Electromagnetic interference suppression method for time domain periodic phase modulation

Abstract

The invention discloses an electromagnetic interference suppression method based on time-domain periodic phase modulation. The electromagnetic interference suppression method comprises the following steps: constructing a mathematical model of a radar echo signal which is modulated by a phase modulation surface of a target, namely is interfered; constructing a reference signal, and performing dechirp processing on the interfered radar echo signal by using the reference signal; performing frequency and duty ratio estimation on a frequency spectrum of a modulation signal, namely an interference signal, through a signal obtained after dechirping processing, and reconstructing the modulation signal at a receiving end according to an estimation result; carrying out time delay on the reconstructed modulation signal, and multiplying the reconstructed modulation signal with an interfered ground radar echo signal to obtain a demodulated signal; carrying out carrier removal processing on the demodulated signal, and then carrying out pulse pressure processing through a matched filter; and changing the time delay value of the reconstructed modulation signal, namely carrying out sliding window operation on the reconstructed modulation signal in the time domain, and determining the modulation starting time by utilizing the relationship between the maximum value of pulse pressure processing and the time delay, thereby recovering a real radar echo signal.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a novel super electromagnetic surface periodic phase modulation interference suppression method. Background Art

[0002] As radar jamming technology gradually matures and diversifies, it has brought great challenges to radar detection. According to the source of interference energy, typical radar jamming can be divided into active jamming and passive jamming. Passive jamming technology usually uses objects such as foil strips to reflect radar signals to generate false echoes, high-power interference, noise echoes, or weaken the target reflection echo signal to achieve the purpose of destroying radar reconnaissance of targets. It has the advantages of quickly generating jamming signals and low exposure probability. However, once the object that generates passive interference is formed, its interference characteristics are fixed and easy to be analyzed and thus fail. Active jamming can be divided into deceptive jamming and suppressive jamming according to the interference effect produced. Suppression interference uses electronic interference to generate large-bandwidth, high-power signals to blur or completely cover up the useful signals received by the enemy's electronic equipment, making it unable to work normally; deceptive interference refers to the intentional transmission or forwarding of intermittent or continuous signals modulated with amplitude, phase, and frequency to disrupt or confuse the enemy's radar, causing it to obtain false information and make wrong judgments. The basic principle of forwarding deceptive interference is to intercept the radar incident wave, estimate its parameters, and then generate a false reflection signal similar to the radar incident signal, so that the receiver makes an incorrect judgment based on the false reflection signal, thereby achieving the purpose of interference.

[0003] As interference technology becomes more flexible and controllable, artificial electromagnetic surfaces are currently a hot topic in the field of electromagnetic interference. From the perspective of regulating the characteristics of electromagnetic waves, it mainly includes amplitude regulation, phase regulation, polarization regulation, beam pointing, and comprehensive regulation. Among them, the artificial electromagnetic surface that realizes phase regulation is also called a phase-switched screen (PSS). It uses the on-off of the active impedance layer to intermittently phase modulate the radar incident wave, so that the phase deviation value of the incident signal changes proportionally with the modulation signal, and the modulated reflected signal produces a spectrum shift effect in the frequency domain, thereby generating deceptive interference. PSS does not actively radiate interfering electromagnetic waves, so it can be regarded as a passive interference device. At the same time, it uses electrical control to change the reflection characteristics of the active impedance layer, thereby changing the interference characteristics, which is not easy to be analyzed. Therefore, PSS combines the effects that can be achieved by active forwarding deception jamming and the advantages of fast response time of passive jamming. At the same time, it overcomes many disadvantages of active jamming, such as high risk of exposure and difficulty in forming jamming signals, and the poor adaptability of passive jamming to the battlefield environment. It disperses the energy at the real target and generates false targets at multiple frequency points. Its characteristics of "strong time-varying", "strong coupling" and "strong similarity" make the detection function of the radar system face huge threats.

[0004] In the face of deceptive jamming, the existing mainstream anti-jamming methods can be divided into deceptive signal detection and deceptive signal elimination. Deceptive signal detection generally detects the presence of interference in the signal through the difference between the jamming signal and the real echo. At present, interference detection is mainly carried out by means of pattern recognition based on the time domain, frequency domain or polarization domain feature difference between the jamming and the echo. However, the current research directly operates on the original signal and its spectrum, which is suitable for single-carrier radar signals under high signal-to-noise ratio. When dealing with low signal-to-noise ratio, the computational complexity of the corresponding method increases. Forwarding deceptive jamming causes multiple false target peaks to be generated after pulse compression at the radar receiving end, and the target constant false alarm rate (CFAR) detection fails, especially when the jamming enters from the main lobe of the beam, it will seriously interfere with the radar's detection effect. At present, the methods of radar anti-main lobe deceptive jamming are essentially divided into two types: one is to optimize the transmitting waveform to reduce the similarity between the jamming and the echo; the other is to suppress the jamming from the perspective of signal processing when the jamming enters the receiver, so as to ensure that the radar can extract the real target information.

[0005] However, there are few existing literatures on methods to suppress new deceptive interference such as time-domain electromagnetic metasurfaces. Compared with active deceptive interference, time-domain electromagnetic metasurface modulation interference has more variable modulation, is more similar to the incident wave, and is difficult to detect and distinguish at the receiving end, making the interference suppression method more complicated. Therefore, it is particularly important to carry out research on time-domain electromagnetic metasurface interference suppression technology. Summary of the invention

[0006] In view of the lack and insufficiency of the current anti-forwarding deception interference method in the application of anti-time domain electromagnetic metasurface interference, the purpose of the present invention is to provide a time domain periodic phase modulation electromagnetic interference suppression method to achieve effective suppression of new interference without changing the existing system and hardware conditions of the radar.

[0007] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0008] A time-domain periodic phase modulation electromagnetic interference suppression method, comprising:

[0009] Construct a mathematical model of the radar echo signal interfered with by the radar transmission signal modulated by the target's phase modulation surface;

[0010] Construct a reference signal and use the reference signal to perform linear frequency modulation processing on the interfered radar echo signal;

[0011] Using the radar echo signal after de-linear frequency modulation, the frequency and duty cycle of the spectrum of the modulation signal are estimated, and the modulation signal is reconstructed according to the estimation results;

[0012] The demodulated signal is obtained by using the result of delay processing of the reconstructed modulated signal and the radar echo signal;

[0013] After removing the carrier wave from the demodulated signal, the signal is subjected to pulse compression through a matched filter;

[0014] A sliding window operation is performed on the reconstructed modulated signal in the time domain, and the relationship between the maximum value of pulse compression processing and the time delay is used to determine the modulation start time, thereby restoring the real radar echo signal.

[0015] Furthermore, the mathematical model of the interfered radar echo signal is expressed as:

[0016]

[0017] In the above formula, t is the time variable, s t (t) is the radar transmission signal incident along the normal phase of the phase modulation surface, l(t) is the modulation signal of the phase modulation surface, rect[·] is the rectangular window function, e is a natural constant, j is an imaginary unit, T r is the pulse width of the pulse radar transmission signal, K is the linear modulation frequency of the linear frequency modulation signal, f c is the center frequency, R represents the radial distance between the target and the radar, c is the speed of light, and t0 represents the modulation moment when the radar transmit signal is incident on the phase modulation surface.

[0018] Furthermore, the construction of the reference signal and the use of the reference signal to perform linear frequency modulation processing on the interfered radar echo signal include:

[0019] The reference signal is expressed as:

[0020]

[0021] Among them, t ref =R ref / c,R ref is the reference distance, and R ref =R+Δr, Δr is the distance resolution, T ref It is the receiving window;

[0022] The process of de-chirping is to mix the echo signal with the conjugate of the reference signal:

[0023] s deChip (t) = s r (t)·s * ref (t)

[0024] The superscript * indicates conjugation.

[0025] Furthermore, the process of frequency estimation of the spectrum of the modulated signal is as follows:

[0026] The radar echo signal s after linear frequency modulation processing deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as:

[0027]

[0028] In the formula, s deChip (n) is s deChip (t) The representation after sampling, N is the number of sampling points, n represents the nth sampling point, D x Indicates deChip The amplitude of the xth harmonic component of (t), t(n) represents the sampling time, t(n) = n / f s , f x =(k x +δ)·Δf is the frequency component corresponding to the xth harmonic, Δf=f s / N is the frequency resolution, δ is the digital frequency deviation, f s is the sampling frequency, k x is the digital frequency;

[0029] For dechip (n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence:

[0030]

[0031] In the formula, S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transformation, δ x is the digital frequency deviation of the xth harmonic;

[0032] Find the digital frequency k corresponding to the first two maximum values ​​of the amplitude spectrum a , k b , let k = k a ±0.5 and k=k b Substitute ±0.5 into S x The expression for (k) yields |S x (k a ±0.5)|、|S x (k b ±0.5)|;

[0033] Then substitute the four calculated spectrum values ​​into the following two formulas:

[0034]

[0035] Calculate δ a and δ b, and then these two values ​​and k a and k b Substitute into the following two expressions:

[0036]

[0037] Calculate f a 、f b , through f p =(f b -f a ) / 2 calculates the modulation frequency f of the modulation signal p .

[0038] Furthermore, the process of estimating the duty cycle of the spectrum of the modulated signal is as follows:

[0039] Select the Fourier coefficient c of the kth harmonic component of the modulated signal in the time domain Fourier expansion k The ratio of the amplitudes of the two largest frequency components in is:

[0040]

[0041] Among them, max1 is c k The maximum value, max2 is c k The second largest value; c1 represents the amplitude of the first harmonic, c -1 represents the amplitude of the first harmonic, c0 represents the amplitude of the fundamental wave, and β represents the duty cycle of the modulated signal spectrum;

[0042] Let ratio2 = c0 / max1, and further subdivide the duty cycle judgment in the interval [26.36%, 50%];

[0043] Through multiple Monte Carlo experiments, ratio1 and ratio2 are calculated, the numerical range they fall into is analyzed, and the duty cycle β is determined based on the analysis results.

[0044] Furthermore, when the modulation frequency f of the modulation signal p After the duty cycle β is accurately estimated, the modulation signal is reconstructed, and the expression is:

[0045]

[0046] Among them, T P =1 / f P , M represents the total number of rectangular pulses of the reconstructed modulation signal, m represents the mth rectangular pulse; MT P In order to reconstruct the length of the modulated signal, the length of the reconstructed signal is required to be greater than the time width T of the radar transmission signal. r .

[0047] Furthermore, after the de-modulated signal is subjected to carrier removal processing, pulse compression processing is performed through a matched filter, including:

[0048] The transfer function of the matched filter constructed according to the radar transmit signal is:

[0049]

[0050] in Represents the transmitted signal s t (t) is the result after deconvolution and conjugation;

[0051] The pulse pressure results are:

[0052]

[0053] Where c0 is the amplitude coefficient of the generated harmonic component, k is the kth harmonic, n = ±1, ±2, ..., ±N is the order of the discrete peak, c n To generate the harmonic component amplitude coefficient, f p ' is the modulation frequency of the modulated interference, t R =2R / c, R represents the radial distance between the target and the radar, c is the speed of light, T r is the pulse width of the pulse radar transmitting signal, T p is the modulation period, and K is the linear modulation rate of the linear frequency modulation signal.

[0054] Furthermore, the reconstructed modulated signal is subjected to a sliding window operation in the time domain, and the relationship between the maximum value of the pulse compression processing and the time delay is used to determine the modulation start time, thereby restoring the real radar echo signal, including:

[0055] Change delay t 0i The value of , the reconstructed modulated signal is operated on the sliding window in the time domain, the entire modulation cycle is traversed, and the maximum value of the pulse compression processing corresponding to each sliding window is recorded to obtain the delay t 0i The corresponding relationship between the maximum value of the pulse pressure and its corresponding value; then, among all the maximum values ​​of the pulse pressure, the maximum value is selected again, and the t corresponding to this maximum value is 0i This is the modulation start time;

[0056] The modulation start time is brought into the expression of the reconstructed modulation signal to multiply it with the radar echo signal, so that the modulation component in the radar echo signal and the reconstructed modulation signal are multiplied to a constant, thereby offsetting the phase modulation interference and restoring the real radar echo signal.

[0057] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor is executed by a computer, the electromagnetic interference suppression method of time domain periodic phase modulation is implemented.

[0058] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the electromagnetic interference suppression method of time-domain periodic phase modulation is implemented.

[0059] Compared with the prior art, the present invention has the following technical features:

[0060] The present invention proposes a method for suppressing electromagnetic interference of a time-domain periodic phase-modulated metasurface. First, an expression of a radar echo signal reflected by a phase-modulated surface is constructed; then, the modulation frequency and duty cycle of the signal after de-linear frequency modulation are estimated in the frequency domain to restore and reconstruct the modulation signal; the reconstructed modulation signal delay is repeatedly multiplied by the echo signal, matched filtering, and the processing flow of recording the pulse pressure peak after matched filtering is performed until the delay value traverses the entire modulation cycle, and the corresponding relationship between the delay size and the pulse pressure peak is established; the delay corresponding to the maximum value of the pulse pressure peak is determined, and the processing flow of reconstructing the signal delay, multiplying the echo signal, and matching filtering is executed to obtain the pulse pressure result after interference suppression. This method utilizes the characteristics of the phase-periodic modulation signal to suppress such multiplicative interference by multiplying the reconstructed signal, obtain the real echo signal, and offset the modulation signal's shifting effect on the spectrum of the real target signal and the energy dispersion effect. Finally, the energy of the real target signal is re-aggregated and the false target disappears, which improves the detection capability of the radar in the scenario of such metasurface interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is an implementation flow chart of an embodiment of the present invention;

[0062] Figure 2 It is a schematic diagram of the time domain of the radar incident wave and the radar echo after being reflected on the PSS surface when the linear frequency modulation signal is used as the radar transmission signal;

[0063] Figure 3 is a time-frequency diagram of the reflected echo in the example of the present invention;

[0064] Figure 4 (a) is the time-frequency diagram of the de-linear frequency modulation reference signal;

[0065] Figure 4 (b) is a spectrum diagram of the de-linear frequency modulation signal obtained by multiplying the echo signal by the conjugate of the de-linear frequency modulation reference signal;

[0066] Figure 4 (c) is the time-frequency diagram of the decoded linear frequency modulation signal;

[0067] Figure 5 It is the duty cycle judgment process;

[0068] Figure 6(a) is a time domain diagram of a reconstructed signal after estimating the modulation frequency and duty cycle of the de-linear frequency modulation signal;

[0069] Figure 6 (b) is the spectrum of the reconstructed signal;

[0070] Figure 6 (c) is the time-frequency diagram of the reconstructed signal;

[0071] Figure 7 (a) is the time-frequency diagram of the demodulated signal obtained by multiplying the reconstructed signal with the echo signal (the periods of the reconstructed signal and the modulated signal are not aligned);

[0072] Figure 7 (b) is the time domain waveform of the de-modulated signal and the pulse compression reference signal after pulse compression (the periods of the reconstructed signal and the modulation signal are not aligned);

[0073] Figure 8 Yes 0i When the value of traverses the entire modulation signal period 0~T, each t 0i The corresponding pulse pressure peak value record;

[0074] Fig. 9 (a) is the time-frequency diagram of the demodulated signal obtained by multiplying the reconstructed signal with the echo signal (the periods of the modulation components in the reconstructed signal and the echo are aligned);

[0075] Fig. 9 (b) is the time domain waveform of the de-modulated signal and the pulse compression reference signal after pulse compression (the period of the modulation component in the reconstructed signal is aligned with that in the echo). DETAILED DESCRIPTION

[0076] Referring to the accompanying drawings, the present invention provides a method for suppressing electromagnetic interference by periodic phase modulation in the time domain. First, the influence of the phase modulation of the time domain electromagnetic metasurface on the radar echo when the active impedance layer is periodically switched between the full-impedance state and the full-pass state is analyzed, and the mathematical expression of the echo signal is derived; then, the modulation parameters of the interference at the radar receiving end are estimated, and the reconstructed modulation signal is multiplied by the received echo to offset the modulation effect of the modulation signal on the echo, thereby realizing the recovery of the energy of the real target and the elimination of the false target. Considering that the time when the phase modulation surface starts modulating the echo is random, the reconstructed modulation signal needs to be multiplied by the echo in the form of a sliding window in the time domain, and the appropriate number of sliding steps of the sliding window is determined by the amplitude of the pulse pressure peak, that is, the time to start modulation is found to achieve interference suppression. The specific implementation process of the present invention is further described in detail below.

[0077] Step 1: construct a mathematical model of the radar echo signal after the radar transmission signal is modulated by the target's phase modulation surface and interfered with. r (t).

[0078] s r (t) = s t (t)×l(t)

[0079] Among them, t is the time variable, s t (t) is the radar transmission signal incident along the normal phase of the phase modulation surface, and l(t) is the modulation signal of the phase modulation surface.

[0080] The radar transmission signal used is s t (t) is a linear frequency modulation signal, and its expression is:

[0081]

[0082] Where rect[·] is the rectangular window function, e is a natural constant, j is an imaginary unit, T r is the pulse width of the pulse radar transmission signal, K is the linear modulation frequency of the linear frequency modulation signal, f c is the center frequency.

[0083] When the active impedance layer of the phase modulation surface is switched between the full-resistance state and the full-pass state, the phase of the harmonic will produce a jump of angle π each time the different states are switched, which is reflected in the amplitude as a jump of "-1" and "+1". The expression of the modulation signal can be written as:

[0084]

[0085] Where N is the total number of pulses that make up l(t), n represents the nth pulse, and T p is the modulation period, then the modulation frequency is f p =1 / T p , τ is the proportion of the duration of the full resistance state, i.e. the amplitude "+1", in the entire cycle, i.e. the duty cycle, NT p is the length of the modulated signal.

[0086] The expression of the modulated signal in the time domain Fourier expansion is:

[0087]

[0088] In the formula, c k is the Fourier coefficient of the kth harmonic component:

[0089]

[0090] The frequency domain representation of the modulated signal is:

[0091]

[0092] Where f is the frequency variable, δ(·) represents the impulse signal, δ(f-kf p ) represents the position where f = kf p The impulse function.

[0093] By analyzing the frequency domain representation of the modulation signal, we can know that the modulation parameters that affect the spectrum distribution of the modulation waveform are the modulation frequency f p The δ(·) in the expression indicates that the Fourier transform of the signal is composed of some impulse functions, and its amplitude is distributed as a sinc(·) function, and these impulses are located at the modulation frequency f in the spectrum. p It can be seen that the modulated signal relies on these impulse functions distributed at various frequency points to shift the spectrum of the real echo signal and disperse the real echo energy.

[0094] Assuming that the target with the phase modulation surface is stationary and the target has only one scattering point, the received echo signal expression is:

[0095]

[0096] In the formula, R represents the radial distance between the target and the radar, c is the speed of light, and T r It is the pulse width of the pulse radar transmitting signal.

[0097] Among them, for the echo receiving end, the time when the waveform starts to be modulated is 2R / c-t0, t0 means that when the radar transmission signal is incident on the phase modulation surface, the modulation wave starts to be modulated from its t0 moment, 0≤t0≤T r . Let 2R / c be t R .

[0098] Step 2: construct a reference signal and use the reference signal to perform linear frequency modulation processing on the interfered radar echo signal.

[0099] After the radar station receives the interfered radar echo signal, it performs de-linear frequency modulation processing; the reference signal is also a linear frequency modulation signal, and the frequency modulation slope and carrier frequency are the same as the transmit signal, but the pulse width is greater than the pulse width of the radar transmit signal. This is to ensure that when detecting under the premise of unknown target distance, the signal processing window can cover the echo signal and ensure that the complete echo sequence is obtained.

[0100] The reference signal can be expressed as:

[0101]

[0102] Among them, t ref =R ref / c,R ref is the reference distance, and R ref=R+Δr, Δr is the distance resolution, T ref is the receiving window, T ref =2R ref / c, generally speaking T ref >T r .

[0103] The process of de-chirping is to mix the echo signal with the conjugate of the reference signal:

[0104]

[0105] The superscript * in the parameter indicates conjugation;

[0106] There are two items in the signal after de-linear frequency modulation that are related to time, namely and l(t+t0-t R ), the first of which is a single-frequency signal; combining the two, it is equivalent to the modulation signal being shifted by k(t ref -t R ).

[0107] Step 3: Use the radar echo signal after de-linear frequency modulation to estimate the frequency and duty cycle of the spectrum of the modulation signal, and reconstruct the modulation signal according to the estimation result.

[0108] (1) Estimation of modulation frequency

[0109] For deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as:

[0110]

[0111] In the formula, s deChip (n) is s deChip (t) The representation after sampling, N is the number of sampling points, n represents the nth sampling point, D x Indicates deChip The amplitude of the xth harmonic component of (t), t(n) represents the sampling time, t(n) = n / f s , f x =(k x +δ)·Δf is the frequency component corresponding to the xth harmonic, Δf=f s / N is the frequency resolution, δ is the digital frequency deviation, and its value range is between -0.5 and 0.5. s is the sampling frequency, k x is the digital frequency.

[0112] For dechip(n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence:

[0113]

[0114] In the formula, S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transformation, δ x is the digital frequency deviation of the xth harmonic.

[0115] Find the digital frequency k corresponding to the first two maximum values ​​of the amplitude spectrum a , k b , let k = k a ±0.5 and k=k b ±0.5 Substitute into S x The expression for (k) yields |S x (k a ±0.5)|、|S x (k b ±0.5)|.

[0116] Then substitute the four calculated spectrum values ​​into the following two formulas:

[0117]

[0118] Calculate δ a and δ b , and then these two values ​​and k a and k b Substitute into the following two expressions:

[0119]

[0120] Calculate f a 、f b , through f p =(f b -f a ) / 2 calculates the modulation frequency f of the modulation signal p .

[0121] (2) Estimation of duty cycle

[0122] Select the Fourier coefficient c of the kth harmonic component of the modulated signal in the time domain Fourier expansion k The ratio of the amplitudes of the two largest frequency components in is:

[0123]

[0124] Among them, max1 is c k The maximum value of c kThe second largest value; c1 represents the amplitude of the first harmonic, c -1 represents the amplitude of the image frequency harmonic, c0 represents the amplitude of the fundamental wave, and β represents the duty cycle of the modulated signal spectrum.

[0125] When the duty cycle is less than 26.36% and greater than 73.64%, ratio1 is the ratio of the first harmonic amplitude to the fundamental amplitude; when the duty cycle is in the range of [26.36%, 73.64%], ratio1 is the ratio of the first harmonic amplitude to its mirror harmonic amplitude, and its value is always equal to 1. It is impossible to further distinguish the duty cycle in the range of [26.36%, 50%]. At this time, the fundamental amplitude is selected and compared with the maximum amplitude to obtain:

[0126] ratio2=c0 / max1

[0127] It is used to further subdivide the duty cycle judgment in the interval [26.36%, 50%]. It is worth noting that the value of ratio2 is 0 when the duty cycle is [0, 26.46%] and the duty cycle is exactly 50%.

[0128] When there is noise and phase jitter error, the values ​​of ratio1 and ratio2 jitter and are random within a certain range. At this time, the duty cycle resolution decreases, and the duty cycle is judged from the ideal value of ratio1 and ratio2 to the numerical range of ratio1 and ratio2. The size of noise and error determines the size of duty cycle resolution.

[0129] Through 500 Monte Carlo tests, under the conditions of signal-to-noise ratio [-2dB, 5dB] and phase jitter error [-10°, 10°], ratio1 and ratio2 were calculated, and the numerical range they fell into was analyzed. Based on the analysis results, a process for determining the duty cycle β was developed; Figure 5 The duty cycle determination process when the resolution is 10% is given.

[0130] When the modulation frequency f p After the duty cycle β is accurately estimated, the modulation signal is reconstructed, and the expression is:

[0131]

[0132] Among them, T P =1 / f P , M represents the total number of rectangular pulses of the reconstructed modulation signal, m represents the mth rectangular pulse; MT P In order to reconstruct the length of the modulated signal, the length of the reconstructed signal is required to be greater than the time width T of the radar transmission signal. r , to ensure that the length of the reconstructed signal can completely cover the modulated signal.

[0133] Step 4: Obtain a demodulated signal using the result of delay processing of the reconstructed modulated signal and the radar echo signal.

[0134] Reconstruct the modulated signal delay Then, multiply it with the interfered radar echo signal:

[0135]

[0136] It can be seen from the above formula that the first part is the true echo expression, and the second part is the key part to cancel interference. Looking at the second part alone, it is actually the multiplication of two square wave signals with the same period and duty cycle. The multiplication result can appear in the following two situations:

[0137] The first is when the delay t R -t0 and When the difference is exactly an integer multiple of the period T of l(t), due to the periodicity of l(t), The two are multiplied to a constant, and the interference is suppressed; the second is if the delay t R -t0 and When the difference is not an integer multiple of the period T of l(t), Get a new modulation interference. R -t0 is fixed, so find the one that meets the first case It is the key to suppress interference.

[0138] Step 5: Demodulate the signal s deModu (t) After the carrier removal process, pulse compression is performed through a matched filter.

[0139] The transfer function of the matched filter constructed according to the radar transmit signal is:

[0140]

[0141] in Represents the transmitted signal s t The result after deconvolution and conjugation of (t).

[0142] The pulse pressure results are:

[0143]

[0144] Where c0 is the amplitude coefficient of the generated harmonic component, k is the kth harmonic, n = ±1, ±2, ..., ±N is the order of the discrete peak, c n To generate the harmonic component amplitude coefficient, f p 'yes The modulation frequency of the newly generated modulated interference.

[0145] Step 6: Change the delay The reconstructed modulated signal is subjected to a sliding window operation in the time domain (each sliding window operation corresponds to a Repeat steps 4 and 5 until the sliding window signal delay traverses the entire modulation cycle, and record the maximum value of the pulse compression processing corresponding to each sliding window to obtain the delay The corresponding relationship between the maximum value of the pulse pressure and its corresponding value; then, among all the maximum values ​​of the pulse pressure, the maximum value is selected again, and the corresponding value of the maximum value is the modulation start time, q is the sliding window number corresponding to the maximum value; the reconstructed modulation signal delay get Multiply it with the echo signal to achieve a constant multiplication of the modulation component in the echo signal and the reconstructed modulation signal, thereby offsetting the phase modulation interference and restoring the real radar echo signal.

[0146] The radar echo expression at this time is:

[0147]

[0148] The pulse pressure results are:

[0149]

[0150] The pulse pressure result is the result of the sinc(·) function, and it can be seen that the peak value is distributed at the time delay t R The pulse pressure result of the echo is the same as that without interference, the interference is suppressed, and the theoretical derivation of this method is established.

[0151] Example:

[0152] Step 1: The transmission signal has a time width of T = 10 μs, a bandwidth of B = 10 MHz, and a linear modulation frequency k = 2 × 10 12 , center frequency f c =0, sampling frequency f s =40MHz, the pulse repetition frequency is 50μs, and the target distance is 3km, then the time delay t caused by the target R = 20μs, add the Gaussian white noise n(t) generated during transmission to the echo signal, its signal-to-noise ratio is 2dB, the reflection phase value is 0, π, the modulation frequency f p f P =1MHz, T p =1MHz duty cycle is 50% modulation start time t0 = 0.2μs, the modulation duration of the modulated wave on the radar incident wave is T, then N = 10, the expression of the radar reflected echo after metasurface modulation is:

[0153]

[0154] Step 2: Set the linear frequency k of the decoded linear frequency modulation signal r = k = 2 × 1012, in order to ensure that the region of interest is included, the pulse width T r =30μs, the received radar echo is demodulated in the area of ​​interest, and the demodulated signal expression is:

[0155]

[0156] Use Matlab's built-in function FFT(·) to calculate s deChip (t) Perform Fourier transform to obtain the spectrum of the de-linear frequency modulation signal.

[0157] Step 3, according to s deChip The frequency spectrum of (t) is used to perform frequency estimation and duty cycle estimation.

[0158] First, perform frequency estimation: get the digital frequency k corresponding to the first two maximum values ​​of the amplitude spectrum a =1831, k b =1771, using the spectrum refinement method to calculate |S(k a -0.5)|=501.1353、|S(k b -0.5)|=479.3976、

[0159] |S(k a +0.5)|=508.6636、|S(k b +0.5)|=497.3538. Substitute the above calculation result into the following formula:

[0160]

[0161] f a =(k a +δ a )Δf、f b =(k b +δ b )Δf、f p =(f a -f b ) / 2

[0162] Calculate respectively: δ a =0.0037, δ b =0.0092, f a =61MHz, f b =59MHz, f p =1MHz, T p =1μs.

[0163] The duty cycle is estimated again: the ratio of the amplitudes of the two frequency components with the largest spectrum amplitudes is ratio1=0.9629, and the ratio of the peak amplitude between the two frequency components to the maximum amplitude is ratio2=0. Based on these two values, it can be determined that the duty cycle β=50%.

[0164] Let the time length of the reconstructed signal be the pulse repetition period, and the expression of the modulated signal reconstructed at the receiving end is:

[0165]

[0166] Where, M = 50;

[0167] Step 4: Multiply the reconstructed signal delay and the reflected echo to obtain the demodulated signal

[0168]

[0169] Step 5, s obtained in step 4 deModu (t) After removing the carrier, the pulse compression is processed through a matched filter to obtain a pulse compression signal.

[0170]

[0171] Step 6: Change the delay The value of , that is, the reconstructed modulated signal is subjected to sliding window operation in the time domain, and steps 4 and 5 are repeated until the sliding window signal delay traverses the entire modulation cycle, and the maximum value of each sliding window pulse pressure processing is recorded to obtain the sliding window delay The corresponding relationship with the pulse pressure peak value; the maximum value of the pulse pressure peak value is found to be 774.9426, at this time q = 16 corresponds to its corresponding Since t0-t R =-19.8μs, That is, the modulated signal has a delay of 19.8μs, and the reconstructed signal has a delay of 1.8μs. The start time of the two signals differs by 18μs, and 18μs is exactly the T of the modulation period. p Eighteen times, indicating that the reconstructed signal and the modulated signal have achieved period alignment. Part 2: Let the reconstruction signal generate delay and multiply it with the echo signal.

[0172] At this time, the result of multiplying the reconstructed signal and the echo signal is:

[0173]

[0174] The pulse pressure results are:

[0175]

[0176] The simulated pulse peak position is 2.0042e-05μs (time delay), and the peak value is 774.9426. When there is no interference, the pulse peak position after pulse compression is 2.0012e-05μs (time delay), and the peak value is 800.00. The interference is considered to be successfully suppressed within the allowable error range.

[0177] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A method for suppressing electromagnetic interference by periodic phase modulation in the time domain, characterized in that: include: Construct a mathematical model of the radar echo signal interfered with by the radar transmission signal modulated by the target's phase modulation surface; Construct a reference signal and use the reference signal to perform linear frequency modulation processing on the interfered radar echo signal; Using the radar echo signal after de-linear frequency modulation, the frequency and duty cycle of the spectrum of the modulation signal are estimated, and the modulation signal is reconstructed according to the estimation results; The demodulated signal is obtained by using the result of delay processing of the reconstructed modulated signal and the radar echo signal; After removing the carrier wave from the demodulated signal, the signal is subjected to pulse compression through a matched filter; A sliding window operation is performed on the reconstructed modulated signal in the time domain, and the relationship between the maximum value of pulse compression processing and the time delay is used to determine the modulation start time, thereby restoring the real radar echo signal.

2. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: The mathematical model of the interfered radar echo signal is expressed as: In the above formula, s t (t) is the radar transmission signal incident along the normal phase of the phase modulation surface, l(t) is the modulation signal of the phase modulation surface, t is the time variable, rect[·] is the rectangular window function, e is a natural constant, j is an imaginary unit, T r is the pulse width of the pulse radar transmission signal, K is the linear modulation frequency of the linear frequency modulation signal, f c is the center frequency, R represents the radial distance between the target and the radar, c is the speed of light, and t0 represents the modulation moment when the radar transmit signal is incident on the phase modulation surface.

3. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: The construction of the reference signal and the use of the reference signal to perform linear frequency modulation processing on the interfered radar echo signal include: The reference signal is expressed as: Among them, t ref =R ref / c,R ref is the reference distance, and R ref =R+Δr, Δr is the distance resolution, T ref It is the receiving window; The process of de-chirping is to mix the echo signal with the conjugate of the reference signal: s deChip (t)=s r (t)·s * ref (t) The superscript * indicates conjugation.

4. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: The process of frequency estimation of the spectrum of the modulated signal is: The radar echo signal s after linear frequency modulation processing deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as: n=0,1,…,N-1 In the formula, s deChip (n) is s deChip (t) The representation after sampling, N is the number of sampling points, n represents the nth sampling point, D x Indicates deChip The amplitude of the xth harmonic component of (t), t(n) represents the sampling time, t(n) = n / f s , f x =(k x +δ)·Δf is the frequency component corresponding to the xth harmonic, Δf=f s / N is the frequency resolution, δ is the digital frequency deviation, f s is the sampling frequency, k x is the digital frequency; For dechip (n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence: k=0,1,…,N-1 In the formula, S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transformation, δ x is the digital frequency deviation of the xth harmonic; Find the digital frequency k corresponding to the first two maximum values ​​of the amplitude spectrum a , k b , let k = k a ±0.5 and k=k b Substitute ±0.5 into S x The expression for (k) yields |S x (k a ±0.5)|、|S x (k b ±0.5)|; Then substitute the four calculated spectrum values ​​into the following two formulas: Calculate δ a and δ b , and then these two values ​​and k a and k b Substitute into the following two expressions: Calculate f a 、f b , through f p =(f b -f a ) / 2 calculates the modulation frequency f of the modulation signal p .

5. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: The process of estimating the duty cycle of the spectrum of the modulated signal is: Select the Fourier coefficient c of the kth harmonic component of the modulated signal in the time domain Fourier expansion k The ratio of the amplitudes of the two largest frequency components in is: Among them, max1 is c k The maximum value of c k The second largest value; c1 represents the amplitude of the first harmonic, c -1 represents the amplitude of the image frequency harmonic, c0 represents the amplitude of the fundamental wave, and β represents the duty cycle of the modulated signal spectrum; Let ratio2 = c0 / max1, and further subdivide the duty cycle judgment in the interval [26.36%, 50%]; Through multiple Monte Carlo experiments, ratio1 and ratio2 are calculated, the numerical range they fall into is analyzed, and the duty cycle β is determined based on the analysis results.

6. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: When the modulation frequency f of the modulation signal p After the duty cycle β is accurately estimated, the modulation signal is reconstructed, and the expression is: Among them, T P =1 / f P , M represents the total number of rectangular pulses of the reconstructed modulation signal, m represents the mth rectangular pulse; MT P In order to reconstruct the length of the modulated signal, the length of the reconstructed signal is required to be greater than the time width T of the radar transmission signal. r .

7. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: After the demodulated signal is subjected to carrier removal processing, pulse compression processing is performed through a matched filter, including: The transfer function of the matched filter constructed according to the radar transmit signal is: in Represents the transmitted signal s t (t) is the result after deconvolution and conjugation; The pulse pressure results are: Where c0 is the amplitude coefficient of the generated harmonic component, k is the kth harmonic, n = ±1, ±2, ..., ±N is the order of the discrete peak, c n To generate the harmonic component amplitude coefficient, f' p is the modulation frequency of the modulated interference, t R =2R / c, R represents the radial distance between the target and the radar, c is the speed of light, T r is the pulse width of the pulse radar transmitting signal, T p is the modulation period, and K is the linear modulation rate of the linear frequency modulation signal.

8. The electromagnetic interference suppression method of time domain periodic phase modulation according to claim 1, characterized in that: The reconstructed modulated signal is subjected to a sliding window operation in the time domain, and the relationship between the maximum value of the pulse compression processing and the time delay is used to determine the modulation start time, thereby restoring the real radar echo signal, including: Change delay The value of is used to perform sliding window operation on the reconstructed modulation signal in the time domain, traverse the entire modulation cycle, record the maximum value of the pulse compression processing corresponding to each sliding window, and obtain the delay The corresponding relationship between the maximum value of the pulse pressure and its corresponding value; then, among all the maximum values ​​of the pulse pressure, the maximum value is selected again, and the corresponding maximum value This is the modulation start time; The modulation start time is brought into the expression of the reconstructed modulation signal to multiply it with the radar echo signal, so that the modulation component in the radar echo signal and the reconstructed modulation signal are multiplied to a constant, thereby offsetting the phase modulation interference and restoring the real radar echo signal.

9. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the electromagnetic interference suppression method of time-domain periodic phase modulation according to any one of claims 1-8 is implemented.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the electromagnetic interference suppression method of time-domain periodic phase modulation according to any one of claims 1-8 is implemented.

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