Joint estimation method for direction of arrival, time delay and carrier frequency offset of array antenna

Abstract

The invention discloses an array antenna direction of arrival, time delay and carrier frequency offset joint estimation method, which comprises the following steps of: establishing a signal receiving model of array elements, constructing a matrix representation form of each array element receiving signal based on the signal receiving model, processing the matrix representation form, and constructing a signal matrix of each array element; dividing signal groups according to subcarriers, and stacking the signal matrix of each array element to construct a stacked matrix; writing the stacked matrix in a tensor form and performing parallel factorization to obtain matrixes respectively containing DOA, time delay and carrier frequency offset; estimating DOA (direction of arrival) and time delay through spectral peak search and a least square method according to a corresponding relation by the matrix after the parallel factorization, and realizing pairing of the DOA and the time delay; and estimating the carrier frequency offset by using the decomposed matrix. The method provided by the invention has relatively high estimation precision for each parameter and relatively good robustness at the same time.

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 deviation of an OFDM signal. Background Art

[0002] Orthogonal Frequency-Division Multiplex (OFDM) has received increasing attention in wireless communications. This technology is highly robust against multipath fading, but it also has certain defects. In the process of receiving OFDM signals, the inherent physical characteristics of the oscillator will cause the transmitter and receiver to not generate carriers of the same frequency, which will in turn cause carrier frequency deviation, affecting the direction finding and positioning of the OFDM signal source. In addition, during the propagation of OFDM signals, multiple paths will be generated due to the presence of scatterers, and the direction of arrival (DOA) and time of arrival of each path to the array are different.

[0003] There are many joint estimation methods for DOA and delay, but considering the carrier frequency offset of OFDM signals will make the system model more complex and the parameter estimation more difficult. There are relatively few existing methods for OFDM signal direction of arrival, delay and carrier frequency offset estimation. 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 receiving model of the array element, constructing a matrix representation of the received signal of each array element based on the signal receiving model and processing the matrix representation, so as to construct a signal matrix of each array element;

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

[0009] The stacked matrix is ​​written in the form of a tensor and factorized in parallel to obtain matrices containing DOA, delay, and carrier frequency offset respectively;

[0010] Based on the corresponding relationship of the matrix decomposed by parallel factors, DOA and time delay are estimated by spectrum peak search and least square method respectively, so as to achieve pairing of DOA and time delay; and the carrier frequency offset is estimated by using the decomposed matrix.

[0011] Furthermore, the establishing of the signal receiving model of the array element includes:

[0012] Assume that the number of OFDM signal subcarriers is N, the number of subcarriers for data transmission 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 received from the OFDM signal source 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 signals, and f offset represents the 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, and the superscript T represents the transposition operation; D m (H1) means taking the mth row of the channel matrix H1 and diagonalizing it, 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 pth subcarrier frequency.

[0015] Furthermore, the 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 the signal matrix of 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 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 of different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It means taking the matrix consisting of the i-th to P-i+1-th columns of H.

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

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

[0020]

[0021] The matrices on the right side of the above formula 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 1~P′, 2~P′+1, …, I~P columns 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, and the number of smoothing times is J. 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 subarray of The smoothed data can be stacked again by rows to form a new stacked matrix:

[0026]

[0027] in The superscript indicates 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 factor decomposition is performed 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 in parallel to obtain M⊙G, as well as The estimated results of

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

[0037] Furthermore, the matrix decomposed by parallel factors estimates DOA and time delay by spectrum peak search and least square method respectively according to the corresponding relationship, so as to achieve pairing of DOA and 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-1 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 The 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 for a column corresponds to The delays solved for the same column in , the two match each other.

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

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

[0046]

[0047] Since the tensor decomposition matrix The order of the columns of the original matrix E will change, so the p-th column here may not be the same as the p-th column of E, so we 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 deviation:

[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 comprises a processor, a memory and a computer program stored in the memory; the characteristic is that when the processor executes the computer program, the method for jointly estimating the direction of arrival, delay and carrier frequency offset of the array antenna is implemented.

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

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

[0060] When the direction finding and positioning of OFDM signals needs to consider the carrier frequency offset, the present invention can realize the joint estimation of multiple parameters of direction of arrival, delay and carrier frequency offset. The separation of the matrix containing the parameters to be estimated is realized by using methods such as data stacking, spatial smoothing and parallel factor decomposition, so as to facilitate subsequent solution. The method has high estimation accuracy for each parameter and 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 relationship diagram between delay estimation accuracy and signal-to-noise ratio in the embodiment;

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

[0066] Since the inherent characteristics of the system itself make it difficult to avoid carrier frequency deviation during OFDM signal positioning, the direction finding positioning accuracy of the signal will be affected. In order to achieve high-precision parameter estimation of OFDM signals, the present invention provides a method for achieving high-precision joint estimation of DOA, delay and carrier frequency deviation through methods such as smoothing and parallel factor decomposition. 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 receiving model for the array element, construct a matrix representation of the signal received by each array element based on the signal receiving model and process the matrix to 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 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.

[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, Δf = f p+1 -f p represents the spacing between adjacent carriers of OFDM signals, and f offset represents the carrier frequency deviation; s(k)=[s1(k),…,s P′ (k)] T represents a set of OFDM signals sent by the signal source in the kth time slot, 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 and diagonalizing it, 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 Indicates the pth subcarrier frequency. In this scheme, it is assumed that there are Q scatterers in the space, so there are Q+1 paths when the OFDM signal reaches the receiving end, including a direct path and Q reflected paths, and each reflected path corresponds to 1 attenuation and delay; this scheme processes the received data and uses the correspondence between the parameters after tensor decomposition (for example, after decomposition, the delay matrix and the position matrix are obtained, and the number of columns of the two matrices must be the same, for example, the second column of the delay matrix and the second column of the position matrix must be the delay and position under the same path). In this way, by estimating the minimum delay, the direct path steering vector can be obtained, because the one with the shortest time to reach the observation station must be direct.

[0072] The first group of signals received by the mth array element in each time slot is written in matrix form as 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 of different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It means taking the matrix consisting of the i-th to P-i+1-th columns of H.

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

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

[0076]

[0077] The matrices on the right side of the above formula 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 1~P′, 2~P′+1, …, I~P columns 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, and the number of smoothing times is J. 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 subarray of The smoothed data can be stacked again by rows to form a new stacked matrix:

[0082]

[0083] in The superscript indicates 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 factor decomposition 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 in parallel to obtain M⊙G, as well as The estimated results of

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

[0093] Step 4: Based on the matrix after parallel factor decomposition, the DOA and time delay are estimated by spectrum peak search and least square method according to the corresponding relationship, 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-1 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 The 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 for 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 tensor decomposition matrix The order of the columns of the original matrix E will change, so the p-th column here may not be the same as the p-th column of E, so we 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 deviation:

[0110]

[0111] Here Consistent with P′.

[0112] This solution implements DOA estimation, and the delay estimation is to use the corresponding relationship between the two, that is, the minimum path delay matches the direction of the direct path, generally for target direction finding or positioning under multipath conditions. The carrier frequency offset is estimated because this error may exist in the system. To achieve high-precision estimation of direction and delay, it must be processed. The estimation of carrier frequency offset mainly occurs at the receiving end of the OFDM signal, such as when the oscillator frequencies of the transmitter and receiver are not completely consistent.

[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 wave arrival directions including the direct path of the OFDM signal, namely θ1 = 45°, θ2 = 0°, θ3 = 30°, and the corresponding relative delays are τ1 = 30ns, τ2 = 60ns, τ3 = 0ns, and the signal-to-noise ratio is -5dB. Figure 2 : This is the spatial power spectrum diagram of the method of the present invention (taking the direct path as an example). It can be seen from the figure that the spatial spectrum of the method of the present invention has a peak in the target incident direction, which proves the effectiveness and accuracy of the DOA estimation of the method of the present invention under low signal-to-noise ratio conditions.

[0116] Experiment 2: Assume that there are three arrival directions including the direct path of the OFDM signal, namely θ1=45°, θ2=0°, θ3=30°, and the corresponding relative delays are τ1=30ns, τ2=60ns, τ3=0ns. Error statistics are performed on DOA, delay and carrier frequency offset. The signal-to-noise ratio ranges from -15dB to 15dB, and the number of Monte Carlo experiments is 200. 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 This 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 This is the RMSE curve of the carrier frequency offset estimation accuracy as the signal-to-noise ratio changes. The curve in the figure shows that this 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 embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna, characterized in that: include: Establishing a signal receiving model of the array element, constructing a matrix representation of the received signal of each array element based on the signal receiving model and processing the matrix representation, so as to construct a signal matrix of each array element; Divide the signal groups according to the subcarriers, and stack the signal matrices of each array element to construct a stacking matrix; The stacked matrix is ​​written in the form of a tensor and factorized in parallel to obtain matrices containing DOA, delay, and carrier frequency offset respectively; Based on the corresponding relationship of the matrix decomposed by parallel factors, DOA and time delay are estimated by spectrum peak search and least square method respectively, so as to achieve pairing of DOA and time delay; and the carrier frequency offset is estimated by using the decomposed matrix.

2. The method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna according to claim 1, characterized in that: The step of establishing a signal receiving model of an array element comprises: Assume that the number of OFDM signal subcarriers is N, the number of subcarriers for data transmission 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 received from the OFDM signal source by the mth array element in the kth time slot can be expressed as the following model: 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 signals, and foffset represents the 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, and the superscript T represents the transposition operation; D m (H1) means taking the mth row of the channel matrix H1 and diagonalizing it, H1 means taking the first P′ columns of H; and H = ABF T , where 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 [f1,f2, … ,f P ] T ,in τ1 represents the path delay corresponding to the first path, f p Indicates the pth subcarrier frequency.

3. The method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna according to claim 2, characterized in that: The method 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 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 the Khatri-Rao product; 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 of different groups of data. The superscript i-1 of the phase shift matrix represents the power. i It means taking the matrix consisting of the i-th to P-i+1-th columns of H.

4. The method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna according to claim 3, characterized in that: The dividing of the signal groups according to the subcarriers and stacking of the signal matrix of each array element to construct a stacking matrix includes: Signal Matrix The left multiplication phase shift matrix is ​​expressed as: The matrices on the right side of the above formula 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: Among them, H1, H2…H I Respectively represent taking 1 of H ～ P′, 2 ～ P′+1,……,I ～ Column P; The superscript Q in the matrix indicates the power; represents the first P′ rows of the matrix F, and the matrix G satisfies: The spatial smoothing method is used, and the number of smoothing times is J. 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 subarray of The smoothed data can be stacked again by rows to form a new stacked matrix: in The superscript indicates 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, delay and carrier frequency offset of an array antenna according to claim 4, characterized in that: The stacked matrix is ​​written into a tensor form and parallel factor decomposition is performed 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 can be decomposed in parallel to obtain M⊙G, as well as The estimated results of Then for M⊙G and The estimation results are stacked in three-dimensional space to form two new three-dimensional arrays. By performing parallel factor decomposition on them, the estimated values ​​of the DOA information matrix M, the delay information matrix G and the carrier frequency offset information matrix E can be obtained respectively. and express.

6. The method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna according to claim 5, characterized in that: The matrix decomposed by parallel factors estimates DOA and time delay by spectrum peak search and least square method according to the corresponding relationship, so as to achieve pairing of DOA and time delay, including: 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-1 vector, then: Where ε1 represents the error parameter, from which the delay τ can be estimated q ; After calculating the delay, take the minimum delay and record it in the delay matrix Column index of The column vector corresponding to the same column index in : 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 for a column corresponds to The delays solved for the same column in , the two match each other.

7. The method for jointly estimating direction of arrival, delay and carrier frequency offset of an array antenna according to claim 5, characterized in that: The method of estimating the carrier frequency offset by using the decomposed matrix includes: From the matrix Take the pth column as: Since the tensor decomposition matrix The order of the columns of the original matrix E will change, so the p-th column here may not be the same as the p-th column of E, so we 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 can estimate Calculate the carrier frequency deviation: Here Consistent with P′.

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

9. 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, delay and carrier frequency offset of the array antenna according to any one of claims 1 to 7.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the method for jointly estimating the direction of arrival, delay and carrier frequency offset of an array antenna according to any one of claims 1 to 7 is implemented.

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