Multi-harmonic peak modulation method based on any phase angle PSS

Abstract

The invention provides a multi-harmonic peak modulation method based on an arbitrary phase angle PSS, and the method comprises the steps: 1, constructing an arbitrary angle phase modulation model; 2, analyzing a PSS modulation signal at any angle; 3, carrying out radar echo modulation analysis; and 4, performing matched filtering analysis. According to the invention, the practical application capability of the PSS in electronic countermeasure is expanded; according to the invention, a non-ideal PSS modulation model is established, and theoretical derivation and simulation analysis are carried out on the modulation signal at any regulation angle to obtain the influence of different modulation parameters on the frequency spectrum of the modulation signal. According to the method, the influence of parameters such as regulation and control angles on the radar echo signal frequency spectrum and matched filtering output is analyzed, and the mapping relation between the modulation parameters and the interference effect is established.

Description

Technical Field

[0001] The present invention relates to a multi-harmonic peak modulation method based on a Phase-Switched Screen (PSS) at any phase angle, belonging to the field of metasurface electromagnetic regulation. Specifically, the present invention explores the modulation mechanism of PSS at any phase regulation angle, establishes a phase modulation model for non-ideal regulation angles, analyzes the influence of parameters such as the regulation angle on the spectrum of the radar echo signal and the harmonic peaks of the matched filter output, and provides theoretical support for improving the electromagnetic regulation effect of PSS.

Background Art

[0002] The Phase-Switched Screen (PSS) is a novel artificial electromagnetic material proposed by Professor B. Chambers and Professor A. Tennant from the University of Sheffield in the UK, with flexible and adjustable electromagnetic scattering characteristics. PSS realizes the intermittent or continuous regulation of the phase of the incident electromagnetic wave by controlling the electromagnetic response of the surface unit, thereby effectively changing the scattering characteristics of the electromagnetic wave and achieving the low detectability of the protected target.

[0003] In 2004, Professor B. Chambers and Professor A. Tennant first experimentally demonstrated the feasibility of the application of PSS in the field of target stealth. The two professors used the PSS structure to reduce the Doppler frequency shift of the radar signal generated by the rotation of the wind turbine blades, and thus reduce the impact of the blade rotation on the airport radar. After that, many scholars from Nanjing University of Posts and Telecommunications, Nanjing University of Aeronautics and Astronautics, and National University of Defense Technology in China have conducted more in-depth research on the theory and application of PSS in the field of radar stealth. Since the above basic research was carried out, the application of PSS in stealth technology has been continuously developed. In 2024, Wang Xueyan, Xi Rui, and Liao Guisheng from Xidian University studied the application of time modulation theory to PSS for angular scattering analysis to realize the movement of the spectrum of the target stealth in the radar-target-receiver channel transmission. In 2025, Wang Xuhui et al. from Northwest University proposed a novel PSS design, which can efficiently reflect the incident wave by changing the states of four PIN diodes.

[0004] In addition to the field of radar stealth, in recent years, more and more scholars have combined electromagnetic modulation metasurface materials with interference technologies to explore their applications in the field of radar jamming. In 2016, Feng Dejun, Xu Letao and others from the National University of Defense Technology first applied PSS to radar jamming technology and studied the matched filtering output characteristics of PSS modulation signals when the modulation frequency is less than the receiver bandwidth, obtaining the effect of range transformation. In addition, Zhang Ran from the National University of Defense Technology conducted in-depth research on the theory, characteristics of PSS and its influence on radar, enriching the relevant theories and application methods of PSS and also proving the feasibility and effectiveness of PSS in the field of electronic countermeasures. Subsequently, Wang Junjie and others from the National University of Defense Technology used the dynamically adjustable electromagnetic scattering characteristics of PSS to generate false targets, thus realizing passive jamming of synthetic aperture radar imaging radar. In 2023, Hao Guoqing, Feng Dejun and others from the National University of Defense Technology analyzed the influence of multiple false target jammings generated by PSS on radar resource allocation and multi-target tracking capabilities, which is beneficial to the application of PSS in interfering with radar resources.

[0005] However, most of the current research on PSS mainly focuses on the ideal 180° regulation angle. In this ideal case, the blanking of the center frequency target can be achieved. But in fact, for actual materials in a wide frequency band, the phase regulation angle can usually only reach 180° within a narrow frequency band range near the resonance frequency point, and it is difficult to achieve the ideal regulation effect at non-resonant frequencies, which limits the wide application of PSS in practice. Therefore, conducting relevant research on PSS under arbitrary phase regulation angles has important theoretical significance and practical application value.

Summary of the Invention

[0006] Aiming at the problem that the existing research on PSS is limited to the ideal 180° regulation angle and it is difficult for actual materials to achieve this effect at non-resonant frequency points, the present invention proposes a multi-harmonic peak modulation method based on PSS with arbitrary phase angles, aiming to comprehensively understand the influence of different phase regulation angles on radar signal processing and expand the application of actual PSS materials in complex electromagnetic environments. The core of the present invention lies in establishing a non-ideal phase modulation model, analyzing the influence of modulation parameters on the harmonics of the matched filtering output, and establishing the mapping relationship between modulation parameters and interference effects. The specific steps are as follows:

[0007] Step 1: Construction of an arbitrary angle phase modulation model

[0008] The method proposed in this application is based on an electrically controlled switch type PSS, which mainly includes a three-layer structure of an active switch impedance layer, a dielectric layer, and a metal backplane. Among them, the active switch impedance layer is usually a two-dimensional periodic array, and each array unit element is connected by a variable impedance component, such as a PIN diode. By intermittently changing the PIN impedance value so that it continuously switches between the on and off states, the reflection phase can be intermittently changed to achieve the phase regulation of the signal by the material. The control angle value is the difference between the reflection phases in the two states. Based on this analysis, the control angle is Modulation model of non-ideal PSS. The PIN diode is controlled to switch intermittently between the on (+1) and off (-1) states, and the relationship between the phase difference between the reflected wave and the incident wave over time is analyzed to obtain the modulated signal waveform.

[0009] Step 2: Analysis of PSS modulation signals at any angle

[0010] First, assume that the PIN state function is a periodic bipolar rectangular pulse train (+1 means on, -1 means off), and set the switching period to T s , modulation frequency f s =1 / T s , duty cycle α = τ / T s , τ is the duration of the high level. Then the amplitude of the modulation signal p(t) remains unchanged, and the phase periodically changes between 0 and Switch between time and frequency domains to derive the modulation signal expression, and then simulate and analyze the influence of modulation parameters on the spectrum characteristics of the modulation signal, including the control angle Modulation frequency f s , duty cycle α. By comparing and analyzing the simulation results with the theoretical derivation results, the consistency between the two is verified.

[0011] Step 3: Radar echo modulation analysis

[0012] The most common radar electromagnetic wave signal is the Linear Frequency Modulation (LFM) signal. When receiving, a matched filter is used to perform pulse compression processing to obtain the final time domain output. The PSS modulated signal at any angle is modulated onto the LFM signal to obtain the modulated reflected signal. After the signal reaches the radar receiver, it is filtered out of the band by a bandpass filter. The passband of the bandpass filter is the same as the LFM signal bandwidth B. At this time, two situations can be considered: s >B, if α=0.5. Theoretical analysis shows that the receiver does not receive any signal at this time, thus achieving target blanking. s <B, if it satisfies α=0.5, the central peak disappears and only the harmonic components exist.

[0013] Step 4: Matched Filtering Analysis

[0014] Perform pulse compression processing on the echo signal through matched filtering, theoretically analyze the output time-domain expression of the matched filter, obtain parameters such as the positions, intervals, peak values, and main lobe widths of each order of output peaks, and observe the influence of parameters such as the control angle through simulation to verify whether it is consistent with the theoretical analysis results, and obtain the mapping relationship between modulation parameters and interference effects.

[0015] The beneficial effects of the present invention include:

[0016] First, innovatively propose a multi-harmonic peak modulation method based on an arbitrary phase angle PSS, which expands the practical application ability of PSS in electronic countermeasures;

[0017] Second, establish a non-ideal PSS modulation model, theoretically deduce and simulate the modulation signal at any control angle, and obtain the influence of different modulation parameters on the spectrum of the modulation signal: the closer the control angle is to 180°, the smaller the peak value of the central peak and the larger the peak value of the harmonic peaks; the larger the modulation frequency f s , the sparser the distribution; the closer the duty cycle α is to 0.5, the smaller the amplitude of the zero-order peak and the larger the amplitude of the harmonic peaks. And when α = 0.5, the central peak disappears, and only odd-order peaks exist.

[0018] Third, analyze the influence of parameters such as the control angle on the radar echo signal spectrum and the output of the matched filter, and establish the mapping relationship between modulation parameters and interference effects. Through theoretical analysis and simulation verification, it is obtained that: the modulation frequency f s is a position parameter, which affects the distribution position of false peaks after matched filtering; the duty cycle α is an energy parameter, which mainly affects the amplitude coefficient of the generated peaks; the control angle is an energy parameter, and the peak values of each order of harmonic peaks in the output of the matched filter under non-ideal conditions are times of those in the ideal case .

[0019] Therefore , the closer the control angle is to 180°, the smaller the amplitude of the central peak and the larger the amplitude of the false peaks; when reaches the ideal 180°, the amplitude of the central peak is the smallest, and the protection effect on the target is the best. This conclusion provides some ideas for solving the problem that the existing PSS research is limited to the ideal control angle of 180°, while it is difficult for actual materials to achieve this ideal control effect at non-resonant frequencies.

Description of the Drawings

[0020] Figure 1 is the schematic diagram of ideal PSS control.

[0021] Figure 2 is the control angle PSS phase modulation model diagram.

[0022] Figure 3 Time-frequency domain waveform diagram of PSS periodic modulation signal ( α = 0.5, f s = 10 MHz).

[0023] Figure 4(a) is the modulation signal spectrum diagram at the regulation angle .

[0024] Figure 4(b) is the modulation signal spectrum diagram at the regulation angle .

[0025] Figure 4(c) is the modulation signal spectrum diagram at the regulation angle .

[0026] Figure 5(a) is the modulation signal spectrum diagram when the modulation frequency f s = 5 MHz.

[0027] Figure 5(b) is the modulation signal spectrum diagram when the modulation frequency f s = 10 MHz.

[0028] Figure 5(c) is the modulation signal spectrum diagram when the modulation frequency f s = 20 MHz.

[0029] Figure 6(a) is the modulation signal spectrum diagram when the duty cycle α = 0.2.

[0030] Figure 6(b) is the modulation signal spectrum diagram when the duty cycle α = 0.6.

[0031] Figure 6(c) is the modulation signal spectrum diagram when the duty cycle α = 0.5.

[0032] Figure 7(a) is the reflected signal spectrum diagram when α = 0.3 and f s > B.

[0033] Figure 7(b) is the reflected signal spectrum diagram when α = 0.5 and f s > B.

[0034] Figure 8(a) is the reflected signal spectrum diagram when α = 0.3 and f s < B.

[0035] Figure 8(b) is the reflected signal spectrum diagram when α = 0.5 and f s < B.

[0036] Figure 9 Peak value diagrams of each order of the matched filter output at different modulation angles.

[0037] Figure 10This is the peak position diagram of each order of matched filter output under different modulation frequencies.

[0038] Figure 11 This is the peak diagram of each order of matched filter output under different duty cycles. [Specific implementation method]

[0039] In order to better understand the method of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments. The specific implementation steps are as follows:

[0040] Step 1: Arbitrary Angle Phase Modulation Model Construction

[0041] Figure 1 This is the ideal PSS control principle diagram. Assuming the carrier frequency is f c , an electromagnetic wave with a wavelength of λ is incident vertically at 90°, and the PSS dielectric layer is filled with a material with a dielectric constant of 1 and a thickness of d=λ / 4. When no power is applied, the resistance of the PIN diode reaches a maximum value, which is equivalent to the circuit being disconnected, and the impedance layer exhibits full transmission; when power is applied, the resistance of the PIN diode reaches a minimum value, which is equivalent to the circuit being turned on, and the impedance layer exhibits full reflection. At the resonant frequency point f0, the reflected wave is cos(f0t) when turned on, and cos(f0t+2βd)=-cos(f0t) when turned off, where the wave number β=2π / λ. Therefore, at the resonant frequency point, the reflection amplitude in the on and off states remains unchanged, and the phase difference is π, that is At the non-resonant frequency point f1, the reflected wave is cos(f1t) when it is turned on, and the reflected wave is Therefore, at the non-resonant point, due to the change in frequency, the wavelength also changes to λ1. At this time, the thickness of the dielectric layer is no longer 1 / 4 wavelength, and the phase difference between the reflected wave and the incident wave is no longer the ideal π, but Right now

[0042] The switch impedance layer is intermittently switched between the on (+1) and off (-1) states, and the control angle is The modulation process of the PSS on the incident signal is: when it is turned on, the phase of the reflected wave remains unchanged, and when it is turned off, the phase of the reflected wave is superimposed. At this time, the phase modulation model is as follows Figure 2 In particular, when The modulation waveform can be viewed as a bipolar rectangular pulse train, with the signal amplitude intermittently switching between +1 and -1.

[0043] Step 2: Analysis of PSS modulation signals at any angle

[0044] Assume that the PIN state function is a periodic bipolar rectangular pulse train (+1 for on, -1 for off), and the switching period is T s , modulation frequency fs = 1 / T s , and the duty cycle α = τ / T s , where τ is the duration of the high level. Then the expression p(t) of the modulation signal at time t can be expressed by the Fourier series as follows:

[0045]

[0046] where F n is the amplitude coefficient of the Fourier series, n is an integer variable representing the harmonic order, j is the imaginary unit, and π is the pi.

[0047] Frequency domain expression:

[0048]

[0049] where δ(·) is the impulse function. Amplitude coefficient:

[0050]

[0051] Substituting into Equation (1) and Equation (2), the time-domain and frequency-domain expressions of the modulation signal are obtained:

[0052]

[0053]

[0054] where δ(f) is the central peak, and δ(f - nf s ) is the discrete spurious peak (n ≠ 0). Specifically, when , the amplitude of the central peak the amplitude of the spurious peak

[0055] Simulation setting: control angle The duty cycle α = 0.5, and the modulation frequency f s = 10 MHz. Then the time-domain and frequency-domain diagrams of the periodic modulation signal are as shown in Figure 3 . When the control angle is 180°, the time-domain of the modulation signal is a bipolar pulse train; the frequency domain is discrete, and the envelope is the sinc function; the central peak disappears, and only spurious peaks exist.

[0056] Next, analyze the influence of modulation parameters on the spectral characteristics of the modulation signal:

[0057] (1) Control angle As can be seen from Equation (5), the larger, the larger the coefficient before δ(f - nf s ), and the smaller the coefficient before δ(f). the coefficient before δ(f) the smaller.

[0058] Therefore, the control angle The closer it is to 180°, the smaller the peak value of the central peak and the larger the peak value of the harmonic peak. The simulation is set with α = 0.5, f s = 10 MHz, Taking 90°, 140°, and 180° respectively, the results are shown in Figures 4(a), 4(b), and 4(c), which are consistent with the theoretical analysis.

[0059] (2) Modulation frequency f s : As can be seen from Equation (5) for δ(f - nf s ), the larger f s , the sparser the distribution, which is a position parameter. The simulation is set with α = 0.5, f s Taking 5, 10, and 20 MHz respectively, the results are shown in Figures 5(a), 5(b), and 5(c), which are consistent with the theoretical analysis.

[0060] (3) Duty cycle α: As can be seen from Equation (5), when the duty cycle is 0.5, the amplitude of the zero-order peak is When the control angle is 180°, the amplitude of the zero-order peak is 0; the amplitude of the harmonic peak is

[0061] Therefore, only odd-order peaks exist. The closer the duty cycle is to 0.5, the smaller the amplitude of the zero-order peak and the larger the amplitude of the harmonic peak. The simulation is set with f s = 10 MHz, Taking α as 0.2, 0.6, and 0.5 respectively, the results are shown in Figures 6(a), 6(b), and 6(c), which are consistent with the theoretical analysis.

[0062] Step 3: Radar echo modulation and matched filtering analysis

[0063] The time-domain and frequency-domain expressions of the modulation signal are shown in Equations (4) and (5). Modulating it onto the LFM signal, the time-domain and frequency-domain expressions of the modulated signal (reflected signal) are:

[0064] r(t) = s(t)·p(t) (6)

[0065]

[0066] where R(f) is the spectrum of the reflected signal r(t), s(t) is the time-domain expression of the LFM signal, S(f) is the spectrum of the LFM signal, represents the convolution operation.

[0067] After the modulated signal arrives at the radar receiver, the out-of-band signal is filtered out by a band-pass filter. The passband of the band-pass filter is the same as that of the LFM signal, which is As can be seen from Equation (7), the nearest frequency points near the central peak are f c ±fs , whose range is Therefore, if i.e., f s > B, after passing through the band - pass filter, only the central carrier - frequency component of the signal remains, and all other harmonic components fall outside the pass - band and are filtered out. And when f s < B, some newly generated harmonic components are still retained within the pass - band, and the maximum number of newly generated sidebands is where represents rounding down. The following is a simulation analysis in two cases:

[0068] When f s > B, the base - band signal obtained by the reflected signal passing through the filter and the mixer is:

[0069]

[0070] where T p is the pulse width of the LFM signal, K is the frequency modulation rate of the LFM signal, and rect(·) represents the rectangular pulse function.

[0071] When α = 0.5, r base (t)=0. At this time, no signal is received in the receiver, achieving the blanking of the target. The simulation sets the carrier frequency f c = 9 GHz, the modulation angle the modulation frequency f s = 50 MHz, the LFM bandwidth B = 20 MHz. Observe the spectra of the reflected signals when α is 0.3 and 0.5 respectively, as shown in Figures 7(a) and 7(b). It can be seen from the figures that when f s > B, except for the central peak, the reflected signal is outside the band - pass of the filter (i.e., the bandwidth of the incident signal in the figure). When α = 0.5, there is no central peak, so there is no signal after filtering; when α≠0.5, the base - band signal has only the central peak.

[0072] When f s < B, the base - band signal obtained by the reflected signal passing through the filter and the mixer is:

[0073]

[0074] If α = 0.5, at this time the central peak is blanked, and only harmonic components exist. The simulation sets the carrier frequency f c = 9 GHz, the modulation angle the modulation frequency f s = 30 MHz, the LFM bandwidth B = 50 MHz. Observe the spectra of the reflected signals when α is 0.3 and 0.5 respectively, as shown in Figures 8(a) and 8(b). It can be seen from the figures that when f s When α < B, the harmonic components of the reflected signal are also within the filter passband. When α = 0.5, there is no central peak, so the central peak is blanked after filtering; when α ≠ 0.5, there are central peaks and harmonic peaks in the baseband signal.

[0075] Step Four: Matched Filter Analysis

[0076] The frequency response function of the matched filter is S * (f), so when f s < B, the matched filter output is:

[0077] Y(f) = R(f)·S * (f) (10)

[0078] Converted to the time domain:

[0079]

[0080] Therefore, the matched filter output is a central zero-order peak and multiple discrete sinc peaks. If and only if α = 0.5, the central peak is blanked. And the output peak position:

[0081]

[0082] Output peak interval:

[0083]

[0084] Amplitude of the nth-order peak (n ≠ 0):

[0085]

[0086] Main lobe width of the nth-order peak:

[0087]

[0088] As can be seen from Equation (14), when , the amplitude of the nth-order peak For other modulation angles, the amplitude of the nth-order peak Therefore, the peak value of each order harmonic peak in the non-ideal case is That is times.

[0089] Next, observe the influence of different parameters through simulation.

[0090] (1) Modulation angle Set the modulation frequency f s = 10 MHz, duty cycle α = 0.5, signal carrier frequency f c = 9 GHz, bandwidth B = 80 MHz. Figure 9Is the regulation angle It is a comparison chart of the peak amplitudes of each order after matched filtering at 45°, 90°, 140°, and 180°. It can be seen from the figure that discrete false interference peaks appear near the central peak after adding PSS interference. As the regulation angle increases, the amplitude of the central zero-order peak decreases, and the amplitude of the false peak increases. When the regulation angle is the ideal 180°, the central peak disappears and the amplitude is 0. In addition, in the figure The first-order peaks at 45°, 90°, 140°, and 180° are 0.2064, 0.3813, 0.5067, and 0.5392 respectively. Calculation shows that they are all times of the ideal value, which is consistent with the theoretical derivation.

[0091] (2) Modulation frequency f s : Set The duty cycle α = 0.5, the signal carrier frequency f c = 9 GHz, and the bandwidth B = 80 MHz. Figure 10 It is a comparison chart of the positions of each order of peaks after matched filtering when the modulation frequency f s is 2, 5, and 10 MHz. It can be seen that as the modulation frequency increases, the output width increases and the distribution of false peaks becomes sparse.

[0092] (3) Duty cycle α: Set The modulation frequency f s = 10 MHz, the signal carrier frequency f c = 9 GHz, and the bandwidth B = 80 MHz. Figure 11 It is a simulation result chart when the duty cycle α is 0.2, 0.4, 0.5, and 0.7. It can be seen that when the duty cycle is 0.5, the amplitude of the central zero-order peak is the smallest, the amplitude of the first-order peak is the largest, and only odd-order peaks are output.

[0093] In summary, the regulation angle is a key energy parameter, which mainly affects the amplitude coefficient of the false peaks generated after matched filtering. The closer the regulation angle is to the ideal 180°, the smaller the amplitude of the central peak, the larger the amplitude of the false peak, and the better the regulation effect. And from the simulation analysis, it is consistent with the theoretical derivation results, verifying the effectiveness of this method.

Claims

1. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS, characterized in that It includes the following steps: Step 1: Construction of an arbitrary-angle phase modulation model It is based on an electronically controlled switch-type PSS. Among them, the active switch impedance layer is a two-dimensional periodic array, and each array unit element is connected by a variable impedance component; the PIN impedance value is intermittently changed to continuously switch between two states of conduction and disconnection, that is, the reflection phase is intermittently changed to achieve the phase control of the material on the signal. The control angle value is the difference in the reflection phase between the two states; the PIN diode is controlled to intermittently switch between the conduction and disconnection states, and the relationship between the phase difference between the reflected wave and the incident wave and time is analyzed, and then the modulation signal waveform is obtained; Step 2: Analysis of the arbitrary-angle PSS modulation signal Let the PIN state function be a periodic bipolar rectangular pulse train, and set the switching period to T s , the modulation frequency f s = 1 / T s , the duty cycle α = τ / T s , where τ is the high-level duration; then the amplitude of the modulation signal p(t) remains unchanged, and the phase periodically switches between 0 and , and the time-frequency domain expression of the modulation signal is obtained, and then the influence of the modulation parameters on the spectral characteristics of the modulation signal is simulated and analyzed; Step 3: Analysis of radar echo modulation The electromagnetic wave signal emitted by the radar is a linear frequency modulation LFM signal. When receiving, a matched filter is used for pulse compression processing to obtain the final time-domain output; the arbitrary-angle PSS modulation signal is modulated onto the LFM signal to obtain the modulated reflected signal. After the signal reaches the radar receiver, the out-of-band signal is filtered by a band-pass filter. The passband of the band-pass filter is the same as the bandwidth B of the LFM signal; Step 4: Matched filtering analysis The echo signal is subjected to pulse compression processing through matched filtering, the time-domain expression of the matched filtering output is analyzed, the parameters of the position, interval, peak value, and main lobe width of each order output peak are obtained, and the influence of the control angle parameter is observed through simulation to obtain the mapping relationship between the modulation parameter and the interference effect.

2. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 1, characterized in that: In step one, let the carrier frequency be f c , an electromagnetic wave with a wavelength of λ is incident vertically at a 90° angle. The PSS dielectric layer is filled with a substance with a dielectric constant of 1 and a thickness of d = λ / 4; when no voltage is applied, the resistance of the PIN diode reaches its maximum value, which is equivalent to the circuit being open at this time, and the impedance layer exhibits total transmission; when voltage is applied, the resistance of the PIN diode reaches its minimum value, which is equivalent to the circuit being conducting at this time, and the impedance layer exhibits total reflection.

3. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 1 or 2, characterized in that: In step one, at the resonant frequency f0, when it is turned on, the reflected wave is cos(f0t), and when it is turned off, the reflected wave is cos(f0t + 2βd) = -cos(f0t), where the wave number β = 2π / λ; therefore, at the resonant frequency, the reflection amplitudes in the on and off states are the same, and the phase difference is π, that is While at the non-resonant frequency f1, when it is turned on, the reflected wave is cos(f1t), and when it is turned off, the reflected wave is Therefore, at the non-resonant point, due to the change in frequency, the wavelength also correspondingly changes to λ1. At this time, the thickness of the dielectric layer is no longer 1 / 4 wavelength, and the phase difference between the reflected wave and the incident wave is no longer the ideal π, but That is 4. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 1, characterized in that: In Step 2, the expression p(t) of the modulation signal at time t is expressed as a Fourier series: where, F n is the amplitude coefficient of the Fourier series, n is an integer variable used to represent the harmonic order, j is the imaginary unit, and π is the pi; Frequency-domain expression: Among them, δ(·) is the impulse pulse function; amplitude coefficient:

5. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 4, characterized in that: In Step 2, substituting Equation (1) and Equation (2), the time-domain and frequency-domain expressions of the modulation signal are obtained: Among them, δ(f) is the central peak, and δ(f - nf s ) is the discrete false peak (n ≠ 0); when , the amplitude of the central peak the amplitude of the false peak 6. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 1 or 5, characterized in that: In Step 3, the time-domain and frequency-domain of the modulation signal are modulated onto the LFM signal, and the time-domain and frequency-domain expressions of the modulated signal are obtained as: r(t) = s(t)·p(t) (6) where \(R(f)\) is the spectrum of the reflected signal \(r(t)\), \(s(t)\) is the time-domain expression of the LFM signal, and \(S(f)\) is the spectrum of the LFM signal. represents the convolution operation.

7. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 6, characterized in that: In step three, after the modulated signal arrives at the radar receiver, the out-of-band signal is filtered out by a band-pass filter. The passband of the band-pass filter is the same as that of the LFM signal, which is The frequency point closest to the center peak is f c ±f s , and its range is Therefore, if That is, when f s > B, only the central carrier frequency component remains after the signal passes through the band-pass filter, and all other harmonic components fall outside the passband and are filtered out; when f s < B, some newly generated harmonic components are still retained within the passband. The maximum number of newly generated sidebands is where represents rounding down.

8. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 7, characterized in that: In step three, when f s > B, the baseband signal obtained from the reflected signal passing through the filter and mixer is: Among them, T p is the pulse width of the LFM signal, K is the frequency modulation rate of the LFM signal, and rect(·) represents the rectangular pulse function; When f s <B, the baseband signal obtained from the reflected signal passing through the filter and mixer is:

9. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 1, characterized in that: In step four, the frequency response function of the matched filter is S * (f), so when f s < B, the matched filter output is: Y(f) = R(f)·S * (f) (10) Converted to the time domain: Therefore, the matched filtering output is the central zero-order peak and multiple discrete sinc peaks.

10. A multi-harmonic peak modulation method based on an arbitrary phase angle PSS according to claim 9, characterized in that: In step four, if and only if α = 0.5, the central peak is blanked; and the output peak position is: Output peak interval: Amplitude of the nth-order peak (n≠0): Main lobe width of the nth-order peak:

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