CN108009373B - Time-space frequency multidimensional modeling method of light-controlled radio frequency beam forming system - Google Patents
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Abstract
The invention discloses a space-time-frequency multi-dimensional modeling method of a light-operated radio frequency beam forming system. It includes: step A, decomposing a light-controlled radio frequency beam forming system into an antenna array consisting of a group of antenna units and a group of parallel microwave photon links corresponding to the antenna units one by one; step B, aiming at the configuration of each microwave photon link in a certain target beam control state of the light-controlled radio frequency beam forming system, mapping the time frequency response of an optical device in each microwave photon link in a light frequency band to be a time frequency sub-model of the microwave photon link in a microwave frequency band, and simultaneously acquiring a radiation sub-model of each antenna unit and establishing a space domain sub-model of antenna array arrangement; and step C, fusing the time frequency, radiation and space domain submodels into a space-time multidimensional frequency spectrum response function of the system. The invention can adapt to various light-operated microwave amplitude-phase delay methods and actual antenna and array conditions, and shows the space-time-frequency multi-dimensional signal processing capability of the system.
Description
Technical Field
The invention relates to a time-space-frequency multi-dimensional modeling method of a light-operated radio frequency beam forming system, belonging to the technical field of intersection of microwave photonics and computer modeling.
Background
The light-operated radio frequency beam forming means that microwave photon technology is utilized to realize control on amplitude, phase, time delay and the like of radio frequency signals in an optical domain so as to realize directional diagram reconstruction functions such as beam scanning and the like of the array antenna. Compared with the traditional pure electric field beam forming mode, the light-operated radio frequency beam forming has obvious advantages in various aspects of low transmission loss, large processing bandwidth, electromagnetic interference resistance, corrosion resistance, light weight and the like, and is an important direction for the research and development of the radio frequency beam forming. In recent years, unit technical innovation and system-level research results related to optically-controlled radio-frequency beam forming are numerous, and various microwave photon phase-shifting and time-delaying modules applying new mechanisms and new structures and beam forming systems formed by the modules are published and reported. However, modeling research for an optical radio frequency beam forming system presents two challenges: firstly, because the implementation modes of the optically controlled microwave amplitude-phase delay are various, the electro-optic modulation mode and the mechanism of the optical domain amplitude-phase delay control device are different, it is necessary to establish a unified model to describe the mapping relationship from the optical spectrum response to the electrical spectrum response under different electro-optic modulation modes. Secondly, the common existing modeling result is a single or multiple directional diagram or array factor of the time point frequency signal, but the complete characteristics and information of the light-controlled broadband radio frequency beam forming system cannot be embodied, the importance of the key parameter of the time frequency in the system analysis is greatly reduced, the key parameter is not matched with the large bandwidth characteristic of the light-controlled broadband radio frequency beam forming system, and the signal processing capability of the light-controlled broadband radio frequency beam forming system in multiple dimensions of time, space, frequency and the like cannot be fully embodied.
To solve these two problems, researchers have proposed a method for describing an optically controlled RF Beamforming system by a space-time two-dimensional response [ x.w.ye, d.zhu, y.m.zhang, s.m.li, and s.l.pan, "Analysis of photonics-based RF Beamforming with Large instant Bandwidth," IEEE/osa journal of Lightwave Technology, vol.35, No.23, pp.5010-5019, dec.2017 ]. The method takes the time frequency list of the signal as an independent variable, is particularly suitable for researching the response of the system under the large instantaneous bandwidth signal, and adapts to the large bandwidth characteristic of the light-controlled beam forming system. Meanwhile, according to the method, different electro-optic modulation processes are unified into complex coefficients of the modulated carrier and positive and negative first-order sidebands through certain approximation, and the mapping relation from optical frequency spectrum response to electrical frequency spectrum response is modeled in a concise mode. However, the spatial frequency and the temporal frequency in this scheme are coupled to each other, and the physical meaning is not clear enough. More importantly, this scheme is too idealized in dealing with antennas and arrays thereof. The antennas in the system are considered as frequency independent isotropic radiators, with the array arranged in one dimension at equal intervals on a straight line. Such a model cannot adapt to the research requirements of an actual system and the new development trends of conformal antennas, random array arrangement and the like.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a time-space-frequency multi-dimensional modeling method of a light-controlled radio-frequency beam forming system so as to adapt to various light-controlled microwave amplitude-phase delay methods and actual antenna and array conditions and show the time-space-frequency multi-dimensional signal processing capability of the system.
The invention relates to a time-space-frequency multi-dimensional modeling method of a light-operated radio frequency beam forming system, which comprises the following steps:
step A, decomposing a light-controlled radio frequency beam forming system into an antenna array consisting of a group of antenna units and a group of parallel microwave photon links corresponding to the antenna units one by one;
step B, aiming at the configuration of each microwave photon link in a certain target beam control state S of the light-controlled radio frequency beam forming system, for each microwave photon link, mapping the time frequency response of the optical device in the microwave photon link in the optical frequency band to be the time frequency sub-model H of the microwave photon link in the microwave frequency bandL(ωtN; s) simultaneously obtaining the radiation sub-model of each antenna unit
And establishing a space domain sub-model of antenna array arrangementWherein ω istIs the time frequency, n is the serial number of the microwave photonic link,
is a normalized space frequency vector independent of time frequency, and has a zenith angle theta and an azimuth angle of the far-field observation point
The relationship of (1) is:
and step C, fusing the time frequency submodel, the radiation submodel and the airspace submodel into a space-time multidimensional frequency spectrum response function of the light-controlled radio frequency beam forming system according to the following formula:
wherein the content of the first and second substances,is a ratio of
A unit direction vector with one more dimension, which represents the direction of the observation angle; and c is the electromagnetic wave propagation speed in the use environment of the antenna array.
Further, the method further comprises:
and D, changing the target beam control state S and repeating the step B and the step C.
Preferably, the time-frequency response of the optical device in the microwave photonic link in the optical frequency band is mapped to a time-frequency submodel of the microwave photonic link in the microwave frequency band, and the specific method is as follows:
step 2, obtaining complex amplitudes of a single-frequency optical carrier wave, a +1 order sideband and a-1 order sideband after passing through the optical device by utilizing the optical frequency band time spectrum response of the optical device;
and 3, respectively beating the single-frequency optical carrier with +1 order sideband and-1 order sideband, and then adding the two beating results.
Further, mapping the time-frequency response of the optical device in the microwave photonic link in the optical frequency band to a time-frequency submodel of the microwave photonic link in the microwave frequency band, further comprising:
and 4, changing the frequency of the single-tone microwave signal and repeating the steps 1 to 3 to obtain a frequency spectrum response model of the microwave photon link under the broadband.
Preferably, the radiation sub-model of the antenna unit is a directional diagram of the antenna unit excited by different single-tone microwave signals.
Preferably, the spatial sub-model of the antenna array is a spatial coordinate set of each antenna unit.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
the modeling method fully considers the correlation of actual antenna response to signal time frequency and far field observation angle, and has no limitation on the arrangement mode of the antenna array and the difference between different antennas in the array. In addition, the scheme of the invention introduces the concept of normalizing spatial frequency, eliminates the coupling between the spatial frequency and time frequency, makes the physical significance of the model more definite, and makes the modeling result more intuitive.
Drawings
FIG. 1 is a flow chart of a method of time-space-frequency multi-dimensional modeling of a light-controlled broadband radio frequency beamforming system of the present invention;
fig. 2 is an exemplary architecture of an optically controlled broadband radio frequency beamforming system;
FIG. 3 is a basic structure of a microwave photonic link;
FIG. 4 is a schematic of the geometry of the antenna array with respect to a far field viewpoint;
FIG. 5 is a block diagram of an optically controlled wideband radio frequency beamforming system in an exemplary embodiment;
FIG. 6 is a modeling result of an antenna element radiation sub-model in an exemplary embodiment;
FIG. 7 is a structure of one of the microwave photonic links broken down in an exemplary embodiment;
FIG. 8 is a time-frequency submodel for each microwave photonic link in a particular embodiment;
FIG. 9 is a modeling result of a specific embodiment.
Detailed Description
Aiming at the defects of the prior art, the invention provides a space-time-frequency multi-dimensional modeling method of a light-controlled radio frequency beam forming system, which comprises the following steps as shown in figure 1:
step A, decomposing a light-controlled radio frequency beam forming system into an antenna array consisting of a group of antenna units and a group of parallel microwave photon links corresponding to the antenna units one by one;
step B, aiming at the configuration of each microwave photon link in a certain target beam control state S of the light-controlled radio frequency beam forming systemFor each microwave photon link, mapping the time-frequency response of the optical device in the microwave photon link in the optical frequency band to a time-frequency sub-model H of the microwave photon link in the microwave frequency bandL(ωtN; s) simultaneously obtaining the radiation sub-model of each antenna unitAnd establishing a space domain sub-model of antenna array arrangement
Wherein ω istIs the time frequency, n is the serial number of the microwave photonic link,
is a normalized space frequency vector independent of time frequency, and has a zenith angle theta and an azimuth angle of the far-field observation point
The relationship of (1) is:
and step C, fusing the time frequency submodel, the radiation submodel and the space domain submodel into a space-time multidimensional frequency spectrum response function of the light-controlled radio frequency beam forming system.
As shown in fig. 2, the optically controlled broadband radio frequency beam forming system is composed of multiple parallel microwave photonic links and an antenna array. Each microwave photon link can be regarded as a two-port microwave network, the amplitude, the phase and the time delay response of the microwave photon link related to time frequency can be adjusted according to a certain target beam control state of the system, and the microwave photon link is the core of the light-controlled broadband radio frequency beam forming system for processing space-time-frequency multi-dimensional signals; the antenna array in the system is composed of a plurality of antenna units with unchanged spatial positions, the number of the antenna units is equal to that of the microwave photon links, and each antenna unit is provided with a microwave photon link corresponding to the antenna unit. In order to construct an integral model of the light-controlled broadband radio frequency beam forming system, microwave photon links, antenna units and array forms of the microwave photon links and the antenna units are respectively modeled.
The modeling target of the microwave photon link is to construct a time-frequency sub-model thereof, namely to obtain the variation relation H of the amplitude, the phase and the delay response with the time frequency of the microwave photon link in a certain target beam control state SL(ωtN; s), where ω istAnd n is the serial number of the microwave photonic link. Figure 3 shows the basic structure of a microwave photonic link. Assume that the optical carrier signal output by the laser is exp (j ω @)ct) where ω iscIs a function of S; the input microwave signal is cos (omega)tt). Without loss of generality, the high order sidebands (≧ 2) are negligible under small signal modulation, then the electro-optically modulated optical signal can be expressed as:
wherein A is-1、A0、A+1Is the complex coefficient of-1 order sideband, carrier wave and +1 order sideband determined by the modulation system. For the commonly used electro-optic intensity modulation based on the quadrature-biased Mach-Zehnder modulator, there is A-1＝A+1＝J1(beta) and A0＝J0(β), wherein β is the modulation index, JnIs an n-th order bessel function of the first kind. If single sideband modulation is applied, then A-1Or A+1The ideal value of (b) is 0. The modulated light then enters a responsive controllable light device. Let the optical frequency band time frequency response function of the optical device in the beam control state S be Hopt(ω; S), the modulated light passing through the optical device can be expressed as:
after photoelectric detection, the optical carrier waves beat with-1 and +1 order sidebands respectively, and the intensity envelope of the optical signal is extracted. Neglecting the direct current term and the quadratic term with small intensity in the envelope, the resulting microwave signal is:
where gamma is a constant determined by both the optical carrier intensity and the responsivity of the photodetector. The formula (3) is compared with the input microwave signal cos (omega)tt) comparing to obtain the time-frequency sub-model of the microwave photon link:
it can be seen that the time frequency response H of the optical device in the optical frequency bandopt(ω; S) has been mapped to the time-frequency response of the microwave photonic link in the microwave frequency band. It is to be noted that A on the right side of the equation (4)0、A-1、A+1、ωcAnd Hopt(ω; S), etc. may be a function of n, if desired, where the variable n is omitted to ensure brevity.
On the other hand, the modeling of the antenna array is to obtain the radiation submodel of each antenna unit and the spatial domain submodel of the array arrangement form of the radiation submodel. The antenna element with n number is used as the radiation sub-model
Is shown in which
Is a normalized spatial frequency vector independent of temporal frequency. By means of the geometrical relations as in fig. 4, it is obtainedThe far field observation angle in the half space with z being more than or equal to 0In a relationship of
In particular, when the viewing angle is at only one angleVariation in degree dimension, i.e.
Or
When the temperature of the water is higher than the set temperature,
degenerated to univariate omegasAt this time have
ωs＝sinθ，θ∈[-π/2,π/2](6)
The radiation sub-model of the antenna element is the time frequency omegatNormalized spatial frequency
And the ternary function of the antenna serial number n can be obtained by measuring the directional diagram of each antenna under the excitation of different single-tone signals, and can also be obtained by electromagnetic simulation or theoretical calculation. The space domain submodel of the antenna array arrangement is composed of
The physical meaning is the spatial coordinates of the nth antenna element. Due to the fact that
The values of (a) are not limited, and the array arrangement modes which can be described include one-dimensional linear arrays arranged at arbitrary intervals along a straight line or a curve, two-dimensional planar arrays arranged at arbitrary intervals on a plane or a curved surface, and other various complex situations.
The submodels of each key part of the light-controlled broadband radio frequency beam forming system can be fused into a space-time multidimensional frequency spectrum response function of the whole system. As shown in FIG. 4, there is a far field observation point A in z ≧ 0 half-space. The normalized spatial frequency corresponding to the observation angle of the antenna element n of the point A is set toThe transmission distance from the antenna unit n to the point A is d (n), and the loss is l (n). According to far fieldSuppose that there are
Wherein l (0), d (0),Respectively the normalized spatial frequency corresponding to the transmission loss, the transmission distance and the observation angle from the origin to the point A,
the unit vector of the line from the origin to the point A can be expressed by adding one dimension
In a certain target beam control state S, the excitation of the light-controlled broadband radio frequency beam forming system is set as the time frequency omegatThe single-tone signal is processed by a microwave photon link n, and the signal sent to an antenna unit n is HL(ωtN; s) and the signal received by point a from antenna element n can be represented as:
the total signal received by point a is the superposition of the signals transmitted by the antenna units:
simultaneous (8) - (10), and omitting the common loss l (0) and delay d (0) from each antenna signal;
scanning the position of the point A in the far field to obtain the space-time multidimensional frequency spectrum response function of the light-controlled broadband radio frequency beam forming system
Thus completing the space-time-frequency multi-dimensional modeling of the light control broadband radio frequency beam forming system. The physical meaning of the model can be understood as the filtering effect of the light-controlled broadband radio frequency beam forming system on the time frequency domain of a signal to be transmitted and the reconstruction effect of a radiation directional diagram of a space domain in a transmitting mode, or the selective gain and attenuation of the light-controlled broadband radio frequency beam forming system on signals with different directions and different time frequencies in a receiving mode.
The method for modeling space-time-frequency multi-dimensions in an optically controlled wideband rf beamforming system according to the present invention will be described in detail with reference to an embodiment.
Consider a simplified optically controlled beamforming system with 16 elements, capable of one-dimensional angular scanning, operating in the X band. As shown in fig. 5, the system is composed of a tunable laser, an electro-optical intensity modulator, a 1-split 16-optical power splitter, 16 optical dispersion devices (n ═ 1,2 …,16) with dispersion value of (n-1) × 30ps/nm, 16 photodetectors, and 16 antenna units. The electro-optic modulation is biased at an orthogonal point, and the modulation index is 0.1. For simplicity, let 16 photodetectors have the same responsivity; the 16 antenna elements have the same radiation characteristics, and the array is arranged at equal intervals along the x-axis at a distance of 0.015 meter.
The light-controlled broadband radio frequency beam forming system is modeled, and the time-space-frequency multidimensional response of the light-controlled broadband radio frequency beam forming system under the setting of a target beam control state S ═ {60 DEG main lobe } is considered. The system is first broken down, the broken down parts being shown in fig. 6. Since 16 antenna units have the same radiation characteristics and the array only performs one-dimensional angle scanning, the radiation sub-model thereof
Can be simplified to A (omega)t,ωs). Now with the antennaAs a result of modeling its radiation submodel, as shown in fig. 6. The data in fig. 6 has been normalized, and the right axis is the far-field viewing angle corresponding to the normalized spatial frequency, which can be determined by equation (6). And the spatial domain submodel of the antenna array arrangement can be expressed asThe broken-down microwave photonic link is shown in fig. 7, in which the 16-way common laser and electro-optic modulator in the original system are divided into individual branches. Since 16 photodetectors have uniform responsivity, and the intensity of the optical carrier and the 1-splitting 16 optical power splitter do not affect the relative amplitude-phase parameters of each microwave photonic link, γ is not set to be 1, and the optical power splitter is omitted. In addition, as known from the modulation system, the sideband coefficient after modulation is A-1＝A+1＝J1(0.1) and A0＝J0(0.1). And the optical time frequency response of the nth microwave photonic link is
Wherein D ═ n-1. times.30 ps/nm is the dispersion value, ω isr＝1.2161×1015rad/s is the reference optical time frequency. At the target beam steering state S ═ 60 ° main lobe setting, the output frequency of the laser should be tuned to 1.21497 × 1015rad/s, then according to (4), calculating out the time-frequency submodel H of each microwave photon linkL(ωtN), as shown in fig. 8. Finally, a space-time multidimensional frequency spectrum response function of the light-controlled broadband radio frequency beam forming system can be obtained according to the formula (12), and modeling of the system is completed, as shown in fig. 9. The data in fig. 9 has been normalized, and the right axis is the far-field viewing angle corresponding to the normalized spatial frequency, which can be determined by equation (6). The time-space-frequency multidimensional model can intuitively display the multidimensional joint processing characteristic of the system, for example, in fig. 9, due to the signal fading problem caused by dispersion, the signals with the time frequency of about 12.5GHz are not effectively concentrated near the normalized space frequency of 0.866. This can provide reference and guidance for the optimization of the system.
Claims (6)
1. The time-space-frequency multi-dimensional modeling method of the light-operated radio frequency beam forming system is characterized by comprising the following steps of:
step A, decomposing a light-controlled radio frequency beam forming system into an antenna array consisting of a group of antenna units and a group of parallel microwave photon links corresponding to the antenna units one by one;
step B, aiming at the configuration of each microwave photon link in a certain target beam control state S of the light-controlled radio frequency beam forming system, for each microwave photon link, mapping the time frequency response of the optical device in the microwave photon link in the optical frequency band to be the time frequency sub-model H of the microwave photon link in the microwave frequency bandL(ωtN; s) simultaneously obtaining the radiation sub-model of each antenna unit
And establishing a space domain sub-model of antenna array arrangement
Wherein ω istIs the time frequency, n is the serial number of the microwave photonic link,
is a normalized space frequency vector independent of time frequency, and has a zenith angle theta and an azimuth angle of the far-field observation point
The relationship of (1) is:
and step C, fusing the time frequency submodel, the radiation submodel and the airspace submodel into a space-time multidimensional frequency spectrum response function of the light-controlled radio frequency beam forming system according to the following formula:
wherein the content of the first and second substances,is a ratio ofA unit direction vector with one more dimension, which represents the direction of the observation angle; and c is the electromagnetic wave propagation speed in the use environment of the antenna array.
2. The method of claim 1, further comprising:
and D, changing the target beam control state S and repeating the step B and the step C.
3. The method as claimed in claim 1 or 2, wherein the time-frequency response of the optical device in the microwave photonic link in the optical frequency band is mapped to a time-frequency submodel of the microwave photonic link in the microwave frequency band by the following specific method:
step 1, obtaining the complex amplitudes of an electro-optically converted optical carrier, a +1 order sideband and a-1 order sideband by utilizing the frequency spectrum relationship of a single-frequency optical carrier after single-tone microwave modulation in an electro-optical modulator;
step 2, obtaining complex amplitudes of a single-frequency optical carrier wave, a +1 order sideband and a-1 order sideband after passing through the optical device by utilizing the optical frequency band time spectrum response of the optical device;
and 3, respectively beating the single-frequency optical carrier with +1 order sideband and-1 order sideband, and then adding the two beating results.
4. The method of claim 3, wherein mapping the time-frequency response of an optical device in a microwave photonic link in an optical frequency band to a time-frequency submodel of the microwave photonic link in a microwave frequency band further comprises:
and 4, changing the frequency of the single-tone microwave signal and repeating the steps 1 to 3 to obtain a frequency spectrum response model of the microwave photon link under the broadband.
5. The method of claim 1 or 2, wherein the radiation sub-model of the antenna unit is a directional pattern of the antenna unit excited by different single-tone microwave signals.
6. The method of claim 1 or 2, wherein the spatial sub-model of the antenna array is a set of spatial coordinates of each antenna element.
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