CN109471064B - Time modulation array direction-finding system based on pulse compression technology - Google Patents

Time modulation array direction-finding system based on pulse compression technology Download PDF

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CN109471064B
CN109471064B CN201811088800.8A CN201811088800A CN109471064B CN 109471064 B CN109471064 B CN 109471064B CN 201811088800 A CN201811088800 A CN 201811088800A CN 109471064 B CN109471064 B CN 109471064B
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CN109471064A (en
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陈靖峰
贺冲
金荣洪
朱卫仁
梁仙灵
耿军平
曹岸杰
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Shanghai Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
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Abstract

The invention provides a time modulation array direction-finding system based on a pulse compression technology, which comprises an antenna array module (1), a radio frequency switch module (2), a digital control module (14), a duplexer (3), a radio frequency local oscillator module (8), a signal transmitting module and a signal receiving module, wherein the antenna array module comprises a plurality of antenna arrays; the antenna array module (1) is sequentially connected with the radio frequency switch module (2) and the duplexer (3), the duplexer (3) is respectively connected with the signal transmitting module and the signal receiving module, the digital control module (14) is respectively connected with the radio frequency switch module (2) and the duplexer (3), and the radio frequency local oscillator module (8) is respectively connected with the signal transmitting module and the signal receiving module. The invention has the characteristics of low cost, simple structure and high direction finding precision, and is suitable for platforms such as miniaturized guidance radars, automobile anti-collision radars, unmanned automobile detection systems and the like.

Description

Time modulation array direction-finding system based on pulse compression technology
Technical Field
The invention relates to the technical field of antenna engineering, in particular to a time modulation array direction-finding system based on a pulse compression technology.
Background
The direction finding technology is widely applied to the fields of radar, sonar, wireless communication and the like, and the traditional direction finding method has the problems of complex hardware structure, high cost, complex calculation degree, low estimation precision and the like. Time modulation arrays have received great attention in recent years as a new type of low cost, low complexity antenna. The array generates harmonic components containing different information contents through periodic modulation, and can be used for realizing functions of direction finding, beam scanning, space division multiple access and the like. The frequency modulation signal is used as a spread spectrum signal with a large time-width bandwidth product, and is also applied to the fields of communication, radar, sonar detection, synthetic aperture radar imaging and the like. In the radar, in order to increase the detection distance of the radar and maintain a certain distance resolution, a linear frequency modulation signal is generally adopted to obtain a large time-bandwidth product; in wireless communication, system identification is carried out by utilizing a linear frequency modulation signal and time-varying filtering; in the synthetic aperture radar imaging technology, the resolution can be enhanced, and the imaging precision can be improved.
Disclosure of Invention
In view of the defects in the prior art, the invention aims to provide a time modulation array direction-finding system based on a pulse compression technology.
The time modulation array direction-finding system based on the pulse compression technology comprises an antenna array module, a radio frequency switch module, a digital control module, a duplexer, a radio frequency local oscillator module, a signal transmitting module and a signal receiving module; the antenna array module is sequentially connected with the radio frequency switch module and the duplexer, the duplexer is respectively connected with the signal transmitting module and the signal receiving module, the digital control module is respectively connected with the radio frequency switch module and the duplexer, and the radio frequency local oscillator module is respectively connected with the signal transmitting module and the signal receiving module.
Preferably, the antenna array module comprises one or more unit printed dipole antenna array units, and the distance between the antenna array units is half wavelength; the radio frequency switch module comprises one or more single-pole single-throw switches; the antenna array units correspond to the single-pole single-throw switches one by one.
Preferably, the signal transmitting module includes a chirp signal generator, a first mixer, a band-pass filter, and a power amplifier, the chirp signal generator is sequentially connected to the first mixer, the band-pass filter, the power amplifier, and the duplexer, and the first mixer is connected to the radio frequency local oscillation module.
Preferably, the signal receiving module includes a low noise amplifier, a second mixer, a low pass filter, a matched filter, and a signal processor, one end of the low noise amplifier is connected to the duplexer, the other end of the low noise amplifier is sequentially connected to the second mixer, the low pass filter, the matched filter, and the signal processor, the second mixer is connected to the radio frequency local oscillation module, and the matched filter is connected to the chirp signal generator.
Preferably, the radio frequency switch module is configured to perform time modulation on the echo signal, the duplexer is configured to switch the transmitting/receiving states, and the digital control module is configured to control a modulation timing of each single-pole single-throw switch of the radio frequency switch module and a state switching of the duplexer.
Preferably, when the system is in a transmitting state, the duplexer is switched to the transmitting branch, and the single-pole single-throw switches of the radio frequency switch module are all in a closed state; the linear frequency modulation pulse signal generated by the linear frequency modulation signal generator is modulated to carrier frequency through the first mixer, power amplification is carried out through the power amplifier after the linear frequency modulation pulse signal is filtered by the band-pass filter, and the amplified signal is radiated to space through the antenna array module after sequentially passing through the duplexer and the radio frequency switch module in a closed state.
Preferably, after the system finishes transmitting the chirp signal, the duplexer switches to a receiving state, the echo signal is received by the antenna array module and is periodically modulated by the radio frequency switch module, wherein the modulated signal is generated by the digital control module, and the modulated signal is down-converted by the second mixer after passing through the duplexer and the low noise amplifier in sequence and then is converted into a baseband signal by the low pass filter.
Preferably, the modulation frequency f of the radio frequency switch modulepThe following relation is satisfied between the chirp rate mu and the chirp signal emitted by the chirp signal generator:
Figure GDA0002482529790000021
modulation frequency f of the radio frequency switch modulepThe following relation is satisfied between the bandwidth B and the chirp rate mu of the chirp signal transmitted by the chirp signal generator:
Figure GDA0002482529790000022
wherein K represents the bandwidth B and the modulation frequency f of the radio frequency switch modulepRatio of (A) to (B), N*Representing a natural number, L representing the chirp rate mu and the modulation frequency f of the RF switch modulepSquared ratio, Z represents an integer.
Preferably, the matched filter performs pulse compression on the baseband signal output by the low-pass filter, including the harmonic component and the fundamental component, to obtain a matched filter output signal with multiple peaks, where the matched filter output signal is expressed as:
Figure GDA0002482529790000031
wherein S iso(theta, t) represents the output signal of the matched filter, theta represents the angle of the incident signal, t represents the time of the signal, Sr(theta, t) represents an echo signal of the transmitted signal,
Figure GDA0002482529790000032
representing the response function of the matched filter, t0Representing the time difference from the transmission of the signal to the reception of the echo signal,urepresenting the delay of the echo signal, m represents the serial number of the mth harmonic, the rect function is represented as rect (T/T) being 1, | T/T | ≦ 1, T is the pulse length of the chirp signal,
Figure GDA0002482529790000033
Figure GDA0002482529790000034
the Fourier coefficient of the mth harmonic wave of the whole array is shown, N represents the number of array elements used in the direction finding of the array, N represents the serial number of the array elements, am，nFourier coefficients representing the mth harmonic of the nth array element, j representing the imaginary sign, β representing the array wavenumber, d representing the array element spacing, fcRepresenting the carrier frequency of the echo signal, the sinc function is denoted sinc (x) sin (pi x)/pi x.
Preferably, the signal processor is used to process the output signal of the matched filter, and obtain the corresponding harmonic coefficient feature by searching, and the signal processor calculates the relationship for the incoming wave direction of the echo signal as follows:
Figure GDA0002482529790000035
wherein, thetanRepresenting the angle of the incident signal, phi, obtained by using the nth and n +1 th harmonic measurementsnRepresenting the nth harmonic coefficient of the array, phin+1Represents the n +1 th harmonic coefficient of the array;
wherein, the phin+1In the form of vectors
Figure GDA0002482529790000036
Expressed as:
Figure GDA0002482529790000037
wherein N × N represents the array element number × harmonics used in the direction finding of the array, the values of the array element number and the harmonics are all equal to N,
Figure GDA0002482529790000038
representing array factor vector, HCMN×NA matrix representing the characteristics of the harmonics,
Figure GDA0002482529790000039
an inverse matrix representing the harmonic characteristic matrix,
Figure GDA00024825297900000310
representing a harmonic coefficient vector;
wherein the array factor vector
Figure GDA00024825297900000311
Wherein, superscript T represents a transpose matrix; the harmonic coefficient vector
Figure GDA00024825297900000312
The harmonic characteristic matrix HCMN×NExpressed as:
Figure GDA0002482529790000041
wherein, am，nIs the Fourier coefficient of the m-th harmonic of the nth array element, wherein k is more than or equal to m and less than or equal to k + N-1, and N is more than or equal to 1 and less than or equal to N.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention adopts the time modulation array and has the characteristics of low complexity and low cost.
2. The invention adopts the pulse compression technology, the accumulated gain of the linear frequency modulation signal can be directly transmitted to the calculation of the echo direction, and the high-precision direction finding of the detection target can be realized.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a block diagram of the basic structure of the present invention.
Fig. 2 is a time-frequency relationship diagram of a transmission signal.
Fig. 3 is a time-frequency relationship diagram of the modulated echo signal.
Fig. 4 is a time-frequency relationship diagram of the echo signal after being modulated in embodiment 1.
Fig. 5 is a time domain waveform of the modulated echo signal in example 1 after pulse compression.
FIG. 6 shows the RMS error of the system direction at SNR of 0dB, 5dB, and 10dB, respectively.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
The invention has two working modes, namely a transmitting mode and a receiving mode. When the system works in a transmitting mode, all the radio frequency switches are in a closed state, so that equal-amplitude in-phase feeding of all the channels is realized, and the linear frequency modulation signals are radiated to the space. When the system finishes the transmission of a single pulse signal, the duplexer controls the system to enter a receiving mode. In the receive mode, the rf switches in each channel are periodically opened and closed to time modulate the received signal. After being modulated, the received chirp echo signal can generate multiple harmonic components in a time-frequency domain. And performing pulse compression on the mixed signal of the fundamental component and the harmonic component through a matched filter to obtain a multi-peak matched filter output signal. And extracting corresponding harmonic coefficient characteristic values of each peak point of the output signal, and substituting the extracted harmonic coefficient characteristic values into a corresponding formula to calculate to obtain the azimuth information of the detection target. The method is suitable for platforms such as miniaturized guidance radars, automobile anti-collision radars, unmanned automobile detection systems and the like.
According to the time modulation array direction-finding system based on the pulse compression technology, as shown in fig. 1, the time modulation array direction-finding system comprises an antenna array module 1, a radio frequency switch module 2, a digital control module 14, a duplexer 3, a radio frequency local oscillator module 8, a signal transmitting module and a signal receiving module; the antenna array module 1 is sequentially connected with the radio frequency switch module 2 and the duplexer 3, the duplexer 3 is respectively connected with the signal transmitting module and the signal receiving module, the digital control module 14 is respectively connected with the radio frequency switch module 2 and the duplexer 3, and the radio frequency local oscillator module 8 is respectively connected with the signal transmitting module and the signal receiving module.
Preferably, the antenna array module 1 comprises one or more unit printed dipole antenna array units, and the spacing between the antenna array units is half wavelength; the radio frequency switch module 2 comprises one or more single-pole single-throw switches; the antenna array units correspond to the single-pole single-throw switches one by one. The antenna array module 1 is used for radiating a pulse signal to a space and receiving an echo signal of a target. The radio frequency switch module 2 is used for time modulation of the echo signal. In a preferred embodiment, the antenna array module 1 comprises eight element printed dipole antenna array elements, and the radio frequency switch module 2 comprises eight single-pole single-throw switches.
Preferably, the signal transmitting module includes a chirp signal generator 7, a first mixer 6, a band-pass filter 5, and a power amplifier 4, the chirp signal generator 7 is sequentially connected to the first mixer 6, the band-pass filter 5, the power amplifier 4, and the duplexer 3, and the first mixer 6 is connected to the radio frequency local oscillation module 8.
Preferably, the signal receiving module includes a low noise amplifier 9, a second mixer 10, a low pass filter 11, a matched filter 12, and a signal processor 13, one end of the low noise amplifier 9 is connected to the duplexer 3, the other end of the low noise amplifier 9 is sequentially connected to the second mixer 10, the low pass filter 11, the matched filter 12, and the signal processor 13, the second mixer 10 is connected to the radio frequency local oscillation module 8, and the matched filter 12 is connected to the chirp signal generator 7.
Preferably, the radio frequency switch module 2 is configured to perform time modulation on the echo signal, the duplexer 3 is configured to switch the transmitting/receiving state, and the digital control module 14 is configured to control the modulation timing of each single-pole single-throw switch of the radio frequency switch module 2 and the state switching of the duplexer 3. In a preferred embodiment, the digital control module 14 comprises an FPGA.
Preferably, when the system is in a transmitting state, the duplexer 3 is switched to the transmitting branch, and the single-pole single-throw switches of the radio frequency switch module 2 are all in a closed state; the linear frequency modulation pulse signal generated by the linear frequency modulation signal generator 7 is modulated to carrier frequency through the first mixer 6, the power amplification is carried out through the power amplifier 4 after the filtering of the band-pass filter 5, and the amplified signal is radiated to the space through the antenna array module 1 after sequentially passing through the duplexer 3 and the radio frequency switch module 2 in a closed state. When the signal is transmitted, the radio frequency switches are all closed, so that equal-amplitude in-phase feeding of all channels is realized, and the linear frequency modulation signal is transmitted to the space.
Preferably, after the system finishes transmitting the chirp signal, the duplexer 3 is switched to a receiving state, the echo signal is received by the antenna array module 1 and then periodically modulated by the radio frequency switch module 2, wherein the modulated signal is generated by the digital control module 14, and after passing through the duplexer 3 and the low noise amplifier 9 in sequence, the modulated signal is down-converted by the second mixer 10 and then is converted into a baseband signal by the low pass filter 11.
Preferably, the modulation frequency f of the radio frequency switch module 2pThe following relation is satisfied with the chirp rate mu of the chirp signal transmitted by the chirp signal generator 7:
Figure GDA0002482529790000061
modulation frequency f of the radio frequency switch module 2pThe following relation is satisfied between the bandwidth B and the chirp rate mu of the chirp signal transmitted by the chirp signal generator 7:
Figure GDA0002482529790000062
wherein K represents the bandwidth B and the switching frequency fpRatio of (A) to (B), N*Representing a natural number, L representing the chirp rate mu and the switching frequency fpThe ratio of the squares, Z represents an integer; the modulation frequency of the rf switch module 2 is also referred to as the switching frequency.
Preferably, the matched filter 12 performs pulse compression on the baseband signal output by the low-pass filter 11, including the harmonic component and the fundamental component, to obtain a matched filter output signal with multiple peaks, where the matched filter output signal is expressed as:
Figure GDA0002482529790000063
wherein S iso(theta, t) represents the output signal of the matched filter, theta represents the angle of the incident signal, t represents the time of the signal, Sr(theta, t) represents an echo signal of the transmitted signal,
Figure GDA0002482529790000064
representing the response function of the matched filter, t0Representing the time difference from the transmission of the signal to the reception of the echo signal,uto representThe echo signal delay, m represents the serial number of the mth harmonic, the rect function represents that rect (T/T) is 1, | T/T | ≦ 1/2, T is the pulse length of the chirp signal,
Figure GDA0002482529790000065
Figure GDA0002482529790000066
the Fourier coefficient of the mth harmonic wave of the whole array is shown, N represents the number of array elements used in the direction finding of the array, N represents the serial number of the array elements, am，nFourier coefficients representing the mth harmonic of the nth array element, j representing the imaginary sign, β representing the array wavenumber, d representing the array element spacing, fcRepresenting the carrier frequency of the echo signal, the sinc function is denoted sinc (x) sin (pi x)/pi x.
Preferably, the signal processor 13 is used to process the output signal of the matched filter, and obtain the corresponding harmonic coefficient feature by searching, and the signal processor 13 calculates the relationship for the incoming wave direction of the echo signal as:
Figure GDA0002482529790000071
wherein, thetanRepresenting the angle of the incident signal, phi, obtained by using the nth and n +1 th harmonic measurementsnRepresenting the nth harmonic coefficient of the array, phin+1Represents the n +1 th harmonic coefficient of the array;
wherein, the phin+1In the form of vectors
Figure GDA0002482529790000072
Expressed as:
Figure GDA0002482529790000073
wherein N × N represents the array element number × harmonics used in the direction finding of the array, the values of the array element number and the harmonics are all equal to N,
Figure GDA0002482529790000074
representing array factor vector, HCMN×NA matrix representing the characteristics of the harmonics,
Figure GDA0002482529790000075
an inverse matrix representing the harmonic characteristic matrix,
Figure GDA0002482529790000076
representing a harmonic coefficient vector;
wherein the array factor vector
Figure GDA0002482529790000077
Wherein, superscript T represents a transpose matrix; the harmonic coefficient vector
Figure GDA0002482529790000078
The harmonic characteristic matrix HCMN×NExpressed as:
Figure GDA0002482529790000079
wherein, am，nIs the Fourier coefficient of the m-th harmonic of the nth array element, wherein k is more than or equal to m and less than or equal to k + N-1, and N is more than or equal to 1 and less than or equal to N.
Example 1:
assuming the carrier frequency of the transmitted chirp signal to be f02GHz, bandwidth B10 MHz, duration T100 mus, chirp rate μ B/T1011. The normal phase direction azimuth angle of the target relative array is 15 degrees, the array element spacing d of the antenna array is 15cm, and the array element spacing d of the antenna array is c/f0C is the speed at which the electromagnetic wave propagates in a vacuum. The time-frequency relationship diagram of the transmitted signals is shown in fig. 2, and the signals have ideal linear relationship in the time-frequency domain.
After the signal transmission is completed, the array is switched to a receiving state. During receiving, the radio frequency switches are sequentially turned on in a unit period for time modulation, and the modulation period is T p1 mus, modulation frequency fp1MHz, each antenna element has an on-time of 0.125 in one modulation periodμ s. The signal is reflected by the target and then received and modulated by the array, and the receiving period number of the whole chirp echo signal is M-T/T p100. Fig. 3 is a time-frequency relationship diagram of a received echo signal after modulation. It can be seen that after the reflected signal has been time modulated, the incident chirp signal can be represented as the sum of infinite chirp harmonic signals with the difference in carrier frequency of adjacent harmonics between those chirp harmonic signals being the modulation frequency of the switch. When the bandwidth of the chirp signal is greater than the modulation frequency of the switch, aliasing occurs between the harmonic signals in both the time domain and the frequency domain, so that the coefficients of the harmonics cannot be accurately obtained by using the conventional fourier transform method.
Fig. 4 shows a time-frequency relationship diagram of the echo signal of the target at 35 ° after being modulated by the switch. It can be seen that after time modulation, the echo signal is expanded in the time-frequency domain to the sum of multiple chirped harmonic signals, and the difference between the carrier frequencies of adjacent harmonics is the modulation frequency of the switch. Meanwhile, because each subharmonic signal has the same modulation frequency, the subharmonic signals can be independently distinguished by the matched filter. In addition, the cross-sectional views of the respective time-frequency graphs are equivalent to the instantaneous power spectra at different time instants. It can be seen that the instantaneous power spectrum curves at different time points are identical except for the carrier frequency, which shows that the harmonic powers of each order have quite stable proportional relationship at different time points. However, when the incoming wave directions of the echo signals are different, the power ratios of the harmonics of the respective orders are different, and the relationship between the power ratios reflects the direction information of the echo signals.
The output time domain waveform of the modulated signal in fig. 4 after passing through the matched filter is shown in fig. 5, and it can be seen that the output signal of the matched filter has a plurality of peak points, which can be regarded as the accumulation of a plurality of harmonic signals after pulse compression. Assuming a time-delayed signal t0The peak point after pulse compression is located at a position t of 0 μ s, which is indicated by a red upper triangular symbol in the figure. The peak point of each order harmonic wave after pulse compression is marked by a blue upper triangular symbol. The distance between adjacent peak points is delta t ═ fp/μ|。
FIG. 6Shown are root mean square error simulation results for various estimated angles at different angles of incidence, wherein the various simulation parameters are the same as in fig. 4 and 5. Wherein the incident angle range is between-65 DEG and +65 DEG and is uniformly distributed with 5 DEG as interval, the environmental signal-to-noise ratio range is between 0dB and 10dB and is uniformly distributed with 5dB as interval, and each simulation point executes 2000 Monte Carlo simulations. Because each harmonic is extracted after matched filtering, the accuracy of harmonic coefficient extraction is improved by the gain of pulse compression, and therefore the method can be seen to obtain higher direction-finding accuracy. The mean root mean square errors in the range of direction finding were 0.032 °, 0.018 °, and 0.010 ° at signal-to-noise ratios of 0dB, 5dB, and 10dB, respectively. Meanwhile, the aperture efficiency of the corresponding array is reduced along with the increase of the incident angle, so the root mean square error of direction finding is increased. It can also be seen that when the echo signals are incident from different angles, the rms error value fluctuates slightly, and the fluctuation level becomes severe as the signal-to-noise ratio decreases. The reason is that the energy values of the harmonics are different at different incident angles, and even in the same signal-to-noise ratio environment, the different harmonics are calculated to obtain thetanAnd thus has a slightly fluctuating influence on the final estimation result.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (8)

1. A time modulation array direction-finding system based on a pulse compression technology is characterized by comprising an antenna array module (1), a radio frequency switch module (2), a digital control module (14), a duplexer (3), a radio frequency local oscillator module (8), a signal transmitting module and a signal receiving module; the antenna array module (1) is sequentially connected with the radio frequency switch module (2) and the duplexer (3), the duplexer (3) is respectively connected with the signal transmitting module and the signal receiving module, the digital control module (14) is respectively connected with the radio frequency switch module (2) and the duplexer (3), and the radio frequency local oscillator module (8) is respectively connected with the signal transmitting module and the signal receiving module;
the signal receiving module comprises a low noise amplifier (9), a second mixer (10), a low pass filter (11), a matched filter (12) and a signal processor (13), one end of the low noise amplifier (9) is connected with the duplexer (3), the other end of the low noise amplifier (9) is sequentially connected with the second mixer (10), the low pass filter (11), the matched filter (12) and the signal processor (13), the second mixer (10) is connected with the radio frequency local oscillation module (8), and the matched filter (12) is connected with the linear frequency modulation signal generator (7);
processing the output signal of the matched filter by using a signal processor (13), and obtaining corresponding harmonic coefficient characteristics through searching, wherein the signal processor (13) has an incoming wave direction calculation relationship of the echo signal as follows:
Figure FDA0002513546660000011
wherein, thetanRepresenting the angle of the incident signal, phi, obtained by using the nth and n +1 th harmonic measurementsnRepresenting the nth harmonic coefficient of the array, phin+1Representing the n +1 th harmonic coefficient of the array, β representing the array wave number, and d representing the array element spacing;
wherein, the phin+1In the form of vectors
Figure FDA0002513546660000012
Expressed as:
Figure FDA0002513546660000013
wherein N × N represents the array element number × harmonics used in the direction finding of the array, the values of the array element number and the harmonics are all equal to N,
Figure FDA0002513546660000014
representing array factor vector, HCMN×NRepresenting harmonicsThe matrix of properties is then used to determine,
Figure FDA0002513546660000015
an inverse matrix representing the harmonic characteristic matrix,
Figure FDA0002513546660000016
representing a harmonic coefficient vector;
the harmonic characteristic matrix HCMN×NExpressed as:
Figure FDA0002513546660000021
wherein, am，nIs the Fourier coefficient of the m-th harmonic of the nth array element, wherein m is more than or equal to k and less than or equal to k + N-1, and N is more than or equal to 1 and less than or equal to N;
the array factor vector
Figure FDA0002513546660000022
Wherein, superscript T represents a transposed matrix, j represents an imaginary number symbol, and theta represents an incident signal angle; the harmonic coefficient vector
Figure FDA0002513546660000023
Figure FDA0002513546660000024
Fourier coefficients representing the mth harmonic of the entire array.
2. The time modulation array direction-finding system based on the pulse compression technology according to claim 1, characterized in that the antenna array module (1) comprises one or more element printed dipole antenna array elements, the spacing between the antenna array elements is half wavelength; the radio frequency switch module (2) comprises one or more single-pole single-throw switches; the antenna array units correspond to the single-pole single-throw switches one by one.
3. The time modulation array direction-finding system based on the pulse compression technology is characterized in that the signal transmitting module comprises a chirp signal generator (7), a first mixer (6), a band-pass filter (5) and a power amplifier (4), the chirp signal generator (7) is sequentially connected with the first mixer (6), the band-pass filter (5), the power amplifier (4) and the duplexer (3), and the first mixer (6) is connected with a radio frequency local oscillator module (8).
4. The time modulation array direction-finding system based on the pulse compression technology according to claim 1, characterized in that the radio frequency switch module (2) is used for time modulating the echo signal, the duplexer (3) is used for switching the transmitting/receiving state, and the digital control module (14) is used for controlling the modulation timing of each single-pole single-throw switch of the radio frequency switch module (2) and the state switching of the duplexer (3).
5. The time modulation array direction-finding system based on the pulse compression technology according to claim 3, characterized in that when the system is in a transmitting state, the duplexer (3) is switched to the transmitting branch, and the single-pole single-throw switches of the radio frequency switch module (2) are all in a closed state; the linear frequency modulation pulse signals generated by the linear frequency modulation signal generator (7) are modulated to carrier frequency through the first mixer (6), the carrier frequency is filtered through the band-pass filter (5) and then subjected to power amplification through the power amplifier (4), and the amplified signals are radiated to the space through the antenna array module (1) after sequentially passing through the duplexer (3) and the radio frequency switch module (2) in a closed state.
6. The time modulation array direction-finding system based on the pulse compression technology according to claim 1, characterized in that after the system finishes transmitting the chirp signal, the duplexer (3) is switched to a receiving state, the echo signal is received by the antenna array module (1) and then is periodically modulated by the rf switch module (2), wherein the modulation signal is generated by the digital control module (14), and after passing through the duplexer (3) and the low noise amplifier (9) in sequence, the modulated signal is down-converted by the second mixer (10) and then is changed into a baseband signal by the low pass filter (11).
7. Time modulation array direction-finding system based on pulse compression technology according to claim 6, characterized in that the modulation frequency f of the radio frequency switch module (2)pThe following relation is satisfied between the chirp rate mu and the chirp signal transmitted by the chirp signal generator (7):
Figure FDA0002513546660000031
the modulation frequency f of the radio frequency switch module (2)pThe following relation is satisfied between the bandwidth B and the frequency modulation slope mu of the chirp signal transmitted by the chirp signal generator (7):
Figure FDA0002513546660000032
wherein K represents the bandwidth B and the modulation frequency f of the radio frequency switch module (2)pRatio of (A) to (B), N*Representing a natural number, L representing the chirp rate mu and the modulation frequency f of the RF switch module (2)pSquared ratio, Z represents an integer.
8. The time modulation array direction-finding system based on the pulse compression technology according to claim 6, characterized in that the matched filter (12) performs pulse compression on the baseband signal output by the low-pass filter (11) including the harmonic component and the fundamental component to obtain a matched filter output signal with a plurality of peaks, and the matched filter output signal is expressed as:
Figure FDA0002513546660000033
wherein S iso(theta, t) represents the output signal of the matched filter, theta represents the angle of the incident signal, t represents the time of the signal, Sr(theta, t) represents an echo signal of the transmitted signal,
Figure FDA0002513546660000034
representing the response function of the matched filter, t0The time difference from signal transmission to echo signal reception is represented, u represents the echo signal delay, m represents the sequence number of the mth harmonic, the rect function is represented as rect (T/T) 1, | T/T | ≦ 1, T is the pulse length of the chirp signal,
Figure FDA0002513546660000035
Figure FDA0002513546660000036
the Fourier coefficient of the mth harmonic wave of the whole array is shown, N shows the array element number used in the direction finding of the array, N shows the array element serial number, am，nFourier coefficients representing the mth harmonic of the nth array element, j representing the imaginary sign, β representing the array wavenumber, d representing the array element spacing, fcRepresenting the carrier frequency of the echo signal, the sinc function is denoted sinc (x) sin (pi x)/pi x.
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