An interference suppression method for random phase modulation electromagnetic metasurface

Abstract

This invention discloses an interference suppression method for a random phase-modulated electromagnetic metasurface, comprising: constructing a mathematical model for the modulated radar echo signal; wherein, a random phase-modulated electromagnetic metasurface is installed on the target surface, the radar transmitted signal is incident on the random phase-modulated electromagnetic metasurface, and the radar echo signal is generated after random time-domain phase modulation; the radar echo signal is subjected to digital down-conversion and delinear frequency modulation, followed by discrete sampling processing, and then self-mixing processing to estimate additional phase information; the radar echo signal after discrete sampling processing is phase-compensated considering noise, and then subjected to time-domain differential transformation and discrete Fourier transform; the phase change time is estimated using a subspace algorithm, and the interference modulation sequence is reconstructed based on the estimation result; the random phase interference is demodulated using the reconstructed interference modulation sequence, and matched filtering processing is performed to obtain the output signal.

Description

Technical Field

[0001] This invention relates to the fields of radar signal processing and electromagnetic interference countermeasures, and in particular to a method for suppressing random phase modulation interference generated when an electromagnetically modulated metasurface is placed on the surface of a camouflaged target. Background Technology

[0002] As an active microwave target detection device, radar possesses all-weather, all-day target detection and perception capabilities, making it a crucial means of situational awareness in air, land, sea, and air battlefields, and playing an irreplaceable role in various surveillance systems. The core of modern electronic warfare lies in gaining information dominance in complex electromagnetic environments, and the importance of radar anti-jamming capabilities is no less than the development of the radar system itself; developing radar equipment with anti-jamming capabilities is key to gaining information and achieving victory in the complex and ever-changing electromagnetic battlefield. With the rapid development of electromagnetic modulation materials, the response speed, deception, and camouflage capabilities of existing new passive jamming systems have been significantly improved, making the electromagnetic battlefield combat environment more dynamic and highly competitive. Currently, jamming forces have effectively achieved integrated stealth and jamming effects by installing electromagnetic modulation metasurfaces on target surfaces, placing higher demands on radar detection.

[0003] Random phase modulation interference is a new type of electromagnetic interference formed by the modulation and retransmission of incident electromagnetic waves by electromagnetic modulation materials. Since the electromagnetic modulation materials themselves do not emit electromagnetic signals, their interference effect is achieved by altering the phase characteristics of the incident wave, classifying it as passive interference. When a radar signal reaches the electromagnetic modulation surface, the dynamic impedance of the electromagnetic material surface shifts the spectrum of the incident signal through phase modulation, weakening the fundamental component while generating a large number of randomly distributed coherent harmonic components. The radar receiver, after matched filtering the modulated echo, generates a large amount of range-dimensional deceptive interference, and the target energy at its true location is significantly weakened, posing a significant threat to radar detection.

[0004] Existing interference suppression methods cannot directly address phase modulation interference, and commonly used anti-interference techniques face the following technical challenges: 1) After the radar transmitted signal is phase-modulated and reflected by the electromagnetic modulation surface, the spectrum of the incident wave signal is redistributed, and the energy of the real target corresponding to the fundamental wave is severely weakened. Simultaneously, harmonic components can generate a large number of highly realistic range-dimensional false targets after matched filtering. Anti-interference methods based on energy feature identification cannot handle situations where the energy of the real target is shifted, or where interference components are suppressed or their features are deceived, under phase modulation interference scenarios; 2) The electromagnetic modulation surface modulates the incident electromagnetic wave very quickly. Compared to intermittent forwarding interference based on digital radio frequency storage technology, it can directly reflect the phase-modulated radar transmitted electromagnetic wave signal with zero delay. When using signal processing algorithms for interference suppression at the receiver, it is impossible to determine the useful target component and interference component based on the delay difference and time-frequency parameter information of the received echo. Anti-interference methods based on time-frequency feature identification cannot cope with strongly coupled phase modulation interference with "parasitic" characteristics.

[0005] In summary, considering the technical bottlenecks of existing anti-jamming methods in phase modulation jamming scenarios, it is urgent to conduct research on phase modulation jamming suppression technology to solve technical problems such as "real target concealment", "jamming feature deception", and "strong coupling between real and false targets", and effectively improve the radar's jamming perception and target detection capabilities in high-dynamic and high-stakes electronic warfare scenarios. Summary of the Invention

[0006] To address the problem that existing anti-jamming technologies cannot detect stealth jamming integrated targets equipped with electromagnetic modulation materials, the present invention aims to provide an effective and accurate method for suppressing phase modulation interference after reconstruction. This method accurately estimates and reconstructs the time-domain phase modulation sequence of random phase modulation interference and effectively suppresses the interfered echoes through signal processing.

[0007] To achieve the above objectives, the present invention employs the following technical solution:

[0008] An interference suppression method for randomly phase-modulated electromagnetic metasurfaces includes:

[0009] A mathematical model is constructed for the modulated radar echo signal; wherein, a random phase modulated electromagnetic metasurface is installed on the target surface, the radar transmitted signal is incident on the random phase modulated electromagnetic metasurface, and the radar echo signal is generated after random time-domain phase modulation.

[0010] Using the parameter information of the radar transmitted signal, the radar echo signal is digitally down-converted and delinearly frequency-modulated before being discretely sampled.

[0011] The additional phase information is estimated by performing self-mixing processing on the discretely sampled echo signal;

[0012] Using the estimation results of the additional phase information, phase compensation is performed on the radar echo signal after discrete sampling, taking noise into account;

[0013] The radar echo signal generated after compensation is subjected to time-domain differential transformation and discrete Fourier transform.

[0014] Based on the sequence after discrete Fourier transform, the phase change time is estimated using a subspace class algorithm, and the interference modulation sequence is reconstructed based on the estimation results;

[0015] The random phase interference is demodulated using the reconstructed interference modulation sequence, and then matched filtering is performed to obtain the output signal.

[0016] Furthermore, the mathematical model for the radar receiving echo signals is expressed as follows:

[0017]

[0018] Where t is the time parameter, Δτ is the time delay between the radar station and the target with the attached electromagnetic modulation metasurface, and T p K is the pulse duration. p For frequency modulation, f0 is the carrier frequency, rect(·) is the rectangular window function, j is the imaginary unit, M is the number of symbols for random phase modulation, m represents the m-th symbol, and T c a is the symbol width. m For the tth m The symbol amplitude φ at time t. m For t m The symbol phase corresponding to the time step, u(t) is the step function, and g(·) is the step function.

[0019] Furthermore, the step of using the parameter information of the radar transmitted signal to perform digital down-conversion and delinear frequency modulation on the radar echo signal, followed by discrete sampling processing, includes:

[0020] s de (t)=s j (t)·exp(-jπK p t 2 )·exp(-jπf0t)

[0021] s de [n] = s de (nT s )

[0022] =β1·β2·p[n]·exp(j2πf r nT s )

[0023] Among them, exp(-jπf0t) and exp(-jπK) p t 2 ) are respectively for s j (t) Performs digital down-conversion and delinear frequency modulation processing, s de [n] represents the pair of s de (t) at sampling frequency f s =1 / T s The discrete expression after discrete sampling; T s The sampling interval is s, where n represents the nth discrete sampling point. de (nT s ) represents s de (t) The time-domain discrete sequence formed after discrete sampling; due to T s It remains unchanged within each sampling interval, thus simplifying s de (nT s ) using s de [n] represents the sampled discrete sequence, p[n] represents the discrete form of the sampled random time-domain phase modulation sequence p(t), β1=exp(j2πf0Δτ), β2=exp(jπK p Δτ 2 ) is a constant term, f r This is an additional phase introduced by the time delay.

[0024] Furthermore, the estimation of additional phase information after self-mixing the discretely sampled echo signal is expressed as follows:

[0025]

[0026] Where FT(·) represents the Discrete Fourier Transform, and f is the frequency domain parameter after the Fourier Transform.

[0027] Furthermore, the step of using the estimation results with additional phase information to perform phase compensation on the discretely sampled radar echo signal, taking noise into account, includes:

[0028]

[0029] Where, N Noise Let represent the noise sequence after discrete sampling, and let s de [n] represents the radar echo signal after discrete sampling processing. Indicates s de [n] is the new sequence generated after phase compensation.

[0030] Furthermore, the step of performing time-domain differential transformation and discrete Fourier transform on the compensated radar echo signal includes:

[0031] For s com After the first-order difference of [n], we can obtain:

[0032]

[0033] in, Indicates s com [n] is processed using first-order difference;

[0034] The sampling time corresponding to d[n]=1 is defined as the phase change time t`. m Then the discrete Fourier transform of the sequence d[n] is:

[0035]

[0036] Where D[k],S com [k] represents the sequences d[n] and s, respectively. com [n] The expression after the Discrete Fourier Transform, where k represents the k-th frequency domain sampling point after the Discrete Fourier Transform, N is the number of points in the Discrete Fourier Transform, M` is the number of phase transition points obtained after time-domain differencing, M`≤M, a m = [-1, 1].

[0037] Furthermore, the step of estimating the phase abrupt change time using a subspace-based algorithm based on the discrete Fourier transform sequence, and reconstructing the interference modulation sequence based on the estimation result, includes:

[0038] Let d s =[D[s],D[s+1],...,D[s+K]] T ,s∈[0,S-1],S=KM`, where D[s] represents the value of the s-th frequency domain sampling point, and K is the order of the autocorrelation matrix, the value of which must satisfy K>M`. Construct the autocorrelation matrix:

[0039]

[0040] in(·) T ,(·) H These represent the transpose and conjugate transpose transformations, respectively.

[0041] For R d After performing eigenvalue decomposition, a noise subspace G = span{μ} is constructed. M`+1 ,μ M`+2 ,…,μ K}, μ M`+1 Represents R d The (M+1)th eigenvalue obtained after eigenvalue decomposition, where span(·) is the span of multiple vectors, is used to classify the phase transition time t'.m The estimated result is:

[0042] a(w) = [1, e -jw ,…,e -j(S-1)w ] H

[0043]

[0044] Where w = 2πf represents the signal angular frequency, f is the signal frequency, and a(w) is the constructed search vector. The peak search step in the multi-signal classification algorithm represents the spectral function. The findpeaks() function is used to search for local maxima in a set of one-dimensional data. Peaks represents the angular frequency value corresponding to the local maxima. in express The time at which the m-th local maximum occurs is the time of phase abrupt change t`. m The estimated results;

[0045] The reconstructed interference modulation sequence is:

[0046] Further, the demodulation of random phase interference using the reconstructed interference modulation sequence and the matching filtering process to obtain the output signal include:

[0047]

[0048] Among them, s j [n] represents the radar echo signal s after reflection via random phase coding modulation. j (t) The result after discrete sampling;

[0049]

[0050] Where DFT and IDFT are the Discrete Fourier Transform and Discrete Inverse Fourier Transform operations, respectively, h[n] is the reference signal in the matched filtering operation, and y[n] is the output signal.

[0051] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor is executed by a computer, it implements the interference suppression method for random phase-modulated electromagnetic metasurfaces.

[0052] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the interference suppression method for random phase-modulated electromagnetic metasurfaces.

[0053] Compared with the prior art, the present invention has the following technical features:

[0054] The random phase modulation interference suppression method proposed in this invention splits the received echo signal of the modulated interference into two paths. One path is used to estimate and reconstruct the modulation parameters of the electromagnetic modulation surface. Utilizing the known parameter information of the transmitted signal, the influence of the carrier frequency term and the second-order term is eliminated through digital down-conversion and demodulation preprocessing. For the additional first-order phase caused by the echo time delay, self-mixing processing is used to estimate and compensate for the additional term. Based on the sparsity of the differential transform of the compensated signal in the time domain, and the fact that the position of the sparse point corresponds to the time of the modulation sequence, a subspace-type signal estimation algorithm is used to estimate the phase change time, ultimately constructing the random phase modulation sequence of the electromagnetic modulation surface. The other path is used to eliminate the influence of random phase modulation interference on the received echo. The reconstructed interference modulation sequence is used to demodulate the random phase interference and then perform matched filtering. This effectively solves the problems of spectrum shifting, spectrum aliasing, and range-dimensional dense false targets caused by random phase modulation interference, improving the robust and accurate detection performance of radar in electromagnetic modulation material countermeasure scenarios. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2 (a) is a schematic diagram of the modulation of radar transmission signals by electromagnetic modulation materials in an example of the present invention;

[0057] Figure 2 (b) is the time-domain envelope diagram of the electromagnetic modulation surface to the incident electromagnetic wave in an example of the present invention;

[0058] Figure 3 This is a comparison chart of the radar received echo spectrum under no-interference conditions in the embodiments of the present invention;

[0059] Figure 4 (a) is a time-frequency analysis diagram of the radar received echo under interference-free conditions in an example of the present invention;

[0060] Figure 4 (b) is a time-frequency analysis diagram of radar received echo under interference conditions in an example of the present invention;

[0061] Figure 5 This is the processing result of the additional phase estimation step in step 3 of the example of the present invention;

[0062] Figure 6 These are the time-domain diagrams after phase compensation in step 5 and after time-domain differential processing in step 6 of this invention.

[0063] Figure 7 This is the jump time estimation result of the subspace class parameter estimation method in step 6 of the present invention;

[0064] Figure 8 This is a comparison result between the reconstructed random phase modulation sequence and the real modulation sequence in the example of this invention;

[0065] Figure 9 This is a comparison of the matched filtering process before and after interference suppression in an example of the present invention. Detailed Implementation

[0066] Referring to the accompanying drawings, this invention provides an interference suppression method for random phase-modulated electromagnetic metasurfaces. First, based on known parameters of the radar transmitted signal, the interference echo signal reflected from the electromagnetic modulation metasurface mounted on the target and received by the radar is digitally down-converted and delinearly frequency-modulated to eliminate the influence of the carrier frequency and modulation frequency on subsequent processing. Considering that the demodulated echo contains an additional phase due to target delay, self-mixing processing is performed to estimate the additional phase. Then, the estimation result from the previous step is used to compensate for the additional phase of the demodulated echo. After performing a time-domain difference operation on the phase-compensated processing result, the phase jump time-domain information of the phase modulation interference is obtained. After the above processing transformation, the interference suppression problem is transformed into a parameter estimation problem, and a subspace class algorithm is used to estimate the modulation sequence of the phase modulation interference. Finally, the reconstructed modulation sequence is multiplied with the received echo to eliminate the phase modulation of the radar incident signal by the time-varying impedance of the electromagnetic modulation surface, ultimately achieving true energy recovery and accurate target detection of camouflaged targets in random phase modulation interference countermeasure scenarios. The specific implementation steps of this invention are further described in detail below.

[0067] Step 1: Due to the propagation time of the radar transmitted signal to the electromagnetic modulation metasurface, there is a delay between the radar transmitted signal and the phase modulation sequence. The magnitude of this delay is equal to the distance between the radar station and the camouflaged target. For simplicity, the radar received echo is modeled as follows:

[0068] Assuming the camouflaged target's surface is completely covered by an electromagnetically modulated metasurface, the mathematical expression for the radar's received echo signal after the radar's transmitted signal is randomly phase-modulated in the time domain by the electromagnetically modulated metasurface is s. J (t):

[0069] s J (t)=s r (t)×p(t)=s t (t-Δτ)×p(t)

[0070] Among them, s r p(t) represents the electromagnetic wave incident along the normal direction of the electromagnetically modulated metasurface, t is a time parameter, Δτ is the time delay between the radar station and the target with the electromagnetically modulated metasurface attached, and p(t) is the random time-domain phase modulation sequence of the electromagnetically modulated metasurface; the radar transmitted signal s tThe expression for (t) is:

[0071]

[0072] Among them, T p K is the pulse duration. p To adjust the frequency, B is the signal bandwidth, and f0 is the carrier frequency. c is the speed of light, λ is the wavelength of the emitted signal, rect(·) is the rectangular window function, and j is the imaginary unit.

[0073] The expression for the random time-domain phase-modulated sequence p(t) is:

[0074]

[0075] Where M is the number of symbols in the random phase modulation, m = 0, 1, ..., M-1 represents the m-th symbol, and T c For symbol width, A m =a m exp(jφ m ), a m For the tth m The symbol amplitude φ at time t. m For t m The symbol phase corresponding to time step, u(t) is the step function, j is the imaginary unit, g(·) is the step function, g(t-mT) c )=u(tt m )-u(tt m+1 ).

[0076] Furthermore, the expression for the radar echo signal after reflection via random phase coding modulation is as follows:

[0077]

[0078] Step 2: Use the known parameter K in the radar transmitted signal to modulate the frequency K. p And carrier frequency f0, for radar echo signal s j (t) Perform digital down-conversion and delinear frequency modulation to eliminate the influence of carrier frequency and frequency modulation on subsequent processing, and perform discrete sampling on the processed radar echo signal; specifically expressed as:

[0079] s de (t)=s j (t)·exp(-jπK p t 2 )·exp(-jπf0t)

[0080] s de [n] = s de (nT s )

[0081] =exp(j2πf0Δτ)·exp(jπK) p Δτ 2 )·p(nT s )·exp(j2πK p nT s Δτ)

[0082] =β1·β2·p[n]·exp(j2πK) p nT s Δτ)

[0083] =β1·β2·p[n]·exp(j2πf r nT s )

[0084] Among them, exp(-jπf0t) and exp(-jπK) p t 2 ) are respectively for s j (t) Performs digital down-conversion and delinear frequency modulation processing, s de [n] represents the pair of s de (t) at sampling frequency f s =1 / T s Discrete representation after discrete sampling; Ts is the sampling interval of discrete sampling, n represents the nth discrete sampling point, s de (nT s ) represents s de (t) The time-domain discrete sequence formed after discrete sampling; p(nT) s ) is based on a fixed sampling interval T s The discrete form of the random time-domain phase-modulated sequence p(t) after sampling, since T s It remains unchanged within each sampling interval, thus simplifying s de (nT s ) using s de [n] represents the sampled discrete sequence, and p[n] represents p(nT) s ); β1=exp(j2πf0Δτ), β2=exp(jπK p Δτ 2 ) is a constant term and can be ignored. r This is an additional phase introduced by the time delay.

[0085] When the discrete modulation sequence p[n] of the electromagnetic modulation metasurface is subjected to single-bit phase modulation (the phase corresponding to p[n] is only 0° and 180°, that is, the phase state is only 0 and 1), at t m Timing symbol amplitude a m =1, symbol phase φ m= [0, π]; When the radar receiver processes the echo signal, if the phase of the single-bit phase-coded modulation sequence p[n] changes continuously between 0° and 180° in an unknown order, the change of p[n] cannot be reconstructed by directly observing the echo time domain; when the phase of p[n] is 0°, the corresponding amplitude is 1, and when the phase of p[n] is 180°, the corresponding amplitude is -1. Therefore, p[n] can be further regarded as a discrete sequence with values ​​randomly changing between 1 and -1; p 2 [n] is a discrete sequence with an amplitude of 1, and its sequence length is the same as that of p[n].

[0086] Step 3: After performing self-mixing processing on the discretely sampled echo signal, the additional phase is estimated.

[0087] Additional phase information can be obtained by performing self-mixing on the discretely sampled echo signal. The specific processing is as follows:

[0088]

[0089] Where FT(·) represents the Discrete Fourier Transform, and f is the frequency domain parameter after the Fourier Transform.

[0090] Step 4: Obtain the estimation results of the additional phase information. After phase compensation processing of the data from step 2, the signal expression is as follows:

[0091]

[0092] In a noise-free ideal condition, the last two terms in the above equation completely cancel each other out, while β1 and β2 are fixed constants; therefore, the sequence s obtained after phase compensation processing... com [n] can reflect the phase change of p[n]; however, in practice, the influence of noise must be considered. Under the assumption of Gaussian white noise, the above formula can be further transformed into:

[0093]

[0094] Where, N Noise Let represent the noise sequence after discrete sampling, and let and They represent s respectively de [n] and N Noise The new sequence generated after multiplying by the compensation term.

[0095] Step 5, Sequence The phase jump information in the original modulation sequence p[n] is consistent with that in s com[n] represents the sequence contaminated with noise. To eliminate the influence of noise and accurately recover the modulation information of p[n], a time-domain difference transformation is performed on it, and then a subspace class parameter estimation algorithm is used to obtain the estimated value of the abrupt change time.

[0096] For s com After the first-order difference of [n], we can obtain:

[0097]

[0098] in, Indicates s com [n] is processed using first-order difference.

[0099] Because s com [n] is a discrete sequence that takes values ​​randomly between -1 and 1. After first-order difference processing, the resulting discrete sequence d[n] takes values ​​of 0 or 1, where d[n] = 0 indicates that s com [n] indicates that the discrete sampling points at consecutive consecutive time points have the same value, and d[n] = 1 indicates that s com [n] The values ​​of discrete sampling points at consecutive consecutive time points are opposite. The sampling time corresponding to d[n]=1 is defined as t` m .

[0100] According to the difference property of the discrete Fourier transform, the discrete Fourier transform of the sequence d[n] is:

[0101]

[0102] Where D[k],S com [k] represents the sequences d[n] and s, respectively. com [n] The expression after the Discrete Fourier Transform, j is the imaginary unit, k represents the k-th frequency domain sampling point after the Discrete Fourier Transform, N is the number of points in the Discrete Fourier Transform, M` is the number of phase transition points obtained after time-domain differencing (M`≤M), a` m = [-1, 1].

[0103] As can be seen, the above equation is a classic spectral estimation problem, and the estimation result is the phase abrupt change time t`. m Considering the impact of noise and estimation accuracy, a subspace-based algorithm is used in subsequent steps to evaluate t'. m Make an estimate.

[0104] Step 6: Reconstruct the interference modulation sequence using a subspace class algorithm.

[0105] Let d s =[D[s],D[s+1],...,D[s+K]] T,s∈[0,S-1],S=KM`, where D[s] represents the value of the s-th frequency domain sampling point, and K is the order of the autocorrelation matrix, the value of which must satisfy K>M`. Construct the autocorrelation matrix:

[0106]

[0107] in(·) T ,(·) H These represent the transpose and conjugate transpose transformations, respectively.

[0108] For R d After performing eigenvalue decomposition, a noise subspace G = span{μ} is constructed. M`+1 ,μ M`+2 ,...,μ K}, μ M`+1 Represents R d The (M+1)th eigenvalue obtained after eigenvalue decomposition, where span(·) is the span of multiple vectors, is used to classify the phase transition time t'. m The estimated result is:

[0109] a(w) = [1, e -jw ,…,e -j (S-1)w] H

[0110]

[0111] Where j is the imaginary unit, N is the number of points in the Fourier transform, w = 2πf represents the signal angular frequency, f is the signal frequency, and a(w) is the constructed search vector. The peak search step in the multi-signal classification algorithm represents the spectral function. The findpeaks() function is used to search for local maxima in a set of one-dimensional data. Peaks represents the angular frequency value corresponding to the local maxima. in express The time at which the m-th local maximum occurs is the time of phase abrupt change t`. m The estimated results.

[0112] The electromagnetic modulation metasurface type in this scheme is single-bit phase modulation. Therefore, the modulation sequence P[n] is essentially a sequence of values ​​that change randomly between [-1, 1]. The reconstructed time parameter in this step actually reflects the change time of the P[n] sequence. P[n] can be effectively reconstructed by using these change times.

[0113] Therefore, the reconstructed interference modulation sequence is:

[0114] Step 7: Demodulate the random phase interference using the reconstructed interference modulation sequence. The specific operation is as follows:

[0115]

[0116] Among them, s j [n] represents the result of discrete sampling of sj(t).

[0117] Step 8: Perform matched filtering on the demodulated signal to obtain the output signal y[n]. The specific operation is as follows:

[0118]

[0119] Where DFT and IDFT are the Discrete Fourier Transform and Discrete Inverse Fourier Transform operations, respectively, and h[n] is the reference signal in the matched filtering operation.

[0120] Example:

[0121] Step 1: The transmitted signal has a duration μ = 10µs, a bandwidth B = 2MHz, and a modulation frequency K. p =2×10 11 The sampling frequency is 10MHz, the carrier frequency is 10GHz, the pulse repetition time is 100us, the target distance is 975m, the corresponding time delay is 6.5us, the input signal-to-noise ratio is 5dB, the time-varying impedance coefficient of the electromagnetic modulation material surface adopts random phase modulation mode, the modulation symbol width is 10us, the modulation sequence within the radar signal time width is [1110101101], the corresponding abrupt change times are [9.9us, 10.9us, 11.8us, 12.8us, 14.9us, 15.9us], where a value of 1 represents a phase modulation state of π, and a value of 0 represents a phase modulation state of 0. The expression for the reflected echo of the radar transmitted signal after modulation by the random phase modulation surface is:

[0122]

[0123] Step 2: Based on the carrier frequency and frequency modulation frequency of the radar transmitted signal, analyze the echo signal s. j (t) After digital downconversion and delinear frequency modulation processing, we can obtain:

[0124] s de [n] = s de (nT s )

[0125] =exp(j2πf0Δτ)·exp(jπK) p Δτ 2 )·p(nT s )·exp(j2πK p nTs Δτ)

[0126] =β1·β2·p[n]·exp(j2πK) p nT s Δτ)

[0127] =β1·β2·p[n]·exp(j2πf r nT s )

[0128] Among them, f r =1.3×10 6 .

[0129] Step 3: After self-mixing the signal after removing the carrier frequency and delinearizing the frequency, the additional phase is estimated.

[0130]

[0131] Calculated The estimated result is 1.2988 × 10⁻⁶. 6 .

[0132] Step 4, based on the estimation results of the first phase After phase compensation processing of the data from step 2, the signal expression is as follows:

[0133]

[0134] Step 5, for s com After difference [n], we get:

[0135]

[0136] According to the difference property of the discrete Fourier transform, the discrete Fourier transform of the sequence d[n] is:

[0137]

[0138] In this case, the number of points in the discrete Fourier transform is N = 100, and the number of phase abrupt change points after time-domain difference processing is M` = 6.

[0139] Step 6: Reconstruct the interference modulation sequence using the subspace class parameter estimation method.

[0140] Let d s =[D[s],D[s+1],...,D[s+K]] T ,s∈[0,S-1],S=KM`, where the order K of the autocorrelation matrix is ​​32, and the number of time-domain transition points of the random phase modulation sequence is 6. Construct the autocorrelation matrix:

[0141]

[0142] For R d After performing eigenvalue decomposition, a noise subspace G = span{μ} is constructed. M`+1 ,μ M`+2 ,...,μ K The phase transition time t` is determined using a multiple signal classification algorithm. m The estimated result is:

[0143] a(w) = [1, e -jw ,…,e -j (S-1 ) w] H

[0144]

[0145] The reconstructed interference modulation sequence is: [9.9us, 11us, 11.9us, 12.9us, 14.9us, 15.9us].

[0146] Step 7: Demodulate the random phase interference using the reconstructed interference modulation sequence. The specific operation is as follows:

[0147]

[0148] Step 8: Perform matched filtering on the demodulated signal to obtain the output signal y[n]. The specific operation is as follows:

[0149]

[0150] After interference suppression processing, the peak position after matched filtering is 6.5 μs, and the measured target distance is 975 m.

[0151] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for suppressing interference from randomly phase-modulated electromagnetic metasurfaces, characterized in that, include: A mathematical model is constructed for the modulated radar echo signal; wherein, a random phase modulated electromagnetic metasurface is installed on the target surface, the radar transmitted signal is incident on the random phase modulated electromagnetic metasurface, and the radar echo signal is generated after random time-domain phase modulation. Using the parameter information of the radar transmitted signal, the radar echo signal is digitally down-converted and delinearly frequency-modulated before being discretely sampled. The additional phase information is estimated by performing self-mixing processing on the discretely sampled echo signal; Using the estimation results of the additional phase information, phase compensation is performed on the radar echo signal after discrete sampling, taking noise into account; The radar echo signal generated after compensation is subjected to time-domain differential transformation and discrete Fourier transform. Based on the sequence after discrete Fourier transform, the phase change time is estimated using a subspace class algorithm, and the interference modulation sequence is reconstructed based on the estimation results; The random phase interference is demodulated using the reconstructed interference modulation sequence, and then matched filtering is performed to obtain the output signal.

2. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The mathematical model of radar echo signals is expressed as follows: in, t For time parameters, The time delay between the radar station and the target with the attached electromagnetic modulation metasurface. T p The duration of the pulse. K p To adjust the frequency, f 0 represents the carrier frequency. For rectangular window functions, j The imaginary unit, M The number of symbols in the random phase modulation. m Representing the m Each code element T c The width of the symbol. a m For the first t m The symbol amplitude corresponding to the time. for t m The symbol phase corresponding to the time, It is a step function. It is a step function.

3. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The process of using parameter information from the radar transmitted signal to perform digital down-conversion and delinear frequency modulation on the radar echo signal, followed by discrete sampling, includes: in, f 0 represents the carrier frequency. The time delay between the radar station and the target with the attached electromagnetic modulation metasurface. K p To adjust the frequency, , They are respectively for Perform digital downconversion and delinear frequency modulation processing. To With sampling frequency Discrete expression after discrete sampling; T s Let n be the sampling interval for discrete sampling, and n represent the nth discrete sampling point. Representative to The time-domain discrete sequence formed after discrete sampling; due to T s It remains constant within each sampling interval, thus simplifying the process. use Represents the discrete sequence after sampling. Represents a random time-domain phase modulation sequence after sampling. p ( t Discrete form of ) , For constant terms, f r This is an additional phase introduced by the time delay.

4. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 3, characterized in that, The estimation of additional phase information after self-mixing the discretely sampled echo signal is expressed as follows: in, Represents the Discrete Fourier Transform. f These are the frequency domain parameters after Fourier transform.

5. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The step of using the estimation results with additional phase information to perform phase compensation on the discretely sampled radar echo signal, taking noise into account, includes: in, Let represent the noise sequence after discrete sampling, and let ; The radar echo signal is after discrete sampling processing. Indicates to The new sequence generated after phase compensation. The estimation result includes additional phase information, where n represents the nth discrete sampling point. T s The sampling interval is for discrete sampling.

6. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The step of performing time-domain differential transformation and discrete Fourier transform on the compensated radar echo signal includes: right After first-order difference, we can obtain: in, Indicates to Perform first-order difference processing; Will The sampling time corresponding to =1 is defined as the phase change time. Then the sequence The discrete Fourier transform is: in, Sequences and The expression after the Discrete Fourier Transform. k Represents the first after the discrete Fourier transform k Each frequency domain sampling point N The number of points in the Discrete Fourier Transform. M ` is the number of phase abrupt change points obtained after time-domain differencing. M ≤ M , , M The number of symbols for random phase modulation.

7. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The sequence based on the discrete Fourier transform is used to estimate the phase abrupt change time using a subspace-based algorithm, and the interference modulation sequence is reconstructed based on the estimation results, including: make ,in D [ s ] indicates the first s The value of each frequency domain sampling point K The order of the autocorrelation matrix must satisfy the following conditions: Construct the autocorrelation matrix: in These represent the transpose and conjugate transpose transformations, respectively. M ` represents the number of phase abrupt changes obtained after time-domain difference; right After performing eigenvalue decomposition, a noise subspace is constructed. , Representative to The first eigenvalue obtained after eigenvalue decomposition 1 eigenvalue, For the span of multiple vectors, a multi-signal classification algorithm is used to identify the phase transition time. t ` m The estimated result is: in, Indicates the angular frequency of the signal. f For signal frequency, For the constructed search vector, This represents the spectral function in the peak search step of a multiple signal classification algorithm. The function is used to search for local maxima in a set of one-dimensional data. Peaks represents the angular frequency value corresponding to the local maxima. ,in express The m The time when each local maximum occurs is the time of phase abrupt change. t ` m The estimated results; N The number of points in the Discrete Fourier Transform; The reconstructed interference modulation sequence is: .

8. The interference suppression method for random phase-modulated electromagnetic metasurfaces according to claim 1, characterized in that, The process of demodulating random phase interference using the reconstructed interference modulation sequence and performing matched filtering to obtain the output signal includes: in, The radar echo signal after being reflected by random phase coding modulation The result after discrete sampling; The reconstructed interference modulation sequence; Where DFT and IDFT are the Discrete Fourier Transform and Discrete Inverse Fourier Transform operations, respectively, and h[n] is the reference signal in the matched filtering operation. This is the output signal.

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; when executed by a computer, the processor implements the interference suppression method for random phase modulation electromagnetic metasurfaces according to any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the interference suppression method for random phase-modulated electromagnetic metasurfaces according to any one of claims 1-8.

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