CN117955557A - Frequency and angle of arrival measuring method based on multipath light undersampling phase shift analysis - Google Patents

Frequency and angle of arrival measuring method based on multipath light undersampling phase shift analysis Download PDF

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CN117955557A
CN117955557A CN202211325121.4A CN202211325121A CN117955557A CN 117955557 A CN117955557 A CN 117955557A CN 202211325121 A CN202211325121 A CN 202211325121A CN 117955557 A CN117955557 A CN 117955557A
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frequency
dpol
antenna
angle
arrival
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王占东
文爱军
李晓阳
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Xidian University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B10/00Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/07Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
    • H04B10/073Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an out-of-service signal
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B10/00Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/11Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02ATECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

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  • Electromagnetism (AREA)
  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • Measuring Phase Differences (AREA)

Abstract

The invention discloses a frequency and angle of arrival measuring method based on multipath light undersampling phase shift analysis, which relates to the technical field of optical communication and microwaves and is used for measuring the frequency and angle of arrival of radio frequency signals. The method comprises an antenna, a mode-locked laser MLL, a direct current source DC, an optical coupler OC, an adjustable optical delay line VODL, an electric power divider EC, a phase distribution line, a dual-polarization Mach-Zehnder modulator DPol-MZM, a polarization controller PC, a polarization beam splitter PBS, a photoelectric detector PD, a low-pass filter LPF, an analog-to-digital converter ADC and a digital signal processing module DSP. The mode-locked laser generates an optical comb, a plurality of undersampled links are constructed by using parallel double-polarization Mach-Zehnder modulators, different relative phase shifts are introduced to undersampled intermediate-frequency signals through optical delay lines and antenna pitches, multi-baseline phase interferometry realizes the non-fuzzy measurement of a large bandwidth angle of arrival, phase shift analysis is carried out on intermediate-frequency signals, and the frequency and angle of arrival of the signals are determined. The invention has simple equipment and strong practical operability.

Description

Frequency and angle of arrival measuring method based on multipath light undersampling phase shift analysis
Technical Field
The invention relates to the technical field of optical communication and the technical field of microwaves, in particular to a frequency and angle of arrival measuring method based on multi-path optical undersampling phase shift analysis in the optical communication technology.
Background
In electronic warfare and radar systems, the ability to acquire the frequency and angle of arrival of radio frequency signals is critical. Since electronic warfare is basically a responsive action to a harsh electronic environment, the receiver should have a wide instantaneous bandwidth, meaning that any signal within the input bandwidth will be received all the time without the need for a switching device.
In the traditional electronic countermeasure and reconnaissance equipment, the electric domain scheme is difficult to realize simultaneous measurement of the frequency and the angle of arrival of the radio frequency signal under the condition of large bandwidth, and has the defects of electromagnetic interference, high power consumption, large volume and the like.
Compared with the traditional electric domain scheme, the microwave photon technology which is rapidly developed in recent years has the advantages of large instantaneous bandwidth, wide frequency coverage range, strong electromagnetic interference resistance and the like, and provides a new scheme for solving the problems encountered by the electric domain scheme.
The current frequency measurement technology based on microwave photons has a plurality of implementation methods, such as time-frequency mapping, amplitude comparison function and down-conversion. The time-frequency mapping-based method can realize high-resolution frequency measurement, but the instantaneous bandwidth is relatively poor. The amplitude comparison function method has the characteristics of simple structure and strong instantaneous capability, is mainly used for an instantaneous frequency measurement receiver, but is difficult to process broadband and multitone signals. The frequency measurement based on down conversion can be realized through frequency scanning and optical sampling, the optical undersampling structure generally comprises a pulse light source, a modulator and a photodiode, the optical undersampling structure has the advantages of low jitter and wide bandwidth, an input radio frequency signal is down-converted to an intermediate frequency range by using an optical undersampling technology, the original frequency of the radio frequency signal can be recovered through the technologies such as intermediate frequency shift, a multi-comb structure, phase shift analysis and the like, and the main disadvantage of the optical undersampling scheme is high cost. Microwave photon technology is also applied to the measurement of angle of arrival, which can be measured by mapping the angle of arrival information of a radio frequency signal to a direct current voltage or power. Down-converting the received signal to an intermediate frequency and using digital signal processing is also a method of measuring the angle of arrival. For a wide-frequency coverage angle of arrival measurement system, the measurement accuracy and the measurement range are mutually restricted by using a single-base-line phase interferometer.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a frequency and angle of arrival measuring method based on multi-path light undersampling phase shift analysis. According to the method, parallel double-polarization Mach-Zehnder modulators are adopted to construct a plurality of optical undersampled links, different relative phase shifts are introduced to different optical sampling intermediate frequency signals through the distances between optical fiber delay lines and different antennas, the arrival angle can be accurately measured in a large frequency range by adopting multi-baseline phase comparison, and the frequency and the arrival angle of a radio frequency signal to be measured can be determined through phase shift analysis of four paths of intermediate frequency signals. The method has the capability of frequency and direction measurement for a plurality of target signals and broadband signals.
The invention adopts the technical scheme for solving the technical problems that: the method comprises an antenna 1, an antenna 2, an antenna 3, a mode-locked laser MLL, a direct current source DC1, a direct current source DC2, an optical coupler OC, an adjustable optical delay line VODL, an electric power divider EC, a phase line, a dual-polarization Mach-Zehnder modulator DPol-MZM1, a dual-polarization Mach-Zehnder modulator DPol-MZM2, a polarization controller PC1, a polarization controller PC2, a polarization beam splitter PBS1, a polarization beam splitter PBS2, a photoelectric detector PD1, a photoelectric detector PD2, a photoelectric detector PD3, a photoelectric detector PD4, a low-pass filter LPF1, a low-pass filter LPF2, a low-pass filter LPF3, a low-pass filter LPF4, an analog-digital converter ADC and a digital signal processing module DSP. The optical pulse signal output by MLL is divided into an upper path and a lower path through OC, the upper path is directly sent into DPol-MZM1, the lower path is sent into DPol-MZM2 after a certain optical delay is introduced into VODL, the radio frequency signal to be measured is received by 3 antennas, a short base line L1 is formed between the antennas 1 and 2, a long base line L2 is formed between the antennas 1 and 3, the signal to be measured received by the antenna 1 is respectively loaded to the sub-modulators MZM1 and DPol-MZM2 of DPol-MZM1 through EC and phase matching line, the signal to be measured received by the antenna 2 is loaded to the sub-modulator MZM2 of DPol-MZM1, the signal to be measured received by the antenna 3 is loaded to the sub-modulator MZM2 of DPol-MZM2, the two DPol-MZMs work at the intersection point QTP, the output ports of the two DPol-MZMs are respectively connected with the input ports of the two PCs, the output ports of the two PCs are respectively connected with the input ports of the two PBSs, the two PBSs are divided into four channels, each channel is connected with the input port of the PD through the output port of the PBS, the output port of the PD is connected with the input port of the LPF, the optical signal of each channel is converted into an electric intermediate frequency signal through the PD, the output ports of the four LPFs are connected with the input port of a four-channel ADC, and the output port of the ADC is connected with the input port of the DSP. The frequency and angle of arrival of the outgoing frequency signal can be calculated from the frequency of the intermediate frequency signal and the phase difference between each intermediate frequency signal.
The invention comprises the following steps in working:
(1) Dividing an optical pulse signal generated by MLL into an upper path and a lower path through an optical coupler, directly sending the upper path into DPol-MZM1, sending the lower path into DPol-MZM2 after passing through an adjustable optical delay line and selecting a frequency measuring range by adjusting the optical delay;
(2) The radio frequency signals to be measured are received by 3 antennas, a short base line L1 is formed between the antennas 1 and 2, a long base line L2 is formed between the antennas 1 and 3, the signals to be measured received by the antennas 1 are respectively loaded to the sub-modulators MZM1 and DPol-MZM2 of DPol-MZM1 through an electric power divider and a phase matching line, the signals to be measured received by the antennas 2 are loaded to the sub-modulator MZM2 of DPol-MZM1, and the signals to be measured received by the antennas 3 are loaded to the sub-modulator MZM2 of DPol-MZM 2;
(3) In DPol-MZM, the injected optical signal is divided into two paths, and is respectively input into the sub-modulators MZM-1 and MZM-2 of the optical signal, the MZM-1 and the MZM-2 are biased at the orthogonal transmission point, the polarization state of the modulated signal output by the MZM-2 is rotated by 90 degrees, and the modulated signal output by the MZM-1 form an orthogonal polarization state;
(4) The orthogonal polarization signals output by the two DPol-MZMs are respectively injected into two PCs, the polarization states are adjusted by the PCs to be aligned with the PBS, the orthogonal polarization signals are separated into two paths of signals according to the polarization states, and the two paths of signals are divided into four paths;
(5) The four paths of PBS output signals are respectively input into the PD for photoelectric conversion to obtain electric signals, and then the electric signals are filtered by a low-pass filter to obtain intermediate frequency signals in a 1 st Nyquist interval.
(6) The four paths of intermediate frequency signals are input into the ADC and the DSP, and the frequency and the angle of arrival of the radio frequency signals to be measured are calculated according to the frequency and the phase difference of the four paths of intermediate frequency signals.
The invention provides a novel method for measuring optical sampling frequency and angle of arrival, which divides an optical pulse signal generated by a mode-locked laser into two paths, introduces time delay to one path, adds an extra phase on the optical pulse through an optical delay line, and generates intermediate frequency signals with different relative phase shifts through optical undersampling by different radio frequency signals. The nyquist band in which the radio frequency signal is located can be determined by the phase shift. Meanwhile, the multi-baseline phase interferometer is adopted to realize high-precision measurement of the angle of arrival in the wide-frequency coverage range, the cost of an optical sampling system is greatly reduced based on a phase shift analysis technology, and the method is also suitable for detection of wide-band and multi-tone signals. The invention has simple equipment and strong practical operability.
The external modulation measurement system constructed by the scheme adopts an all-optical modulation system, is not limited by the bandwidth of an electric field device, the frequency measurement range of the whole system only depends on the modulation bandwidth of DPol-MZM and the repetition frequency of an optical comb, the overall frequency dependence of the system is small, the working bandwidth is large, the wave arrival angle measurement of the system adopts multi-baseline interference, the accurate measurement of the wave arrival angle is ensured, and the measurement precision of the wave arrival angle is improved.
The invention realizes the sharing of devices based on the frequency and the angle of arrival measurement of the multi-path light undersampled phase shift analysis, and provides technical support for a microwave photon integrated system.
Drawings
FIG. 1 is a schematic diagram of a frequency and angle of arrival measurement method based on multi-path optical undersampled phase shift analysis in accordance with the present invention; FIG. 2 is a graph of the fit of the phase shift DeltaPhi 1 between channel 3 and channel 1, with frequency ranging from 0.608GHz to 31.579GHz, spacing 300.698MHz, and an enlarged graph of the phase shift DeltaPhi 1 in each Nyquist band, each Nyquist band having a frequency width of 285MHz, spacing 15MHz, for a total of 20 points; FIG. 3 is a phase shiftFitting a curve, wherein the frequency ranges from 0.608GHz to 31.579GHz, the interval is 300.698MHz, and the amplified diagram shows the phase shift/>, in each Nyquist bandThe frequency width of each Nyquist band is 285MHz, the interval is 15MHz, and the total number of the Nyquist bands is 20 points; FIG. 4 shows the theoretical and experimental values of the phase difference of the RF signal, and the measurement error, FIG. 4 (a) shows the phase difference/>, when the frequency of the RF signal is 15GHzWherein the solid line is a theoretical curve and the circle O represents/>The black inverted triangle indicates the error between the theoretical value and the experimental value, and FIG. 4 (b) shows the phase difference/>, when the frequency of the RF signal is 15GHzWherein the solid line is a theoretical curve and the circle O represents/>The black inverted triangle indicates the error of the theoretical value from the experimental value.
Detailed Description
Examples of embodiments of the invention are described in detail below with reference to the attached drawing figures: the embodiment example is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode and a specific operation process are provided, but the protection scope of the invention is not limited to the following embodiment example.
FIG. 1 is a schematic diagram of a frequency and angle of arrival measurement method based on multi-path optical undersampled phase shift analysis in accordance with the present invention. The method comprises a mode locking laser MLL, an optical coupler OC, an adjustable optical delay line VODL, an electric power divider EC, a phase distribution line, a dual-polarization Mach-Zehnder modulator DPol-MZM, a polarization controller PC, a polarization beam splitter PBS, a photoelectric detector PD, a low-pass filter LPF, an analog-to-digital converter ADC and a digital signal processing module DSP. The optical pulse signal optical coupler output by the MLL divides an optical pulse signal into an upper path and a lower path, the upper path is directly sent into DPol-MZM1, the lower path is sent into DPol-MZM2 after a certain optical delay is introduced through an adjustable optical delay line, a radio frequency signal to be detected generated by a radio frequency source is received by 3 antennas, a short base line L1 is formed between the antenna 1 and the antenna 2, a long base line L2 is formed between the antenna 1 and the antenna 3, and the phase difference between the antenna receiving signals is simulated through the phase shift of an electric phase shifter. The signal to be measured received by the antenna 1 is respectively loaded to the sub-modulators MZM1 and DPol-MZM2 of DPol-MZM1 through the power divider and the phase matching line, the signal to be measured received by the antenna 2 is loaded to the sub-modulator MZM2 of DPol-MZM1, and the signal to be measured received by the antenna 3 is loaded to the sub-modulator MZM2 of DPol-MZM 2; the upper and lower sub-modulators of the DC source control DPol-MZM are biased at the quadrature transmission point to modulate the signals received by the antenna, respectively. The polarization state of the modulated signal output by the MZM2 is rotated by 90 degrees, and the modulated signal output by the MZM1 and the modulated signal form an orthogonal polarization state. The orthogonal polarization signals output by the two DPol-MZMs are respectively injected into two PCs, the polarization states are adjusted by the PCs to be aligned with the PBS, the orthogonal polarization signals are separated into two paths of signals according to the polarization states, and the signals are divided into four paths in total. The four paths of output signals of the PBS are respectively input into the PD to be subjected to photoelectric conversion to obtain electric signals, the electric signals are filtered by a low-pass filter to obtain intermediate frequency signals in a1 st Nyquist interval, the intermediate frequency signals are then sent into the ADC to be subjected to analog-to-digital conversion, and digital signals output by the ADC are sent into a digital signal processing module to be processed and analyzed to recover the radio frequency initial frequency and the phase difference information.
In this example, the method comprises the following specific implementation steps:
step one: the mode-locked laser generates an optical pulse signal with the repetition frequency of 601.396 MHz;
step two: the radio frequency signals to be detected generated by the radio frequency source are received by 3 antennas, a short base line L1 is formed between the antenna 1 and the antenna 2, a long base line L2 is formed between the antenna 1 and the antenna 3, the antenna 2 and the antenna 3 are respectively subjected to phase shifting by an electric phase shifter to simulate the phase difference between antenna receiving signals, and the radio frequency signals received by each antenna can be expressed as:
Where V 0 denotes the amplitude of the RF signal, f RF denotes the frequency of the RF signal, Indicating the phase difference of the signals received by antenna 1 and antenna 2,/>The phase difference of the signals received by the antennas 1 and 2 is shown, and M is an integer. The relationship of the short baseline L1 and the long baseline L2 can be expressed as:
step three: the output optical pulse signal optical coupler divides the optical pulse signal into an upper path and a lower path, the upper path is directly fed into DPol-MZM1, the lower path is fed into an adjustable optical delay line, then the signal output by the adjustable optical delay line is input into DPol-MZM2, and the optical pulse signals at the input ends of DPol-MZM1 and DPol-MZM2 can be expressed as:
Wherein E U、EL represents the light pulse intensity of the upper path and the lower path respectively, P p is the pulse peak power, T r is the sampling light pulse repetition period, the right side of the equation is the frequency domain Fourier expansion expression of the pulse, c n is the coefficient of each subharmonic, f r is the frequency of each subharmonic, and f r=1/Tr is present, the coefficient of the harmonic is related to the pulse shape, and τ represents the light delay introduced by the lower path.
Step four: in DPol-MZM, the injected optical signal is divided into two paths, and is respectively input into the sub-modulators MZM-1 and MZM-2, wherein the MZM-1 and the MZM-2 are biased at the orthogonal transmission point, the polarization state of the modulated signal output by the MZM-2 is rotated by 90 degrees, the modulated signal output by the MZM-1 and the modulated signal output by the MZM-1 form the orthogonal polarization state, and under the condition of small signal modulation, the transmission function of the MZM can be expressed as follows:
Where V π is the half-wave voltage of the sub-modulator MZM. Considering the ideal case, i.e. c n =1, the two DPol-MZM outputs can be expressed as:
Step five: the orthogonal polarization signals output by the two DPol-MZMs are respectively injected into two PCs, the polarization states are adjusted by the PCs to be aligned with the PBS, the orthogonal polarization signals are separated into two paths of signals according to the polarization states, and the signals are divided into four paths in total.
Step six: the output end of the PBS is connected with the photoelectric detector to perform beat frequency to obtain an electric signal, then a low-pass filter is used to obtain an intermediate frequency signal in the (0, f r/2) frequency band, and the output end of the four-way low-pass filter can be expressed as:
Wherein ψ m (), m=1, 2,3,4 and a m (), m=1, 2,3,4 represent the non-ideal phase-frequency response and the amplitude-frequency response of the four-channel device between PD and ADC, f IF=|Nfr-fRF | represents the intermediate frequency signal frequency, the integer N represents the optical comb number nearest to the radio frequency signal frequency in the frequency spectrum, and k can be expressed as:
Step seven: the frequency and phase of the intermediate frequency signal can be obtained by fast Fourier transformation, and the output intermediate frequency signals of different channels comprise And/>Three sets of phase shifts, which can be expressed as:
In which the phase is shifted ΔΦ 1 is the phase shift between channel 3 and channel 1, ΔΦ 2 is the phase shift between channel 2 and channel 1, ΔΦ 3 is the phase shift between channel 4 and channel 3, sweep signals with intervals of 300.698MHz are signals to be measured, wherein the electrical signals in each frequency range are comb signals with intervals of 15MHz, ΔΦ 1、△Φ2 and ΔΦ 3 are obtained by linear fitting, the phase shift between channel 3 and channel 1 ΔΦ 1 is obtained by linear fitting, the slope of the fitted curve is the optical delay τ, i.e., τ= 15.527ps is shown in fig. 2. And ψ 3(fIF)-ψ1(fIF) is equal to the fitted phase shift curve minus the phase shift introduced by the optical delay τ, and values ψ 2(fIF)-ψ1(fIF) and ψ 4(fIF)-ψ3(fIF) are obtained in the same way. By fitting the phase shift curve and the phase frequency response, the/>And/>Phase shift/>, from 0.608GHz to 31.579GHzThe measurement results are shown in fig. 3. By measuring/>The values of k and N can be obtained, and the radio frequency f RF can be expressed as:
fRF=Nfr-kfIF
step eight: adjusting the frequency of the input radio frequency signal to 15GHz, respectively adjusting an electric phase shifter connected with the antenna 2 and an electric phase shifter connected with the antenna 3, measuring 20 data points from 0 DEG to 360 DEG, and measuring the phase shift And/>Finally, the theoretical value and the experimental value of the phase difference of the radio frequency signals are compared to obtain a measurement error, as shown in fig. 4. From the measured phase shift/>And/>The angle of arrival θ can be obtained and can be expressed as:
Where round () represents a rounding function.
In conclusion, the invention utilizes the optical comb undersampling and parallel DPol-MZM and the like to realize the frequency measurement and the angle of arrival measurement of signals, the system has simple structure, is easy to realize, is not affected by electromagnetic interference and has wide working bandwidth, the angle of arrival measurement of the system adopts multi-baseline interference, thereby not only ensuring the accurate measurement of the angle of arrival, but also improving the measurement precision of the angle of arrival. In actual operation, the measurement result of the angle of arrival can be calibrated by measuring the phase spectrum of the system. Larger operating bandwidths can be achieved with wider DPol-MZMs.
In summary, the above embodiments are merely examples of the present invention, and are not intended to limit the scope of the present invention, it should be noted that, for those skilled in the art, equivalent modifications and substitutions may be made on the disclosure of the present invention, the frequency of the optical comb repetition frequency, the output power of the mode-locked laser, the broadband or multi-frequency point of the signal to be measured, etc., and in addition, any module with digital signal processing capability may be connected to the LPF to process the final signal. Such equivalent variations and substitutions and adjustments of the frequency ranges should also be considered to be within the scope of the present invention.

Claims (1)

1. The utility model provides a frequency and angle of arrival measurement method based on multichannel light undersampled phase shift analysis, including antenna 1, antenna 2, antenna 3, mode locking laser MLL, DC source DC1, DC source DC2, optocoupler OC, adjustable optical delay line VODL, electric power divider EC, join in marriage the phase line, dual polarization Mach-Zehnder modulator DPol-MZM1, dual polarization Mach-Zehnder modulator DPol-MZM2, polarization controller PC1, polarization controller PC2, polarization beam splitter PBS1, polarization beam splitter PBS2, photodetector PD1, photodetector PD2, photodetector PD3, photodetector PD4, low pass filter LPF1, low pass filter LPF2, low pass filter LPF3, low pass filter LPF4, analog-digital converter ADC, digital signal processing module DSP, wherein DPol-M is inside totally integrated two Mach-Zehnder modulators MZM1 and MZM2, polarization beam combiner PBC and a polarization rotator 90 DEG, characterized in that: the optical pulse signal output by MLL is divided into an upper path and a lower path through OC, the upper path is directly sent into DPol-MZM1, the lower path is sent into DPol-MZM2 after a certain optical delay is introduced into VODL, the radio frequency signal to be measured is received by 3 antennas, a short base line L1 is formed between the antennas 1 and 2, a long base line L2 is formed between the antennas 1 and 3, the signal to be measured received by the antenna 1 is respectively loaded into the sub-modulators MZM1 and DPol-MZM2 of DPol-MZM1 through EC and phase matching line, the signal to be measured received by the antenna 2 is loaded into the sub-modulator MZM2 of DPol-MZM1, the signal to be measured received by the antenna 3 is loaded into the sub-modulator MZM2 of DPol-MZM2, both DPol-MZM work at a positive QTP, the output ports of the two DPol-MZMs are respectively connected with the input ports of the two PCs, the output ports of the two PCs are respectively connected with the input ports of the two PBSs, the two PBSs are divided into four channels, each channel is connected with the input port of the PD by the output port of the PBS, the output port of the PD is connected with the input port of the LPF, the optical signals of each channel are converted into electric intermediate frequency signals through the PD, the output ports of the four LPFs are connected with the input port of a four-channel ADC, the output port of the ADC is connected with the input port of the DSP, and the frequency and the angle of arrival of the outgoing frequency signals can be calculated according to the frequency of the intermediate frequency signals and the phase difference between each intermediate frequency signal.
CN202211325121.4A 2022-10-27 2022-10-27 Frequency and angle of arrival measuring method based on multipath light undersampling phase shift analysis Pending CN117955557A (en)

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