CN109738854A - A Method for Estimating the Arrival Angle of the Arrival Direction of the Antenna Array - Google Patents

Abstract

This application discloses the angle-of- arrival estimation methods of aerial array arrival bearing a kind of, pass through the self calibration based on subspace, according in the phase of first array element of receiving antenna array only include calibration error information, the calibration error of adjacent array element is mutually indepedent, and include the angle of arrival information component of arrival bearing in phase difference, building is maximum to be overlapped submatrix, and obtain array phase calibration error, the accurate initial estimate of angle of arrival, then the orthogonality of signal subspace and noise subspace is utilized, design iteration optimization algorithm, realize angle of arrival, the iteration of phase alignment error more new estimation, obtain accurate angle estimation.The invention can there are excellent angle estimation performance is still obtained when biggish phase alignment error in array element.

Description

A Method for Estimating the Arrival Angle of the Arrival Direction of the Antenna Array

technical field

The present invention relates to the multi-antenna field of broadband wireless communication, in particular, to a method for estimating the angle of arrival of the incoming wave direction of an antenna array.

Background technique

In order to alleviate the shortage of spectrum resources in the microwave frequency band, millimeter wave communication technology has become the key technology of next-generation mobile communication. The millimeter-wave frequency band has abundant spectrum resources and can achieve Gbps-level wireless transmission rates; its short wavelength makes it possible to use large-scale antenna arrays to achieve beamforming in a small physical size, so as to obtain high gain to compensate for the high gain. Severe path loss and fading on the frequency band. Because beamforming technology requires accurate azimuth information, the estimation of the angle of arrival of the incoming wave from the antenna array becomes the premise and foundation of millimeter wave communication. Limited by the technological level, the actual antenna array generally has a large initial phase error of the array element, which will seriously affect the performance of the angle of arrival estimation and beamforming.

In order to solve the influence of the initial phase error of the array element on the performance of the angle of arrival estimation, many experts and scholars have done a lot of research work in recent years. According to their different emphasis, they can be divided into two research directions: First, do not deal with existing algorithms, and find algorithms that are insensitive to array errors or have minimal sensitivity, thereby reducing the impact of arrays on the estimation of the angle of arrival. However, this kind of algorithm usually increases the complexity of the algorithm and loses the performance of the algorithm; the second is to design the algorithm to estimate the array error, and to calibrate the phase error through the estimated value.

In the second research direction above, the methods of array error calibration research are as follows:

1. Active calibration method.

The core idea of the active calibration method is to introduce an auxiliary positioning source, use the accurate angle of arrival information of the auxiliary positioning source to solve the array error, then use the obtained error value to calibrate the array error, and finally use the conventional angle of arrival estimation algorithm to calculate the angle of arrival. estimate.

The paper "Jia Yongkang, Bao Zheng, Wu Huan. An active calibration method for the position, amplitude and phase errors of array antenna elements [J]. Journal of Electronics, 1996, (03): 47-52." proposed a The active calibration algorithm is suitable for the errors of different array forms. When the arrival angle of the signal source is known, the minimum mean square error criterion is used to solve the array calibration error.

The paper "Zhang Ming, Zhu Zhaoda. Single-source calibration method for inconsistency of array channels without accurately known calibration source direction [J]. Journal of Electronic Science, 2009, (01): 20-25." The source constructs the cost function and realizes the amplitude and phase error calibration algorithm through the minimum cost function. The algorithm is not affected by the array form.

Patent "Sun Yimao, Wang Li, Fan Rong, Liu Yang, Hu Zepeng, Zou Lin, Yin Jihao, Wan Qun. A method of calibrating the amplitude and phase error of antenna array with unknown source position. CN201610865202.1" using the signal source existing in the external environment As a calibration source, when the position of the calibration source is unknown, the antenna array is used to repeatedly measure the calibration source signal in a grid whose spatial position is accurately known to determine the amplitude and phase error of the calibration antenna array element.

Such methods based on auxiliary positioning sources usually require precise auxiliary positioning source positions or receiving array positions, and slight deviations in known positions can cause significant degradation in the performance of AOA estimation. Therefore, in order to achieve better performance, the active calibration algorithm puts forward higher requirements on the manufacturing process or construction technology, and it is difficult to popularize and apply in practical engineering.

2. Array self-calibration algorithm.

The array self-calibration algorithm completes the angle of arrival estimation of the incoming wave direction of the antenna array without an auxiliary positioning source, but the array error seriously affects the estimation of the target angle of arrival. Because the characteristic law of the array manifold is destroyed, the angle of arrival estimation algorithm cannot uniquely identify the array. Error information and angle of arrival information. In addition, the joint estimation method is usually sensitive to the initial value of the angle of arrival and the array error, resulting in unstable algorithm performance.

Paper 'H.Liu,L.Zhao,Y.Li,X.Jing and T.K.Truong,"A Sparse-Based Approachfor DOA Estimation and Array Calibration in Uniform Linear Array,"in IEEESensors Journal, vol.16,no.15, pp.6018-6027, Aug.1, 2016. 'Proposed an angle of arrival estimation algorithm that can solve the mutual coupling effect of the array, the position deviation of the array element and the error of the amplitude and phase of the array element, using the sparseness of the array matrix for convex optimization Search solution, poor performance when the calibration error of the array is large.

The patent "Zhang Gong, Liu Shuai. MIMO radar array position error self-calibration method based on genetic algorithm. CN200910264135.8" proposes a genetic algorithm-based MIMO radar array position error self-calibration method. The invention constructs an adaptive weight function for weighted summation of spatial spectral values in different directions, and then combines the MUSIC method to construct an individual fitness function. Based on the genetic algorithm, the joint online estimation of the array element position error and DOA is realized. The algorithm requires relatively accurate initial estimates, so it is suitable for antenna arrays with small calibration errors.

The patent "Cao Xiang. Signal direction of arrival self-calibration method for sensor arrays. CN201611243005.2" proposes a signal direction of arrival self-calibration method for sensor arrays. Initialize the array error of the sensor array, use the MUSIC algorithm to estimate the initial value of the incoming wave direction of the signal from the noise subspace matrix; use the Lagrangian multiplier method to minimize the constructed Hermitian positive definite matrix to get the array error estimate; then use the MUSIC algorithm to estimate Direction of arrival of the signal; iterate the above steps repeatedly until the iteration stop condition is met. The performance of this method is limited by the initial estimation value, and the estimation performance deteriorates when the array calibration error is large.

From the perspective of various existing self-calibration algorithms, there are mainly the following types of problems:

1) It is suitable for antenna arrays with small calibration errors.

2) The performance is not ideal under low signal-to-noise ratio.

3) The performance is unstable and is greatly affected by the initial value.

Therefore, the research focus of phase error calibration technology is to avoid or reduce the dependence of the algorithm on the initial value, enhance the estimation performance under the signal-to-noise ratio, and still ensure the estimation performance when the array calibration error is large.

SUMMARY OF THE INVENTION

The invention provides a method for estimating the arrival angle of the incoming wave direction of the antenna array, so as to improve the accuracy of the arrival angle estimation when the array calibration error is large.

A method for estimating the angle of arrival of the incoming wave direction of an antenna array provided by the present invention includes:

A method for estimating the angle of arrival of the incoming wave direction of an antenna array, characterized in that the method comprises:

Eliminate pilot symbols from the received signal of each symbol period to obtain a first received signal vector;

The first received signal vector of at least one symbol period is spliced into an M×K-dimensional first received signal matrix, where M is the number of elements of the receiving antenna array, and K is the number of signal sources;

The first received signal matrix is divided into two sub-arrays with the maximum degree of coincidence, and the corresponding elements of each row of the two sub-arrays are respectively subjected to cancellation processing to obtain the first maximum coincident sub-arrays containing incoming wave direction information in each row;

Average the phases of all the row vectors of the first maximum coincident sub-array to obtain the initial estimated value of the arrival angle of each signal source wave direction;

According to the initial estimated value of the angle of arrival, the angle of arrival component in the first maximum coincident sub-array is eliminated to obtain the second maximum coincident sub-array; based on the second maximum coincident sub-array, it is calculated that all elements except the first antenna array element are obtained. The initial estimated value of the difference between the phase calibration errors of the other array elements and the first antenna element;

Iterate as follows:

Normalizing the random error of the first antenna in the first received signal matrix to obtain the second received signal;

Perform singular value decomposition on the covariance matrix of the second received signal to obtain a signal subspace eigenvector matrix and a noise subspace eigenvector matrix;

Based on the orthogonality between the eigenvector matrix of the signal subspace and the eigenvector matrix of the noise subspace, the current cost function is constructed according to the initial estimated value of the phase calibration error of each array element, and the initial estimated value of the angle of arrival of the direction of arrival of each signal source is used. solve the transformation matrix;

Minimize the current cost function according to the transformation matrix, and solve the first estimated value of the phase calibration error of each array element;

By decomposing the structure of the signal subspace eigenvector matrix, two signal subspace eigenvector submatrices are obtained;

According to the two signal subspace eigenvector submatrices and the first estimated value of the phase calibration error of each array element, solve the first estimated value of the arrival angle of each signal source wave direction;

Calculate the first cost function according to the first estimated value of the phase calibration error of each array element and the first estimated value of the angle of arrival of the direction of arrival of each signal source;

Determine whether the absolute value of the difference between the first cost function and the second cost function is less than a preset threshold, wherein the second cost function is zero in the first iteration,

If yes, stop the iteration, and output the first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of each signal source direction of arrival as the estimation result,

Otherwise, the first estimated value of the phase calibration error of each array element is used as the initial estimated value of the phase calibration error of each array element, and the first estimated value of the arrival angle of each signal source direction of arrival is used as the angle of arrival of each signal source. For the initial estimated value, the first cost function is used as the second cost function, and the next iteration is performed.

According to the self-calibration based on subspace, the present invention only includes calibration error information in the phase of the first array element of the receiving antenna array, the calibration errors of adjacent array elements are independent of each other, and the phase difference includes the arrival angle information of the incoming wave direction. components, construct the maximum coincident subarray, and obtain relatively accurate initial estimates of the phase calibration error and angle of arrival of the array, and then use the orthogonality of the signal subspace and the noise subspace to design an iterative optimization algorithm to achieve the angle of arrival and phase calibration errors. Iteratively update the estimate to obtain an accurate angle estimate. The invention can still obtain excellent angle estimation performance when the array element has a large phase calibration error.

Description of drawings

FIG. 1 is a schematic diagram of a system block diagram of a millimeter wave communication system;

FIG. 2 is a schematic flowchart of a method for estimating the angle of arrival of an incoming wave of an antenna array according to an embodiment of the present invention.

FIG. 3 is a simulation comparison diagram of the estimation error RMSE of the angle of arrival using the traditional angle estimation method (ESPRIT algorithm) and the estimation method of the present invention respectively in the embodiment of the present invention.

FIG. 4 is a simulation comparison diagram of the RMSE of the phase calibration error of the array element using the uncorrected angle estimation method and the angle of arrival estimation method of the present invention respectively in an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical means and advantages of the present application more clear, the present application will be further described in detail below with reference to the accompanying drawings.

According to the structure characteristics of the received signal of the uniform linear antenna array, the present invention divides the received signal matrix into two sub-matrices with the maximum degree of coincidence, and the phase information contained in the matrix after the corresponding elements are divided by the two sub-arrays row by row has repetition. According to the law, the initial estimated value of the incoming wave direction is obtained by canceling it, and the estimated value is close to the true value when the number of array elements is large. The initial estimated value of the direction of origin can further obtain the initial estimated value of the phase calibration error of the array element. The estimated value has high precision, and the accurate initial estimated value ensures the stable estimation performance of the subsequent iterative processing.

In addition, based on the orthogonality of the signal subspace and the noise subspace, an iterative algorithm is designed to iteratively update the estimated value of the arrival angle of the incoming wave direction and the estimated value of the phase calibration error, and realize the accurate calculation of the arrival angle of the incoming wave direction and the phase calibration error. estimate.

Referring to FIG. 1, FIG. 1 is a schematic diagram of a system block diagram of a millimeter wave communication system. A millimeter-wave communication system using a large-scale antenna array consists of a transmitter including K signal sources and a receiver; the receiver adopts a uniform linear array with M array elements to receive K signal sources from the transmitter, and, at the In millimeter wave communication systems,

1) When the wireless signal emitted by the signal source reaches the receiver antenna array, it can be regarded as a plane wave, that is, far-field communication;

2) The signals of the signal source are independent of each other;

3) The number M of antenna array elements is greater than the number K of signal sources;

4) The phase calibration errors of the antenna array elements are independent and have a uniform and identical distribution;

5) The received signal is superimposed with Gaussian white noise with zero mean and variance ^σ2 . The noise and the signal are independent of each other.

6) The channel is a slow fading channel, that is, the channel basically remains unchanged within a frame time.

The baseband received signal model is:

Y=GAS+n (1)

in, is an M-dimensional diagonal matrix composed of the phase calibration errors of the array elements, diag(·) represents the diagonal matrix, and φ _m is the phase calibration error on the mth array element; A=[a(θ ₁ ), a(θ ₂ ),...,a(θ _K )] is the steering matrix composed of M×K-dimensional array element steering vectors, where the steering vector is the signal steering vector, θ _k is the arrival angle of the kth signal source, d and λ are the array element spacing and wavelength, respectively, and d=λ/2; S is the energy-normalized pilot signal matrix, different signals The signals of the source are orthogonal to each other, that is, E{SS ^H }=I _K ; n is the white noise vector, and there is

Referring to FIG. 2 , FIG. 2 is a schematic flowchart of a method for estimating the angle of arrival in the direction of arrival of an antenna array according to an embodiment of the present invention.

Step 201: Eliminate the pilot signal from the baseband received signal according to equation (2) to obtain the first received signal from which the pilot signal has been eliminated

Step 202, according to the arrival of the incoming wave direction included in the phase of the first array element in the receiving antenna array, only the phase calibration error is included, the calibration errors of adjacent array elements are independent of each other, and the phase difference between adjacent array elements is included. angle information, construct the first maximum coincident sub-array; due to the first received signal matrix Adjacent columns contain the same arrival angle of arrival and different phase calibration errors, so the first received signal matrix is divided into two sub-matrices with the maximum degree of coincidence and the same dimension as the first received signal matrix. The number of rows of the matrix is the same, and the elements of the corresponding rows in the two sub-matrices are divided row by row to obtain the first maximum coincident sub-matrix, that is, the first row of the first received signal matrix to the M-1th row, The K dimension is used as the first sub-array of the first received signal matrix; the second row to the M-th row and the K dimension are used as the second sub-array of the first received signal matrix, and the elements of each row in the second sub-array are compared with the first The elements of each row in the sub-array are divided correspondingly to obtain the (M-1)×K-dimensional first largest coincident sub-matrix:

in express The submatrix consisting of the mth row to the nth row of . Then the nth row of the (M-1)×K-dimensional matrix R:

Step 203, obtain the initial estimates of the arrival angles of the K signal sources in the direction of arrival:

It can be seen from formula (4) that each row of the first maximum coincident sub-array R contains the same arrival angle information of the incoming wave direction. Add and average the phases of all row vectors of R to obtain the initial estimate of the angle of arrival in the direction of the incoming wave

When the number of antennas M is large, The initial estimated values of the arrival angles of the incoming waves of the K signal sources are respectively about:

Step 204, by the above-mentioned estimated value of the angle of arrival of the direction of arrival, can eliminate the angle of arrival information of the direction of arrival from formula (4), obtain the second maximum coincidence sub-array R ′ that eliminates the angle of arrival information of the direction of arrival:

Step 205: Perform addition and phase calculation on the second largest coincident sub-array R', and from R', it is possible to estimate the difference between the phase calibration errors of the other array elements except the first antenna array element and the first antenna array element. Bad initial estimate:

The following is an iterative update based on the initial estimated value of the angle of arrival in the direction of arrival of each signal source k obtained in the above steps, to obtain the estimated value of the angle of arrival in the direction of arrival and the estimated value of the phase calibration error.

Step 206, normalize the random error of the received signal of the first antenna in the first received signal matrix, that is, divide the elements of each row of the first received signal matrix by the corresponding elements of the first row to obtain the second received signal:

where ./ is the dot division operation.

Step 207, for the second received signal The covariance matrix of is carried out singular value (SVD) decomposition, and the eigenvector matrix E _s corresponding to the signal subspace and the eigenvector matrix E _n corresponding to the noise subspace are obtained:

where E _s is the signal subspace matrix composed of the signal eigenvectors, E _n is the noise subspace matrix composed of the noise eigenvectors, ∑ _s and ∑ _n are the diagonals composed of the signal subspace eigenvalues and the noise subspace eigenvalues, respectively matrix, from which E _n is calculated.

Step 208, based on the principle that the signal subspace and the noise subspace are orthogonal, construct the current cost function J according to formula 12,

in, Obtained by Equation 10, is the M-dimensional diagonal matrix composed of the phase calibration errors of the array elements, A=[a(θ ₁ ), a(θ ₂ ), ..., a(θ _K )] is the M×K-dimensional array element guidance Steering matrix composed of vectors;

because

From this we get:

In the formula, is a diagonal matrix with steering vector a(θ _k ) as its diagonal elements, is the initial estimated value vector of the phase calibration error;

Therefore, the transformation matrix T(θ) _is obtained based on Equation 11-1 and the En calculated in step 208:

Step 209: Minimize the constructed cost function to obtain the first estimated value of the phase calibration error vector of each antenna array: Specifically, the cost function is minimized according to Equation 12,

Among them, argmin represents the set of all phase calibration error estimates that make the cost function J achieve the minimum value;

Substitute the transformation matrix T(θ) obtained in step 208 into formula 12, thereby obtaining the first estimated value of the phase calibration error of each antenna array

Step 210: Obtain eigenvector matrices corresponding to the two signal subspaces of the first received signal matrix by singular value decomposition, wherein the two signal subspaces of the first received signal matrix are respectively the first received signal constructed in step 202. A subarray and a second subarray.

E _S1 = P ₁ E _s (13)

E _S2 =P ₂ E _s (14)

E _S1 and E _S2 are the first sub-array and the second sub-array of the signal subspace eigenvector matrix, respectively, P ₁ =[I _M-1 0], P ₂ =[0 I _M-1 ], where I is the unit matrix; is the rotation matrix containing the arrival angle information in the direction of arrival.

Step 211, by E _S1 and E _S2 , and the first estimated value of the phase calibration error of each array element, solve the first estimated value Θ of the reaching angle:

Due to:

Therefore:

in,

Step 212: Substitute the first estimated value of the phase calibration error and the first estimated value of the angle of arrival into Formula 11-1 to obtain a first cost function.

Step 213, judging whether the absolute value of the difference between the first cost function and the second cost function is less than a preset threshold, wherein, in the first iteration, the second cost function is 0;

When the absolute value of the first cost function and the second cost function is smaller than the preset threshold, step 214 is executed, the iteration is stopped, and the first estimated value of the phase calibration error and the first estimated value of the angle of arrival are used as the final estimate The result is output, otherwise, go to step 215, take the first estimated value of the phase calibration error as the initial value of the phase calibration error, the first estimated value of the angle of arrival as the initial value of the angle of arrival, and take the first cost function as the second cost function , return to step 206, and proceed to the next iteration.

The invention provides a method for estimating the arrival angle of the incoming wave direction of an antenna array, when the array element has a large phase calibration error, the arrival angle is accurately estimated based on the incoming wave direction of the array self-calibration. Its advantages are:

1. The phase calibration error estimated according to the signal structure characteristics and the initial value of the arrival angle of the incoming wave have high precision, which greatly improves the stability of the algorithm performance.

2. When the phase calibration error of the array element is large, the estimation accuracy is high and stable.

3. In a millimeter-wave communication system with a large-scale antenna array, it overcomes the problem of high complexity of the existing angle of arrival estimation method and is only suitable for a small range of phase errors, so it has a good prospect of popularization and application.

Referring to FIG. 3 and FIG. 4 , FIG. 3 is a simulation comparison diagram of the estimation error RMSE of the angle of arrival using the traditional angle estimation method (ESPRIT algorithm) and the estimation method of the present invention respectively in the embodiment of the present invention. FIG. 4 is a simulation comparison diagram of the RMSE of the phase calibration error of the array element using the uncorrected angle estimation method and the angle of arrival estimation method of the present invention respectively in the embodiment of the present invention.

The simulation performed by the method of the present invention: under the condition of the additive white Gaussian noise channel, the simulation implementation test diagram with the iteration number i of 1000 times is randomly generated, wherein the number of signal sources K=2, the number of elements of the receiving array M=100, The received signal-to-noise ratio is 20dB, and the phase calibration error of the array element is independent and identically distributed and obeys a uniform distribution with standard deviation σ _φ , that is, in evenly distributed among them. The standard deviation _σφ varies from 0 to 10 degrees in the simulation. The arrival angles of the two signal sources are θ ₁ =10° and θ ₂ =15°, respectively; J ⁽⁰⁾ =100, Th=10 ⁻⁶ . The estimated performance measure uses the estimated error standard deviation, namely: in represents the estimated value of the phase calibration error of the mth antenna in the nth simulation, in represents the estimated value of the mth angle of arrival in the nth simulation. It can be seen from the simulation results that the estimation performance of the angle of arrival and the phase calibration error of the array element in the embodiment of the present invention is far superior to the classical ESPRIT algorithm, which indicates that the present invention can still accurately estimate the angle of arrival and the phase calibration error when the receiving antenna array has a large phase calibration error. Element phase calibration error value.

In this document, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such existence between these entities or operations. The actual relationship or sequence. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, article or device that includes a list of elements includes not only those elements, but also includes not explicitly listed or other elements inherent to such a process, method, article or apparatus. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in a process, method, article or apparatus that includes the element.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the present invention. within the scope of protection.

Claims (10)

1. a method for estimating the angle of arrival of the incoming wave direction of an antenna array, characterized in that the method comprises, Eliminate pilot symbols from the received signal of each symbol period to obtain a first received signal vector; The first received signal vector of at least one symbol period is spliced into an M×K-dimensional first received signal matrix, where M is the number of elements of the receiving antenna array, and K is the number of signal sources; The first received signal matrix is divided into two sub-arrays with the maximum degree of coincidence, and the corresponding elements of each row of the two sub-arrays are respectively subjected to cancellation processing to obtain the first maximum coincident sub-arrays containing incoming wave direction information in each row; Average the phases of all the row vectors of the first maximum coincident sub-array to obtain the initial estimated value of the arrival angle of each signal source wave direction; According to the initial estimated value of the angle of arrival, the angle of arrival component in the first maximum coincident sub-array is eliminated to obtain the second maximum coincident sub-array; based on the second maximum coincident sub-array, it is calculated that all elements except the first antenna array element are obtained. The initial estimated value of the difference between the phase calibration errors of the other array elements and the first antenna element; Iterate as follows: Normalizing the random error of the first antenna in the first received signal matrix to obtain the second received signal; Perform singular value decomposition on the covariance matrix of the second received signal to obtain a signal subspace eigenvector matrix and a noise subspace eigenvector matrix; Based on the orthogonality between the eigenvector matrix of the signal subspace and the eigenvector matrix of the noise subspace, the current cost function is constructed according to the initial estimated value of the phase calibration error of each array element, and the initial estimated value of the angle of arrival of the direction of arrival of each signal source is used. solve the transformation matrix; Minimize the current cost function according to the transformation matrix, and solve the first estimated value of the phase calibration error of each array element; By decomposing the structure of the signal subspace eigenvector matrix, two signal subspace eigenvector submatrices are obtained; According to the two signal subspace eigenvector submatrices and the first estimated value of the phase calibration error of each array element, solve the first estimated value of the arrival angle of each signal source wave direction; Calculate the first cost function according to the first estimated value of the phase calibration error of each array element and the first estimated value of the angle of arrival of the direction of arrival of each signal source; Determine whether the absolute value of the difference between the first cost function and the second cost function is less than a preset threshold, wherein the second cost function is zero in the first iteration, If yes, stop the iteration, and output the first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of each signal source direction of arrival as the estimation result, Otherwise, the first estimated value of the phase calibration error of each array element is used as the initial estimated value of the phase calibration error of each array element, and the first estimated value of the arrival angle of each signal source direction of arrival is used as the angle of arrival of each signal source. For the initial estimated value, the first cost function is used as the second cost function, and the next iteration is performed. 2. The method according to claim 1, wherein the signal model of the received signal of each symbol period is: Y=GAS+n in, is an M-dimensional diagonal matrix composed of the phase calibration errors of the array elements, diag(·) represents the diagonal matrix, and φ _m is the phase calibration error on the mth array element; A=[a(θ ₁ ), a(θ ₂ ),...,a(θ _K )] is the steering matrix composed of M×K-dimensional array element steering vectors, where the steering vector is the signal steering vector, θ _k is the angle of arrival of the kth signal source, d and λ are the array element spacing and wavelength, respectively, and d=λ/2; S is the energy-normalized pilot signal matrix, and E {SS ^H }=I _K ; n is a white noise vector and has I is the identity matrix; The removing the pilot symbol from the received signal of each symbol period to obtain the first received signal vector includes: according to the formula obtaining the first received signal vector; The first received signal matrix is divided into two sub-arrays with the maximum degree of coincidence, and the corresponding elements of each row of the two sub-arrays are respectively subjected to cancellation processing to obtain the first maximum coincident sub-arrays containing the information of the incoming wave direction in each row. include, Take the first row to the M-1th row and the K dimension of the first received signal matrix as the first sub-array of the first received signal, and take the second row to the Mth row and the K dimension of the first received signal matrix as the first sub-array. a second subarray for receiving signals; Point division is performed correspondingly to each row of elements in the second sub-matrix and each row of elements in the first sub-matrix to obtain a (M-1)×K-dimensional first maximum coincident sub-matrix. 3. The method according to claim 1, wherein, according to the initial estimated value of the angle of arrival, eliminating the angle of arrival component in the first maximum coincident sub-array to obtain the second maximum coincident sub-array comprises, according to formula The second maximum coincident sub-array R′ is obtained by calculation, wherein R is the first maximum coincident sub-array, and θ _k is the initial estimated value of the arrival angle of the incoming wave of the signal source k. 4. The method according to claim 1, wherein, based on the second maximum coincident sub-array, the phase calibration of each array element and the first antenna array element except the first antenna array element is obtained by calculation An initial estimate of the difference in error includes, According to the formula Calculate the initial estimated value of the difference between the phase calibration errors of the other array elements except the first antenna array element and the first antenna array element, wherein, φ ₁ is the phase calibration error value of the first wire array element; phase is the phase calculation operation, and R′(n) represents the n-th row element in the second maximum coincident sub-array. 5. The method of claim 1, wherein the normalizing the random error of the first antenna in the first received signal matrix to obtain the second received signal comprises: The elements of each row of the first received signal matrix are respectively divided by the corresponding elements of the first row to obtain the second received signal. 6. method as claimed in claim 1 is characterized in that, the described covariance matrix of the second received signal is carried out singular value decomposition, obtains signal subspace eigenvector matrix and noise subspace eigenvector matrix and comprises, According to the formula The signal subspace eigenvector matrix E _s and the noise subspace eigenvector matrix E _n are calculated, wherein Σ _s and Σ _n are diagonal matrices formed by signal subspace eigenvalues and noise subspace eigenvalues, respectively. 7. The method according to claim 1, wherein, constructing a current cost function based on the signal subspace eigenvector matrix and the noise subspace eigenvector matrix being orthogonal, and solving the transformation matrix comprises, According to the formula Construct the current cost function J, where E _n is the noise subspace eigenvector matrix, is an M-dimensional diagonal matrix composed of the initial estimates of phase calibration errors of M array elements, A=(a(θ ₁ ), a(θ ₂ ), ..., a(θ _k )] is an M×K dimension The steering matrix formed by the array element steering vector α(θ _k ) of ; Based on the noise subspace eigenvector matrix E _n , according to the formula Calculate the transformation matrix T(θ), where, is a diagonal matrix with the steering vector α(θ _k ) as the diagonal elements. 8. The method according to claim 1, wherein the minimizing the current cost function and solving the first estimated value of the phase calibration error of each array element according to the transformation matrix comprises, according to formula 1 Obtain the set of all phase calibration error estimates that make the cost function J obtain the minimum value, wherein argmin represents the set of all phase calibration error estimates that make the cost function J obtain the minimum value; Substituting the obtained transformation matrix T(θ) into the formula 1, we get is the first estimated value vector of the phase calibration error of the M array elements; According to the first estimated value vector of the phase calibration error of the M array elements, according to the formula Obtain the first estimated value of the phase calibration error of each antenna array 9. The method according to claim 2, characterized in that, obtaining two signal subspace eigenvector submatrices by decomposing the structure of the signal subspace eigenvectors comprises, according to formula E _S1 =P ₁ E _s and E _S2 =P ₂ E _s , respectively obtain the signal subspace E _S1 corresponding to the first subarray of the first received signal, and the signal subspace E corresponding to the second subarray of the first received signal _S2 , where P ₁ =[I _M-1 0], P ₂ =[0 I _M-1 ], and I is an identity matrix. 10 . The method according to claim 1 , wherein, according to the first estimated value of the phase calibration error of the two received signal matrix sub-matrices and each array element, the first estimated value of the angle of arrival in the direction of arrival of each signal source is calculated. 11 . An estimate includes, According to the formula Solve for the first estimate of the angle of arrival, where, The calculating the first cost function according to the first estimated value of the phase calibration error of each of the array elements and the first estimated value of the arrival angle of the incoming wave direction of each signal source includes: Substitute the obtained first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of each signal source direction of arrival into the formula J=g ^H T(θ)g to obtain a first cost function.