CN114488027A - Wave beam zero setting and widening method of conformal array antenna - Google Patents

Wave beam zero setting and widening method of conformal array antenna Download PDF

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CN114488027A
CN114488027A CN202111543818.4A CN202111543818A CN114488027A CN 114488027 A CN114488027 A CN 114488027A CN 202111543818 A CN202111543818 A CN 202111543818A CN 114488027 A CN114488027 A CN 114488027A
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许京伟
刘英楚
朱圣棋
张续莹
王建
张教镭
阚庆云
王建新
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Xidian University
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Abstract

The invention provides a wave beam zeroing and widening method of a conformal array antenna, which mainly solves the problem that the output performance of wave beam formation is seriously reduced when interference angle errors exist in the prior art. The implementation scheme is as follows: constructing a conformal array model; carrying out original covariance estimation on echo data received by the conformal array by using a maximum likelihood method; expanding the position of the interference source and calculating the broadening function of the interference source; adding a broadening function to the original covariance matrix, and calculating to obtain a broadened covariance matrix; calculating the expanded self-adaptive weight vector according to the expanded covariance matrix; and carrying out beam scanning on the widened self-adaptive weight vector, and outputting a null-setting widened array directional diagram. The invention can match with the weight of the beam former in real time when the interference presents non-stationarity, keeps stronger stability, improves the interference suppression performance and can be used for electronic countermeasure.

Description

Wave beam zero setting and widening method of conformal array antenna
Technical Field
The invention belongs to the technical field of radar signal processing, and further relates to an antenna beam nulling and broadening method which can be used for electronic countermeasure.
Background
Radar contrast with interference is one of the persistent topics of radar technology development. Generally, the incoming wave directions of the signal and the interference are different, the array weighting coefficient is adaptively adjusted to enhance the signal and suppress the interference, so that a beam can be formed in the signal azimuth, and a null can be formed in the interference. Although the antijam algorithm has been studied for many years, in practical applications, the interference signal may exhibit non-stationary variations in both time domain and space domain. In terms of airspace, the non-stationarity of the interference signal is represented by the change of the incident angle of the interference on the receiving antenna; in the time domain, the non-stationary effect of the interference signal is characterized by the time variation of the parameters of the interference signal or the intermittent presence of the interference signal in time.
Aiming at the non-stationarity caused by the change of the relative position of an interference source and a radar receiving platform, Zatman provides a null broadening method of covariance matrix tapering, the principle of null broadening is explained from the perspective of space-time equivalence, the extension of the angle of the interference source in a time domain is embodied as the diffusion of frequency in a frequency domain, and the diffusion degree of the angle is in direct proportion to the signal bandwidth, so that an incident narrowband interference source can be converted into a broadband interference source with a certain virtual bandwidth, and the null broadening of the interference position is realized. However, the method can only be applied to linear arrays by utilizing space-time equivalence to realize wide nulls.
The university of west ampere electronic technology under its grant bulletin number: CN104360338B patent document proposes an array antenna adaptive beam forming method based on diagonal loading, which first uses diagonal loading to correct the data covariance matrix, then uses the corrected data covariance matrix to estimate the steering vector of the target signal, and then solves the optimization problem with constraints based on the corrected data covariance matrix, so as to implement interference suppression. The method can improve the problems of inaccurate covariance matrix estimation and expected signal mismatch, has robustness, but has larger data requirement amount because only the situation that a support data set does not contain a strong target can be processed, and the diagonal loading factor is obtained through experience, thereby causing unstable interference suppression performance.
The method proposed in the document "adaptive antenna pattern interference null-broadening method research" published by Lerong peak et al on modern radar starts from a statistical model, deduces the null-broadening technology when the interference normal distribution characteristic exists, and proves the interference uniform distribution, and the method is equivalent to the Zatman method, and the method is used for broadening the null, which is based on the premise that the expected signal guide vector is accurately known, when the expected signal direction has a pointing error, the performance is seriously reduced, and the applied normal model is only suitable for linear arrays.
In the study of array beam null broadening algorithm, a self-adaptive null technique irrelevant to interference is deduced by performing left-right rotation on an interference guide vector and utilizing numerical processing on a covariance matrix. Under the condition of more interference number, the method is equivalent to a Zatman method, although the method is simple to implement, the method is only suitable for a linear array, because more and denser nulls exist, the widening effect is limited, and when the number of array elements is less, the width of a main lobe is very wide, the main lobe can be deformed while the nulls are formed, and the expansion of an angle is influenced.
In recent years, the research of conformal array antenna technology becomes a hot spot of attention of researchers, and compared with the conventional uniform linear array, the conformal array has superior structural characteristics and good lateral performance, and meanwhile, has the advantages of saving the structural space of a carrier and reducing the scattering sectional area of a radar, and is widely applied to the field of aerospace, wherein the cylindrical conformal array antenna is the most common conformal antenna form. However, most of the existing anti-interference methods for conformal array antennas are common adaptive beamforming algorithms, such as LCMV, when the methods are affected by antenna rotation or interference source position disturbance and other factors, interference is very stable, and the weight of the conventional adaptive algorithms cannot be matched with the non-stable interference in real time, so that the interference suppression performance of the conventional adaptive algorithms is sharply reduced.
Disclosure of Invention
The invention aims to provide a beam zeroing and widening method of a conformal array antenna aiming at the defects of the prior art, so that the reduction of the output performance when the direction of an interference signal has a pointing error is reduced, the beam zeroing and widening method can be matched with the weight of a beam former in real time when the interference presents non-stationarity, and the strong robustness is kept, thereby improving the interference suppression performance.
In order to achieve the above object, the technical solution of the present invention includes the following:
(1) determining wave number vector k according to the actually selected coordinate system and the expected signal model0The incoming wave direction u of the signal0Each array element position vector p and signal steering vector a (u)0) And then the conformal array model is established by taking the information as prior information;
(2) obtaining echo receiving data of the array according to the conformal array model, and performing maximum likelihood estimation on the echo receiving data to obtain an original covariance matrix R;
(3) and (3) expanding the interference source, and determining the broadening width:
(3a) uniformly distributing a plurality of virtual interference sources with equal power and irrelevant envelops near each interference source, and calculating the actual angle interval of a single virtual interference source according to a set expansion angle:
Figure BDA0003415110820000031
Figure BDA0003415110820000032
wherein u is a normalized direction vector corresponding to the incoming wave direction, theta,
Figure BDA0003415110820000033
Respectively representing the azimuth angle and the pitch angle corresponding to the incoming wave direction of the signal, delta theta,
Figure BDA0003415110820000034
Respectively, the expansion angles in the azimuth and pitch dimensions, [ Delta u ]]θ、
Figure BDA0003415110820000035
Respectively representing the angle intervals between the spatial interference sources which are discretely distributed on the azimuth dimension and the pitch dimension;
(3b) obtaining a final spreading function according to the angle interval and the number of the virtual interference sources:
Wθ、
Figure BDA0003415110820000036
respectively representing broadening functions in an azimuth dimension and a pitch dimension, and I represents the number of virtual interferences;
(4) adding I discrete virtual interference sources into an original covariance matrix R to obtain a broadened covariance matrix
Figure BDA0003415110820000037
Figure BDA0003415110820000038
Wherein, < > indicates a Hadamard product, T1、T2And the coning matrixes respectively represent an azimuth dimension and a pitch dimension, the two coning matrixes are both represented in the form of sinc functions, and the m-th row and the n-th column of the coning matrixes respectively have the following elements:
Figure BDA0003415110820000039
pmand pnRespectively representing the positions of the mth array element and the nth array element relative to the reference array element, wherein lambda is the wavelength;
(5) according to the signal steering vector a (u)0) And the broadened covariance matrix
Figure BDA00034151108200000310
Calculating the self-adaptive weight vector w after zero setting and broadening:
Figure BDA00034151108200000311
wherein, a (u)0) The signal guide vector is Nx 1, and N represents the number of array elements;
(6) an azimuth angle theta and a pitch angle corresponding to the direction of the incoming wave of the signal
Figure BDA00034151108200000312
Performing beam scanning, and obtaining the space-time steering vector of the array according to the actually selected coordinate system and the expected signal model
Figure BDA00034151108200000313
Space-time steering vector of array with variation of spatial scanning angle
Figure BDA00034151108200000314
Searching an interference angle matched with the self-adaptive weight vector w, and outputting a zeroing widening directional diagram after interference is suppressed:
Figure BDA00034151108200000315
wherein, H represents the conjugate transpose,
Figure BDA0003415110820000041
is a directional pattern function.
Compared with the prior art, the invention has the following advantages:
firstly, the invention expresses the covariance taper matrix as a function of Euclidean distance between each array element and directional diagram zero setting broadening coefficient by first-order approximation of array steering vector, and provides a basis for solving the broadening function expression.
Secondly, the invention applies the zeroing and broadening algorithm to the conformal antenna array to realize the zeroing and broadening of the azimuth pattern, thereby effectively resisting the non-stationary interference and improving the robustness of the anti-interference algorithm.
Thirdly, the invention realizes the suppression of the non-stationary interference by adjusting the value of the adaptive weight vector, which is independent of the array configuration, thus being applicable to any array configuration, including linear arrays, planar arrays and conformal arrays.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a conformal array geometry model constructed in the present invention;
FIG. 3 is a graph comparing the output patterns before and after zeroing and broadening of the present invention;
FIG. 4 is the nulling broadening pattern of FIG. 3 in a different orientation;
fig. 5 is a graph of the loss of the output signal to interference plus noise ratio after suppressing interference according to the present invention.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the invention are as follows:
step 1, constructing a conformal array geometric model.
Referring to fig. 2, the specific implementation of this step is as follows:
1.1) selecting an actual coordinate system as shown in FIG. 2(a), and defining a pitch angle as an included angle between the position of an array element and a Z axis and expressing the included angle as the position of the array element and the Z axis
Figure BDA0003415110820000042
Defining the azimuth angle as the included angle between the projection of the array element position on the XOY plane and the X axis, and expressing the included angle as theta;
1.2) taking the actually selected coordinate system as a reference, taking the position vectors of the azimuth angle and the pitch angle defined in the coordinate system as the position vector of each array element, and combining the wave number vector k0The incoming wave direction u of the signal0Each array element position vector p and signal steering vector a (u)0) Establishing a conformal array geometric model:
1.2.1) obtaining a direction vector u corresponding to the incoming wave direction of the signal according to the azimuth angle and the pitch angle0：
Figure BDA0003415110820000043
Wherein,
Figure BDA0003415110820000051
and theta0Respectively representing the pitch angle and the azimuth angle of the incoming wave direction,
1.2.2) the array narrowband model of any useful signal is represented as: a (u)0)s(t)，
Where s (t) is the signal baseband envelope, a (u)0) A signal steering vector, wherein the steering vector corresponding to the nth unit is:
Figure BDA0003415110820000052
in the formula, Fn() represents the element pattern of the nth array element; fn(u0) Indicates the nth unit corresponds to u0Array element directional diagram coefficients of the direction; g (u)n,u0) Reflecting the shielding problem of the array surface for an irradiation function, wherein the problem indicates whether the array element can receive signals or not;
Figure BDA0003415110820000053
for the corresponding phase relation of the electromagnetic wave propagation, unIs the normal direction vector of the n array element, pnIs the position coordinate vector of the nth array element,
Figure BDA0003415110820000054
representing the wave number vector, T representing transpose;
the resulting steering vector a (u)0) The method includes array element position vector information, normal direction and irradiation relation, and obtains a conformal array basic model according to the information, which is shown in fig. 2 (b).
And 2, calculating a covariance matrix R of the original received data.
According to the constructed conformal array model, echo receiving data comprising N array elements is actually obtained and comprises an expected target signal, a plurality of interference signals and noise;
setting the position of the m-th array element and the position of the n-th array element relative to the reference array element as pmAnd pnThe nth array element corresponds to a receiver noise power of
Figure BDA0003415110820000055
Power of the q-th interference signal is
Figure BDA0003415110820000056
The pitch angle and azimuth angle of the interference position are respectively
Figure BDA0003415110820000057
And thetaqAnd calculating an original covariance matrix R corresponding to the original covariance matrix R, wherein the m-th row and the n-th column are represented as:
Figure BDA0003415110820000058
wherein, m, N is 1,2, the., N, Q is 1,2, the., Q represents the quantity of interference, and the normalized direction vector corresponding to the Q interference is
Figure BDA0003415110820000059
δ (n, m) is a two-dimensional Kronecker function expressed as
Figure BDA00034151108200000510
And step 3, determining a broadening function.
Arranging I virtual interference sources which are uniformly distributed, have equal power and are not related to envelope near each interference source, and setting azimuth angles and pitch angles corresponding to incoming wave directions as theta, and theta, and theta, and theta, and theta, and theta, and delta, and delta,
Figure BDA0003415110820000061
obtaining a corresponding normalized direction vector u:
Figure BDA0003415110820000062
the direction vector u is subjected to first-order approximate derivation in the azimuth direction and the pitch direction respectively to obtain the angle interval delta u between the discretely distributed spatial interference sources, which can be respectively expressed as:
Figure BDA0003415110820000063
Figure BDA0003415110820000064
wherein, [ Delta u ]]θ、
Figure BDA0003415110820000065
Respectively representing the angle intervals between spatial interference sources which are discretely distributed in the azimuth dimension and the pitch dimension;
obtaining a final broadening function according to the angle interval delta u between the spatial interference sources in discrete distribution:
Wθ＝I·Δθ·[Δu]θ
Figure BDA0003415110820000066
wherein, Wθ、
Figure BDA0003415110820000067
Representing the spread function in the azimuth and pitch dimensions, respectively; delta theta,
Figure BDA0003415110820000068
The spread angle in the azimuth and pitch dimensions, respectively.
And 4, constructing a tapering matrix according to the widened covariance matrix.
I virtual interference sources which are uniformly distributed are respectively arranged in the pitching and azimuth directions corresponding to the interference, so that the position of the interference source is expanded in the pitching and azimuth dimensions, and echo receiving data comprising N array elements comprises an expected target signal, an interference signal, a plurality of virtual interference sources and noise;
setting the positions of the m-th array element and the n-th array element relative to the reference array element as p respectivelymAnd pnThe nth array element corresponds to a receiver noise power of
Figure BDA0003415110820000069
Power of the q-th interference signal is
Figure BDA00034151108200000610
The pitch angle and azimuth angle of the disturbance position are respectively
Figure BDA00034151108200000611
And thetaqThe angular intervals between the discretely distributed spatial interference sources are respectively delta uθ、
Figure BDA00034151108200000612
The spread function in the azimuth direction and the pitch direction is Wθ、
Figure BDA00034151108200000613
Calculating the covariance matrix after its corresponding broadening
Figure BDA00034151108200000614
Wherein the mth row and nth column elements are represented as:
Figure BDA0003415110820000071
where m, N is 1, 2., N, Q is 1, 2., Q represents the number of interferers, λ represents the wavelength, and the normalized direction vector corresponding to the Q-th interferer is the vector of Q
Figure BDA0003415110820000072
δ (n, m) is a two-dimensional Kronecker function, which can be expressed as
Figure BDA0003415110820000073
The zero-set and widened covariance matrix
Figure BDA0003415110820000074
Compared with the covariance matrix R of the original interferer, it adds a sinc function term, which depends only on the signal wavelength λ and the relative position of the array elements, since the sinc function is independent of the interferer angle. Therefore, the determined null width and the fixed number of virtual interference sources can determine a unique sinc function, so that the elements of the m-th row and the n-th column of the widened covariance matrix after zero adjustment are carried out
Figure BDA0003415110820000075
Further expressed as:
Figure BDA0003415110820000076
wherein, the conical-clipped matrix of the azimuth dimension and the elevation dimension, which indicates the Hadamard product, is T1、T2The T is1、T2The m-th row and the n-th column of the element are respectively:
Figure BDA0003415110820000077
step 5, constructing a zero-setting broadening self-adaptive weight vector:
steering the vector a (u) according to the desired signal0) And the broadened covariance matrix
Figure BDA0003415110820000078
Obtaining a self-adaptive weight vector w after zero setting and broadening:
Figure BDA0003415110820000079
wherein, a (u)0) The signal guide vector is Nx 1, and N represents the number of array elements.
And 6, outputting the widened directional diagram.
Azimuth angle theta and pitch angle corresponding to incoming wave direction
Figure BDA0003415110820000081
Performing beam scanning to obtain space-time steering vector of the array according to the selected coordinate system and the expected signal model
Figure BDA0003415110820000082
Space-time steering vector of array with variation of spatial scanning angle
Figure BDA0003415110820000083
Searching interference matched with the self-adaptive weight vector w, and outputting a zeroing widening directional diagram after the interference is suppressed:
Figure BDA0003415110820000084
wherein, H represents the conjugate transpose,
Figure BDA0003415110820000085
is a directional pattern function.
The effect of the present invention is further explained by combining the simulation experiment as follows:
1. simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is Intel (R) core (TM) i7-10700 CPU, the main frequency is 2.90GHz, and the memory is 16 GB.
The software platform of the simulation experiment of the invention is as follows: the Windows 10 operating system and MATLAB R2020 b.
The parameters of the simulation experiment of the invention are set as follows:
the whole conformal array antenna array of the radar consists of 106 array elements, and the specific arrangement is shown in fig. 2 (b).
Setting the center frequency of the signal to f01.3GHz, the radar working wavelength is lambda 0.23m, the signal-to-noise ratio is SNR-10, and the incoming wave direction of the signal corresponds to the pitch angle
Figure BDA0003415110820000086
Azimuth angle theta 00 deg.. The number of interference is 1, the dry-to-noise ratio is JNR (60), and the interference position corresponds to the pitch angle
Figure BDA0003415110820000087
Azimuth angle theta j40 DEG, and an expansion angle Delta theta,
Figure BDA0003415110820000088
Are each 1.
2. Simulation content and result analysis:
simulation 1, adopting the present invention to perform interference suppression on the signal echoes generated under the above simulation conditions, and obtaining the directivity diagrams output before and after the null-steering broadening, as shown in fig. 3, the null-steering broadening directivity diagrams of fig. 3 in different directions are shown in fig. 4, where:
FIG. 3(a) is the normalized directional diagram result output before zeroing and broadening, the X-axis represents the azimuth angle, the Y-axis represents the pitch angle, and the Z-axis is the normalized output power;
FIG. 3(b) is a normalized directional diagram output after the anti-interference device is used, wherein the X axis represents an azimuth angle, the Y axis represents a pitch angle, and the Z axis is normalized output power;
fig. 4(a) shows the result of broadening of the nulled and broadened directional diagram in the azimuth dimension, where the X-axis represents the azimuth angle and the Y-axis is the normalized output power;
fig. 4(b) shows the widening result of the nulled and widened directional diagram in the pitch dimension, where the X axis represents the azimuth angle and the Y axis represents the normalized output power.
Comparing fig. 3(a) and fig. 3(b), before the zero-set broadening is not performed, the null generated by the anti-interference is very narrow, and the anti-interference performance is susceptible to the interference pointing error; after the zero-setting widening is carried out, the null of the position corresponding to the interference in the directional diagram is obviously widened, and the widening effect of the position and the pitch dimension behind the zero-setting widening can be obviously seen from the graph 4(a) and the graph 4(b), which shows that the invention can reduce the reduction of the output performance when the direction error exists in the direction of the interference signal, can keep stronger robustness when the interference presents non-stationarity, and can improve the robustness of the interference resistance.
Simulation 2, the output result after the interference suppression is adopted to perform 100 monte carlo experiments to obtain an output signal to interference plus noise ratio loss curve, and the result is shown in fig. 5, wherein the X axis represents the output signal to interference plus noise ratio, and the Y axis represents the output signal to interference plus noise ratio loss.
As can be seen from the simulation result of FIG. 5, the loss of the output SINR is kept at 1-2 dB under the condition of zero setting and broadening, which shows that the method can effectively resist non-stationary interference pointing errors and improve the robustness of interference resistance on the premise of ensuring the output performance.
The simulation result verifies the correctness, effectiveness and reliability of the invention, and the invention can widen the null under the condition of ensuring the output performance and improve the anti-interference robustness of the conformal array.

Claims (4)

1. A method for widening and nulling beams of a conformal array antenna is characterized by comprising the following steps:
(1) determining wave number vector k according to the actually selected coordinate system and the expected signal model0The incoming wave direction u of the signal0Each array element position vector p and signal steering vector a (u)0) And then the conformal array model is established by taking the information as prior information;
(2) obtaining echo receiving data of the array according to the conformal array model, and performing maximum likelihood estimation on the echo receiving data to obtain an original covariance matrix R;
(3) and (3) expanding the interference source, and determining the broadening width:
(3a) uniformly distributing a plurality of virtual interference sources with equal power and irrelevant envelops near each interference source, and calculating the actual angle interval of a single virtual interference source according to a set expansion angle:
Figure FDA0003415110810000011
Figure FDA0003415110810000012
wherein u is a normalized direction vector corresponding to the incoming wave direction, theta,
Figure FDA0003415110810000013
Respectively representing the azimuth angle and the pitch angle corresponding to the direction of the incoming wave, delta theta,
Figure FDA0003415110810000014
Respectively, the expansion angles in the azimuth and pitch dimensions, [ Delta u ]]θ、
Figure FDA0003415110810000015
Respectively representing the angle intervals between the spatial interference sources which are discretely distributed on the azimuth dimension and the pitch dimension;
(3b) obtaining a final spreading function according to the angle interval and the number of the virtual interference sources:
Wθ、
Figure FDA0003415110810000016
respectively representing broadening functions in an azimuth dimension and a pitch dimension, and I represents the number of virtual interferences;
(4) adding I discrete virtual interference sources into an original covariance matrix R to obtain a broadened covariance matrix
Figure FDA0003415110810000017
Figure FDA0003415110810000018
Wherein, < > indicates a Hadamard product, T1、T2And the coning matrixes respectively represent an azimuth dimension and a pitch dimension, the two coning matrixes are both represented in the form of sinc functions, and the m-th row and the n-th column of the coning matrixes respectively have the following elements:
Figure FDA0003415110810000021
pmand pnRespectively representing the positions of the mth array element and the nth array element relative to the reference array element, wherein lambda is the wavelength;
(5) according to the signal steering vector a (u)0) And the broadened covariance matrix
Figure FDA0003415110810000022
Calculating the self-adaptive weight vector w after zero setting and broadening:
Figure FDA0003415110810000023
wherein, a (u)0) The signal guide vector is Nx 1, and N represents the number of array elements;
(6) an azimuth angle theta and a pitch angle corresponding to the direction of the incoming wave of the signal
Figure FDA0003415110810000024
Performing beam scanning to obtain the space-time steering vector of the array according to the actually selected coordinate system and the expected signal model
Figure FDA0003415110810000025
Space-time steering vector of array with variation of spatial scanning angle
Figure FDA0003415110810000026
Searching an interference angle matched with the self-adaptive weight vector w, and outputting a zeroing widening directional diagram after interference is suppressed:
Figure FDA0003415110810000027
wherein, H represents the conjugate transpose,
Figure FDA00034151108100000211
is a directional pattern function.
2. The method of claim 1, wherein the conformal array model is established in (1) as follows:
(1a) defining a pitch angle as an included angle between the position of the array element and the Z axis and expressing the included angle as
Figure FDA0003415110810000028
Defining an azimuth angle as an included angle between the projection of the array element position on the XOY plane and the X axis, and expressing the included angle as theta;
(1b) calculating the incoming wave direction vector u of the expected signal0And different normal direction vectors unVector inner product of (1), element directional diagram coefficient Fn(u0)：
Figure FDA0003415110810000029
Wherein,
Figure FDA00034151108100000210
for the incoming direction vector u of the desired signal0And different normal direction vectors unThe angle of,
(1c) from the direction vector u of the incoming wave of the desired signal0And different normal direction vectors unIs obtained as the vector inner product of (c) to obtain the illumination function g (u)n,u0)：
Figure FDA0003415110810000031
(1d) Vector k of wave number0And the n-th array element position coordinate vector pnPerforming exponential operation to obtain an electromagnetic wave propagation phase vector with dimension of Nx 1
Figure FDA0003415110810000032
Calculating the signal guide vector [ a (u) of the n array element0)]n：
Figure FDA0003415110810000033
(1e) And calculating the signal steering vector of the nth array element to obtain the signal steering vectors of all array elements with dimension size of Nx 1, and finishing the establishment of the conformal array model.
3. The method of claim 1, wherein the original covariance matrix R is calculated in (2) as follows:
(2a) obtaining training sample data X with dimension size of NxL from received echo data, wherein N is the array element number contained in the conformal array, and L is the selected airspace fast beat number;
(2b) according to training sample data X, calculating through maximum likelihood to obtain an original covariance matrix R with dimension of NxN:
Figure FDA0003415110810000034
where H denotes a conjugate transpose.
4. The method of claim 1, wherein (5) a space-time steering vector is constructed
Figure FDA0003415110810000035
The method is realized as follows:
(5a) calculating the incoming wave direction vector of omnidirectional scanning
Figure FDA0003415110810000036
And different normal direction vectors unVector inner product of (2), cell pattern coefficient
Figure FDA0003415110810000037
Figure FDA0003415110810000038
Wherein,
Figure FDA0003415110810000039
incoming wave direction vector for omnidirectional scanning
Figure FDA00034151108100000310
And different normal direction vectors unThe angle of,
(5b) incoming wave direction vector by omnidirectional scanning
Figure FDA00034151108100000311
And different normal direction vectors unIs multiplied by the vector to obtain the illumination function
Figure FDA00034151108100000312
Figure FDA0003415110810000041
(5c) Calculating a scanning beam vector k through an incoming wave direction vector of the omnidirectional scanning:
Figure FDA0003415110810000042
(5d) transposing a scanning wave number vector k and an n-th array element position coordinate vector pnPerforming exponential operation to obtain an electromagnetic wave propagation phase vector with dimension of Nx 1
Figure FDA0003415110810000043
Computing space-time steering vector of nth array element
Figure FDA0003415110810000044
Figure FDA0003415110810000045
(5e) Calculating the space-time steering vector of each array element to obtain the space-time steering vectors of all array elements with dimension size of Nx 1
Figure FDA0003415110810000046
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115015846A (en) * 2022-05-27 2022-09-06 西安电子科技大学 Generalized self-adaptive monopulse angle measurement method based on conformal array antenna
CN115114780A (en) * 2022-06-27 2022-09-27 北京雷久科技有限责任公司 Method for forming wave beam of circular truncated cone array antenna
CN117914364A (en) * 2024-03-19 2024-04-19 艾索信息股份有限公司 Method and device for generating wide null beam, electronic equipment and storage medium

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115015846A (en) * 2022-05-27 2022-09-06 西安电子科技大学 Generalized self-adaptive monopulse angle measurement method based on conformal array antenna
CN115114780A (en) * 2022-06-27 2022-09-27 北京雷久科技有限责任公司 Method for forming wave beam of circular truncated cone array antenna
CN117914364A (en) * 2024-03-19 2024-04-19 艾索信息股份有限公司 Method and device for generating wide null beam, electronic equipment and storage medium
CN117914364B (en) * 2024-03-19 2024-05-31 艾索信息股份有限公司 Method and device for generating wide null beam, electronic equipment and storage medium

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