A method for joint estimation of direction of arrival, time delay and carrier frequency offset of an array antenna

Abstract

The application discloses a kind of array antenna wave direction, time delay and carrier frequency offset joint estimation method, comprising: the signal receiving model of array element is established, based on signal receiving model, the matrix representation form of each array element received signal is constructed and is handled, and the signal matrix of each array element is constructed;Signal group is divided according to subcarrier, and the signal matrix of each array element is stacked, and the stacked matrix is constructed;The stacked matrix is written into the form of tensor and is parallel factor decomposition, and the matrix containing DOA, time delay and carrier frequency offset is obtained respectively;From the matrix after parallel factor decomposition, DOA and time delay are estimated by spectral peak search and least square method according to the corresponding relationship respectively, the pairing of DOA and time delay is realized;And carrier frequency offset is estimated using the matrix after decomposition.The method of the application has high estimation accuracy for each parameter, and better robustness.

Description

Technical Field

[0001] The present invention relates to the field of array signal processing, and in particular to a method for jointly estimating the direction of arrival, time delay and carrier frequency offset of an OFDM signal. Background Art

[0002] Orthogonal Frequency-Division Multiplex (OFDM) is gaining increasing attention in wireless communications. While this technology is highly robust against multipath fading, it also has certain drawbacks. During OFDM signal reception, the inherent physical characteristics of the oscillator prevent the transmitter and receiver from generating carriers with identical frequencies, resulting in carrier frequency deviation and impacting the direction-finding and positioning of the OFDM signal source. Furthermore, OFDM signals propagate along multiple paths due to the presence of scatterers, each with a different direction of arrival (DOA) and time of arrival at the array.

[0003] Currently, there are many joint estimation methods for DOA and delay, but considering the carrier frequency offset of OFDM signals further complicates the system model and makes parameter estimation more difficult. Existing methods for OFDM signal direction of arrival, delay, and carrier frequency offset estimation are relatively limited. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for jointly estimating the direction of arrival, time delay and carrier frequency offset of an array antenna, so as to achieve high-precision parameter estimation of an OFDM signal.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna, comprising:

[0007] Establishing a signal reception model for the array element, constructing a matrix representation of the signal received by each array element based on the signal reception model and processing the matrix to construct a signal matrix for each array element;

[0008] Divide the signal groups by subcarriers, and stack the signal matrices of each array element to construct a stacking matrix;

[0009] Write the stacked matrix into tensor form and perform parallel factorization to obtain matrices containing DOA, delay and carrier frequency offset respectively;

[0010] The matrix after parallel factor decomposition is used to estimate the DOA and time delay through spectrum peak search and least squares method according to the corresponding relationship, thereby achieving the pairing of DOA and time delay; and the carrier frequency offset is estimated using the decomposed matrix.

[0011] Furthermore, establishing a signal reception model of an array element includes:

[0012] Assume that the number of OFDM signal subcarriers is N, the number of subcarriers transmitting data is P, and the frequency of the pth carrier is f p The signal cyclic prefix is ​​L; the number of uniform linear array elements is M, the wavelength is λ, and the element spacing is d; there is an OFDM signal source in space, Q is the number of scatterers in space, and the number of signal time slots is K; the first group of signals from the OFDM signal source received by the mth array element in the kth time slot can be expressed as the following model:

[0013]

[0014] Where E=diag{1,e 2πΔf ,…,e 2π(N-1)Δf}·F P′ , F P′ represents the first P′ columns of the matrix obtained by performing inverse discrete Fourier transform on the received OFDM signal, e represents a natural constant, j is an imaginary unit, P′ represents the number of subcarriers contained in the first group of signals, Δf = f p+1 -f p represents the spacing between adjacent carriers of OFDM signal, and f offset Indicates carrier frequency deviation; s(k)=[s1(k),…,s P′ (k)] T represents a set of OFDM signals sent by the k-th time slot signal source, where s1(k) represents the OFDM signal corresponding to the first subcarrier, and the superscript T represents the transposition operation; D m (H1) means taking the mth row of the channel matrix H1 for diagonalization, H1 means taking the first P′ columns of H; and H=ABF T , where the array flow pattern A=[a(θ1),a(θ2),…,a(θ Q+1 )], where the qth (q=1,2,...,Q+1)th steering vector θ q represents the DOA corresponding to the qth path including the direct path, B=diag[β1,…,β Q+1 ] represents the path attenuation matrix, where β1 represents the attenuation corresponding to the first path, and the matrix F containing all delay information is F = [f1,f2,…,f P ] T ,in τ1 represents the path delay corresponding to the first path, f p Indicates the p-th subcarrier frequency.

[0015] Furthermore, constructing a matrix representation of the signal received by each array element based on the signal reception model and processing the matrix representation to construct a signal matrix for each array element includes:

[0016] The first group of signals received by the mth array element in each time slot is written in matrix form as It is vectorized, and then the first group of signals received by all array elements in each time slot are vectorized and stacked in columns, which is expressed as Where vec(·) represents vectorization processing, ⊙ represents Khatri-Rao product;

[0017] The difference between each group of received signals is that the subcarriers used to transmit data are different, namely 1~P′, 2~P′+1, …, I~P, where I is the total number of signal groups; therefore, the i-th group of signals received by the m-th array element can be expressed as the signal matrix The phase shift matrix The phase shift is caused by different carrier waves in different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It represents the matrix consisting of the i-th to P-i+1-th columns of H.

[0018] Furthermore, the division of the signal groups by subcarriers and stacking of the signal matrices of each array element to construct a stacked matrix includes:

[0019] Signal Matrix The left-multiplied phase shift matrix is ​​expressed as:

[0020]

[0021] The matrices on the right side of the above equation are stacked row by row to form a new signal matrix that can be written in the form of Khatri-Rao product, as shown below:

[0022]

[0023] Among them, H1, H2…H I They represent the columns 1 to P′, 2 to P′+1, …, I to P of H respectively; The superscript Q in the matrix indicates the power; represents the first P' rows of the matrix F, and the matrix G satisfies:

[0024]

[0025] The spatial smoothing method is used, the number of smoothing times is J, and the array flow type is represented by A1. Compared with the original array flow type A, A1 takes the first J rows, so each sub-array contains I-J+1 array elements, so the signal matrix is ​​taken The first sub-matrix of The smoothed data can be stacked again by rows to form a new stacked matrix:

[0026]

[0027] in The superscript represents the power; and the matrix M satisfies:

[0028]

[0029] The stacked matrix after adding noise is expressed as:

[0030]

[0031] Where W represents the noise matrix.

[0032] Furthermore, the stacked matrix is ​​written into a tensor form and parallel factorized to obtain matrices containing DOA, delay, and carrier frequency offset, respectively, including:

[0033] Since the matrix B is a diagonal matrix, the stacked matrix can be written as follows:

[0034]

[0035] The matrix is ​​stacked in three-dimensional space to obtain a three-dimensional array, which can be decomposed into parallel factors to obtain M⊙G, as well as The estimated results of

[0036] Then M⊙G and The estimation results are stacked in three-dimensional space to form two new three-dimensional arrays. The estimated values ​​of DOA information matrix M, delay information matrix G and carrier frequency offset information matrix E can be obtained by performing parallel factor decomposition on them respectively. and express.

[0037] Furthermore, the matrix decomposed by the parallel factorization estimates the DOA and the time delay by using the spectrum peak search and the least square method according to the corresponding relationship, thereby achieving the pairing of the DOA and the time delay, including:

[0038] Pair Matrix and Further parameter estimation is performed from the matrix Take the qth column as Taking the logarithm and then the imaginary part of each element in the column vector can get b(τ q )=2πτ q [0,1,…,I-1] T , let t = [0, 1, ..., I-1] T ; define T1 = [1 I×1 ,t], where 1 I×1 represents an L×1 dimensional all-one vector, then:

[0039]

[0040] Where ε1 represents the error parameter, from which the delay τ can be estimated q ;

[0041] After calculating the delay, take the minimum delay and record it in the delay matrix Column index of Column vector corresponding to the same column index in :

[0042]

[0043] Find the covariance matrix R of the column vector q , perform eigendecomposition on the covariance matrix and obtain the noise subspace The spectrum peak search function is determined according to the orthogonality of the subspace and the DOA is estimated; The DOA solved in a column corresponds to The delays solved for the same column in , the two match each other.

[0044] Furthermore, estimating the carrier frequency offset using the decomposed matrix includes:

[0045] From the matrix Take the pth column as:

[0046]

[0047] Since the matrix after tensor decomposition The order of the columns of the original matrix E will be transformed, so the p-th column here may not be the same as the p-th column of E, so use express;

[0048] Taking the logarithm of each element in the column vector yields:

[0049]

[0050] Let m = [0, 1, ..., N-1] T , define T2=[1 N×1 ,m], where 1 N×1represents an N×1 dimensional all-1 vector, then:

[0051]

[0052] Where ε2 represents the error parameter, from which we can estimate

[0053] Calculate the carrier frequency offset:

[0054]

[0055] Here Consistent with P′.

[0056] A receiving station, after receiving an OFDM signal, performs signal processing according to the array antenna direction of arrival, time delay and carrier frequency offset joint estimation method.

[0057] A terminal device includes a processor, a memory, and a computer program stored in the memory; characterized in that when the processor executes the computer program, it implements the method for jointly estimating the array antenna direction of arrival, delay and carrier frequency offset.

[0058] A computer-readable storage medium having a computer program stored therein; wherein when the computer program is executed by a processor, the method for jointly estimating the direction of arrival, time delay and carrier frequency offset of an array antenna is implemented.

[0059] Compared with the prior art, the present invention has the following technical features:

[0060] When direction finding and positioning of OFDM signals requires consideration of carrier frequency offset, the present invention enables joint estimation of multiple parameters, including direction of arrival (DOA), delay, and carrier frequency offset. By utilizing methods such as data stacking, spatial smoothing, and parallel factorization, the matrix containing the parameters to be estimated is separated, facilitating subsequent solution. This method achieves high estimation accuracy for each parameter and exhibits good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a schematic diagram of the receiving station array model;

[0062] Figure 2 It is the DOA estimation spatial spectrum in the embodiment;

[0063] Figure 3 : is a relationship diagram between DOA estimation accuracy and signal-to-noise ratio in the embodiment;

[0064] Figure 4 This is a diagram showing the relationship between delay estimation accuracy and signal-to-noise ratio in an embodiment;

[0065] Figure 5Graph showing the relationship between carrier frequency offset estimation accuracy and signal-to-noise ratio in an embodiment. DETAILED DESCRIPTION

[0066] During OFDM signal positioning, the inherent characteristics of the system make carrier frequency deviation difficult to avoid, which can affect the direction-finding accuracy of the signal. To achieve high-precision parameter estimation of OFDM signals, the present invention provides a method for high-precision joint estimation of DOA, delay, and carrier frequency deviation through methods such as smoothing and parallel factorization. The method is applied to a signal receiving end, which can be, for example, an observation station composed of a multi-antenna array. The method comprises the following steps:

[0067] Step 1: Establish a signal reception model for the array element, construct a matrix representation of the signal received by each array element based on the signal reception model, process the matrix representation, and construct a signal matrix for each array element.

[0068] Establish an OFDM signal parameter estimation model: Assume that the number of OFDM signal subcarriers is N, the number of subcarriers transmitting data is P, and the frequency of the pth carrier is f p ; The signal cyclic prefix is ​​L; the number of array elements in the uniform linear array is M, the wavelength is λ, and the array element spacing is d; there is an OFDM signal source in space, Q is the number of scatterers in space, and the number of signal time slots is K.

[0069] According to the model assumption, the first group of signals received by the mth array element from the OFDM signal source in the kth time slot can be expressed as the following model:

[0070]

[0071] Where E=diag{1,e 2πΔf ,…,e 2π(N-1)Δf}·F P′ , F P′ represents the first P′ columns of the matrix obtained by performing an N×N-dimensional inverse discrete Fourier transform on the original received signal, e represents a natural constant, j is an imaginary unit, P′ represents the number of subcarriers contained in the first group of signals, and Δf = f p+1 -f p represents the spacing between adjacent carriers of OFDM signal, and f offset Indicates carrier frequency deviation; s(k)=[s1(k),…,s P′ (k)] T represents a set of OFDM signals sent by the k-th time slot signal source, where s1(k) represents the OFDM signal corresponding to the first subcarrier, and the superscript T represents the transposition operation, the same below; D m (H1) means taking the mth row of the channel matrix H1 for diagonalization, H1 means taking the first P′ columns of H; and H=ABFT , where the array flow pattern A=[a(θ1),a(θ2),…,a(θ Q+1 )], where the qth (q=1,2,...,Q+1)th steering vector θ q represents the DOA corresponding to the qth path including the direct path, B=diag[β1,…,β Q+1 ] represents the path attenuation matrix, where β1 represents the attenuation corresponding to the first path, and the matrix F containing all delay information is F = [f1,f2,…,f P ] T ,in τ1 represents the path delay corresponding to the first path, f p Represents the pth subcarrier frequency. This scheme assumes that there are Q scatterers in space. Thus, the OFDM signal has Q+1 paths to the receiver, including a direct path and Q reflected paths. Each reflected path corresponds to an attenuation and delay. This scheme processes the received data and exploits the correspondence between parameters after tensor decomposition (for example, the delay matrix and position matrix obtained after decomposition must have the same number of columns; for example, the second column of the delay matrix and the second column of the position matrix must represent the delay and position for the same path). By estimating the minimum delay, the direct path steering vector can be obtained, because the path with the shortest arrival time at the observation station is definitely the direct path.

[0072] The first group of signals received by the mth array element in each time slot is written in matrix form as It is vectorized, and then the first group of signals received by all array elements in each time slot are vectorized and stacked in columns, which is expressed as Where vec(·) represents vectorization processing, ⊙ represents Khatri-Rao product;

[0073] The difference between each group of received signals is that the subcarriers used to transmit data are different, namely 1~P′, 2~P′+1, …, I~P, where I is the total number of signal groups; therefore, the i-th group of signals received by the m-th array element can be expressed as the signal matrix The phase shift matrix The phase shift is caused by different carrier waves in different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It represents the matrix consisting of the i-th to P-i+1-th columns of H.

[0074] Step 2: Divide the signal groups by subcarriers, and stack the signal matrices of each array element to construct a stacking matrix.

[0075] Signal Matrix The left-multiplied phase shift matrix is ​​expressed as:

[0076]

[0077] The matrices on the right side of the above equation are stacked row by row to form a new signal matrix that can be written in the form of Khatri-Rao product, as shown below:

[0078]

[0079] Among them, H1, H2…H I They represent the columns 1 to P′, 2 to P′+1, …, I to P of H respectively; The superscript Q in the matrix indicates the power; represents the first P' rows of the matrix F, and the matrix G satisfies:

[0080]

[0081] The spatial smoothing method is used, the number of smoothing times is J, and the array flow type is represented by A1. Compared with the original array flow type A, A1 takes the first J rows, so each sub-array contains I-J+1 array elements, so the signal matrix is ​​taken The first sub-matrix of The smoothed data can be stacked again by rows to form a new stacked matrix:

[0082]

[0083] in The superscript represents the power; and the matrix M satisfies:

[0084]

[0085] The stacked matrix after adding noise is expressed as:

[0086]

[0087] Where W represents the noise matrix.

[0088] Step 3: Write the stacked matrix into a tensor form and perform parallel factorization to obtain matrices containing DOA, delay, and carrier frequency offset respectively.

[0089] Since the matrix B is a diagonal matrix, the stacked matrix can be written as follows:

[0090]

[0091] The matrix is ​​stacked in three-dimensional space to obtain a three-dimensional array, which can be decomposed into parallel factors to obtain M⊙G, as well as The estimated results of

[0092] Then M⊙G and The estimation results are stacked in three-dimensional space to form two new three-dimensional arrays. The estimated values ​​of DOA information matrix M, delay information matrix G and carrier frequency offset information matrix E can be obtained by performing parallel factor decomposition on them respectively. and express.

[0093] Step 4: Based on the corresponding relationship, the matrix after parallel factor decomposition is used to estimate the DOA and time delay through spectrum peak search and least square method respectively, so as to achieve the pairing of DOA and time delay.

[0094] Pair Matrix and Further parameter estimation is performed from the matrix Take the qth column as Taking the logarithm and then the imaginary part of each element in the column vector can get b(τ q )=2πτ q [0,1,…,I-1] T , let t = [0, 1, ..., I-1] T ; define T1 = [1 I×1 ,t], where 1 I×1 represents an L×1 dimensional all-one vector, then:

[0095]

[0096] Where ε1 represents the error parameter, from which the delay τ can be estimated q ;

[0097] After calculating the delay, take the minimum delay and record it in the delay matrix Column index of Column vector corresponding to the same column index in :

[0098]

[0099] Find the covariance matrix R of the column vector q , perform eigendecomposition on the covariance matrix and obtain the noise subspace The spectrum peak search function is determined according to the orthogonality of the subspace and the DOA is estimated; The DOA solved in a column corresponds to The delays solved for the same column in , the two match each other.

[0100] Step 5: Estimate the carrier frequency offset from the matrix after parallel factor decomposition.

[0101] From the matrix Take the pth column as:

[0102]

[0103] It should be pointed out that since the matrix after tensor decomposition The order of the columns of the original matrix E will be transformed, so the p-th column here may not be the same as the p-th column of E, so use express.

[0104] Taking the logarithm of each element in the column vector yields:

[0105]

[0106] Let m = [0, 1, ..., N-1] T , define T2=[1 N×1 ,m], where 1 N×1 represents an N×1 dimensional all-1 vector, then:

[0107]

[0108] Where ε2 represents the error parameter, from which we can estimate

[0109] Calculate the carrier frequency offset:

[0110]

[0111] Here Consistent with P′.

[0112] This solution estimates direction of arrival (DOA), while delay estimation leverages the corresponding relationship between the two—that is, matching the minimum path delay with the direction of the direct path. This approach is typically used for direction finding or positioning targets under multipath conditions. Carrier frequency offset estimation addresses potential errors in the system, which must be addressed to achieve high-precision direction and delay estimation. Carrier frequency offset estimation primarily occurs at the OFDM signal receiving end, for example, when the oscillator frequencies at the transmitter and receiver are not completely aligned.

[0113] Example:

[0114] The basic configuration of this embodiment is as follows: a uniform linear array consisting of 7 antenna elements is used, the element spacing is half the wavelength of the incident signal, and the OFDM signal carrier frequency f k =28GHz, bandwidth is 100MHz, total number of subcarriers is 64, number of subcarriers for data transmission is 40, number of time slots is 50, carrier frequency deviation is f offset=0.15ω, where ω=2π / N; the number of spatial smoothing times is 4, the number of data groups is 4, the number of subcarriers transmitting information in each group of data is 37, the observation spatial angle range is [-90°, 90°], and the spatial grid division interval is 0.01.

[0115] Experiment 1: Assume that there are three directions of arrival including the direct path of the OFDM signal, namely θ1 = 45°, θ2 = 0°, and θ3 = 30°. The corresponding relative delays are τ1 = 30ns, τ2 = 60ns, and τ3 = 0ns. The signal-to-noise ratio is -5dB. Figure 2 Figure 2 shows the spatial power spectrum of the proposed method (taking the direct path as an example). As can be seen from the figure, the spatial spectrum of the proposed method exhibits a sharp peak in the target incident direction, demonstrating the effectiveness and accuracy of the proposed method in DOA estimation under low signal-to-noise ratio conditions.

[0116] Experiment 2: Assume that there are three directions of arrival (DOA) including the direct path of the OFDM signal: θ1 = 45°, θ2 = 0°, and θ3 = 30°. The corresponding relative delays are τ1 = 30 ns, τ2 = 60 ns, and τ3 = 0 ns. Error statistics are performed on the DOA, delay, and carrier frequency offset. The signal-to-noise ratio varies from -15 dB to 15 dB, and 200 Monte Carlo experiments are performed. Figure 3 RMSE curve of the DOA estimation accuracy of the method of the present invention as the signal-to-noise ratio changes. It can be seen from the figure that the method of the present invention has a higher angle estimation accuracy. Figure 4 Figure 2 is the RMSE curve of the delay estimation accuracy changing with the signal-to-noise ratio. It can be seen that this method also has a high delay estimation accuracy. Figure 5 The RMSE curve of the carrier frequency offset estimation accuracy as the signal-to-noise ratio changes is shown in FIG. 1 . The curve in the figure shows that the method also has a high accuracy for carrier frequency offset estimation.

[0117] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna, characterized in that: include: Establishing a signal reception model for the array element, constructing a matrix representation of the signal received by each array element based on the signal reception model and processing the matrix to construct a signal matrix for each array element; Divide the signal groups by subcarriers, and stack the signal matrices of each array element to construct a stacking matrix; The stacked matrix is ​​written as a tensor and factored in parallel to obtain matrices containing DOA, delay, and carrier frequency offset, including the estimated value of the DOA information matrix Estimated value of the delay information matrix And the estimated value of the carrier frequency offset information matrix Based on the corresponding relationship between the matrix after parallel factorization, the DOA and time delay are estimated by spectrum peak search and least squares method respectively, thus achieving the pairing of DOA and time delay, including: right and Further parameter estimation is performed from the matrix Take the qth column as Take the logarithm and then the imaginary part of each element in the column vector to get b(τ q )=2πτ q [0,1,…,I-1] T , let t = [0, 1, ..., I-1] T ; define T1 = [1 I×1 ,t], where 1 I×1 represents an L×1 dimensional all-one vector, then: Where e represents a natural constant, j is an imaginary unit, Δf represents the spacing between adjacent carriers of the OFDM signal, I is the total number of signal groups, the superscript T represents the transposition operation, and ε1 represents the error parameter, thereby estimating the delay τ q ; After calculating the delay, take the minimum delay and record it in Column index of Column vector corresponding to the same column index in : Where d is the array element spacing, λ is the wavelength, θ q represents the DOA corresponding to the qth path including the direct path, and J is the smoothing number; Find the column vector c q The covariance matrix R q , perform eigendecomposition on the covariance matrix and obtain the noise subspace The spectrum peak search function is determined according to the orthogonality of the subspace and the DOA is estimated; The DOA solved in a column corresponds to The delays solved for the same column in ,the two are matched with each other; The decomposed matrix is ​​used to estimate the carrier frequency offset; the decomposed matrix is ​​the estimated value of the carrier frequency offset information matrix 2. The method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna according to claim 1, wherein: The establishing of the signal receiving model of the array element includes: Assume that the number of OFDM signal subcarriers is N, the number of subcarriers transmitting data is P, and the frequency of the pth carrier is f p The signal cyclic prefix is ​​L; the number of uniform linear array elements is M; there is an OFDM signal source in space, Q is the number of scatterers in space, and the number of signal time slots is K; the first group of signals from the OFDM signal source received by the mth array element in the kth time slot is represented by the following model: Where E=diag{1,e 2πΔf ,…,e 2π(N-1)Δf }·F P′ , F P′ It represents the first P′ columns of the matrix obtained by performing inverse discrete Fourier transform on the received OFDM signal, where P′ represents the number of subcarriers contained in the first group of signals, and Δf = f p+1 -f p , and f offset Indicates carrier frequency deviation; s(k)=[s1(k),…,s P′ (k)] T represents a set of OFDM signals sent by the kth time slot signal source, where s1(k) represents the OFDM signal corresponding to the first subcarrier; D m (H1) means taking the mth row of the channel matrix H1 for diagonalization, H1 means taking the first P′ columns of H; and H=ABF T , where the array flow pattern A=[a(θ1),a(θ2),…,a(θ Q+1 )], where the qth (q=1,2,...,Q+1)th steering vector B=diag[β1,…,β Q+1 ] represents the path attenuation matrix, where β1 represents the attenuation corresponding to the first path, and the matrix F containing all delay information is F = [f1,f2,…,f P ] T ,in τ1 represents the path delay corresponding to the first path, f p Indicates the p-th subcarrier frequency.

3. The method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna according to claim 2, wherein: The step of constructing a matrix representation of a signal received by each array element based on the signal reception model and processing the matrix representation to construct a signal matrix of each array element includes: The first group of signals received by the mth array element in each time slot is written in matrix form as It is vectorized, and then the first group of signals received by all array elements in each time slot are vectorized and stacked in columns, which is expressed as Where vec(■) represents vectorization processing and represents Khatri-Rao product; The difference between each group of received signals is that the subcarriers used for transmission data are different, namely 1~P′, 2~P′+1, …, I~P; therefore, the i-th group of signals received by the m-th array element is represented by the signal matrix The phase shift matrix The phase shift is caused by different carrier waves in different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It represents the matrix consisting of the i-th to P-i+1-th columns of H.

4. The method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna according to claim 3, wherein: The dividing of the signal groups by subcarriers and stacking the signal matrices of each array element to construct a stacking matrix includes: Signal Matrix The left-multiplied phase shift matrix is ​​expressed as: The matrices on the right side of the above equation are stacked row by row to form a new signal matrix written in the form of Khatri-Rao product, as shown below: Among them, H1, H2…H I They represent the columns 1 to P′, 2 to P′+1, …, I to P of H respectively; The superscript Q in the matrix indicates the power; represents the first P' rows of the matrix F, and the matrix G satisfies: Using the spatial smoothing method, the array flow type is represented by A1. Compared with the original array flow type A, A1 takes the first J rows, so each sub-array contains I-J+1 array elements, so the signal matrix is The first sub-matrix of The smoothed data is stacked again by rows to form a new stacked matrix: in The superscript represents the power; and the matrix M satisfies: The stacked matrix after adding noise is expressed as: Where W represents the noise matrix.

5. The method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna according to claim 4, wherein: The stacked matrix is ​​written into a tensor form and subjected to parallel factor decomposition to obtain matrices containing DOA, delay, and carrier frequency offset, respectively, including: Since the matrix B is a diagonal matrix, the stacked matrix can be written as follows: The matrix is ​​stacked in three-dimensional space to obtain a three-dimensional array, which is then subjected to parallel factor decomposition to obtain M⊙G, as well as The estimated results of Then M⊙G and The estimation results are stacked in three-dimensional space to form two new three-dimensional arrays, which are then decomposed into parallel factors to obtain the estimated values ​​of the DOA information matrix M, the time delay information matrix G, and the carrier frequency offset information matrix E, respectively. and express.

6. The method for jointly estimating direction of arrival, time delay, and carrier frequency offset of an array antenna according to claim 5, wherein: The estimating the carrier frequency offset by using the decomposed matrix includes: From the matrix Take the pth column as: Since the matrix after tensor decomposition The order of the columns of the original matrix E will be transformed, so the p-th column here may not be the same as the p-th column of E, so use express; Taking the logarithm of each element in the column vector yields: Let m = [0, 1, ..., N-1] T , define T2=[1 N×1 ,m], where 1 N×1 represents an N×1 dimensional all-1 vector, then: Where ε2 represents the error parameter, from which we estimate Calculate the carrier frequency offset: Here Consistent with P′.

7. A receiving station, which, after receiving an OFDM signal, performs signal processing according to the method for jointly estimating direction of arrival, time delay and carrier frequency offset of an array antenna according to any one of claims 1 to 6.

8. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, it implements the method for jointly estimating the direction of arrival, time delay and carrier frequency offset of the array antenna according to any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the method for jointly estimating the direction of arrival, time delay and carrier frequency offset of an array antenna according to any one of claims 1 to 6 is implemented.

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