CN112731279A - Arrival angle estimation method based on hybrid antenna subarray - Google Patents

Arrival angle estimation method based on hybrid antenna subarray Download PDF

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CN112731279A
CN112731279A CN202011429950.8A CN202011429950A CN112731279A CN 112731279 A CN112731279 A CN 112731279A CN 202011429950 A CN202011429950 A CN 202011429950A CN 112731279 A CN112731279 A CN 112731279A
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CN112731279B (en
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郭子钰
曾晓洋
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Fudan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/46—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
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Abstract

The invention discloses an arrival angle estimation method based on a hybrid antenna subarray. The method specifically comprises the following steps: optimizing the number of antennas of each subarray; constructing an output signal model of the sub array under the optimized mixed antenna sub array structure; calculating the cross correlation between output signals of each subarray; extracting the phase of the cross-correlation and performing a modulus operation; constructing an optimization problem for estimating the arrival angle and solving an optimal solution; and converting according to the optimal solution of the optimization problem to obtain the zenith angle and the azimuth angle of the incoming wave. The invention avoids the angle fuzzy effect of the arrival angle estimation by optimizing the number of the antennas of the subarray, and does not need complex operations such as matrix decomposition, inversion and the like in the calculation process. The invention is suitable for an actual communication system adopting the mixed antenna subarray, can effectively realize high-precision arrival angle estimation by utilizing digital signal processing with low power consumption, low cost and low time delay, and provides a precondition guarantee for subsequent signal processing technologies such as beam forming, space division multiplexing, wavelength division multiple access and the like.

Description

Arrival angle estimation method based on hybrid antenna subarray
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to an arrival angle estimation method based on a hybrid antenna subarray.
Background
In order to compensate for the path loss of the high-band electromagnetic wave signal, a large-scale antenna array and a beamforming technique are usually used to improve the received signal-to-noise ratio of the target user. It should be noted that this signal-to-noise ratio improvement is directional, i.e., the received signal-to-noise ratio of the target user is improved only when it is beam-aligned. Therefore, to improve the signal-to-noise ratio of the target user, the direction information of the target user must be obtained through the angle-of-arrival estimation.
In order to reduce power consumption and cost, large-scale antenna arrays often employ hybrid antenna sub-array structures. In this structure, the number of radio frequency channels (RF chain) is much smaller than the number of antennas, and the connection relationship between them is as follows: all antennas are divided into non-overlapping sub-arrays, and antennas belonging to the same sub-array are connected with a single radio frequency channel. This particular structure complicates the angle-of-arrival estimation problem.
The traditional arrival angle estimation methods mainly comprise a signal subspace method represented by MUSIC and ESPRIT and a compressive sensing method, the computation complexity of the methods is high, the methods are not suitable for being applied to a portable wireless terminal, and the methods have the problem of angle blurring effect, namely, the estimation result of the arrival angle is not unique, and the algorithm cannot identify a real arrival angle from the estimation result. The arrival angle estimation method using low-complexity beam scanning is capable of avoiding the angle ambiguity effect, but if a high estimation accuracy is to be achieved, it needs to occupy a lot of time domain resources, which may cause a high delay in an actual communication system.
An arrival angle estimation method is proposed based on a hybrid antenna sub-array structure, x.huang, y.jay Guo and j.d.bunton (a hybrid adaptive antenna array, "IEEE trans. wireless commun., vol.9, No.5, pp.1770-1779,2010, 5 months). This method produces an angle blurring effect. Wu, W.Ni, T.Su, R.P.Liu and Y.J.Guo (Robust unambiguated estimation of angle-of-arrival in hybrid array with localized analog subarrays, "IEEE trans.Wireless Commun., vol.17, No.5, pp.2987-3002,2018, month 5) propose an angle-of-arrival estimation method. The method avoids the angle blurring effect, but adds constraints to the beam pointing directions of each sub-array, which greatly limits the application of the method in practical scenes.
Disclosure of Invention
The invention provides a new arrival angle estimation method based on a hybrid antenna subarray aiming at the problems in the background technology, which mainly solves the following technical problems: eliminating the angle fuzzy effect on the premise of not restricting the sub-array beam direction; and the high-precision arrival angle estimation is realized by using low-complexity operation and less time domain resources.
In order to solve the technical problems, the invention adopts the following technical scheme.
An arrival angle estimation method based on a hybrid antenna sub-array comprises the following steps:
optimizing the number of antennas of each subarray;
constructing an output signal model of the sub array under the optimized mixed antenna sub array structure;
calculating the cross correlation between output signals of each subarray; extracting the phase of the cross-correlation and performing a modulus operation;
constructing an optimization problem for estimating the arrival angle and solving an optimal solution;
and converting according to the optimal solution of the optimization problem to obtain the zenith angle and the azimuth angle of the incoming wave.
Specifically, in the invention, the optimized hybrid antenna subarray structure can eliminate the angle blurring effect, and has the following characteristics:
1)Nxline NyColumn total NxNyThe antennas are uniformly arranged in the horizontal and vertical directions with an arrangement interval d in the horizontal directionyThe arrangement interval in the vertical direction is dx；
2) In the vertical direction, NxThe line antenna is divided into L blocks, where the L-th block has a number of lines
Figure BDA0002826292900000021
3) In the horizontal direction, NyThe column antennas are divided into K blocks, where the number of columns of the K block is
Figure BDA0002826292900000022
4) By dividing the characteristics 2) and 3), the antenna array is divided into L × K sub-arrays, wherein the (L, K) th sub-array has
Figure BDA0002826292900000023
A root antenna;
5) l and K are both greater than or equal to 3;
6) for the division in feature 2), there is a certain subscript i, which corresponds to
Figure BDA0002826292900000024
Is an odd number, i is more than or equal to 1 and less than or equal to L-1;
7) for the division in feature 3), there is some subscript j, which corresponds to
Figure BDA0002826292900000025
Is odd number, j is more than or equal to 1 and less than or equal to K-1;
8) for the index i in feature 6), there is another different index
Figure BDA0002826292900000026
It corresponds to
Figure BDA0002826292900000027
And
Figure BDA0002826292900000028
the quality of the mixture is relatively prime,
Figure BDA0002826292900000029
9) for the index j in feature 7), there is another different index
Figure BDA00028262929000000210
It corresponds to
Figure BDA00028262929000000211
And
Figure BDA00028262929000000212
the quality of the mixture is relatively prime,
Figure BDA00028262929000000213
10) in thatThe sub-array described in feature 4) has each antenna directly connected to a phase shifting device, so that the (l, k) th sub-array has
Figure BDA00028262929000000214
And the output signals of the phase shifters are superposed together and are sent to the radio frequency channels corresponding to the sub-arrays one by one for digital sampling.
Further, on the basis of the above-mentioned characteristic hybrid antenna sub-array structure, a method for estimating an angle of arrival is provided, which includes the following steps:
1) order to
Figure BDA00028262929000000215
Denotes the beam pointing of the (l, k) th sub-array, wherein
Figure BDA00028262929000000216
And
Figure BDA00028262929000000217
can be taken as (-pi, pi)]Any value in the range, the (l, k) th sub-array may be represented as a phase modulation factor
Figure BDA00028262929000000218
Wherein
Figure BDA0002826292900000031
Represents the kronecker product, and
Figure BDA0002826292900000032
then order slk(t) represents the sampled output of the RF channel corresponding to the (L, k) th sub-array at time t, then preferably with the subscript k fixed, L-1 cross-correlation observations can be obtained
Figure BDA0002826292900000033
Where K is an arbitrary value from 1 to K, T represents the number of samples, (x)*Meaning that the conjugate is taken for x,
Figure BDA0002826292900000034
and
Figure BDA0002826292900000035
defined in features 2) and 3), respectively;
2) similar to step 1), preferably fixing the subscript l makes it possible to obtain K-1 cross-correlation observations
Figure BDA0002826292900000036
Wherein L is any value from 1 to L;
3) the L-1 observations obtained in step 1) were processed as follows
Figure BDA0002826292900000037
Where < (x) denotes the phase taken for x, mod(-π,π]{ x } denotes the interval (- π, π) for x]Taking a mould internally;
4) the K-1 observations obtained in step 2) were processed as follows
Figure BDA0002826292900000038
5) Order to
Figure BDA0002826292900000039
The elements are given in step 3), and q is then made to be [ q ]1,…,qL-1]TFor any L-1 dimensional vector, a new vector is defined
Figure BDA00028262929000000310
Wherein
Figure BDA00028262929000000313
Representing the multiplication of corresponding elements and then solving the following optimization problem, preferably using an exhaustive method
Figure BDA00028262929000000311
Where max { x } represents the maximum value of vector x, min { x } represents the minimum value of vector x, preferably DqRepresenting a solution space
Figure BDA00028262929000000312
The optimal solution to the optimization problem is recorded as
Figure BDA0002826292900000041
6) Order to
Figure BDA0002826292900000042
The element is given in step 4), and p is ═ p1,…,pK-1]TDefining new vectors for arbitrary K-1 dimensional vectors
Figure BDA0002826292900000043
The following optimization problem is then solved, preferably by means of an exhaustive method
Figure BDA0002826292900000044
Wherein preferably DpRepresenting a solution space
Figure BDA0002826292900000045
Recording the optimal solution of the optimization problemIs composed of
Figure BDA0002826292900000046
7) Order to
Figure BDA0002826292900000047
Wherein
Figure BDA00028262929000000413
And
Figure BDA0002826292900000048
given in step 5) of the method,
Figure BDA0002826292900000049
and
Figure BDA00028262929000000410
given in step 6), the estimated values of the azimuth angle and the zenith angle are respectively
Figure BDA00028262929000000411
And
Figure BDA00028262929000000412
where λ denotes the wavelength of the electromagnetic wave, sign (x) denotes the sign of x, dyAnd dxDefined in feature 1), tan-1(. ang.) and sin-1(. cndot.) denotes arctan and arcsine functions, respectively.
Compared with the prior art, the invention has the following technical effects:
1) the invention eliminates the angle fuzzy effect problem of the arrival angle estimation under the mixed antenna subarray structure by optimizing the number of the antennas contained in the subarray, does not need to carry out special constraint on the beam direction of the subarray, and provides great convenience for solving the arrival angle estimation problem in an actual system;
2) the arrival angle estimation method provided by the invention does not need complex matrix operations such as eigenvalue decomposition, inversion, SVD decomposition and the like, and can effectively reduce the calculation complexity and the power consumption of a hardware operation unit;
3) the arrival angle estimation method provided by the invention is an off-grid (off-grid) method, namely, the angle domain does not need to be quantized, so that ultrahigh angle resolution can be realized.
Drawings
Fig. 1 is a schematic diagram of the hybrid antenna sub-array antenna partitioning of the present invention.
Fig. 2 is a schematic diagram of the hybrid antenna sub-array phase shifter and rf channel connection of the present invention.
Fig. 3 is a schematic view of the zenith and azimuth angles of the present invention.
FIG. 4 is a computational flow diagram of the present invention.
Fig. 5 shows the average error of the angle-of-arrival estimation under different signal-to-noise ratios.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in FIG. 1, NxLine NyColumn total NxNyThe antennas are uniformly arranged in the horizontal and vertical directions with an arrangement interval d in the horizontal directionyThe arrangement interval in the vertical direction is dx. In the vertical direction, NxThe line antenna is divided into L blocks, where the L-th block has a number of lines
Figure BDA0002826292900000051
In the horizontal direction, NyThe column antennas are divided into K blocks, where the number of columns of the K block is
Figure BDA0002826292900000052
K is 1, K. Thereby obtaining L × K antenna sub-arrays, wherein the (L, K) th sub-array has
Figure BDA0002826292900000053
A root antenna. In order to avoid the angle ambiguity effect of the arrival angle estimation, the number of the antennas of the sub-array is optimized as follows:
1) ensuring that both L and K are greater than or equal to 3;
2) ensuring the presence of a certain index i, corresponding thereto
Figure BDA0002826292900000054
Is an odd number, i is more than or equal to 1 and less than or equal to L-1;
3) ensuring the presence of a certain index j, which corresponds to
Figure BDA0002826292900000055
Is odd number, j is more than or equal to 1 and less than or equal to K-1;
4) for the index i in 2), it is ensured that a different index is present
Figure BDA0002826292900000056
It corresponds to
Figure BDA0002826292900000057
And
Figure BDA0002826292900000058
the quality of the mixture is relatively prime,
Figure BDA0002826292900000059
5) for the index j in 3), it is ensured that a different index is present
Figure BDA00028262929000000510
It corresponds to
Figure BDA00028262929000000511
And
Figure BDA00028262929000000512
the quality of the mixture is relatively prime,
Figure BDA00028262929000000513
at each oneIn the antenna subarray, each antenna is directly connected with a phase shifter, output signals of the phase shifters are superposed together, and the superposed signals are sent to radio frequency channels corresponding to the subarray one by one to carry out digital sampling. FIG. 2 shows an example, where Nx1, i.e. corresponding to a one-dimensional linear array, skAnd (t) represents the digital sampling output of the kth radio frequency channel at the time t, wherein K is 1, … and K.
Based on the optimized antenna subarray structure, the arrival angle estimation is carried out according to the following mode:
as shown in FIG. 3, let θ and φ denote the zenith and azimuth angles of the incoming wave, respectively; reissue to order
Figure BDA00028262929000000514
And
Figure BDA00028262929000000515
where λ represents the wavelength of the electromagnetic wave signal, then the output of the radio frequency channel corresponding to the (l, k) sub-array can be expressed as
Figure BDA0002826292900000061
Wherein
Figure BDA0002826292900000062
Denotes the beam pointing direction of the (l, k) th sub-array, s (t) denotes the received complex signal, wlk(t) represents a noise term.
As shown in fig. 4, the calculation process of the present invention preferably includes cross-correlation calculation, phase extraction, optimization problem solving, and arrival angle demapping, and the correlation calculation process is further described below.
Preferably, by fixing the index k, L-1 cross-correlation observations can be obtained
Figure BDA0002826292900000063
Where K is an arbitrary value from 1 to K, T represents the number of samples, (x)*Representing the conjugation of x;similarly, preferably the fixed subscript l can obtain K-1 cross-correlation observations
Figure BDA0002826292900000064
Where L is any value from 1 to L.
The observed quantity can be obtained by processing
Figure BDA0002826292900000065
And
Figure BDA0002826292900000066
where < (x) denotes the phase taken for x, mod(-π,π]{ x } denotes the interval (- π, π) for x]And (6) internal mold taking.
Order to
Figure BDA0002826292900000067
Let q be [ q ]1,…,qL-1]TFor any L-1 dimensional vector, a new vector is defined
Figure BDA0002826292900000068
Wherein
Figure BDA00028262929000000610
Representing the multiplication of corresponding elements and then solving the following optimization problem, preferably using an exhaustive method
Figure BDA0002826292900000069
Where max { x } represents the maximum value of vector x, min { x } represents the minimum value of vector x, preferably DqRepresenting a solution space
Figure BDA0002826292900000071
The optimal solution to the optimization problem is recorded as
Figure BDA0002826292900000072
Memo
Figure BDA0002826292900000073
Order to
Figure BDA0002826292900000074
The element is given in step 4), and p is ═ p1,…,pK-1]TDefining new vectors for arbitrary K-1 dimensional vectors
Figure BDA0002826292900000075
The following optimization problem is then solved, preferably by means of an exhaustive method
Figure BDA0002826292900000076
Wherein preferably DpRepresenting a solution space
Figure BDA0002826292900000077
The optimal solution to the optimization problem is recorded as
Figure BDA0002826292900000078
Memo
Figure BDA0002826292900000079
The final azimuth angle estimation and zenith angle evaluation values of the incoming wave are respectively as follows:
Figure BDA00028262929000000710
and
Figure BDA00028262929000000711
wherein λ represents the wavelength of the electromagnetic wave, sign (x) represents the sign of x, tan-1(. ang.) and sin-1(. cndot.) denotes arctan and arcsine functions, respectively.
A verification example of the present invention is given below by computer simulation. The simulation parameters are set as follows: n is a radical ofx＝L＝1，Ny＝32，K＝4，
Figure BDA00028262929000000712
φ＝0，θ∈(-π,π]，dyThe signal-to-noise ratio is defined as the ratio of the power of the signal at the antenna end to the power of the noise. In the simulation process, the invention determines the beam direction of each sub-array through coarse scanning
Figure BDA0002826292900000081
The simulation result is shown in fig. 5, when the signal-to-noise ratio reaches 15dB, the average value of the estimation error of the arrival angle of the invention is less than 1 degree, and the invention has good direction-finding performance.
The above examples are only preferred embodiments of the present invention, it being noted that: it is obvious to those skilled in the art that various modifications can be made based on the technical idea of the present invention, and these modifications also belong to the protection scope of the present invention.

Claims (1)

1. An arrival angle estimation method based on a mixed antenna subarray is characterized by comprising the following specific steps:
step one, optimizing the number of antennas of each sub array;
Nxline NyColumn total NxNyThe antennas are uniformly arranged in the horizontal and vertical directions with an arrangement interval d in the horizontal directionyIn the vertical directionColumn interval dx. In the vertical direction, NxThe line antenna is divided into L blocks, where the L-th block has a number of lines
Figure FDA0002826292890000011
In the horizontal direction, NyThe column antennas are divided into K blocks, where the number of columns of the K block is
Figure FDA0002826292890000012
Thereby obtaining L × K antenna sub-arrays, wherein the (L, K) th sub-array has
Figure FDA0002826292890000013
A root antenna; in order to avoid the angle ambiguity effect of the arrival angle estimation, the number of the antennas of the sub-array is optimized as follows:
1) ensuring that both L and K are greater than or equal to 3;
2) ensuring the presence of a certain index i, corresponding thereto
Figure FDA0002826292890000014
Is an odd number, i is more than or equal to 1 and less than or equal to L-1;
3) ensuring the presence of a certain index j, which corresponds to
Figure FDA0002826292890000015
Is odd number, j is more than or equal to 1 and less than or equal to K-1;
4) for the index i in 2), it is ensured that a different index is present
Figure FDA0002826292890000016
It corresponds to
Figure FDA0002826292890000017
And
Figure FDA0002826292890000018
the quality of the mixture is relatively prime,
Figure FDA0002826292890000019
5) for the index j in 3), it is ensured that a different index is present
Figure FDA00028262928900000110
It corresponds to
Figure FDA00028262928900000111
And
Figure FDA00028262928900000112
the quality of the mixture is relatively prime,
Figure FDA00028262928900000113
in each antenna subarray, each antenna is directly connected with a phase shifter, output signals of the phase shifters are superposed together, and the superposed signals are sent to radio frequency channels corresponding to the subarrays one by one for digital sampling;
secondly, constructing an output signal model of the sub array under the optimized mixed antenna sub array structure;
let theta and phi denote the zenith angle and azimuth angle of the incoming wave, respectively; reissue to order
Figure FDA00028262928900000114
And
Figure FDA00028262928900000115
where λ represents the wavelength of the electromagnetic wave signal, then the output of the radio frequency channel corresponding to the (l, k) sub-array is represented as
Figure FDA00028262928900000116
Wherein
Figure FDA00028262928900000117
Denotes the (l, k)Beam pointing of the sub-array, s (t) representing the received complex signal, wlk(t) represents a noise term;
step three, calculating the cross correlation among output signals of each subarray;
obtaining L-1 cross-correlation observations by fixing subscript k
Figure FDA00028262928900000118
Where K is an arbitrary value from 1 to K, T represents the number of samples, (x)*Representing the conjugation of x;
the fixed subscript l can obtain K-1 cross-correlation observations
Figure FDA0002826292890000021
Wherein L is any value from 1 to L;
step four, extracting the phase of the cross correlation and performing a modulus operation;
the observed quantity is obtained by processing
Figure FDA0002826292890000022
And
Figure FDA0002826292890000023
where < (x) denotes the phase taken for x, mod(-π,π]{ x } denotes the interval (- π, π) for x]Taking a mould internally;
step five, constructing an optimization problem for estimating the arrival angle and solving an optimal solution;
order to
Figure FDA0002826292890000024
Let q be [ q ]1,...,qL-1]TFor any L-1 dimensional vector, a new vector is defined
Figure FDA0002826292890000025
Wherein
Figure FDA0002826292890000026
Representing the multiplication of corresponding elements and then solving the following optimization problem, preferably using an exhaustive method
Figure FDA0002826292890000027
Where max { x } represents the maximum value of vector x, min { x } represents the minimum value of vector x, DqRepresenting a solution space:
Figure FDA0002826292890000028
the optimal solution to the optimization problem is recorded as
Figure FDA0002826292890000029
Memo
Figure FDA00028262928900000210
Order to
Figure FDA00028262928900000211
The element is given by step four, and p is then made to be [ p ]1,...,pK-1]TDefining new vectors for arbitrary K-1 dimensional vectors
Figure FDA0002826292890000031
The following optimization problem is then solved using an exhaustive method
Figure FDA0002826292890000032
Wherein DpRepresenting a solution space
Figure FDA0002826292890000033
The optimal solution to the optimization problem is recorded as
Figure FDA0002826292890000034
Memo
Figure FDA0002826292890000035
Step six, converting according to the optimal solution of the optimization problem to obtain zenith angles and azimuth angles of incoming waves
Figure FDA0002826292890000036
And
Figure FDA0002826292890000037
wherein λ represents the wavelength of the electromagnetic wave, sign (x) represents the sign of x, tan-1(. ang.) and sin-1(. cndot.) denotes arctan and arcsine functions, respectively.
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张辉等: "DOA矩阵类方法中角度兼并问题的分析与改进", 《数据采集与处理》 *
王亦之等: "TDS-OFDM时变信道估计和均衡的BEM-LSQR方法", 《复旦学报(自然科学版)》 *
许文龙等: "一种基于子阵列合成的DOA估计算法", 《电子学报》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113447887A (en) * 2021-09-02 2021-09-28 广东省新一代通信与网络创新研究院 Full-space positioning method, device, equipment and computer readable storage medium
CN113447887B (en) * 2021-09-02 2022-01-21 广东省新一代通信与网络创新研究院 Full-space positioning method, device, equipment and computer readable storage medium

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