Distance and angle joint parameter estimation method based on OFDM (Orthogonal Frequency Division Multiplexing) signal

Abstract

The invention provides a distance and angle joint parameter estimation method based on an OFDM signal. The method comprises a target function establishment step of converting a distance and angle parameter estimation problem into a two-dimensional optimization problem of a corresponding distance value and an angle value when a spectral function is solved to be maximum in a distance range and an angle range; a coarse estimation step: performing global search on the two-dimensional optimization problem, and outputting a coarse search spectrum peak position; and a fine estimation step: performing high-precision local fine search on the basis of the coarse search spectrum peak position, and outputting the finally estimated distance value and angle value of the OFDM signal for OFDM positioning. According to the method, the approximate position of the spectrum peak is found through rapid coarse search, high-precision fine search is carried out on the basis, high-precision rapid estimation of parameters is finally achieved, the problems of coupling complexity and high precision in the prior art are solved, and the corresponding problems are solved step by step. And low complexity and high estimation precision are both obtained in combined parameter estimation of the distance and the angle of the OFDM signal.

Description

Technical Field

[0001] The present invention relates to radar communication perception integration technology, and in particular to a distance angle joint parameter estimation technology based on OFDM signals. Background Art

[0002] With the development of 6G technology, Integrated Sensing and Communication (ISAC) technology has become an important development trend by realizing the deep integration of communication and perception functions through shared spectrum, hardware platform and signal processing algorithm. In the application of 6G, high-precision positioning technology is crucial as the basis for precise control and decision-making in applications such as smart medical care, smart transportation, and drones. Therefore, in the context of 6G application requirements and the development of ISAC technology, it is of great significance to propose a method for high-precision positioning based on communication signals. Among them, positioning technology based on orthogonal frequency division multiplexing (OFDM) signals shows great potential. As an advanced multi-carrier modulation technology, OFDM technology has high spectrum utilization and the ability to resist multipath fading and interference by decomposing high-speed data signals into multiple low-speed parallel sub-data streams and transmitting them on multiple orthogonal sub-carriers. These characteristics enable OFDM signals to perform well in complex communication environments, providing new possibilities for high-precision positioning.

[0003] In the OFDM positioning problem, if the two important positioning parameters of distance and angle can be estimated simultaneously, the positioning system overhead can be effectively reduced and the system efficiency can be improved, which is more advantageous than the positioning based on one-dimensional parameter estimation. For example, the distance and angle are jointly estimated using the two-dimensional rotation invariance technique (Two Dimensional Estimating Signal Parameter via Rotational Invariance Techniques, 2D-ESPRIT), and the angle parameters are first obtained by the closed-form solution using the rotation factor, and then the diagonal elements of the delay parameters are solved by the column correspondence attributes composed of orthogonal matrix operations and the delay vector matrix constructed by the exchange rule. Alternatively, the distance and angle are jointly estimated using the two-dimensional multiple signal classification (Two Dimensional Multiple Signal Classification, 2D-MUSIC), by constructing the covariance matrix of the array received signal, and using the orthogonality of the signal subspace and the noise subspace to construct the MUSIC two-dimensional spectrum function, and the spectrum function is traversed in the observation space to search for peaks to obtain the estimated value. However, the distance and angle parameter joint estimation method usually takes a long time and is difficult to apply in actual systems because it requires search and estimation in two-dimensional space. The parameter estimation accuracy of the 2D-ESRPIT algorithm is low, especially when the signal-to-noise ratio is low. The 2D-MUSIC algorithm is complex and its estimation accuracy is limited by the spectral peak search step size. Under the requirement of high-precision parameter estimation, the computational complexity of the algorithm increases sharply, making it difficult to use in actual systems.

[0004] Reduced-Dimension Multiple Signal Classification (RD-MUSIC) is used to split the high-dimensional spectrum function into multiple one-dimensional spectrum functions based on the idea of ​​matrix dimensionality reduction, and the distance and angle are estimated using the 1D-MUSIC algorithm. The RD-MUSIC algorithm reduces the computational complexity by reducing the dimensionality, but still uses traversal search to find the spectrum peak, so it does not really solve the problem of high complexity and limited accuracy of 2D-MUSIC.

[0005] In summary, the drawback of existing joint parameter estimation technology is that it is difficult to achieve both estimation accuracy and estimation speed. For example, the 2D-ESPRIT algorithm can quickly solve the parameter estimation value with a closed-form solution, but its estimation accuracy under low signal-to-noise ratio cannot meet the 6G high-precision positioning requirements. Both the 2D-MUSIC algorithm and the RD-MUSIC algorithm have the ability to estimate parameters with high precision, but their estimation accuracy is limited by the spectral peak search step size. When a small search step size is used to achieve high-precision estimation, the estimation time will increase accordingly, resulting in the inability to achieve both estimation accuracy and speed. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a distance angle joint parameter estimation method with low complexity and high precision in the OFDM signal positioning scenario, in view of the problem that the existing distance angle parameter joint estimation method is too complex and time-consuming under the 6G high-precision positioning requirements.

[0007] The technical solution adopted by the present invention to solve the above technical problems is a distance angle joint parameter estimation method based on OFDM signals, comprising the steps of:

[0008] Objective function establishment steps: use the matrix form of channel frequency response to obtain the covariance matrix of channel frequency response, then perform eigenvalue decomposition on the covariance matrix of channel frequency response to obtain the noise subspace, and use the noise subspace and the steering vector in the matrix form of channel frequency response to construct the spectral function; transform the parameter estimation problem of distance and angle into a two-dimensional optimization problem of solving the distance value and angle value corresponding to the maximum of the spectral function within the distance range and angle range;

[0009] Rough estimation step: performing a global search on the two-dimensional optimization problem and outputting a rough search spectrum peak position;

[0010] Fine estimation step: Based on the coarse search of the spectrum peak position, a high-precision local fine search is performed, and the final estimated distance value and angle value of the OFDM signal are output for OFDM positioning.

[0011] The present invention transforms the original 2D-MUSIC spectrum peak search into an optimization problem, and proposes a two-step optimization method. In the first step, a fast coarse search is used to find the approximate position of the spectrum peak. On this basis, a high-precision fine search is performed in the second step, and finally a high-precision rapid estimation of the parameters is achieved. This two-step estimation technical solution decouples the complexity and high-precision problems of coupling in the original technology, and solves the corresponding problems step by step, that is, the first step of fast search is used to greatly reduce the complexity of the original technical solution, and then the second step is used to compensate the accuracy of the rough estimation result of the first step to achieve high-precision estimation. Since the main purpose of the first step is to reduce the complexity of the algorithm rather than directly achieve high-precision parameter estimation, an optimization method with fast convergence speed and relatively high accuracy is required for search.

[0012] Preferably, the dung beetle optimization algorithm is used for fast and rough global search, and the stochastic gradient descent method is used for high-precision local search. Dung beetle optimization is a bionic optimization algorithm with fast convergence speed and relatively high precision. It simulates the behavior of different types of dung beetles in the natural dung beetle population, and iterates and updates the parameters of different dung beetles in the population in parallel, so as to quickly find the optimal value of the objective function. Although the dung beetle algorithm can be solved in a short time, it is often difficult to accurately control the search direction when facing local optimization, and its estimation accuracy is still far from the requirements of 6G high-precision positioning applications. In contrast, the stochastic gradient descent method can quickly approach the local optimal solution through intuitive gradient calculation, which is particularly suitable for optimization scenarios with high precision requirements. Therefore, the second step of the present invention uses the stochastic gradient descent method as a precision compensation strategy for dung beetle optimization to further improve the accuracy of parameter estimation. Based on the approximate estimated position obtained in the first step, the precise position of the spectrum peak is iteratively searched in a small range according to the gradient information of the function. It is worth noting that since the initial iteration value of the second step is the approximate value of the spectral peak position obtained in the first step, the complexity of the search process is very low and can be ignored. This two-step optimization strategy not only inherits the global search capability of the dung beetle algorithm, but also takes advantage of the high precision of the gradient descent method in local search.

[0013] The beneficial effect of the present invention is that low complexity and high estimation accuracy are achieved in the joint parameter estimation of the range angle of the OFDM signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The angle RMSE and distance RMSE changes of different technical solutions when the signal-to-noise ratio is 0-25dB; (a) is the angle RMSE change; (b) is the distance RMSE change.

[0015] Figure 2 The angle and distance estimation performance of the technical solution of the present invention under different numbers of antennas when the number of subcarriers is 256; (a) is the angle estimation performance; (b) is the distance estimation performance.

[0016] Figure 3 The angle and distance estimation performance of the present invention under different numbers of subcarriers when the number of antennas is 16; (a) is the angle estimation performance; (b) is the distance estimation performance. DETAILED DESCRIPTION

[0017] The present invention transforms the original 2D-MUSIC spectrum peak search into an optimization problem, and the specific solution process is: 1) constructing an optimization objective function based on the 2D-MUSIC spectrum function; 2) quickly and roughly estimating the distance angle parameters in the function; 3) performing high-precision fine estimation based on the estimation result obtained by the rough estimation.

[0018] Step 1: Construct an optimization objective function based on 2D-MUSIC spectrum:

[0019] Consider an OFDM positioning system with a symbol time of T S , the number of subcarriers is N c , the total number of array elements is M. k is the subcarrier number variable, k=1,2,...,N c . is a time variable. The receiving end is a uniform linear array with M antennas, and the array element spacing is d = λ / 2, where λ represents the carrier wavelength. t is a time variable, and the transmitted signal writing:

[0020]

[0021] Where X(k) is the pilot information carried by the kth subcarrier, and j is an imaginary unit. Assuming that the distance between the target and the antenna array satisfies the far-field condition, that is, the arrival angle of the received signal to each array element is the same, then the received signal y of the mth array element is m (t) is expressed as:

[0022]

[0023] Where α represents the fading coefficient, r represents the distance from the target to the antenna array, θ represents the angle of arrival, and n m (t) represents the noise on the mth array element, the array element number variable m = 1, 2, ..., M, c represents the speed of light. For the convenience of representation, the received signal is converted into the frequency domain by FFT:

[0024]

[0025] Where Δf is the subcarrier spacing, N m (k) Yes Since X(k) is the known pilot information, the channel frequency response can be obtained by dividing the received signal by X(k). The channel frequency response is expressed in vector form as follows:

[0026] h=d(r,θ)α+z;

[0027] Where h represents the vector form of the channel frequency response, h = [h1(1),...,h1(N c ),...,h m (1),...,h m (k),...,h m (N c ),...,h M (1),...,h M (N c )] T , T represents transpose, hm (k) represents the frequency response of the kth subcarrier on the mth array element; z is the additive random complex Gaussian white noise vector, z = [z1(1),...,z1(N c ),...,z m (1),...,z m (k),...,z m (N c ),...,z M (1),...,z M (N c )] T , z m (k) represents the additive random complex Gaussian white noise of the kth subcarrier on the mth array element, and N m (k) divided by X(k); d(r,θ) represents the steering vector, in represents the Kronecker product, the steering angle component a M (θ) and the steering distance component It can be further written as:

[0028]

[0029] Where e is a natural constant.

[0030] The covariance matrix R of the channel frequency response is:

[0031]

[0032] Where N s Indicates the number of samples, the sampling sequence variable n s =1,2,...,N s , H represents conjugate transpose. Perform eigenvalue decomposition on the covariance matrix R, and the eigenvector of the covariance matrix r contains two parts:

[0033]

[0034] The eigenvectors after decomposition of the covariance matrix R are sorted from large to small according to the eigenvalue size. Where u1 is the eigenvector with the largest eigenvalue, is the eigenvector corresponding to other smaller eigenvalues; represents the maximum eigenvalue, and u1 constitutes the signal subspace U S , U S =u1; the other part is MN c -1 other smaller eigenvalue The corresponding eigenvector U N , including MN c -1 feature u mk, U N Construct the noise subspace, mk is the feature serial number;

[0035] Using the noise subspace U N Orthogonality with the signal subspace, construct the 2D-MUSIC spectrum function P(r,θ):

[0036]

[0037] Based on the spectral function, the parameter estimation problem of distance r and angle θ is transformed into the following two-dimensional optimization problem:

[0038] argmaxP(r,θ)str l ≤r≤r u ,θ l ≤θ≤θ u ;

[0039] Among them [r l ,r u ] is the observation interval of distance r, [θ l ,θ u ] is the observation interval of angle θ, r l is the minimum distance, r u Maximum distance, θ l is the minimum angle, θ u Maximum angle.

[0040] Step 2: Quick rough estimate:

[0041] Step 2 mainly uses the dung beetle optimization idea to quickly iterate and obtain the solution to the above two-dimensional optimization problem.

[0042] At the tth iteration, the distance angle optimization parameter of the i-th dung beetle in the population is It is expressed as:

[0043]

[0044] Where L represents the number of dung beetles in the population, i is the dung beetle serial number variable, and r i 1 and They belong to [r l ,r u ] and [θ l ,θ u] is an independent random variable. There are four different types of dung beetles in the dung beetle population, which simulate different behaviors of dung beetles in nature to update the distance angle parameters: a1 rolling dung beetles, a2 breeding dung beetles, a3 small dung beetles and (L-a1-a2-a3) stealing dung beetles. In each iteration, the rolling dung beetle will update its parameters first, and the other three dung beetles will be updated in parallel according to the updated parameters of the rolling dung beetle. The updated optimized parameters of the rolling dung beetle are used as the distance angle optimization parameters for the next iteration. i=1,2,...,a1, substitute the optimization target spectrum function, and the dung beetle optimization parameter with the largest corresponding spectrum function value calculated at this time is called the local optimal parameter for the next iteration This local optimal parameter will be used to update the parameters of the other three dung beetles in this iteration. At the end of each iteration, the new distance angle parameters of the four dung beetles are substituted into the spectral function to calculate the corresponding P i t+1 Among them, the distance angle optimization parameter with the minimum spectral function value is called the worst parameter The distance angle optimization parameter corresponding to the maximum spectrum function value at this time is called the global optimal parameter That is, the optimal solution to the two-dimensional optimization problem in the current iteration.

[0045] The specific update rules for the four types of dung beetles are as follows:

[0046] 1) The rolling dung beetle performs straight-line rolling behavior in barrier-free mode with a probability of 90%. The update rule of the straight-line rolling behavior is:

[0047]

[0048] Among them, γ, k and b are all linear rolling behavior update parameters, γ is ±1, k∈(0,0.2], b∈(0,1), and represent the distance angle optimization parameters of the i-th dung beetle at the t-th iteration and the t-1-th iteration, respectively. is the worst parameter of the tth iteration.

[0049] The dancing behavior with obstacle mode is performed with a probability of 10%. The update rule of the dancing behavior with obstacle mode can be expressed as:

[0050]

[0051] Where φ is a dancing behavior random variable, and its value range is [0,π].

[0052] 2) The parameter update rule for breeding dung beetles is:

[0053]

[0054] in is the local optimal parameter of the tth iteration; b1 and b2 are the update parameters of the breeding dung beetle, which are independent random vectors of size 1×2; the intermediate quantity and Further written as:

[0055]

[0056] The minimum amount Z lb =[r l ,θ l ] T , maximum amount Z ub =[r u ,θ u ] T , T1 represents the maximum number of iterations of dung beetle optimization.

[0057] 3) The parameter update rule of the dung beetle is:

[0058]

[0059] Among them, c1 and c2 are the update parameters of the dung beetle. c1 is a random number that obeys the normal distribution, c2 is a random vector with a value range of (0,1), and the intermediate quantity and It can be further written as:

[0060]

[0061] in is the global optimal parameter of the tth iteration.

[0062] 4) The parameter update rule for the stealing dung beetle is:

[0063]

[0064] Where d and g are the update parameters of the stealing dung beetle, d is a constant, and g is a random vector that follows a normal distribution.

[0065] When the number of iterations reaches the maximum allowed number T1, the new distance angle parameters of the four dung beetles are substituted into the spectrum function to calculate the corresponding P i t+1 , the new distance angle parameter with the largest spectrum function value is the global optimal parameter Global optimal parameters This is the final result of a quick rough estimate.

[0066] Step 3: High-precision detailed estimation:

[0067] High-precision fine estimation Iterates along the gradient direction to find the exact value of the spectrum peak, where the initial value of the iteration is the result of the fast rough estimation Since the target spectral function has high dimension and the derivative calculation takes a long time, a two-dimensional finite difference is used instead of a partial derivative. The spectral function is calculated at point The gradients G(r) and G(θ) with respect to distance and angle are expressed as:

[0068]

[0069] Where h represents the difference interval, G(r) represents the gradient of the spectral function with respect to the distance parameter, and G(θ) represents the gradient of the spectral function with respect to the angle parameter. represents the distance parameter value at the tth iteration, represents the angle parameter value at the tth iteration. The parameter update rule can be expressed as:

[0070]

[0071] Among them l r Represents the learning rate of distance parameter update, l θ Represents the learning rate of the angle parameter update. When the number of iterations reaches the maximum allowed number T2, That is the final distance angle joint parameter estimation value of the OFDM signal.

[0072] Simulation experiment:

[0073] Using the Monte Carlo method, the distance angle parameter estimation RMSE of the technical solution of the present invention is compared with other technical solutions: solution 1 RD-MUSIC, solution 2 2D-MUSIC and solution 3 2D-ESPRIT. The root mean square error RMSE of the distance and angle parameters is defined as:

[0074]

[0075] Where N t is the Monte Carlo number, and is the estimated value of distance and angle in the nth Monte Carlo experiment, r and θ are the true values ​​of distance and angle respectively. Assume that the source position (angle, distance) is (35°, 41.775m), the number of uniform linear array antennas at the receiving end is 16, the array element spacing is λ / 2, the number of OFDM subcarriers is 256, the subcarrier spacing is 600kHz, the number of Monte Carlo is 1000, the total number of dung beetles in the population is L30, the number of rolling dung beetles a1 is 6, the number of breeding dung beetles a2 is 6, the number of small dung beetles a3 is 7, the maximum number of iterations of fast rough estimation T1 is 80, the maximum number of iterations of high-precision fine estimation T2 is 200, and the distance and angle parameter observation spaces are [0, 50m] and [-90°, 90°] respectively. In order to further illustrate the limiting relationship between the estimation accuracy and the search step size in the original technical scheme, the scheme 1 RD-MUSIC and scheme 2 2D-MUSIC with (angle, distance) step sizes of (0.3°, 0.05m) and (0.01°, 0.01m) were set in the experiment for comparison.

[0076] Figure 1 (a) is the change of angle RMSE of different technical solutions when the signal-to-noise ratio is 0-25dB. The angle RMSE of the technical solution of the present invention is significantly smaller than that of solution one RD-MUSIC and solution three 2D-ESPRIT. When solution two 2D-MUSIC adopts an angle search step of 0.3°, the angle RMSE of the technical solution of the present invention is significantly smaller than that of solution two 2D-MUSIC. When solution two 2D-MUSIC adopts an angle search step of 0.01°, the angle RMSE of the technical solution of the present invention is equivalent to that of solution two 2D-MUSIC.

[0077] Figure 1 (b) is the change of distance RMSE of different technical solutions when the signal-to-noise ratio is 0-25dB. The distance RMSE of the technical solution of the present invention is significantly smaller than that of the third solution 2D-ESPRIT. When the distance RMSE of the first solution RD-MUSIC and the second solution 2D-MUSIC is 0.05m, the distance RMSE of the technical solution of the present invention is significantly smaller than that of the two technical solutions. When the distance RMSE of the first solution RD-MUSIC and the second solution 2D-MUSIC is 0.01m, the distance RMSE of the technical solution of the present invention is generally equivalent to that of the two solutions. However, when the signal-to-noise ratio is greater than 15dB, the distance RMSE of the technical solution of the present invention still decreases with the increase of the signal-to-noise ratio, while the distance RMSE of the first solution RD-MUSIC and the second solution 2D-MUSIC enters a plateau period and no longer decreases with the increase of the signal-to-noise ratio.

[0078] Figure 2 (a) and Figure 2(b) respectively show the angle and distance estimation performance of the technical solution of the present invention under different numbers of antennas when the number of subcarriers is 256. Figure 3 (a) and Figure 3 (b) The angle and distance estimation performance of the present invention under different numbers of subcarriers when the number of antennas is 16. Figure 2 (a) and Figure 3 (a) It can be found that the performance of angle estimation will improve with the increase of the number of antennas or the number of subcarriers, but the number of antennas has a greater impact on the performance of angle estimation, especially when the number of antennas is relatively small. Figure 2 (b) and Figure 3 (b) It can be found that the performance of distance estimation will also improve with the increase of the number of antennas or the number of subcarriers. However, it is obvious that the number of subcarriers has a more obvious impact on distance estimation.

[0079] The following table compares the complexity of different technical solutions in different scenarios. As the number of subcarriers and antennas increases, the complexity of different technical solutions increases. When the search step size of 2D-MUSIC in solution 2 is set to (0.01°, 0.01m), its complexity is about 10 times that of the technical solution of the present invention. 4 When the search step size of RD-MUSIC in solution 1 is set to (0.01°, 0.01m), its complexity is about 10 times that of the technical solution of the present invention. 3 When the search step size of RD-MUSIC in Scheme 1 and 2D-MUSIC in Scheme 2 is set to (0.3°, 0.05m), the complexity of the technical solution of the present invention is still 10-100 times lower than that of the two solutions. The complexity of the technical solution of the present invention is slightly higher than that of 2D-ESPRIT in Scheme 3, that is, the complexity is not 10 times higher.

[0080]

Claims

1. A distance angle joint parameter estimation method based on OFDM signal, characterized in that: Includes steps: Objective function establishment steps: use the vector form of the channel frequency response to obtain the covariance matrix of the channel frequency response, then perform eigenvalue decomposition on the covariance matrix of the channel frequency response to obtain the noise subspace, and use the noise subspace and the steering vector in the vector form of the channel frequency response to construct the spectral function; The parameter estimation problem of distance and angle is transformed into a two-dimensional optimization problem of solving the distance value and angle value corresponding to the maximum of the spectrum function within the distance range and the angle range; Rough estimation step: performing a global search on the two-dimensional optimization problem and outputting a rough search spectrum peak position; Fine estimation step: Based on the coarse search of the spectrum peak position, a high-precision local fine search is performed, and the final estimated distance value and angle value of the OFDM signal are output for OFDM positioning.

2. The method according to claim 1, characterized in that: The spectral function P(r,θ) is expressed as: Among them, P(r,θ) is the spectral function corresponding to the distance r and the angle θ, U N is the noise subspace, d(r,θ) is the steering vector corresponding to the distance r and the angle θ, H represents the conjugate transpose.

3. The method according to claim 2, characterized in that: Steering vector a M (θ) is the steering angle component, is the turning distance component, represents the Kronecker product; to M (θ)=[1,e -j2πd / λsinθ ,...,And -j2π(m-1)d / λsinθ ,...,And -j2π(M-1)d / λsinθ ] T Where d is the array element spacing of the OFDM antenna, d = λ / 2, λ represents the carrier wavelength, Δf is the subcarrier spacing, N s Indicates the number of samples, the number of subcarriers is N c , the total number of array elements is M, the array element number variable m=1,2,...,M, the subcarrier number variable k=1,2,...,N c , c represents the speed of light, T represents transposition, and e is a natural constant.

4. The method according to claim 3, characterized in that: The noise subspace is composed of eigenvectors corresponding to smaller eigenvalues ​​except the eigenvector corresponding to the maximum eigenvalue after eigenvalue decomposition is performed on the covariance matrix of the channel frequency response.

5. The method according to claim 3 or 4, characterized in that: The two-dimensional optimization problem is expressed as: argmaxP(r,θ)str l ≤r≤r u ,i l ≤θ≤θ u ; Among them, [r l ,r u ] is the observation interval of distance r, r l is the minimum distance, r u The maximum distance; [θ l ,θ u ] is the observation interval of angle θ, θ l is the minimum angle, θ u Maximum angle.

6. The method according to claim 1, characterized in that: The global search uses the dung beetle optimization algorithm.

7. The method according to claim 1, characterized in that: In the global search using the dung beetle optimization algorithm, each iteration uses four dung beetle update rules, namely, rolling dung beetles, breeding dung beetles, small dung beetles and stealing dung beetles, to update the distance and angle values. When the number of iterations reaches the maximum number allowed by the dung beetle optimization algorithm, the distance and angle values ​​obtained by the four dung beetle update rules are substituted into the spectrum function, and the distance and angle values ​​with the largest spectrum function values ​​are taken as the global optimal parameters. The global optimal parameters are the rough search spectrum peak position.

8. The method according to claim 1, characterized in that: The high-precision local fine search adopts the stochastic gradient descent method, which uses the rough search spectrum peak position as the iteration initial value and iteratively searches for the exact value of the spectrum peak of the spectrum function in the gradient direction.

9. The method according to claim 8, characterized in that In the stochastic gradient descent method, the spectral function is at the point The distance gradient G(r) and angle gradient G(θ) are expressed as: in, represents the distance value at the tth iteration of the stochastic gradient descent method, represents the angle value at the tth iteration of the stochastic gradient descent method; h represents the difference interval; The update rules of distance value and angle value during the iteration are: Among them l r Represents the learning rate of distance parameter update, l θ Represents the learning rate of angle parameter update; represents the distance value at the t+1th iteration of the stochastic gradient descent method, Represents the angle value at the t+1th iteration of the stochastic gradient descent method; When the number of iterations reaches the maximum number allowed by the stochastic gradient descent method, the distance value and angle value obtained by the current iteration update are the final estimated distance value and angle value of the OFDM signal.

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