CN109738854B - Arrival angle estimation method for arrival direction of antenna array - Google Patents
Arrival angle estimation method for arrival direction of antenna array Download PDFInfo
- Publication number
- CN109738854B CN109738854B CN201811529049.0A CN201811529049A CN109738854B CN 109738854 B CN109738854 B CN 109738854B CN 201811529049 A CN201811529049 A CN 201811529049A CN 109738854 B CN109738854 B CN 109738854B
- Authority
- CN
- China
- Prior art keywords
- matrix
- signal
- array
- phase
- array element
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Abstract
The application discloses an arrival angle estimation method of an antenna array incoming wave direction, which comprises the steps of constructing a maximum coincidence subarray 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 through subspace-based self-calibration, obtaining an initial estimation value with more accurate array phase calibration errors and arrival angles, designing an iterative optimization algorithm by utilizing the orthogonality of a signal subspace and a noise subspace, achieving iterative updating estimation of the arrival angles and the phase calibration errors, and obtaining accurate angle estimation. The method can obtain excellent angle estimation performance when the array elements have larger phase calibration errors.
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. L iu, L, ZHao, Y. L i, X.Jning and T.K.Truong, "A space-Based applied elevation for DOA Estimation and alignment in Uniform L inner Array," in IEEESensors Journal, vol.16, No.15, pp.6018-6027, and Aug.1, 602' propose an arrival angle Estimation algorithm that can solve the mutual coupling effect, the position deviation of the Array elements and the amplitude and phase error of the Array elements, and carry out convex optimization search solution by using the sparsity of the Array matrix, and have poor performance when the Calibration error of the Array is large.
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 × K-dimensional first receiving signal matrix, wherein M is the number of array elements of a receiving antenna array, and K is the number of signal sources;
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.
Drawings
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 the content of the first and second substances,
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)]Is a steering matrix formed by M × K-dimensional 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 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 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 matrix
Adjacent columns contain the same incoming wave direction arrival angle and doAnd the same phase calibration error is obtained, 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 the corresponding row in the two sub-matrixes is subjected to line-by-line point 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 a first sub-matrix of the first received signal matrix, the second row to the M-th row and the K dimensionality are taken as a second sub-matrix of the first received signal matrix, each row element in the second sub-matrix and each row element in the first sub-matrix are respectively subjected to point division to obtain a (M-1) × K dimensionality first maximum coincidence sub-matrix:
wherein
To represent
The (M-1) × K-dimensional matrix R has an nth row:
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:
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.
where/is a dot division operation.
Wherein E issIs a signal subspace matrix formed by the signal eigenvectors, EnA noise subspace matrix formed by the noise feature vectors, ∑sAnd ∑nE 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 the content of the first and second substances,
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 steering matrix is formed by array element steering vectors of M × K dimensions;
due to the fact that
This gives:
in the formula (I), the compound is shown in the specification,
is guided byVector a (θ)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):
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
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.
because of having:
therefore, the following steps are carried out:
wherein the content of the first and second substances,
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 is
Independently identically distributed and subject to a standard deviation of σφAre uniformly distributed, i.e. in
Are uniformly distributed. Standard deviation sigma in simulationφVarying from 0 degrees to 10 degrees. The arrival angles of the two signal sources are respectively theta 110 ° and θ2＝15°；J(0)＝100，Th＝10-6. The estimated performance metric uses the standard deviation of the estimation error, i.e.:
wherein
Representing the estimated phase alignment error for the mth antenna in the nth simulation,
wherein
Representing 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 × K-dimensional first receiving signal matrix, wherein M is the number of array elements of a receiving antenna array, and K is the number of signal sources;
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 the content of the first and second substances,
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)]Is a steering matrix formed by array element steering vectors of M × K dimension, wherein,
the removing the pilot symbols from the received signal in each symbol period to obtain a first received signal vector includes: according to the formula
Obtaining the first received signal vector, wherein,
in order to eliminate white noise after pilot frequency symbols;
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 an (M-1) × K-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 formula
Calculating to obtain the second maximum coincidence subarray R', wherein R is the first maximum coincidence subarray thetakIs the incoming wave direction of signal source kAn initial estimate of the angle of arrival.
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 formula
Calculating the initial estimation value of the difference between the phase calibration errors of the first antenna array element and the other array elements except the first antenna array element, 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 formula
Calculating the signal subspace eigenvector matrix EsNoise subspace eigenvector matrix EnWherein, ∑sAnd ∑nRespectively, 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 the current cost function based on the signal subspace eigenvector matrix being orthogonal to the noise subspace eigenvector matrix and solving for the transformation matrix comprises, according to a formula
Constructing 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 calibration errors of M array elements, and A ═ a (theta)1)，a(θ2)，...，a(θK)]Is an array element guide vector a (theta) of M × K dimensionk) A steering matrix is formed;
feature vector matrix E based on noise subspacenAccording to the formula
A transformation matrix T (theta) is calculated, wherein,
is the guide vector a (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;
the obtained transformationSubstituting the matrix T (theta) into the formula 1 to obtain
A 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 formula
Obtaining a first estimated value of phase calibration error of each antenna array
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 formula
Solving 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.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811529049.0A CN109738854B (en) | 2018-12-14 | 2018-12-14 | Arrival angle estimation method for arrival direction of antenna array |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811529049.0A CN109738854B (en) | 2018-12-14 | 2018-12-14 | Arrival angle estimation method for arrival direction of antenna array |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109738854A CN109738854A (en) | 2019-05-10 |
| CN109738854B true CN109738854B (en) | 2020-07-10 |
Family
ID=66359436
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811529049.0A Active CN109738854B (en) | 2018-12-14 | 2018-12-14 | Arrival angle estimation method for arrival direction of antenna array |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109738854B (en) |
Families Citing this family (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114391229B (en) * | 2019-10-04 | 2023-04-11 | 华为技术有限公司 | Low complexity angle of arrival (AOA) array calibration |
| CN110687500B (en) * | 2019-10-28 | 2023-05-16 | 武汉大学 | Identification and positioning method and system for acquiring wireless signal arrival angle by intelligent antenna |
| CN112904321B (en) * | 2019-12-03 | 2023-01-17 | 复旦大学 | Method for calibrating even linear array cross coupling and array element gain-phase error |
| CN111413668B (en) * | 2020-04-15 | 2022-04-01 | 南京航空航天大学 | DOA estimation method based on DFT enhancement in large-scale array |
| CN111983556B (en) * | 2020-08-19 | 2023-01-24 | 杭州电子科技大学 | Device and method for estimating angle of arrival |
| CN112285641B (en) * | 2020-09-16 | 2023-12-29 | 西安空间无线电技术研究所 | ICA-based DOA (direction of arrival) estimation method and device |
| CN112305494B (en) * | 2020-10-23 | 2023-12-12 | 北京邮电大学 | Sensor position calibration method and device |
| CN112986935B (en) * | 2021-02-24 | 2022-12-20 | 湖北中南鹏力海洋探测系统工程有限公司 | Multi-element array channel passive calibration method based on landform conformal arrangement |
| CN113242099B (en) * | 2021-03-19 | 2022-11-15 | 天津科畅慧通信息技术有限公司 | Phased array antenna installation parameter calibration method based on gradient descent algorithm |
| CN113114390B (en) * | 2021-04-30 | 2023-04-07 | 网络通信与安全紫金山实验室 | Array OTA (over the air) array form calibration method and calibration system based on broadband signals |
| CN113821907B (en) * | 2021-08-19 | 2024-03-19 | 南京理工大学 | Amplitude and phase automatic calibration method for large planar antenna array system |
| CN114339991B (en) * | 2022-01-14 | 2024-02-02 | 网络通信与安全紫金山实验室 | AoA estimation method, device, base station, storage medium and computer program product |
| CN114609579B (en) * | 2022-03-23 | 2023-05-12 | 电子科技大学 | Defocus direction finding error correction method |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5583502A (en) * | 1993-11-04 | 1996-12-10 | Mitsubishi Denki Kabushiki Kaisha | A-D converter testing circuit and D-A converter testing circuit |
| GB2347036A (en) * | 1999-01-06 | 2000-08-23 | Nec Corp | Estimating arrival direction of a repeatedly transmitted signal, using cross-correlation |
| SU1840427A1 (en) * | 1986-02-20 | 2007-03-20 | Нижегородский научно-исследовательский институт радиотехники | Adaptive antenna array |
| CN104375133A (en) * | 2014-11-11 | 2015-02-25 | 西北大学 | Estimation method for space two-dimensional DOA |
| CN104407335A (en) * | 2014-10-24 | 2015-03-11 | 哈尔滨工业大学深圳研究生院 | DOA estimation method of 3-axis cross array |
| CN104698430A (en) * | 2015-03-27 | 2015-06-10 | 北京邮电大学 | Virtual array antenna based angle estimation method for improving accuracy |
| CN105246086A (en) * | 2015-10-08 | 2016-01-13 | 北京邮电大学 | Method and equipment for determining antenna angles |
| CN105891771A (en) * | 2016-04-06 | 2016-08-24 | 北京邮电大学 | Continuous distribution-based angle estimation method and device for improving estimation precision |
| CN108872930A (en) * | 2018-08-28 | 2018-11-23 | 天津大学 | Extend aperture two dimension Joint diagonalization DOA estimation method |
-
2018
- 2018-12-14 CN CN201811529049.0A patent/CN109738854B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SU1840427A1 (en) * | 1986-02-20 | 2007-03-20 | Нижегородский научно-исследовательский институт радиотехники | Adaptive antenna array |
| US5583502A (en) * | 1993-11-04 | 1996-12-10 | Mitsubishi Denki Kabushiki Kaisha | A-D converter testing circuit and D-A converter testing circuit |
| GB2347036A (en) * | 1999-01-06 | 2000-08-23 | Nec Corp | Estimating arrival direction of a repeatedly transmitted signal, using cross-correlation |
| CN104407335A (en) * | 2014-10-24 | 2015-03-11 | 哈尔滨工业大学深圳研究生院 | DOA estimation method of 3-axis cross array |
| CN104375133A (en) * | 2014-11-11 | 2015-02-25 | 西北大学 | Estimation method for space two-dimensional DOA |
| CN104698430A (en) * | 2015-03-27 | 2015-06-10 | 北京邮电大学 | Virtual array antenna based angle estimation method for improving accuracy |
| CN105246086A (en) * | 2015-10-08 | 2016-01-13 | 北京邮电大学 | Method and equipment for determining antenna angles |
| CN105891771A (en) * | 2016-04-06 | 2016-08-24 | 北京邮电大学 | Continuous distribution-based angle estimation method and device for improving estimation precision |
| CN108872930A (en) * | 2018-08-28 | 2018-11-23 | 天津大学 | Extend aperture two dimension Joint diagonalization DOA estimation method |
Non-Patent Citations (2)
| Title |
|---|
| An Enhanced Channel Estimation Method for Millimeter Wave Systems With Massive Antenna Arrays;Yuexing Peng et al.;《IEEE COMMUNICATIONS LETTERS》;20150930;第1592-1595页 * |
| 基于抵消干扰信号相关阵的DOA估计;王维新 等;《东南大学学报(自然科学版)》;20040531;第301-304页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109738854A (en) | 2019-05-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109738854B (en) | Arrival angle estimation method for arrival direction of antenna array | |
| CN109765519B (en) | Angle estimation method of analog-digital hybrid antenna array | |
| CN112130111B (en) | Single-snapshot two-dimensional DOA estimation method in large-scale uniform cross array | |
| CN111239678A (en) | Two-dimensional DOA estimation method based on L-shaped array | |
| CN113189592B (en) | Vehicle-mounted millimeter wave MIMO radar angle measurement method considering amplitude mutual coupling error | |
| CN111239677A (en) | Multi-beam passive monopulse angle measurement method based on digital array | |
| CN112255629A (en) | Sequential ESPRIT two-dimensional incoherent distribution source parameter estimation method based on combined UCA array | |
| CN113835063B (en) | Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method | |
| CN109725298B (en) | Array flow pattern error calibration and direction of arrival estimation method based on rank loss root-finding | |
| Li et al. | Joint calibration algorithm for gain-phase and mutual coupling errors in uniform linear array | |
| Ateşavcı et al. | DoA estimation in the presence of mutual coupling using root-MUSIC algorithm | |
| Li et al. | Mutual coupling self-calibration algorithm for uniform linear array based on ESPRIT | |
| Luo et al. | Direction finding for bistatic MIMO radar using a sparse moving array with sensor position errors | |
| Ping et al. | Study of 2D DOA estimation for uniform circular array in wireless location system | |
| CN109407047B (en) | Amplitude-phase error calibration and direction-of-arrival estimation method based on rank loss root finding | |
| Dai et al. | Central direction-of-arrival estimation of coherently distributed sources for antenna arrays with gain-phase errors | |
| CN111352063A (en) | Two-dimensional direction finding estimation method based on polynomial root finding in uniform area array | |
| Peng et al. | An improved gain-phase error self-calibration method for robust DOA estimation | |
| Qin et al. | DOA estimation and mutual coupling calibration algorithm for array in plasma environment | |
| Hu et al. | Adaptive beamforming based on compressed sensing with gain/phase uncertainties | |
| Du et al. | An effective algorithm for gain-phase error and angle estimation in MIMO radar | |
| Xu et al. | Direction of arrival estimation with gain-phase uncertainties in unknown nonuniform noise | |
| Dai et al. | A calibration method for linear arrays in the presence of gain-phase errors | |
| Thet et al. | Reduced-rank joint estimation of DOA with mutual coupling | |
| Elbir et al. | Terahertz-Band Direction Finding With Beam-Split and Mutual Coupling Calibration |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |