CN109738854A - A kind of angle-of- arrival estimation method of aerial array arrival bearing - Google Patents
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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
Technical Field
The present invention relates to the field of multiple antennas in broadband wireless communication, and in particular, to a method for estimating an arrival angle of an antenna array in an incoming wave direction.
Background
In order to alleviate the shortage of spectrum resources in the microwave frequency band, the millimeter wave communication technology becomes a key technology of next generation mobile communication. The millimeter wave frequency band has rich spectrum resources, and can realize the wireless transmission rate of Gbps level; due to the characteristic of short wavelength, the large-scale antenna array can be used for realizing beam forming on a smaller physical size, so that high gain is obtained to make up for serious path loss and fading on a high frequency band. Because the beam forming technology needs accurate azimuth information, the arrival angle estimation of the incoming wave direction of the antenna array becomes the premise and the basis of millimeter wave communication. Due to the limitation of the process level, a large initial phase error of an array element generally exists in an actual antenna array, which seriously affects the performance of angle of arrival estimation and beam forming.
In order to solve the influence of the initial phase error of the array element on the estimation performance of the arrival angle, a lot of research works have been done by a plurality of expert scholars in recent years. From the differences of the respective emphasis points, two research directions can be distinguished: firstly, the existing algorithm is not processed, and an algorithm which is insensitive or has extremely small sensitivity to array errors is searched, so that the influence of the array on the estimation of the arrival angle is reduced. However, this class of algorithms typically comes at the cost of increased complexity and loss of algorithm performance; secondly, the array error is estimated by a design algorithm, and the phase error is calibrated through the estimated value.
In the second study direction, the array error calibration study method includes the following steps:
1. active calibration method.
The core idea of the active calibration method is to introduce an auxiliary positioning source, solve array errors by means of accurate arrival angle information of the auxiliary positioning source, then calibrate the array errors through the obtained error values, and finally estimate the arrival angles by adopting a conventional arrival angle estimation algorithm.
An active calibration method for array element position, amplitude and phase errors of an array antenna [ J ] electronics, 1996, (03):47-52 ] proposes an active calibration algorithm suitable for errors in different array forms, and solves the array calibration error by adopting a minimum mean square error criterion when the arrival angle of a signal source is known.
The paper "zhanming, zhangda, single source calibration method of array channel inconsistency without accurately knowing the calibration source direction [ J ]. electronics science, journal, 2009, (01): 20-25" proposes an algorithm for constructing a cost function by using a known source and realizing amplitude and phase error calibration through minimum cost function, and the algorithm is not influenced by the array form.
CN201610865202.1 "uses a signal source present in the external environment as a calibration source, and repeatedly measures the calibration source signal in a grid whose spatial position is precisely known, using an antenna array in the case of an unknown calibration source position, to determine the calibration antenna array element amplitude-phase error.
Such assisted localization source-based methods typically require accurate assisted localization source or receive array locations, while slight deviations in the known locations can cause significant degradation in the angle-of-arrival estimation performance. Therefore, the active calibration algorithm has high requirements on the manufacturing process or construction technology and the like to achieve good performance, and is difficult to popularize and apply in practical engineering.
2. An array self-calibration algorithm.
The array self-calibration algorithm completes the arrival angle estimation of the incoming wave direction of the antenna array without the auxiliary positioning source condition, but the array error seriously affects the target arrival angle estimation, and the arrival angle estimation algorithm cannot uniquely identify the array error information and the arrival angle information due to the fact that the characteristic rule of the array manifold is damaged. In addition, joint estimation methods are generally sensitive to the initial values of the arrival angle and array errors, resulting in unstable algorithm performance.
The paper 'H.Liu, L.ZHao, Y.Li, X.lacing and T.K.Truong,' A space-Based application for DOA Estimation and Array Calibration in Uniform Linear Array, 'in IEEESensors Journal, vol.16, No.15, pp.6018-6027, Aug.1, 2016' proposes an arrival angle Estimation algorithm which can solve the mutual coupling effect, the Array element position deviation and the Array element amplitude and phase error of the Array, and utilizes the sparsity of the Array matrix to carry out convex optimization search solving, and has poor performance when the Calibration error of the Array is larger.
The patent of Zhang Bo, Liushuai, MIMO radar array position error self-calibration method based on genetic algorithm CN200910264135.8 provides a MIMO radar array position error self-calibration method based on genetic algorithm. The method constructs an adaptive weight function for carrying out weighted summation on spatial spectrum values in different directions, then constructs an individual fitness function by combining an MUSIC method, and realizes the combined online estimation of array element position errors and DOAs based on a genetic algorithm. The algorithm needs a more accurate initial estimation value, and is therefore suitable for antenna arrays with smaller calibration errors.
The patent "Cao Xiang. self-calibration method of signal arrival direction for sensor array. CN 201611243005.2" proposes a self-calibration method of signal arrival direction for sensor array. Initializing array errors of the sensor array, and estimating initial values of incoming wave directions of signals by a noise subspace matrix through an MUSIC algorithm; obtaining the estimation of the array error by minimizing the constructed Hermitian positive definite matrix by a Lagrange multiplier method; estimating the direction of arrival of the signal by using an MUSIC algorithm; and repeating the iteration of the steps until an iteration stop condition is met. The method performance is limited to the initial estimate and the estimate performance deteriorates when the array calibration error is large.
From the existing various self-calibration algorithms, the following problems mainly exist:
1) the method is suitable for the antenna array with small calibration error.
2) The performance is not ideal at low signal to noise ratio.
3) The performance is unstable and greatly affected by the initial value.
Therefore, the research of the phase error calibration technology mainly aims to avoid or reduce the dependence of the algorithm on the initial value, enhance the estimation performance under the signal-to-noise ratio and ensure the estimation performance when the array calibration error is large.
Disclosure of Invention
The invention provides an arrival angle estimation method of an antenna array incoming wave direction, which aims to improve the accuracy of arrival angle estimation when the array calibration error is large.
The invention provides a method for estimating the arrival angle of an antenna array incoming wave direction, which comprises the following steps,
a method for estimating arrival angle of incoming wave direction of antenna array is characterized in that the method includes,
eliminating pilot symbols from the received signal of each symbol period to obtain a first received signal vector;
splicing first receiving signal vectors of at least more than one symbol period into an M multiplied by K dimension first receiving signal matrix, wherein M is the array element number of a receiving antenna array, and K is the signal source number;
dividing the first received signal matrix into two sub-arrays with the maximum coincidence degree, and performing cancellation processing on corresponding elements of each row of the two sub-arrays respectively to obtain first maximum coincidence sub-arrays of each row containing incoming wave direction information;
averaging the phases of all the row vectors of the first maximum coincidence subarray to obtain an initial estimation value of the arrival angle of the incoming wave direction of each signal source;
eliminating an arrival angle component in the first maximum coincidence subarray according to the initial estimation value of the arrival angle to obtain a second maximum coincidence subarray; based on the second maximum coincidence subarray, calculating to obtain an initial estimation value of the difference between the phase calibration errors of other array elements except the first antenna array element and the first antenna array element;
iteration is carried out according to the following steps:
normalizing the random error of the first antenna in the first received signal matrix to obtain a second received signal;
performing 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;
constructing a current cost function based on the orthogonality of the signal subspace eigenvector matrix and the noise subspace eigenvector matrix according to the initial estimation value of the phase calibration error of each array element, and solving a transformation matrix according to the initial estimation value of the arrival angle of each signal source in the incoming wave direction;
solving a first estimated value of the phase calibration error of each array element according to the transformation array minimized current cost function;
obtaining two signal subspace characteristic vector submatrices through the structural decomposition of the signal subspace characteristic vector matrixes;
according to the two signal subspace characteristic vector quantum matrixes and the first estimated value of the phase calibration error of each array element, solving the first estimated value of the arrival angle of the incoming wave direction of each signal source;
calculating a 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 arrival angle of the incoming wave direction of each signal source;
judging whether the absolute value of the difference between the first cost function and the second cost function is smaller than a preset threshold value, wherein the second cost function is zero in the first iteration,
if so, stopping iteration, and outputting the first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of the incoming wave direction of each signal source as estimation results,
otherwise, taking the first estimated value of the phase calibration error of each array element as the initial estimated value of the phase calibration error of each array element, taking the first estimated value of the arrival angle of the incoming wave direction of each signal source as the initial estimated value of the arrival angle of the incoming wave direction of each signal source, taking the first cost function as the second cost function, and performing the next iteration.
According to the method, through self calibration based on subspace, a maximum coincidence subarray is constructed according to the fact that the phase of a first array element of a receiving antenna array only contains calibration error information, the calibration errors of adjacent array elements are mutually independent, and the phase difference contains the arrival angle information component of the incoming wave direction, an initial estimation value with more accurate array phase calibration errors and arrival angles is obtained, then an iterative optimization algorithm is designed by utilizing the orthogonality of a signal subspace and a noise subspace, iterative update estimation of the arrival angles and the phase calibration errors is achieved, and accurate angle estimation is obtained. The method can obtain excellent angle estimation performance when the array elements have larger phase calibration errors.
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FIG. 1 is a system block diagram schematic diagram of a millimeter wave communication system;
fig. 2 is a schematic flow chart of a method for estimating an arrival angle of an incoming wave direction 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 in the embodiment of the present invention, in which the conventional angle estimation method (ESPRIT algorithm) and the estimation method of the present invention are respectively adopted.
Fig. 4 is a simulation comparison diagram of array element phase calibration errors RMSE in the embodiment of the present invention, which respectively adopt the uncorrected angle estimation method and the arrival angle estimation method of the present invention.
Detailed Description
For the purpose of making the objects, technical means and advantages of the present application more apparent, the present application will be described in further detail with reference to the accompanying drawings.
According to the structural characteristics of the received signals of the uniform linear antenna array, the received signal matrix is divided into two sub-matrices with the maximum coincidence degree, phase information contained in the matrix after corresponding element points of the two sub-matrices are divided line by line has a repetition rule, the phase information is subjected to cancellation processing to obtain an initial estimated value of an incoming wave direction, and the estimated value approaches to a true value when the number of array elements is large. The initial estimation value of the phase calibration error of the array element can be further obtained by the initial estimation value of the incoming wave direction, the accuracy of the estimation value is high, and the accurate initial estimation value ensures the stable estimation performance of the subsequent iteration processing.
And based on the orthogonality of the signal subspace and the noise subspace, an iterative algorithm for iteratively updating the arrival angle estimation value of the incoming wave direction and the phase calibration error estimation value is designed, and accurate estimation of the arrival angle of the incoming wave direction and the phase calibration error is realized.
Referring to fig. 1, fig. 1 is a system block diagram of a millimeter wave communication system. A millimeter wave communication system adopting a large-scale antenna array is composed of a sending end comprising K signal sources and a receiver; the receiving end adopts a uniform linear array with M array elements to receive K signal sources from the transmitting end, and in a millimeter wave communication system,
1) when a wireless signal transmitted by a signal source reaches an antenna array of a receiver, the wireless signal can be regarded as plane wave, namely far-field communication;
2) the signals of the signal sources 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 uniform and same distribution;
5) received signal is superposed with zero mean and variance of sigma2White gaussian noise. The noise is independent of the signal to noise.
6) The channel is a slow fading channel, i.e., the channel remains substantially unchanged for a frame time.
The baseband received signal model is:
Y＝GAS+n (1)
wherein,is an M-dimensional diagonal matrix formed by the phase calibration errors of the array elements, diag (a) represents the diagonal matrix, phimCalibrating the phase error of the m array element; a ═ a (θ)1)，a(θ2)，...，a(θK)]A steering matrix formed by M × K array element steering vectorsFor signal steering vectors, thetakD and lambda are the array element spacing and the wavelength respectively, and d is lambda/2; s is a pilot signal matrix with energy normalization, the signals of different signal sources are mutually orthogonal, i.e. there is E { SSH}＝IK(ii) a n is a white noise vector and has
Referring to fig. 2, fig. 2 is a schematic flow chart of a method for estimating an arrival angle of an incoming wave direction of an antenna array according to an embodiment of the present invention.
Step 201, removing the pilot signal from the baseband received signal according to equation (2) to obtain a first received signal with the pilot signal removed
Step 202, constructing a first maximum coincidence subarray according to arrival angle information of an incoming wave direction, wherein the phase of a first array element in the receiving antenna array only contains phase calibration errors, the calibration errors of adjacent array elements are mutually independent, and the phase difference between the adjacent array elements contains; due to the first received signal matrixAdjacent columns contain the same arrival angle in the incoming wave direction and different phase calibration errors, so that the first received signal matrix is divided into two sub-matrixes with the maximum coincidence degree and the same dimensionality as the first received signal matrix, the row numbers of the two sub-matrixes are the same, each element of a corresponding row in the two sub-matrixes is subjected to row-by-row dot division to obtain a first maximum coincidence sub-matrix, namely, the first row to the (M-1) th row and the K dimensionality of the first received signal matrix are taken as the first sub-matrix of the first received signal matrix; taking the dimensions from the second row to the Mth row and K as a second sub-array of the first receiving signal matrix, and correspondingly performing point division on each row of elements in the second sub-array and each row of elements in the first sub-array respectively to obtain a (M-1) xK-dimensional first maximum coincidence sub-array:
whereinTo representAnd (4) the m-th row to the n-th row of the matrix. Then the nth behavior of the (M-1) xK dimensional matrix R:
step 203, obtaining initial estimates of arrival angles of incoming wave directions of K signal sources:
as can be seen from equation (4), each row of the first maximum coincidence subarray R contains the same arrival angle information of the incoming wave direction. The phases of all the row vectors of R are added and averaged, so that the initial estimated value of the arrival angle of the incoming wave direction can be obtained
When the number of antennas M is large,the initial estimated values of the arrival angle of the incoming wave direction of the K signal sources are respectively about:
step 204, by using the estimated arrival angle of the incoming wave direction, the arrival angle information of the incoming wave direction can be eliminated from the formula (4), and a second maximum coincidence subarray R' for eliminating the arrival angle information of the incoming wave direction is obtained:
step 205, add the second maximum coincidence subarray R 'to obtain a phase operation, so as to estimate an initial estimation value of a difference between phase calibration errors of other array elements except the first antenna array element and the first antenna array element from R':
then, based on the initial arrival angle estimation value of the arrival direction of each signal source k obtained in the above steps, iterative updating is performed to obtain an arrival angle estimation value and a phase calibration error estimation value of the arrival direction.
Step 206, normalizing the random error of the first antenna received signal in the first received signal matrix, i.e. dividing each row element of the first received signal matrix by the corresponding element of the first row to obtain a second received signal:
where/is a dot division operation.
Step 207, for the second received signalThe covariance matrix is decomposed by Singular Value (SVD) to obtain an eigenvector matrix E corresponding to the signal subspacesEigenvector matrix E corresponding to noise subspacen：
Wherein E issIs a signal subspace matrix formed by the signal eigenvectors, EnIs a noise subspace matrix, Σ, formed by noise feature vectorssSum ΣnE is calculated from a diagonal matrix of signal subspace eigenvalues and noise subspace eigenvalues, respectivelyn。
And step 208, constructing a current cost function J according to the formula 12 based on the principle that the signal subspace is orthogonal to the noise subspace,
wherein,as is obtained from the equation 10, the,is an M-dimensional diagonal matrix formed by array element phase calibration errors, A ═ a (theta)1)，a(θ2)，...，a(θK)]The matrix is a guide matrix formed by M multiplied by K array element guide vectors;
due to the fact that
This gives:
in the formula,is the guide vector a (theta)k) Is a diagonal matrix of diagonal elements,a vector of initial estimated values of phase calibration errors;
thus, E is calculated based on equation 11-1, and step 208nTo find the transformation matrix T (θ):
step 209, minimizing the constructed cost function to obtain a first estimation value of the phase calibration error vector of each antenna array: specifically, the cost function is minimized according to equation 12,
wherein argmin represents the set of all phase calibration error estimates that make the cost function J take a minimum;
substituting the transformation matrix T (theta) obtained in step 208 into equation 12 to obtain a first estimated value of the phase calibration error of each antenna array
Step 210, obtaining eigenvector matrixes corresponding to 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 the first subarray and the second subarray of the first received signal constructed in step 202, respectively.
ES1＝P1Es(13)
ES2＝P2Es(14)
ES1And ES2First and second subarrays, P, respectively, of a signal subspace eigenvector matrix1＝[IM-10],P2＝[0 IM-1]Wherein I is an identity matrix;is a rotation matrix containing information of arrival angle of incoming wave direction.
Step 211, from ES1And ES2And the first estimation value of the phase calibration error of each array element, and solving the first estimation value of the angle of arrival theta:
because of having:
therefore, the following steps are carried out:
wherein,
and 212, substituting the first estimated phase calibration error value and the first estimated arrival angle value into a formula 11-1 to obtain a first cost function.
Step 213, determining whether an absolute value of a difference between the first cost function and the second cost function is smaller than a preset threshold, wherein the second cost function is 0 in the first iteration;
and if the absolute values of the first cost function and the second cost function are smaller than the preset threshold, executing step 214, stopping iteration, and outputting the first estimated phase calibration error value and the first estimated arrival angle value as final estimation results, otherwise, executing step 215, taking the first estimated phase calibration error value as an initial phase calibration error value and the first estimated arrival angle value as an initial arrival angle value, taking the first cost function as a second cost function, and returning to step 206 for the next iteration.
According to the method for estimating the arrival angle of the incoming wave direction of the antenna array, provided by the invention, when the array elements have large phase calibration errors, the arrival angle is accurately estimated based on the incoming wave direction of the array self-calibration. The advantages are that:
1. the phase calibration error estimated according to the signal structure characteristics and the initial value of the arrival angle of the incoming wave direction have high precision, and the stability of the performance of the algorithm is greatly improved.
2. When the phase calibration error of the array element is large, the estimation precision is high and stable.
3. In a millimeter wave communication system with a large-scale antenna array, the method solves the problems that the existing arrival angle estimation method is high in complexity and only suitable for phase errors in a small range, and has good popularization and application prospects.
Referring to fig. 3 and 4, fig. 3 is a simulation comparison diagram of the estimation error RMSE of the angle of arrival in the embodiment of the present invention, which respectively adopts the conventional angle estimation method (ESPRIT algorithm) and the estimation method of the present invention. Fig. 4 is a simulation comparison diagram of array element phase calibration errors RMSE in the embodiment of the present invention, which respectively adopt the uncorrected angle estimation method and the arrival angle estimation method of the present invention.
The simulation performed by the method of the invention: under the condition of an additive white Gaussian noise channel, a simulation implementation test chart with 1000 times of iteration times i is randomly generated, wherein the number K of signal sources is 2, the number M of array elements of a receiving array is 100, the receiving signal-to-noise ratio is 20dB, and the phase calibration error of the array elements isIndependently identically distributed and subject to a standard deviation of σφAre uniformly distributed, i.e. inAre uniformly distributed. Standard deviation sigma in simulationφVarying from 0 degrees to 10 degrees. The arrival angles of the two signal sources are respectively theta110 ° and θ2＝15°；J(0)＝100，Th＝10-6. The estimated performance metric uses the standard deviation of the estimation error, i.e.:whereinRepresents the m-th simulation in the n-th simulationThe phase alignment error estimate for the root antenna,whereinRepresenting the estimated value of the mth angle of arrival in the nth simulation. The simulation result shows that the estimation performance of the calibration error of the arrival angle and the phase of the array element in the embodiment of the invention is far better than that of the classical ESPRIT algorithm, which shows that when the receiving antenna array has larger phase calibration error, the method can still accurately estimate the calibration error value of the arrival angle and the phase of the array element.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for estimating arrival angle of incoming wave direction of antenna array is characterized in that the method includes,
eliminating pilot symbols from the received signal of each symbol period to obtain a first received signal vector;
splicing first receiving signal vectors of at least more than one symbol period into an M multiplied by K dimension first receiving signal matrix, wherein M is the array element number of a receiving antenna array, and K is the signal source number;
dividing the first received signal matrix into two sub-arrays with the maximum coincidence degree, and performing cancellation processing on corresponding elements of each row of the two sub-arrays respectively to obtain first maximum coincidence sub-arrays of each row containing incoming wave direction information;
averaging the phases of all the row vectors of the first maximum coincidence subarray to obtain an initial estimation value of the arrival angle of the incoming wave direction of each signal source;
eliminating an arrival angle component in the first maximum coincidence subarray according to the initial estimation value of the arrival angle to obtain a second maximum coincidence subarray; based on the second maximum coincidence subarray, calculating to obtain an initial estimation value of the difference between the phase calibration errors of other array elements except the first antenna array element and the first antenna array element;
iteration is carried out according to the following steps:
normalizing the random error of the first antenna in the first received signal matrix to obtain a second received signal;
performing 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;
constructing a current cost function based on the orthogonality of the signal subspace eigenvector matrix and the noise subspace eigenvector matrix according to the initial estimation value of the phase calibration error of each array element, and solving a transformation matrix according to the initial estimation value of the arrival angle of each signal source in the incoming wave direction;
solving a first estimated value of the phase calibration error of each array element according to the transformation array minimized current cost function;
obtaining two signal subspace characteristic vector submatrices through the structural decomposition of the signal subspace characteristic vector matrixes;
according to the two signal subspace characteristic vector quantum matrixes and the first estimated value of the phase calibration error of each array element, solving the first estimated value of the arrival angle of the incoming wave direction of each signal source;
calculating a 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 arrival angle of the incoming wave direction of each signal source;
judging whether the absolute value of the difference between the first cost function and the second cost function is smaller than a preset threshold value, wherein the second cost function is zero in the first iteration,
if so, stopping iteration, and outputting the first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of the incoming wave direction of each signal source as estimation results,
otherwise, taking the first estimated value of the phase calibration error of each array element as the initial estimated value of the phase calibration error of each array element, taking the first estimated value of the arrival angle of the incoming wave direction of each signal source as the initial estimated value of the arrival angle of the incoming wave direction of each signal source, taking the first cost function as the second cost function, and performing the next iteration.
2. The method of claim 1, wherein the signal model of the received signal for each symbol period is:
Y＝GAS+n
wherein,is an M-dimensional diagonal matrix formed by the phase calibration errors of the array elements, diag (a) represents the diagonal matrix, phimCalibrating the phase error of the m array element; a ═ a (θ)1)，a(θ2)，...，a(θK)]A steering matrix formed by M × K array element steering vectors
For signal steering vectors, thetakD and lambda are the array element spacing and the wavelength respectively, and d is lambda/2; s is an energy-normalized pilot signal matrix, and E { SSH}＝IK(ii) a n is a white noise vector and hasI is an identity matrix;
the removing the pilot symbols from the received signal in each symbol period to obtain a first received signal vector includes: according to the formulaObtaining the first received signal vector;
the first receiving signal matrix is divided into two sub-arrays with the maximum coincidence degree, corresponding elements of each row of the two sub-arrays are subjected to destructive processing respectively to obtain first maximum coincidence sub-arrays of each row containing incoming wave direction information,
taking the first row to the M-1 th row and the K dimension of a first receiving signal matrix as a first subarray of a first receiving signal, and taking the second row to the M-th row and the K dimension of the first receiving signal matrix as a second subarray of the first receiving signal;
and correspondingly performing point division on each row of elements in the second subarray and each row of elements in the first subarray respectively to obtain a (M-1) xK-dimensional first maximum coincidence subarray.
3. The method of claim 1, wherein said removing the angle-of-arrival component from the first maximum coincidence sub-array based on the initial estimate of the angle-of-arrival to obtain the second maximum coincidence sub-array comprises, according to a formulaCalculating to obtain the second maximum coincidence subarray R', wherein R is the first maximum coincidence subarray thetakThe initial estimated value of the arrival angle of the incoming wave direction of the signal source k is obtained.
4. The method of claim 1 wherein computing an initial estimate of the difference between the phase alignment errors of the elements other than the first antenna element and the first antenna element based on the second maximum coincidence subarray comprises,
according to the formulaCalculating to obtain the phase calibration error of other array elements except the first antenna array element and the first antenna array elementThe initial estimate of the difference between the differences, wherein,
φ1calibrating an error value for the phase of the first wire array element; phase is a phase operation, and R' (n) represents the nth row element in the second maximum coincidence subarray.
5. The method of claim 1, wherein normalizing the random error of the first antenna in the first received signal matrix to obtain the second received signal comprises,
and dividing each row element of the first receiving signal matrix by the corresponding element of the first row to obtain the second receiving signal.
6. The method of claim 1, wherein the performing a 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 comprises,
according to the formulaCalculating the signal subspace eigenvector matrix EsNoise subspace eigenvector matrix EnWherein, sigmasSum ΣnRespectively, the diagonal arrays are formed by the signal subspace characteristic values and the noise subspace characteristic values.
7. The method of claim 1, wherein constructing a current cost function based on the signal subspace eigenvector matrix being orthogonal to a noise subspace eigenvector matrix and solving for a transform matrix comprises,
according to the formulaConstructing a current cost function J, wherein EnIs a matrix of noise subspace feature vectors,is an M-dimensional diagonal matrix formed by initial estimation values of phase alignment errors of M array elements, wherein A is (a (theta)1)，a(θ2)，...，a(θk)]Is an M x K dimensional array element steering vector α (theta)k) A steering matrix is formed;
feature vector matrix E based on noise subspacenAccording to the formulaA transformation matrix T (theta) is calculated, wherein,is the guide vector α (theta)k) Is a diagonal matrix of diagonal elements.
8. The method of claim 1, wherein minimizing the current cost function and solving the first estimate of the phase alignment error for each array element based on the transformation array comprises, according to equation 1
Solving a set of all phase calibration error estimation values enabling the cost function J to obtain a minimum value, wherein argmin represents the set of all phase calibration error estimation values enabling the cost function J to obtain the minimum value;
substituting the obtained transformation matrix T (theta) into the formula 1 to obtainA first estimated value vector of phase calibration errors of M array elements;
according to the first estimated value vector of the phase calibration errors of the M array elements and a formulaObtaining a first estimate of the phase calibration error for each antenna arrayEvaluating value
9. The method of claim 2, wherein said obtaining two signal subspace eigenvector submatrices by structural decomposition of the signal subspace eigenvector comprises, according to formula
ES1＝P1EsAnd ES2＝P2EsRespectively obtaining the signal subspaces E corresponding to the first subarrays of the first received signalS1The signal subspace E corresponding to the second subarray of the first received signalS2Wherein P is1＝[IM-10]，P2＝[0 IM-1]And I is an identity matrix.
10. The method of claim 1 wherein said solving for a first estimate of the arrival angle of the incoming wave direction of each signal source based on said two sub-matrices of received signals and a first estimate of the phase alignment error for each array element comprises,
according to the formulaSolving for the first estimate of the angle of arrival, wherein,
the calculating 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 arrival angle of the incoming wave direction of each signal source comprises,
and substituting the obtained first estimated value of the phase calibration error of each array element and the first estimated value of the arrival angle of the incoming wave direction of each signal source into a formula J-gHT (theta) g, to obtain a first cost function.
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