CN112968299A - Basic unit, super-surface and arrival angle estimation method based on information super-surface - Google Patents
Basic unit, super-surface and arrival angle estimation method based on information super-surface Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
- H01Q15/14—Reflecting surfaces; Equivalent structures
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
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- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
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- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
- H01Q15/14—Reflecting surfaces; Equivalent structures
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Abstract
The basic unit structure is formed by periodically arranging the basic units, an information super surface can be formed, and a switch diode in each basic unit can be controlled by an external circuit so as to present different electromagnetic responses; the electromagnetic response states of the basic units can be distributed in a spatial dimension according to a spatial coding sequence and can also be periodically circulated in a time dimension according to a time coding sequence; by designing a corresponding space-time coding matrix, the information super-surface can realize the simultaneous regulation and control of electromagnetic waves on a space domain and a frequency domain; the arrival angle estimation of the incident electromagnetic wave can be realized by carrying out signal analysis on the controlled electromagnetic wave, so that an information super-surface-based arrival angle estimation and electromagnetic control integrated method is formed, and the incident angle of the electromagnetic wave which irradiates the information super-surface can be independently controlled while being rapidly estimated in real time.
Description
Technical Field
The invention belongs to the technical field of artificial electromagnetic materials, and particularly relates to a basic unit, a super surface and an arrival angle estimation method based on the information super surface.
Background
The novel artificial electromagnetic surface, also known as a super surface, can control the parameters of amplitude, phase, polarization, wave beam, orbital angular momentum and the like of electromagnetic waves by designing the unit characteristics and spatial arrangement of the surface, realizes the functions of deflection, focusing, wave absorption and the like of electromagnetic energy, and can be used in the fields of antennas, imaging and the like. By introducing an adjustable technology, an adjustable super surface capable of controlling various parameters of electromagnetic waves in real time can be designed. The control signal of the traditional adjustable super surface is static or is changed at a very low frequency, so that the adjustable super surface is a linear device and can only adjust and control some linear characteristics of electromagnetic waves, such as amplitude, phase, polarization and the like. The information super-surface provides an additional degree of freedom in a time dimension by dynamically changing a control signal of the coding super-surface at a high speed, so that the information super-surface becomes a nonlinear device on the premise of not using a nonlinear material, and a series of harmonic components can be generated. Therefore, the information super surface has potential application value in the fields of communication, stealth and imaging.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the invention is to provide an information super-surface-based arrival angle estimation and electromagnetic regulation and control integration method, which can perform independent regulation and control while performing real-time and rapid estimation on the incident angle of electromagnetic waves irradiating the information super-surface.
The technical scheme of the invention is as follows: the invention provides a basic unit, which comprises an upper surface structure, a dielectric substrate and a lower surface structure, wherein the upper surface structure comprises a first metal strip and a metal rectangular patch, the first metal strip and the metal rectangular patch are connected through a switch diode, the first metal strip and the metal rectangular patch are arranged on the upper surface of the dielectric substrate in parallel, and the first metal strip is vertically connected with two edges of the upper surface of the dielectric substrate; the lower surface structure is a second metal strip which is positioned on the lower surface of the medium base, the direction of the second metal strip is orthogonal to the direction of the first metal strip on the upper surface, and the second metal strip is vertically connected with two edges of the lower surface of the medium substrate; the metal rectangular patch on the upper surface of the unit is connected with the second metal strip on the lower surface of the unit through the metal through hole; the switch diode of each basic unit is controlled by an external circuit and presents different electromagnetic responses; the electromagnetic response states of the basic units are distributed in an arrangement mode in a space dimension according to the space coding sequence or periodically circulate in a time dimension according to the time coding sequence.
Furthermore, the information super-surface is formed by the periodic arrangement of the basic units, N columns of basic units are shared, the first metal strips of the same column of units are connected with each other, external control signals are shared, the first metal strips are controlled by the same group of time coding sequences, the electromagnetic responses are the same, and the second metal strips of the same row of units are connected with each other.
The invention also provides a method for estimating the angle of arrival of the information super-surface pair, which comprises the following steps:
(1) determining a time coding sequence and a period of a reflection coefficient of each row of units on the super surface, and calculating the amplitude and the phase of each order of harmonic component in each row of unit reflection waves through Fourier transform;
(2) forming a space-time coding matrix according to the time coding sequences of the row units, and calculating a far field directional diagram corresponding to each order of harmonic;
(3) selecting M-order nonzero harmonic components from the harmonic amplitude and phase results in the step (1), wherein M is larger than or equal to N, calculating amplitude phase values of corresponding harmonics at the position of theta 0 degrees according to the harmonic far-field directional diagram obtained in the step (2), and combining the harmonic amplitude and phase results and the calculation formula used in the step (2) to form a linear equation set and obtain a coefficient matrix of the linear equation set;
(4) obtaining a generalized inverse matrix of the coefficient matrix in the step (3) through matrix inversion, and calculating an estimated value theta of the incident angle of the incident electromagnetic wave by utilizing matrix row-column transformatione。
Further, the specific method of the step (1) is as follows: the super surface comprises N columns of units, the reflection coefficient of each column of units is controlled by a corresponding time coding sequence, wherein the specific expression gamma of the periodic time-varying reflection coefficient of the p-th column of units in one periodp(t) is of the form:
wherein T is the period of the time-varying reflection coefficient,
for time shifting
The basic pulse function of (2) is specifically defined as:
wherein the content of the first and second substances,
is a complex number with specific amplitude phase, representing the L-th bit code in the time code sequence with length L;
when the frequency of the incident electromagnetic wave is fcMeanwhile, the electromagnetic wave reflected by the p-th row unit of the super surface is modulated and changed into a periodic reciprocal f of a reflection coefficient by taking the frequency of an incident wave as a center 01/T is a mixed frequency signal with harmonic frequency interval, and the frequency domain expression is
Wherein, delta (f-kf)0-fc) Representing the frequency shift as kf0-fcAn impulse function of
Then represents the k-th harmonic kf in the reflected wave of the p-th column unit0+fcThe complex coefficient (c) is obtained by performing fourier transform theoretical calculation on the formula (1), and is specifically expressed as:
wherein j is an imaginary unit, pi is a circumference ratio,
in the form of a standard sampling function,
representing an amplitude of 1 and a phase of
According to the formula (3), the k-th harmonic kf of the electromagnetic wave after unit modulation is calculated0+fcCorresponding amplitude and phase.
Further, the specific method of the step (2) is as follows: for an information super surface with N columns of units, N time coding sequences with the length of L are shared to form a space-time coding matrix with the dimension of NxL, and when electromagnetic waves form an angle theta with the normal direction of the super surfaceiWhen the direction of (a) is incident, the time domain expression f (theta, t) of the far field directional diagram is as follows:
wherein E isp(theta) cos theta is the scattering pattern function of the basic cell, theta is defined as the angle between the observation direction and the normal of the super-surface, and lambdacThe wavelength of an incident wave in free space is subjected to Fourier transform, and the far field directional diagram of the k-th harmonic is as follows:
wherein λ iskAnd d is the distance between each row of units, and the directional diagram of each order of harmonic of the information super-surface under a certain time-space coding matrix can be respectively calculated by the formula (5).
Further, the specific method of step (3) is as follows: according to the formula (3), the calculation result of each order of harmonic amplitude phase in the reflection coefficient of each row of units on the super surface can be obtained, and M-order non-zero harmonic components are selected from the calculation result and are sequentially written as k1,k2,…,kMAccording to equation (5), the k-th harmonic component in the reflected wave spectrum at which the super surface θ is 0 ° is obtained as:
at this time, the selected harmonic band is respectively put into formula (6), and the corresponding result is obtained and is simultaneously formed into a linear equation system, and is written into a matrix form:
equation (7) is further written as:
wherein the content of the first and second substances,
is a harmonic column vector, of length M,
is a matrix of the harmonic coefficients and is,
is the incident wave angle column vector with length N.
Further, the specific method of the step (4) is as follows: as can be seen from equation (7), A is a two-dimensional matrix of M × N, and is represented as A assuming that it has a generalized inverse matrix with dimensions of N × M-1Then the incident light can be obtainedThe wave angle column vector is:
as can be seen from the formula (7),
in fact, an equivalent series, whose common value can be obtained according to the adjacent term on the right of equation (9):
wherein the content of the first and second substances,
is a column vector
The nth row element can obtain the incident wave angle as follows according to the formula:
in which sin-1(. cndot.) is an arcsine function, and angle (. cndot.) is a complex phase operation, the above formula being applied to the incident wave angle θiN-1 times of calculation are carried out in total, and the result of each time is recorded as
Taking the average value of the calculation results of the N-1 times as a final incident angle estimation value:
the invention also proposes a computer processing device comprising a processor, a memory and a computer program stored on said memory and executable on said processor, said computer program, when executed by said processor, implementing the steps of the method of information hyper-surface-pair angle of arrival estimation as claimed in claims 3 to 7.
The invention also proposes a computer-readable storage medium, characterized in that it has stored thereon a computer program which, when being executed by said processor, carries out the steps of the method for information hyper-surface-pair angle of arrival estimation of claims 3 to 7.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
(1) the arrival angle estimation method has a simple principle, and can estimate the incident direction of the electromagnetic wave only by carrying out spectrum analysis on the super-surface reflected wave;
(2) compared with the traditional reaching angle estimation method, the method does not need an additional sensor and a complex signal processing system, and has the advantages of low cost, quick and accurate result and the like;
(3) the invention can independently regulate and control the electromagnetic wave while estimating the angle, perfectly integrates the functions of two different systems without mutual influence, has the characteristics of high integration, quick response and the like, and can be used for designing and manufacturing only systems which have different regulation and control functions on the electromagnetic wave with different incidence angles.
Drawings
FIG. 1 is a schematic diagram of simultaneous estimation of arrival angle and modulation of electromagnetic waves for an information super-surface according to the present invention.
Fig. 2 is a schematic diagram of an upper surface structure of an information super-surface unit according to an exemplary embodiment of the present invention, where (a) is a schematic diagram of an upper surface structure of an information super-surface unit according to the present invention, (b) is a schematic diagram of a lower surface structure of an information super-surface unit according to the present invention, (c) is a simulation result diagram of a reflection amplitude/phase of an information super-surface unit according to the present invention as a function of a control voltage, and (d) is a schematic diagram of an information super-surface composed of information super-surface units according to the present invention.
FIG. 3(a) is a space-time coding matrix designed according to the present invention, wherein the code '0' represents the phase of the unit reflection coefficient is 0, and the code '1' represents the phase of the unit reflection coefficient is 180.
FIG. 3(b) shows the incident angle θiWhen the angle is 45 degrees, the electromagnetic wave reflected by the super surface used by the invention is calculated in the spectrum distribution of the normal direction.
FIG. 3(c) shows the incident angle θiAnd when the angle is 45 degrees, calculating the far-field scattering directional diagram of each order of harmonic waves of the electromagnetic waves reflected by the super surface used by the invention.
FIG. 4(a) is a graph showing the incident angle θ during the experimental verification process of the present inventioniAt 45 °, the spectral data received in the direction of the normal to the super surface, where the dots represent the calculation results for the comparison.
FIG. 4(b) is a graph showing the incident angle θ during the experimental verification process of the present inventioniAt 45 °, the far-field scattering pattern of the reflected wave +1 order harmonic, where the solid/dashed lines represent the measured/calculated results, respectively.
FIGS. 4(c) and (d) are respectively the estimated reaching angle θ under different incident angles in the experimental verification process of the present inventioneAnd the absolute error between the absolute value and the actual value, the measuring range is [ -90 degrees, 90 degrees °]The measurement interval was 3 °.
Detailed Description
Fig. 1 shows an integrated method of arrival angle estimation and electromagnetic modulation based on an information super-surface, which can perform time domain-space domain-frequency domain joint modulation on incident electromagnetic waves through the information super-surface and simultaneously perform rapid and accurate estimation on the arrival angle.
The information super-surface is formed by periodically arranging the same basic units, and a plurality of basic units form an array through a feed network, similar to a planar reflective array, and the unit reflection coefficients can be regulated and controlled in real time through an external voltage control signal.
The structure of the basic unit 1 used by the invention is shown in figure 2 and is divided into three layers: an upper surface structure (see fig. 2a), a dielectric substrate and a lower surface structure (see fig. 2 b). The upper surface structure consists of a metal strip 11 and a rectangular patch 12, and a switching diode 13 is bridged in the middle; the intermediate medium substrate is made of TLY-5, the dielectric constant is 2.2, and the thickness is 1.59 mm; the lower surface structure is a full-face metal back plate 14. In addition, the unit upper layer rectangular patch is connected with the lower layer back plate through a metal through hole 15.
The basic unit 1 shown in fig. 2 has the following geometrical dimensions: the length and the width of the whole unit 1 are both 5mm, the thickness is 1.59mm, the width of the metal strip 11 is 1mm, the length of the rectangular patch 12 is 1.7mm, the width of the rectangular patch is 1.7mm, and the through hole 15 is positioned in the center of the rectangular patch; the operating state of the switching diode 13 is changed by the bias voltage, so that the reflection characteristic of the basic unit can be regulated, and a simulation result graph is shown in fig. 2 (c). It can be seen that the reflection amplitude of the basic unit is very stable within 23 GHz-25 GHz, the loss is lower than 1dB, and the phase response has a phase difference of 180 °.
Further, as shown in fig. 2d, the basic cells 1 are arranged periodically, i.e. the information super surface 2 can be formed, wherein the above cells 1 are formed in an array form controlled by columns, and the cells 1 and the switching diodes 13 thereof of each column are controlled by bias supply lines 21 to realize voltage or current control.
The specific method for simultaneously carrying out time domain-space domain-frequency domain combined regulation and control and arrival angle estimation on electromagnetic waves based on the information super surface comprises the following steps:
(1) determining a time coding sequence and a period of a reflection coefficient of each row of units on the super surface, and calculating the amplitude and the phase of each order of harmonic component in each row of unit reflection waves through Fourier transform;
the invention has the basic principle that the incident electromagnetic wave frequency spectrum is regulated and controlled by utilizing the periodic time-varying reflection coefficient. The super surface comprises N columns of units, the reflection coefficient of each column of units is controlled by a corresponding time coding sequence, wherein the specific expression gamma of the periodic time-varying reflection coefficient of the p-th column of units in one periodp(t) is of the form:
wherein, T is a period,
for time shifting
The basic pulse function of (2) is specifically defined as:
wherein the content of the first and second substances,
is a complex number with a specific amplitude phase and represents the ith bit code in a time code sequence with length L. The above formula embodies the control mode of the time coding sequence to the unit reflection coefficient, so that the periodic time-varying reflection coefficient of the basic unit can be represented only by a period of time coding sequence.
When the frequency of the incident electromagnetic wave is fCWhen the wave passes through the surface unit, the reflected wave is modulated and changed into the reciprocal f of the reflection coefficient period with the incident wave frequency as the center0Mixing signals with harmonic frequency spacing of 1/T
Wherein E isr(f) Representing the frequency domain expression of the reflected wave, delta (f-kf)0-fc) Representing the frequency shift as kf0-fcAn impulse function of
Then represents the k-th harmonic kf0+fcThe complex coefficient (c) can be obtained by performing fourier transform theoretical calculation on the formula (1), and is specifically expressed as:
wherein j is an imaginary unit, pi is a circumference ratio,
in the form of a standard sampling function,
representing an amplitude of 1 and a phase of
Is a natural exponential function of (a). According to the formula (3), the k-th harmonic kf of the electromagnetic wave after unit modulation is calculated0+fcCorresponding amplitude and phase.
(2) And forming a space-time coding matrix according to the time coding sequences of the column units, and calculating a far field directional diagram corresponding to each order of harmonic.
For an information super-surface with N columns of units, there are N different time-coded sequences Lp(t), an N L space-time coding matrix can be formed. When the electromagnetic wave is from the angle theta of the super surfaceiWhen the direction of (a) is incident, the time domain expression f (θ, t) of the far field pattern thereof can be written as:
wherein Ep(theta) cos theta is the scattering pattern function of the elementary cell approximation, theta being defined as the angle between the normal to the hypersurface and lambdacIs the wavelength of the incident wave in free space. After Fourier transform, the far field pattern of the kth harmonic is:
λkand d is the unit distance, the directional diagram of each order of harmonic wave of the information super-surface under a certain time-space coding matrix can be respectively calculated by the formula (5), and the time-space-frequency domain combined regulation and control of the incident electromagnetic wave are completed.
(3) And (3) selecting M-order (M is more than or equal to N) nonzero harmonic components from the harmonic amplitude and phase results in the step (1), wherein N represents the number of super-surface unit rows, calculating amplitude phase values of corresponding harmonics at the position of theta 0 degrees according to the harmonic far-field directional diagram obtained in the step (2), and finally establishing a linear equation set and obtaining a coefficient matrix of the linear equation set.
According to equation (5), the k-th harmonic component in the reflected wave spectrum at the supersurface θ equal to 0 ° (line of defense is found) can be obtained as follows:
at the moment, M-order (M is more than or equal to N) nonzero harmonic components are selected according to the calculation result and are sequentially written as k1,k2,…,kMRespectively calculating harmonic components and then combining the harmonic components into a matrix form:
for simplicity, equation (7) can be further written as:
wherein
Is a harmonic column vector with length M, A is a harmonic coefficient matrix,
is the incident wave angle column vector with length N.
(4) Obtaining a generalized inverse matrix of the coefficient matrix in the step (3) through matrix inversion, and finally calculating to obtain an estimated value theta of the incident electromagnetic wave angle by utilizing matrix row-column transformatione。
As can be seen from equation (7), a is a two-dimensional matrix of M × N. It is assumed to have a generalized inverse matrix with dimension N × M, denoted as a-1Then, the obtained incident wave angle column vector is:
the formula (7) shows
In fact, an equivalent series, whose common value can be obtained according to the adjacent term on the right of equation (9):
wherein
Is a column vector
Line n elements. According to the above formula, the incident wave angle can be obtained as follows:
in which sin-1(. cndot.) is an arcsine function, and angle (. cndot.) is a complex phase operation. Angle theta of incident waveiN-1 times of calculation are carried out in total, and the result of each time is recorded as
Theoretically, the results of the N-1 calculations should all be consistent, but taking the measurement error into consideration, the average value is taken as the final incident angle estimation value:
(5) and designing a corresponding control signal according to the mapping relation between the reflection coefficient of the super-surface unit and the control signal, designing a corresponding program to carry out data processing required by the estimation of the angle of arrival, and constructing a corresponding signal control, acquisition and processing platform.
The mapping relation between the unit reflection coefficient and the control signal of the information super-surface with different forms and structures is different. Therefore, the space-time coding matrix required by the super-surface calculated in step (2) needs to be mapped into a corresponding control signal according to the actual situation, and the control signal is sent to a special control platform to be generated and loaded onto a super-surface corresponding unit. In addition, based on the arrival angle estimation methods in steps (3) and (4), a corresponding signal acquisition and data processing platform is required, the electromagnetic wave signals reflected by the super surface are acquired and subjected to spectrum analysis in the far field normal direction (θ ═ 0 °), and the amplitude phase of the selected harmonic component is extracted for data processing to obtain an estimated value of the arrival angle. Finally, once the super-surface is (f) loaded with the control signalc，θi) The electromagnetic wave excitation can estimate the incidence direction of the electromagnetic wave while performing electromagnetic regulation and control on the electromagnetic wave excitation.
In order to show the technical scheme provided by the invention, according to the information material basic unit and the super-surface typical embodiment thereof shown in fig. 2, an information super-surface is processed as an experimental verification sample. The super surface comprises 10 multiplied by 10 basic units, each row of the units can be controlled by the same control signal, the bias voltage for changing the working state of the diode in practical application is 0V/1.5V respectively, and the reflection coefficient phase of the units can be 0 DEG/180 DEG respectively. The signal control platform consists of an FPGA and a driving circuit, and can generate a high-speed and stable control signal to be loaded on the super surface.
According to the number of the super-surface independent controllable unit columns and the electrical performance of the signal control platform, a 10 × 32 space-time coding matrix is designed, and consists of 10 independent time coding sequences with the length of 32, as shown in fig. 3a, wherein a code '0' represents that the phase of the unit reflection coefficient is 0 °, and a code '1' represents that the phase of the unit reflection coefficient is 180 °. The matrix modulation period is 16 mus, meaning that the harmonic frequency spacing of the reflected wave is 62.5 kHz. By taking the correlation parameter into formula (6), the current incident angle theta is calculatediAt 45 deg., the spectral distribution of the reflected wave in the normal direction is shown in fig. 3 b. As can be seen,theoretically, only odd harmonic components exist in the reflected wave, in order to obtain higher signal-to-noise ratio in practice, all odd harmonics from-9 order to +9 order (10 order harmonics in total) are selected to be brought into formula (7) to obtain a corresponding harmonic coefficient matrix, and finally the angle theta is estimated according to the method of the inventione. In addition, fig. 3c shows the calculation result of the far-field scattering pattern of each order of harmonics (all odd harmonics within the range from-3 to + 3) in this case by the solid line, and the dotted line shows the far-field scattering pattern of the base wave in the modulation of the super-surface non-time space coding matrix. The result shows that the information super-surface has a function of harmonic wave beam deflection for electromagnetic waves incident at 45 degrees, and deflects the +1 order harmonic waves to the normal direction.
Next, in order to verify the validity of the proposed solution of the present invention, experimental verification was performed using the processed super-surface sample in combination with a dedicated signal control, acquisition, processing platform. When the designed space-time coding matrix is applied to the super-surface, the correlation results at 45 ° incidence at 24GHz frequency are first measured. FIG. 4a shows the spectral data received over the normal to the surface, where the dots represent the calculation for the comparison. Fig. 4b shows the measured/calculated far-field scattering pattern for the +1 th harmonic in this case in solid/dashed lines. Fig. 4c and 4d show the estimated angle of arrival and the absolute error for different incident angles, respectively, with a measurement range of-90 ° and a measurement interval of 3 °. From the results, the invention can accurately estimate the incidence angle in the range of [ -60 degrees, 60 degrees ] under the condition that the error threshold is 3 degrees. Meanwhile, the super-surface can also perform beam deflection on each order of harmonic component in the incident electromagnetic wave.
The information super-surface integrating the arrival angle estimation and the electromagnetic regulation controls the space-frequency distribution of incident electromagnetic waves by utilizing a space-time coding matrix, and meanwhile, the arrival angle can be estimated in real time by analyzing the frequency spectrum in the normal direction. The invention has simple principle, low cost, high integration level and easy realization, thereby having great application value in the fields of communication, stealth and imaging.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (9)
1. A basic unit is characterized in that the unit structure comprises an upper surface structure, a dielectric substrate and a lower surface structure, wherein the upper surface structure comprises a first metal strip and a metal rectangular patch, the first metal strip and the metal rectangular patch are connected through a switch diode, the first metal strip and the metal rectangular patch are arranged on the upper surface of the dielectric substrate in parallel, and the first metal strip is vertically connected with two edges of the upper surface of the dielectric substrate; the lower surface structure is a second metal strip which is positioned on the lower surface of the medium base, the direction of the second metal strip is orthogonal to the direction of the first metal strip on the upper surface, and the second metal strip is vertically connected with two edges of the lower surface of the medium substrate; the metal rectangular patch on the upper surface of the unit is connected with the second metal strip on the lower surface of the unit through the metal through hole; the switch diode of each basic unit is controlled by an external circuit and presents different electromagnetic responses; the electromagnetic response states of the basic units are distributed in an arrangement mode in a space dimension according to the space coding sequence or periodically circulate in a time dimension according to the time coding sequence.
2. The information super-surface constructed by the basic units as claimed in claim 1, wherein the information super-surface is formed by the above basic units being arranged periodically, and N columns of basic units are provided, the first metal strips of the same column of units are connected with each other, share the external control signal, are controlled by the same group of time-coded sequences, have the same electromagnetic response, and the second metal strips of the same row of units are connected with each other.
3. A method for estimating the angle of arrival of information pairs according to claim 2, characterized in that the method comprises the steps of:
(1) determining a time coding sequence and a period of a reflection coefficient of each row of units on the super surface, and calculating the amplitude and the phase of each order of harmonic component in each row of unit reflection waves through Fourier transform;
(2) forming a space-time coding matrix according to the time coding sequences of the row units, and calculating a far field directional diagram corresponding to each order of harmonic;
(3) selecting M-order nonzero harmonic components from the harmonic amplitude and phase results in the step (1), wherein M is larger than or equal to N, calculating amplitude phase values of corresponding harmonics at the position of theta 0 degrees according to the harmonic far-field directional diagram obtained in the step (2), and combining the harmonic amplitude and phase results and the calculation formula used in the step (2) to form a linear equation set and obtain a coefficient matrix of the linear equation set;
(4) obtaining a generalized inverse matrix of the coefficient matrix in the step (3) through matrix inversion, and calculating an estimated value theta of the incident angle of the incident electromagnetic wave by utilizing matrix row-column transformatione。
4. The method for estimating the angle of arrival according to claim 3, wherein the specific method of step (1) is as follows: the super surface comprises N columns of units, the reflection coefficient of each column of units is controlled by a corresponding time coding sequence, wherein the specific expression gamma of the periodic time-varying reflection coefficient of the p-th column of units in one periodp(t) is of the form:
wherein T is the period of the time-varying reflection coefficient,
for time shifting
The basic pulse function of (2) is specifically defined as:
wherein the content of the first and second substances,
is a complex number with specific amplitude phase, representing the L-th bit code in the time code sequence with length L;
when the frequency of the incident electromagnetic wave is fcMeanwhile, the electromagnetic wave reflected by the p-th row unit of the super surface is modulated and changed into a periodic reciprocal f of a reflection coefficient by taking the frequency of an incident wave as a center01/T is a mixed frequency signal with harmonic frequency interval, and the frequency domain expression is
Wherein, delta (f-kf)0-fc) Representing the frequency shift as kf0-fcAn impulse function of
Then represents the k-th harmonic kf in the reflected wave of the p-th column unit0+fcThe complex coefficient (c) is obtained by performing fourier transform theoretical calculation on the formula (1), and is specifically expressed as:
wherein j is an imaginary unit, pi is a circumference ratio,
in the form of a standard sampling function,
representing an amplitude of 1 and a phase of
According to the formula (3), the k-th harmonic kf of the electromagnetic wave after unit modulation is calculated0+fcCorresponding amplitude and phase.
5. The method for estimating the angle of arrival according to claim 4, wherein the specific method of step (2) is as follows: for an information super surface with N columns of units, N time coding sequences with the length of L are shared to form a space-time coding matrix with the dimension of NxL, and when electromagnetic waves form an angle theta with the normal direction of the super surfaceiWhen the direction of (a) is incident, the time domain expression f (theta, t) of the far field directional diagram is as follows:
wherein E isp(theta) cos theta is the scattering pattern function of the basic cell, theta is defined as the angle between the observation direction and the normal of the super-surface, and lambdacThe wavelength of an incident wave in free space is subjected to Fourier transform, and the far field directional diagram of the k-th harmonic is as follows:
wherein λ iskAnd d is the distance between each row of units, and the directional diagram of each order of harmonic of the information super-surface under a certain time-space coding matrix can be respectively calculated by the formula (5).
6. The method for estimating the angle of arrival according to claim 5, wherein the specific method of step (3) is as follows: according to the formula (3), the calculation result of each order of harmonic amplitude phase in the reflection coefficient of each row of units on the super surface can be obtained, and M-order non-zero harmonic components are selected from the calculation result and are sequentially written as k1,k2,…,kMAccording to equation (5), the k-th harmonic component in the reflected wave spectrum at which the super surface θ is 0 ° is obtained as:
at this time, the selected harmonic band is respectively put into formula (6), and the corresponding result is obtained and is simultaneously formed into a linear equation system, and is written into a matrix form:
equation (7) is further written as:
wherein the content of the first and second substances,
is a harmonic column vector, of length M,
is a matrix of the harmonic coefficients and is,
is the incident wave angle column vector with length N.
7. The method for estimating the angle of arrival according to claim 6, wherein the specific method of step (4) is as follows: as can be seen from equation (7), A is a two-dimensional matrix of M × N, and is represented as A assuming that it has a generalized inverse matrix with dimensions of N × M-1Then, the obtained incident wave angle column vector is:
as can be seen from the formula (7),
in fact, an equivalent series, whose common value can be obtained according to the adjacent term on the right of equation (9):
wherein the content of the first and second substances,
is a column vector
The nth row element can obtain the incident wave angle as follows according to the formula:
in which sin-1(. cndot.) is an arcsine function, and angle (. cndot.) is a complex phase operation, the above formula being applied to the incident wave angle θiN-1 times of calculation are carried out in total, and the result of each time is recorded as
Taking the average value of the calculation results of the N-1 times as a final incident angle estimation value:
8. a computer processing device comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, the computer program when executed by the processor implementing the steps of the method of information hyper-surface-pair angle of arrival estimation of claims 3-7.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a computer program which, when being executed by the processor, carries out the steps of the method of information hyper-surface-pair angle-of-arrival estimation of claims 3-7.
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