set of the coarse grid grouping is defined as: (8), In formula (8), , represents the two-dimensional super-resolution coefficient, represents the super-resolution coefficient of the delay dimension, represents the Doppler dimension super-resolution coefficient, represents the floor function; Step 502: Use the EM algorithm to estimate the variance of the hyperparameter sparse variables Variance of observed model ;The EM algorithm is divided into two steps, the E step to find the expectation and the M step to maximize; Step E is to transform the observed variables As a hidden variable, find the joint probability density function about This step is equivalent to combining the sparse vector probability density function with the SBL observation model to obtain the marginal probability density function: (9), In formula (9), represents the marginal probability variance, Represents a unit matrix of size MN; The M step maximizes the marginal probability density function, which is equivalent to minimizing the SBL cost function, as shown below (10), Use the cost function to derive the three variables separately, and get the expression of the three variables that satisfies the derivative of 0, which is the minimized expression. The variance of the hyperparameter sparse variable Variance of observed model The iterative formula is: (11), (12), In formulas (11) and (12), It means finding the trace of the matrix, and The iterative expression is: (13), (14).

[0010] Furthermore, in step 6 Rearrange into rows and columns , The matrix is ​​transformed linearly to obtain the delay-Doppler domain perception result; the specific process is: The latest posterior matrix estimated after the iteration Rearrange into rows and columns , Matrix ,at this time The delay dimension has scale, and convert it into normalized delay , for The delay index is, similarly, the normalized Doppler is , for Doppler index of Normalized time delay and distance between scattering point and radar The relationship is: (15), In formula (15), Indicates the OFDM subcarrier spacing, represents the speed of light; Normalized Doppler and radial velocity of the scattering point relative to the radar The relationship is: (16), In formula (16), Indicates the OFDM carrier frequency; At this time, the matrix It can be called a range-velocity diagram, where each element represents the signal reflection strength of the range-velocity unit.

[0011] The beneficial effects of the present invention are: 1. This invention eliminates the interference caused by random communication symbols and constructs an OFDM echo compressed sensing model. Using EM to derive the hyperparameter iteration formula in the SBL algorithm iteration ensures sparsity and improves perception accuracy. This invention proposes a coarse grid block sparse hyperprior, which utilizes the internal structure of the signal to achieve faster algorithm convergence and solve the problem of a large number of false targets appearing under low signal-to-noise ratio conditions. 2. The present invention can efficiently and quickly complete OFDM echo perception, and has higher accuracy and convergence speed than the standard SBL algorithm; 3. The significance of the present invention is to enhance the accuracy of OFDM echo perception and eliminate the influence of communication random symbols so as to meet the needs of ISAC in future 6G networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flowchart of the present invention; Figure 2 It is a schematic diagram of coarse grid grouping; Figure 3 This is a schematic diagram of the DD domain perception results of the four methods at a signal-to-noise ratio of 5dB; Figure 3 (a) is a schematic diagram of coarse grid block sparse SBL; Figure 3 (b) is a schematic diagram of a standard SBL; Figure 3 (c) is a schematic diagram of OMP; Figure 3 (d) is a schematic diagram of MUSIC; Figure 4 It is a schematic diagram of the results of the perceptual accuracy of OMP, standard SBL and coarse grid block sparse SBL changing with SNR; Figure 5 It is a schematic diagram showing the results of the number of iterations of standard SBL and coarse grid block sparse SBL changing with SNR. DETAILED DESCRIPTION

[0013] Specific implementation method 1: Figure 1 As shown in FIG, the OFDM echo perception method based on coarse grid block sparse prior sparse Bayesian learning includes the following steps: Step 1: Preprocess the OFDM echo to obtain the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated. ,in , are the number of subcarriers and symbols of the OFDM signal respectively; Construct a sparse Bayesian compressed sensing model to determine the maximum number of delay and Doppler dimensions in a super-resolution fine grid and , both of which are and an integer multiple of ; The process of OFDM echo preprocessing is as follows: Step 101: Receive The OFDM echo of the symbol duration is sampled and the cyclic prefix is ​​removed to obtain the baseband signal. ; Step 102: Rearrange into rows and columns , Matrix .right Fast Fourier transform of each column and point-by-point division of the communication modulation information matrix , the first Rank The elements in the column represent the OFDM signal The subcarrier in the The modulation information carried on the symbol is finally obtained, and the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated is obtained. ; Step 103: Vectorization, building a compressed sensing model, (1), In formula (1), yes The vectorization of is called the observation variable, is the dictionary matrix, its The columns are represented as: (2), In formula (2), represents the Kronecker product, is a sparse vector, It's noise. and are the maximum number of delay and Doppler dimensions in the super-resolution fine grid, respectively; Step 104: Construct a sparse Bayesian model. Assume Each element All have zero mean and variance Gaussian distribution, then the probability density function of the sparse vector can be described as: (3), In formula (3), Represents a sparse vector The variance of is a diagonal matrix, the first The elements are , the rest of the elements are 0; The SBL algorithm assumes that the observed variables conform to the Gaussian likelihood model: (4), In formula (4), represents the observed model variance; Step 2: Initialize the iterative parameters used to control the SBL algorithm, including the maximum number of iterations and error tolerance ; Initialize the hyperparameters estimated by SBL, including the variance of sparse variables , observation model variance , intra-block variance , block sparse variance ; The number of iterations Set to 1; Step 3: Based on the initialized hyperparameters and , use the sparse Bayesian compressed sensing model constructed in step 1 to calculate the posterior mean and the posterior variance ; Posterior mean and the posterior variance The calculation process is: Combining formula (3) and formula (4) and using the Bayesian formula to obtain the posterior probability , and then get the posterior mean and the posterior variance The iterative expression is: (5), (6); Step 4: If or Stop iteration and execute step 6; otherwise, execute step 5; Step 5: Based on the posterior mean obtained from the previous iteration and the posterior variance , combining coarse grid block sparse hyper prior with expectation maximization algorithm to estimate the variance of sparse variables of hyper parameters Variance of observed model , the number of iterations increases by one, and then execute step 3; Combining coarse grid block sparse hyperprior with EM algorithm to estimate the variance of sparse variables of hyperparameters Variance of observed model The process is: Step 501: Define a coarse grid hyper-prior; group the sparse variable elements that conform to the coarse grid distribution into a group, each group has a block sparse coefficient, and finally redefine the variance of each sparse variable element as follows: (7), In formula (7), represents the intra-block variance, It is Block sparse variance, It is The vector index set of the coarse grid grouping is defined as: (8), In formula (8), , represents the two-dimensional super-resolution coefficient, represents the super-resolution coefficient of the delay dimension, represents the Doppler dimension super-resolution coefficient, represents the floor function; Step 502: Use the EM algorithm to estimate the variance of the hyperparameter sparse variables Variance of observed model ;The EM algorithm is divided into two steps, the E step to find the expectation and the M step to maximize; Step E is to transform the observed variables As a hidden variable, find the joint probability density function about This step is equivalent to combining the sparse vector probability density function with the SBL observation model to obtain the marginal probability density function: (9), In formula (9), represents the marginal probability variance, Represents a unit matrix of size MN; The M step maximizes the marginal probability density function, which is equivalent to minimizing the SBL cost function, as shown below (10), Use the cost function to derive the three variables separately, and get the expression of the three variables that satisfies the derivative of 0, which is the minimized expression. The variance of the hyperparameter sparse variable Variance of observed model The iterative formula is: (11), (12), In formulas (11) and (12), It means finding the trace of the matrix, and The iterative expression is: (13), (14); Step 6: Rearrange into rows and columns , The matrix is ​​linearly transformed to obtain the delay-Doppler domain sensing result; Will Rearrange into rows and columns , The matrix is ​​transformed linearly to obtain the delay-Doppler domain perception result; the specific process is: The latest posterior matrix estimated after the iteration Rearrange into rows and columns , Matrix ,at this time The delay dimension has scale, and convert it into normalized delay , for The delay index is, similarly, the normalized Doppler is , for Doppler index of Normalized time delay and distance between scattering point and radar The relationship is: (15), In formula (15), Indicates the OFDM subcarrier spacing, represents the speed of light; Normalized Doppler and radial velocity of the scattering point relative to the radar The relationship is: (16), In formula (16), Indicates the OFDM carrier frequency; At this time, the matrix It can be called a range-velocity diagram, where each element represents the signal reflection strength of the range-velocity unit.

[0014] Table 1 Symbol Description

[0015] Example Number of OFDM subcarriers Set to 16, the number of symbols Set to 16, modulation information matrix For random 4-QAM, the maximum number of iterations is set to , the error tolerance is set to , the number of scattering points is 5, the signal-to-noise ratio changes from 5dB to 30dB in increments of 5dB, and the comparison algorithms are standard SBL, OMP and MUSIC.

[0016] like Figure 3 As shown, Figure 3 Figure 2 shows the DD domain perception results of the four algorithms under a signal-to-noise ratio of 5dB. It can be seen that the coarse grid prior SBL has the sparsest result and does not estimate false scattering points; both OMP and MUSIC estimate false scattering points; the amplitude calculated by MUSIC is incorrect, and the result is not sparse.

[0017] Since MUSIC estimates the pseudo spectrum, it cannot correctly estimate the echo intensity, such as Figure 4 As shown, Figure 4 The comparison of perception accuracy of different algorithms under different signal-to-noise ratios is given in

[15] , except for MUSIC. It can be seen that the coarse grid prior SBL has the best result.

[0018] like Figure 5 As shown, Figure 5 The number of iterations of the two SBL algorithms is given in , and it can be seen that the coarse grid prior SBL converges faster.

[0019] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. OFDM echo perception method based on coarse grid block sparse prior sparse Bayesian learning, characterized by: The specific steps include: Step 1: Preprocess the OFDM echo to obtain the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated. ,in , are the number of subcarriers and symbols of the OFDM signal respectively; Construct a sparse Bayesian compressed sensing model to determine the maximum number of delay and Doppler dimensions in a super-resolution fine grid and , both of which are and an integer multiple of ; Step 2: Initialize the iterative parameters used to control the SBL algorithm, including the maximum number of iterations and error tolerance ; Initialize the hyperparameters estimated by SBL, including the variance of sparse variables , observation model variance , intra-block variance , block sparse variance ; The number of iterations Set to 1; Step 3: Based on the initialized hyperparameters and , use the sparse Bayesian compressed sensing model constructed in step 1 to calculate the posterior mean and the posterior variance ; Step 4: If or Stop iteration and execute step 6; otherwise, execute step 5; Step 5: Based on the posterior mean obtained from the previous iteration and the posterior variance , combining coarse grid block sparse hyper prior with expectation maximization algorithm to estimate the variance of sparse variables of hyper parameters Variance of observed model , the number of iterations increases by one, and then execute step 3; Step 6: Rearrange into rows and columns , The matrix is ​​linearly transformed to obtain the delay-Doppler domain sensing result.

2. The OFDM echo perception method based on coarse grid block sparse prior sparse Bayesian learning according to claim 1, characterized in that The OFDM echo preprocessing process in step 1 is: Step 101: Receive The OFDM echo of the symbol duration is sampled and the cyclic prefix is ​​removed to obtain the baseband signal. ; Step 102: Rearrange into rows and columns , Matrix .right Fast Fourier transform of each column and point-by-point division of the communication modulation information matrix , the first Rank The elements in the column represent the OFDM signal The subcarrier in the The modulation information carried on the symbol is finally obtained, and the OFDM echo time-frequency domain representation signal with the communication modulation information eliminated is obtained. ; Step 103: Vectorization, building a compressed sensing model, （1）， In formula (1), yes The vectorization of is called the observation variable, is the dictionary matrix, its The columns are represented as: （2）， In formula (2), represents the Kronecker product, is a sparse vector, It's noise. and are the maximum number of delay and Doppler dimensions in the super-resolution fine grid, respectively; Step 104: Construct a sparse Bayesian model. Assume Each element All have zero mean and variance Gaussian distribution, then the probability density function of the sparse vector can be described as: （3）， In formula (3), Represents a sparse vector The variance of is a diagonal matrix, the first The elements are , the rest of the elements are 0; The SBL algorithm assumes that the observed variables conform to the Gaussian likelihood model: （4）， In formula (4), represents the observed model variance.

3. The OFDM echo perception method based on coarse grid block sparse prior sparse Bayesian learning according to claim 1 or 2, characterized in that: The posterior mean in step 3 and the posterior variance The calculation process is: Combining formula (3) and formula (4) and using the Bayesian formula to obtain the posterior probability , and then get the posterior mean and the posterior variance The iterative expression is: （5）， （6）。 4. The OFDM echo sensing method based on coarse grid block sparse prior sparse Bayesian learning according to claim 1, characterized in that: In step 5, the coarse grid block sparse hyperprior is combined with the EM algorithm to estimate the variance of the sparse variable of the hyperparameter Variance of observed model The process is: Step 501: Define a coarse grid hyper-prior; group the sparse variable elements that conform to the coarse grid distribution into a group, each group has a block sparse coefficient, and finally redefine the variance of each sparse variable element as follows: （7）， In formula (7), represents the intra-block variance, It is Block sparse variance, It is The vector index set of the coarse grid grouping is defined as: （8）， In formula (8), , represents the two-dimensional super-resolution coefficient, represents the super-resolution coefficient of the delay dimension, represents the Doppler dimension super-resolution coefficient, represents the floor function; Step 502: Use the EM algorithm to estimate the variance of the hyperparameter sparse variables Variance of observed model ;The EM algorithm is divided into two steps, the E step to find the expectation and the M step to maximize; Step E is to transform the observed variables As a hidden variable, find the joint probability density function about This step is equivalent to combining the sparse vector probability density function with the SBL observation model to obtain the marginal probability density function: （9）， In formula (9), represents the marginal probability variance, Represents a unit matrix of size MN; The M step maximizes the marginal probability density function, which is equivalent to minimizing the SBL cost function, as shown below （10）， Use the cost function to derive the three variables separately, and get the expression of the three variables that satisfies the derivative of 0, which is the minimized expression. The variance of the hyperparameter sparse variable Variance of observed model The iterative formula is: （11）， （12）， In formulas (11) and (12), It means finding the trace of the matrix, and The iterative expression is: （13）， （14）。 5. The OFDM echo sensing method based on coarse grid block sparse prior sparse Bayesian learning according to claim 1, characterized in that: In step 6, Rearrange into rows and columns , The matrix is ​​linearly transformed to obtain the delay-Doppler domain sensing result; The specific process is: The latest posterior matrix estimated after the iteration Rearrange into rows and columns , Matrix ,at this time The delay dimension has scale, and convert it into normalized delay , for The delay index is, similarly, the normalized Doppler is , for Doppler index of Normalized time delay and distance between scattering point and radar The relationship is: （15）， In formula (15), Indicates the OFDM subcarrier spacing, represents the speed of light; Normalized Doppler and radial velocity of the scattering point relative to the radar The relationship is: （16）， In formula (16), Indicates the OFDM carrier frequency; At this time, the matrix It can be called a range-velocity diagram, where each element represents the signal reflection strength of the range-velocity unit.

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