A time-domain periodic phase modulation method for electromagnetic interference suppression

Abstract

The present invention discloses a time-domain periodic phase modulation electromagnetic interference suppression method, comprising: constructing a mathematical model of a radar echo signal modulated by a target's phase modulation surface, i.e., an interfered radar echo signal; constructing a reference signal, and using the reference signal to perform de-linear frequency modulation processing on the interfered radar echo signal; estimating the frequency and duty cycle of the spectrum of the modulation signal, i.e., the interference signal, using the signal obtained after the de-linear frequency modulation processing, and reconstructing the modulation signal at a receiving end according to the estimation result; delaying the reconstructed modulation signal, and then multiplying the signal with the interfered radar echo signal to obtain a de-modulated signal; performing carrier removal processing on the de-modulated signal, and then performing pulse compression processing through a matched filter; changing the time delay value of the reconstructed modulation signal, i.e., performing a sliding window operation on the reconstructed modulation signal in the time domain, and determining the modulation start time by using the relationship between the maximum value of the pulse compression processing and the time delay, thereby restoring the true radar echo signal.

Description

Technical Field

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

[0002] As a key electronic device, radar provides critical information for various combat operations and has become an indispensable part of modern warfare.

[0003] However, the gradual maturity and diversification of radar jamming technology has posed significant challenges to radar detection. Based on the source of the jamming energy, typical radar jamming can be categorized as active jamming and passive jamming. Passive jamming typically uses objects such as foil to reflect radar signals, generating false echoes, high-power jamming, noise echoes, or weakening the target's reflected echo signal to disrupt radar detection. This technology offers advantages such as rapid jamming signal generation and low exposure. However, once the passive jamming object is formed, its jamming characteristics become fixed, making it easily deciphered and ineffective. Active jamming can be categorized as deceptive jamming and suppressive jamming based on the jamming effect. Suppression jamming uses electronic interference to generate large-bandwidth, high-power signals to blur or completely mask the useful signals received by the enemy's electronic equipment, making it unable to work normally; deceptive jamming 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 jamming is to intercept the radar incident wave, estimate its parameters, and generate a false reflection signal close 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.

[0004] As interference technologies become increasingly flexible and controllable, artificial electromagnetic surfaces (AESs) are currently a research hotspot in the field of electromagnetic interference. From the perspective of controlling electromagnetic wave characteristics, these primarily include amplitude control, phase control, polarization control, beam pointing, and comprehensive control. A phase-switched screen (PSS) that achieves phase control uses an active impedance layer to intermittently phase-modulate the radar's incident wave. This causes the phase deviation of the incident signal to vary proportionally with the modulated signal, and the modulated reflected signal to produce a spectrum shift in the frequency domain, thereby generating deceptive interference. A PSS does not actively radiate interfering electromagnetic waves and can therefore be considered a passive interference device. Furthermore, it uses electrical control to alter the reflection characteristics of the active impedance layer, thereby changing the interference characteristics and making them difficult to analyze. 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 exposure risk 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 variation", "strong coupling" and "strong similarity" make the detection function of the radar system face huge threats.

[0005] Current mainstream anti-jamming methods for deceptive jamming can be categorized as deceptive signal detection and deceptive signal elimination. Deceptive signal detection generally detects the presence of interference by comparing the jamming signal with the true echo. Currently, interference detection primarily relies on pattern recognition techniques based on the differences in the time, frequency, or polarization domain characteristics between the jammer and the echo. However, current research directly operates on the original signal and its spectrum, which is suitable for single-carrier radar signals with high signal-to-noise ratios. However, the computational complexity of these methods increases when dealing with low signal-to-noise ratios. Forward-type deceptive jamming generates multiple false target peaks after pulse compression at the radar receiver, rendering constant false alarm rate (CFAR) detection ineffective. This is especially true when the jammer enters from the mainlobe of the beam, severely disrupting radar detection. Currently, radar anti-mainlobe deceptive jamming methods essentially fall into two categories: one is to optimize the transmit waveform to reduce the similarity between the jammer and the echo; the other is to suppress the jammer through signal processing when it enters the receiver, ensuring that the radar can extract true target information.

[0006] However, there are few existing literature on methods for suppressing new deceptive jamming methods such as time-domain electromagnetic metasurfaces. Compared with active deceptive jamming, time-domain electromagnetic metasurface modulation jamming has more variable modulation, is more similar to the incident wave, and is difficult for the receiver to detect and distinguish, making interference suppression more complex. Therefore, research on time-domain electromagnetic metasurface interference suppression technology is particularly important. Summary of the Invention

[0007] In view of the lack and insufficiency of the current anti-forwarding deception jamming 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 radar system and hardware conditions.

[0008] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0009] A time-domain periodic phase modulation electromagnetic interference suppression method, comprising:

[0010] Construct a mathematical model of the radar echo signal after the radar transmit signal is modulated by the target's phase modulation surface;

[0011] Construct a reference signal and use the reference signal to perform linear frequency modulation on the interfered radar echo signal;

[0012] Using the radar echo signal after de-linear frequency modulation, the frequency and duty cycle of the modulation signal spectrum are estimated, and the modulation signal is reconstructed based on the estimation results;

[0013] The demodulated signal is obtained by using the result of delay processing of the reconstructed modulated signal and the radar echo signal;

[0014] After removing the carrier wave from the modulated signal, the signal is pulse compressed by a matched filter.

[0015] 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.

[0016] Furthermore, the mathematical model of the interfered radar echo signal is expressed as:

[0017]

[0018] 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 frequency modulation rate 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.

[0019] Furthermore, the construction of the reference signal and the use of the reference signal to perform de-linear frequency modulation processing on the interfered radar echo signal include:

[0020] The reference signal is expressed as:

[0021]

[0022] 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;

[0023] The process of dechirping is to mix the echo signal with the conjugate of the reference signal:

[0024] s deChip (t) = s r (t)·s * ref (t)

[0025] The superscript * indicates conjugation.

[0026] Furthermore, the process of frequency estimation of the spectrum of the modulated signal is as follows:

[0027] The radar echo signal s after de-linear frequency modulation deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as:

[0028]

[0029] n=0,1,…,N-1

[0030] Where 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 s 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;

[0031] to s dechip (n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence:

[0032]

[0033] k=0,1,…,N-1

[0034] Where S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transform, δ x is the digital frequency deviation of the xth harmonic;

[0035] 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)|;

[0036] Then substitute the four calculated spectrum values ​​into the following two formulas:

[0037]

[0038] Calculate δ a and δ b , and then these two values ​​and k a and k b Substitute into the following two expressions:

[0039]

[0040] Calculate f a 、f b , through f p =(f b -f a ) / 2 to calculate the modulation frequency f of the modulation signal p .

[0041] Furthermore, the process of estimating the duty cycle of the spectrum of the modulated signal is as follows:

[0042] Select the Fourier coefficient c of the kth harmonic component of the modulation signal in the time domain Fourier expansion k The ratio of the amplitudes of the two largest frequency components in is:

[0043]

[0044] 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 -1represents 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;

[0045] Let ratio2 = c0 / max1, and further subdivide the duty cycle judgment within the interval [26.36%, 50%];

[0046] 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.

[0047] Furthermore, when the modulation frequency f p After accurately estimating the duty cycle β, we begin to reconstruct the modulated signal, which is expressed as:

[0048]

[0049] 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 .

[0050] Furthermore, after the demodulated signal is subjected to carrier removal processing, pulse compression processing is performed through a matched filter, including:

[0051] The transfer function of the matched filter constructed according to the radar transmit signal is:

[0052]

[0053] in Represents the transmitted signal s t (t) is the result after deconvolution and conjugation;

[0054] The pulse pressure results are:

[0055]

[0056] Among them, c0′ is the amplitude coefficient of the generated harmonic component, k′ is the k′th harmonic, n′=±1, ±2,……, ±N′ is the order of the discrete peak, c n ′ is the amplitude coefficient of the generated harmonic component, 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 transmission signal, T p is the modulation period, and K is the linear modulation frequency of the linear frequency modulation signal.

[0057] 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 utilized to determine the modulation start time, thereby restoring the true radar echo signal, including:

[0058] Changing the delay 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 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;

[0059] The modulation start time is brought into the expression of the reconstructed modulation signal and multiplied with the radar echo signal so that the modulation component in the radar echo signal and the reconstructed modulation signal are multiplied into a constant, thereby offsetting the phase modulation interference and restoring the real radar echo signal.

[0060] 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.

[0061] 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.

[0062] Compared with the prior art, the present invention has the following technical features:

[0063] This invention proposes a method for suppressing electromagnetic interference using a time-domain periodic phase-modulated metasurface. First, an expression for the radar echo signal reflected by a phase-modulated surface is constructed. Then, the modulation frequency and duty cycle are estimated in the frequency domain for the de-linear frequency modulated signal to restore and reconstruct the modulated signal. The reconstructed modulated signal is repeatedly delayed and multiplied by the echo signal, followed by matched filtering and recording the peak pulse pressure after matched filtering until the delay value traverses the entire modulation period. A corresponding relationship between the delay and the peak pulse pressure is established. The delay corresponding to the maximum pulse pressure peak is determined, and the signal delay, multiplication by the echo signal, and matched filtering are executed to obtain the pulse pressure result after interference suppression. This method utilizes the characteristics of periodic phase-modulated signals to suppress this type of multiplicative interference by multiplying the reconstructed signal, obtaining a true echo signal and offsetting the modulation signal's shifting effect on the true target signal's spectrum and energy dispersion. Ultimately, the true target signal's energy is refocused and the false target disappears, improving the radar's detection capability in scenarios involving such metasurface interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is an implementation flow chart of an embodiment of the present invention;

[0065] Figure 2 It is a time domain diagram 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;

[0066] Figure 3 is a time-frequency diagram of the reflected echo in the example of the present invention;

[0067] Figure 4 (a) is the time-frequency diagram of the de-linear frequency modulation reference signal;

[0068] Figure 4 (b) is a spectrum diagram of the dechirped signal obtained by multiplying the echo signal by the conjugate of the dechirped reference signal;

[0069] Figure 4 (c) is the time-frequency diagram of the decoded linear frequency modulation signal;

[0070] Figure 5 It is the duty cycle judgment process;

[0071] Figure 6 (a) is a time domain diagram of the reconstructed signal after estimating the modulation frequency and duty cycle of the de-linear frequency modulation signal;

[0072] Figure 6 (b) is the spectrum of the reconstructed signal;

[0073] Figure 6 (c) is the time-frequency diagram of the reconstructed signal;

[0074] Figure 7 (a) is the time-frequency diagram of the demodulated signal obtained by multiplying the reconstructed signal and the echo signal (the periods of the reconstructed signal and the modulated signal are not aligned);

[0075] 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);

[0076] Figure 8 yes When the value of traverses the entire modulation signal period 0~T, each The corresponding pulse pressure peak value record;

[0077] Figure 9 (a) is the time-frequency diagram of the demodulated signal obtained by multiplying the reconstructed signal and the echo signal (the periods of the modulation components in the reconstructed signal and the echo are aligned);

[0078] Figure 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

[0079] Referring to the accompanying drawings, the present invention provides a method for suppressing electromagnetic interference using time-domain periodic phase modulation. First, the method analyzes the effect of time-domain electromagnetic metasurface phase modulation on radar echoes when the active impedance layer is periodically switched between the full-resistance state and the full-pass state, and derives the mathematical expression of the echo signal. Then, the modulation parameters of the interference are estimated at the radar receiving end, and the reconstructed modulation signal is multiplied by the received echo to offset the modulation effect of the modulation signal on the echo, thereby achieving the recovery of the real target energy and the elimination of false targets. 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.

[0080] Step 1: Construct a mathematical model of the radar echo signal after the radar transmit signal is modulated by the target's phase modulation surface. r (t).

[0081] s r (t) = s t (t)×l(t)

[0082] 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.

[0083] The radar transmission signal s used t (t) is a linear frequency modulation signal, and its expression is:

[0084]

[0085] 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 frequency modulation rate of the linear frequency modulation signal, f c is the center frequency.

[0086] When the active impedance layer of the phase modulation surface switches 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 switch, which is reflected in the amplitude as a jump of "-1" and "+1". The expression of the modulated signal can be written as:

[0087]

[0088] 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.

[0089] The expression of the modulated signal in the time domain Fourier expansion is:

[0090]

[0091] Where c k is the Fourier coefficient of the kth harmonic component:

[0092]

[0093] The frequency domain representation of the modulated signal is:

[0094]

[0095] 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.

[0096] 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 and duty cycle τ; 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 in the spectrum these impulses are located at the modulation frequency f p It can be seen that the modulation 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.

[0097] Assuming that the target with the phase modulation surface is stationary and has only one scattering point, the received echo signal expression is:

[0098]

[0099] Where R represents the radial distance between the target and the radar, c is the speed of light, and T r is the pulse width of the pulse radar transmitting signal.

[0100] 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 transmit 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 .

[0101] Step 2: construct a reference signal and use the reference signal to perform linear frequency modulation on the interfered radar echo signal.

[0102] After receiving the interfered radar echo signal, the radar station 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 transmitted 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 obtain the complete echo sequence.

[0103] The reference signal can be expressed as:

[0104]

[0105] 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 .

[0106] The process of dechirping is to mix the echo signal with the conjugate of the reference signal:

[0107]

[0108] The superscript * in the parameter indicates conjugation;

[0109] There are two time-related items in the signal after de-linear frequency modulation, namely and l(t+t0-t R ), where the first one is a single-frequency signal; combining the two, it is equivalent to the modulation signal being shifted by k(t ref -t R ).

[0110] Step 3: Use the radar echo signal after de-linear frequency modulation to estimate the frequency and duty cycle of the modulation signal spectrum, and reconstruct the modulation signal according to the estimation results.

[0111] (1) Estimation of modulation frequency

[0112] to s deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as:

[0113]

[0114] n=0,1,…,N-1

[0115] Where 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 s 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.

[0116] to s dechip (n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence:

[0117]

[0118] k=0,1,…,N-1

[0119] Where S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transform, δ x is the digital frequency deviation of the xth harmonic.

[0120] 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 is substituted into S x The expression for (k) yields |S x (k a ±0.5)|、|S x (k b ±0.5)|.

[0121] Then substitute the four calculated spectrum values ​​into the following two formulas:

[0122]

[0123] Calculate δ a and δ b , and then these two values ​​and k a and k b Substitute into the following two expressions:

[0124]

[0125] Calculate f a 、f b , through f p =(f b -f a ) / 2 to calculate the modulation frequency f of the modulation signal p .

[0126] (2) Duty cycle estimation

[0127] Select the Fourier coefficient c of the kth harmonic component of the modulation signal in the time domain Fourier expansion k The ratio of the amplitudes of the two largest frequency components in is:

[0128]

[0129] Among them, max1 is c k The maximum value of c, max2 is k The second largest value; c1 represents the amplitude of the first harmonic, c -1 represents the amplitude of the image frequency harmonics, c0 represents the amplitude of the fundamental wave, and β represents the duty cycle of the modulated signal spectrum.

[0130] 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. Its value is always equal to 1. It is impossible to further distinguish the duty cycle in the range of [26.36%, 50%]. In this case, the fundamental amplitude is selected and compared with the maximum amplitude to obtain:

[0131] ratio2=c0 / max1

[0132] 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%.

[0133] When noise and phase jitter errors are present, the values ​​of ratio1 and ratio2 fluctuate and exhibit randomness within a certain range. This reduces the duty cycle resolution, and the duty cycle is determined by the range of values ​​within which ratio1 and ratio2 fall, rather than the ideal value. The magnitude of the noise and error determines the duty cycle resolution.

[0134] Through 500 Monte Carlo experiments, under the conditions of signal-to-noise ratio (SNR) in the range of [-2dB, 5dB] and phase jitter error in the range of [-10°, 10°], ratio1 and ratio2 were calculated and analyzed. The numerical ranges in which they fell were analyzed, and a process for determining the duty cycle β was developed based on the analysis results. Figure 5 The judgment process of duty cycle when the resolution is 10% is given.

[0135] When the modulation frequency f p After accurately estimating the duty cycle β, we begin to reconstruct the modulated signal, which is expressed as:

[0136]

[0137] 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.

[0138] Step 4: Obtain a demodulated signal using the result of delay processing on the reconstructed modulated signal and the radar echo signal.

[0139] Delay the reconstructed modulated signal Then, multiply it with the interfered radar echo signal:

[0140]

[0141] As can be seen from the above formula, 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 be the following two situations:

[0142] The first is when the delay t R -t0 with 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 with When the difference is not an integer multiple of the l(t) period T, Get a new modulated interference. R -t0 is fixed, so find the one that meets the first case It is the key to suppress interference.

[0143] Step 5: Demodulate the signal s deModu (t) After the carrier is removed, pulse compression is performed through a matched filter.

[0144] The transfer function of the matched filter constructed according to the radar transmit signal is:

[0145]

[0146] in Represents the transmitted signal s t The result after deconvolution and conjugation of (t).

[0147] The pulse pressure results are:

[0148]

[0149] Among them, c0′ is the amplitude coefficient of the generated harmonic component, k′ is the k′th harmonic, n′=±1, ±2,……, ±N′ is the order of the discrete peak, c n ′ is the amplitude coefficient of the generated harmonic component, f p 'yes The modulation frequency of the new modulated interference generated.

[0150] Step 6: Change the delay The value of , the reconstructed modulated signal is subjected to 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 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.

[0151] The radar echo expression at this time is:

[0152]

[0153] The pulse pressure results are:

[0154]

[0155] The pulse pressure result is the result of sinc(·) function, which shows 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.

[0156] Example:

[0157] 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, the duty cycle is 50%, the modulation start time t0 = 0.2μs, the modulation duration of the modulated wave on the radar incident wave is T, then N = 10, and the expression of the radar reflected echo after metasurface modulation is:

[0158]

[0159] Step 2: Set the linear frequency k of the 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 expression of the demodulated signal is:

[0160]

[0161] Use Matlab's built-in function FFT(·) to calculate s deChip (t) Perform Fourier transform to obtain the spectrum of the delinear frequency modulation signal.

[0162] Step 3, according to s deChip The frequency spectrum of (t) is used to estimate the frequency and duty cycle.

[0163] 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, and the spectrum refinement method is used to calculate |S(ka -0.5)|=501.1353、|S(k b -0.5)|=479.3976、

[0164] |S(k a +0.5)|=508.6636、|S(k b +0.5)|=497.3538. Substitute the above calculation result into the following formula:

[0165]

[0166] f a =(k a +δ a )Δf、f b =(k b +δ b )Δf、f p =(f a -f b ) / 2

[0167] Calculate respectively: δ a =0.0037, δ b =0.0092, f a =61MHz, f b =59MHz, f p =1MHz, T p =1μs.

[0168] Then the duty cycle is estimated: 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, the duty cycle β can be determined to be 50%.

[0169] 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:

[0170]

[0171] Where, M = 50;

[0172] Step 4: Multiply the reconstructed signal delay and the reflected echo to obtain the demodulated signal.

[0173]

[0174] Step 5, s obtained in step 4 deModu (t) After removing the carrier, pulse compression is performed through a matched filter to obtain a pulse compression signal.

[0175]

[0176] 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 774.9426, at this time q = 16 corresponds to its corresponding Since t0-t R =-19.8μs, That is, the modulated signal generates a delay of 19.8μs, and the reconstructed signal generates 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 reconstructed signal generate and multiplied by the echo signal.

[0177] At this time, the result of multiplying the reconstructed signal and the echo signal is:

[0178]

[0179] The pulse pressure results are:

[0180]

[0181] The simulated pulse peak position is 2.0042e-05μs (delay) and the peak value is 774.9426. When there is no interference, the pulse peak position after pulse compression is 2.0012e-05μs (delay) and the peak value is 800.00. The interference is considered to be successfully suppressed within the allowable error range.

[0182] 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, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for suppressing electromagnetic interference using time-domain periodic phase modulation, characterized in that: include: Construct a mathematical model of the radar echo signal after the radar transmit signal is modulated by the target's phase modulation surface; Construct a reference signal and use the reference signal to perform linear frequency modulation on the interfered radar echo signal; Using the radar echo signal after de-linear frequency modulation, the frequency and duty cycle of the modulation signal spectrum are estimated, and the modulation signal is reconstructed based on 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 modulated signal, the signal is pulse compressed by 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 frequency modulation rate 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 2, characterized in that: The construction of the reference signal and the use of the reference signal to perform de-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 dechirping 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 de-linear frequency modulation deChip (t) Perform N-point FFT operation, after sampling, s deChip (t) The sequence can be expressed as: n=0,1,…,N-1 Where 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 s 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; to s dechip (n) Performing N-point discrete Fourier transform can obtain the spectrum expression of the echo signal sequence: k=0,1,…,N-1 Where S x (k) represents the k-th Fourier coefficient of the x-th harmonic after Fourier transform, 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 to calculate the modulation frequency f of the modulation signal p .

5. The electromagnetic interference suppression method of time-domain periodic phase modulation according to claim 4, 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 modulation 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, max2 is k The second largest value; c1 represents the amplitude of the first harmonic, c -1 represents the amplitude of the image frequency harmonics, 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 within 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 5, characterized in that: When the modulation frequency f p After accurately estimating the duty cycle β, we begin to reconstruct the modulated signal, which is expressed as: 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 c'0 is the amplitude coefficient of the generated harmonic component, k' is the k'th harmonic, n'=±1, ±2, ..., ±N' is the order of the discrete peak, c n ′ is the amplitude coefficient of the generated harmonic component, 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 transmission signal, T p is the modulation period, and K is the linear modulation frequency 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 method of performing a sliding window operation on the reconstructed modulated signal in the time domain and determining the modulation start time by utilizing the relationship between the maximum value of the pulse compression processing and the time delay, thereby restoring the true radar echo signal, includes: Changing the delay 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 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 and multiplied with the radar echo signal so that the modulation component in the radar echo signal and the reconstructed modulation signal are multiplied into 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 to 8 is implemented.

10. A computer-readable storage medium storing a computer program; wherein: 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 to 8 is implemented.

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