Non-uniform double-pulse modulation method based on TCM

Abstract

The invention provides a non-uniform double-pulse modulation method based on a TCM. The non-uniform double-pulse modulation method comprises the steps that 1, a non-uniform double-pulse period modulation model is constructed; 2, carrying out radar echo modulation analysis; 3, analyzing a pulse compression result; and step 4, regulation and control effect analysis based on a CFAR detector. According to the method, the key parameter of the time delay factor is innovatively introduced, the modulation flexibility and unpredictability are greatly improved through the collaborative design of three degrees of freedom, and the problems of insufficient flexibility and the like existing in a radar target feature regulation and control method are solved. Compared with a regulation and control method based on TCM uniform monopulse period modulation, the generated harmonic peak amplitude distribution is diversified, screening of regular signals by a radar CFAR detector is effectively avoided, and the number of effective harmonic peaks passing detection is remarkably increased. According to the invention, precise suppression or enhancement of specific-order harmonics can be realized, and a technical approach is provided for implementing flexible and dynamic radar target feature regulation and control.

Description

TECHNICAL FIELD

[0001] The present application relates to a non-uniform double pulse modulation method based on a temporal-coded metasurface (TCM), and belongs to the technical field of metasurface electromagnetic regulation. Specifically, based on the modulation mechanism of TCM, the present application introduces a time delay factor as a core degree of freedom and establishes an amplitude modulation model of non-uniform double pulses, analyzes the influence of parameters such as the time delay factor on the radar echo signal spectrum and the harmonic peak output by the matched filter, and provides technical support for improving the electromagnetic regulation effect of TCM. BACKGROUND

[0002] Temporal-Coded Metasurface (TCM) integrates PIN diodes, field effect transistors and other active devices in traditional frequency selective surfaces, so that the reflection, transmission or absorption characteristics of electromagnetic waves can be dynamically adjusted by external electrical signals, realizing real-time control of phase, amplitude, polarization and other parameters.

[0003] Based on the advantages of such dynamic regulation, radar target feature modulation technology based on TCM has been widely studied. On the one hand, researchers use electromagnetic regulation surfaces to change radar target characteristics, which has been applied to high-resolution range profile (HRRP) modulation, radar cross section (RCS) simulation, etc. In HRRP regulation, Guo et al. derived a non-periodic time modulation model of time-coding digital metasurface (TCDM), and theoretically proved that a single TCDM with a specific non-periodic sequence can accurately simulate the complex scattering point distribution in HRRP [1] . In RCS simulation, Fang et al. proposed a multifunctional space-time modulation metasurface that can simultaneously perform direction of arrival estimation and RCS manipulation in a single system [2] . On the other hand, modulation waveform design based on TCM has also gradually attracted the attention of researchers, mainly divided into periodic and random waveforms, which can realize discrete and continuous Doppler frequency shift of incident signals, respectively, and form harmonic peaks or block regions in the range direction after matched filtering. For example, Kong et al. proposed a double pulse cyclic intermittent modulation method for active frequency selective surface (AFSS) reflector electromagnetic scattering state switching, which can improve its variability and flexibility in radar target simulation [3]Li et al. proposed a dynamic random coded metasurface for generating and directly manipulating random electromagnetic signals, laying the theoretical and technical foundation for the application of dynamic random metasurfaces in the field of radar technology. [4] .

[0004] However, existing TCM-based radar target modulation methods still face significant challenges. First, the harmonic peaks generated by existing TCM-based radar feature modulation follow a highly regular sinc function distribution, resulting in low modulation flexibility. Second, these harmonic peaks are easily filtered out during subsequent signal processing. For example, modern radars typically use CFAR detection technology to filter out background or stationary noise; effective modulation can only be achieved when the harmonic peaks exceed the CFAR detection threshold. However, harmonic peaks generated by TCM often fail to pass this detection, significantly limiting the modulation effect. It is worth noting that how to flexibly allocate echo energy in the radar target feature space is also a long-standing challenge for electromagnetic metasurface-based radar target feature modulation.

[0005] The references are as follows:

[0006] [1]Guo J, Guan D, Liu Z, et al. Radar Target HRRP Imitation Based on Non-Periodic Time-Coding Digital Metasurface[J]. IEEE Transactions on Antennas andPropagation, 2025.

[0007] [2]Fang X, Li M, Lai Z, et al. Multifunctional space–time-modulated metasurface for direction of arrival estimation and RCS manipulation in asingle system [J]. IEEE Transactions on Microwave Theory and Techniques, 2023, 72(6): 3797-3808.

[0008] [3] Yameng K, Guoyu W, Dejun F. AFSS reflector double pulse cycle intermittent modulation method [J]. Systems Engineering & Electronics, 2022, 44(12).

[0009] [4]Li JC,Cui T J.Controlling stochastic electromagnetic process by dynamically random coding metasurface[J].Advanced Materials Technologies, 2025:2401888. [Summary of the Invention]

[0010] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a non-uniform dual-pulse modulation method based on TCM. This method effectively breaks the regularity of harmonic peak amplitude distribution by introducing new modulation degrees of freedom, significantly increasing the number of effective harmonic peaks that can overcome radar CFAR detection. To achieve the above objective, the specific steps of this invention are as follows:

[0011] Step 1: Construct a non-uniform double-pulse periodic modulation model

[0012] This invention defines a periodic, non-uniform double-pulse modulated signal, wherein each modulation period T s It contains two rectangular pulses: the first pulse has a duty cycle of β, and the second pulse has a duty cycle of α. The second pulse has a time delay relative to the first pulse, which is determined by a delay factor γ, and the delay time is γT. s In reality, a non-uniform double-pulse periodic signal is the superposition of two uniform single-pulse periodic signals in the time domain. The time-frequency domain expression of the modulation signal is derived, and then the influence of modulation parameters on the spectral characteristics of the modulation signal is simulated and analyzed, including the time delay factor γ and the modulation frequency f. s Duty cycles α and β were determined. The consistency between the simulation results and the theoretical derivation results was verified by comparing and analyzing them.

[0013] Step 2: Radar Echo Modulation Analysis

[0014] The method proposed in this invention application is based on TCM expansion, which can realize the switching between absorption and reflection states, i.e., amplitude modulation. A linear frequency modulation (LFM) signal is used as the radar transmission signal, which is incident on the TCM loaded with a non-uniform double-pulse periodic modulation signal to obtain a modulated reflected signal. After the signal reaches the radar receiver, it is filtered by a bandpass filter to remove out-of-band signals, resulting in the echo baseband signal.

[0015] Step 3: Pulse Compression Result Analysis

[0016] The echo baseband signal obtained in step two of this invention undergoes pulse compression processing via matched filtering. Theoretical analysis of the time-domain expression of the matched filter output yields parameters such as the position, interval, and amplitude coefficient of each output peak. It is deduced that the time delay factor is a key energy parameter, primarily affecting the amplitude coefficient of the harmonic peaks generated after matched filtering. Furthermore, simulation analysis of the influence of parameters such as the time delay factor verifies the consistency with the theoretical analysis results, thus establishing the mapping relationship between modulation parameters and the control effect.

[0017] Step 4: Analysis of the Modulation Effect Based on the CFAR Detector

[0018] Under the non-uniform dual-pulse periodic amplitude control of TCM, the amplitude-modulated echo, after radar signal processing in steps two and three, will form a series of harmonic peaks with controllable amplitude. The harmonic peak amplitude distribution generated by the method proposed in this invention is controllable, breaking the sinc envelope limitation of traditional uniform single-pulse modulation. This effectively realizes the improved flexibility and unpredictability of radar feature modulation, and also enables more harmonic peaks to successfully pass through the constant false alarm rate (CFAR) detector in the radar system.

[0019] The beneficial effects of this invention are as follows:

[0020] First, the innovative introduction of the time delay factor as a key parameter, through the collaborative design of three degrees of freedom, can generate rich harmonic peak amplitude distributions, greatly improving the flexibility and unpredictability of modulation, and solving the problems of insufficient flexibility in radar target feature control methods.

[0021] Second, compared with the control method based on TCM uniform single-pulse periodic modulation, the harmonic peak amplitude distribution generated in this paper is diverse, which effectively avoids the filtering of regular signals by the radar CFAR detector and significantly increases the number of effective harmonic peaks that pass the detection.

[0022] Third, by utilizing the coupling effect of the nonlinear relationship between parameters, it is possible to accurately suppress or enhance specific order harmonics, providing a technical approach for implementing flexible and dynamic radar target characteristic control. [Attached Image Description]

[0023] Figure 1 This is a diagram illustrating the amplitude control principle of TCM.

[0024] Figure 2 This is a schematic diagram of a non-uniform double-pulse signal design.

[0025] Figure 3(a) shows f s The spectrum of a non-uniform double pulse signal when 10MHz, γ=0.5, β=0.1, α=0.2.

[0026] Figure 3(b) shows fs The spectrum of a non-uniform double pulse signal at 20MHz, γ=0.5, β=0.1, α=0.2.

[0027] Figure 3(c) shows f s The spectrum of a non-uniform double-pulse signal when ω = 20MHz, γ = 0.6, β = 0.2, α = 0.2.

[0028] Figure 4(a) shows the variation of the discrete peak amplitude distribution with time delay factor when β≠α.

[0029] Figure 4(b) shows the variation of the discrete peak amplitude distribution with time delay factor when β=α.

[0030] Figure 5 This is a diagram illustrating the effect of non-uniform double-pulse periodic modulation.

[0031] Figure 6(a) shows the pulse compression results of non-uniform double-pulse periodic modulation based on TCM when γ=0.5.

[0032] Figure 6(b) shows the pulse compression results of non-uniform double-pulse periodic modulation based on TCM when γ = 0.6.

[0033] Figure 6(c) shows the pulse compression results of non-uniform double-pulse periodic modulation based on TCM when γ = 0.7.

[0034] Figure 7(a) shows the pulse compression results based on TCM non-uniform double-pulse periodic modulation when γ=0.5 and β=α=0.2.

[0035] Figure 7(b) shows the pulse compression results based on TCM non-uniform double-pulse periodic modulation when γ=0.6 and β=α=0.2.

[0036] Figure 7(c) shows the pulse compression results based on TCM non-uniform double-pulse periodic modulation when γ=0.5, β=0.2, α=0.1.

[0037] Figure 7(d) shows the pulse compression results based on TCM non-uniform double-pulse periodic modulation when γ=0.6, β=0.2, α=0.1.

[0038] Figure 8(a) shows the CFAR detection results when the uniform single pulse has a duty cycle of α = 0.4.

[0039] Figure 8(b) shows the CFAR detection results when the uniform single pulse has a duty cycle of α = 0.5.

[0040] Figure 8(c) shows the CFAR detection results when there is a non-uniform double pulse with γ = 0.5, β = 0.1, and α = 0.2.

[0041] Figure 8(d) shows the CFAR detection results when there is a non-uniform double pulse with γ = 0.6, β = 0.1, and α = 0.2.

[0042] Figure 9 The cost of CFAR detection for different modulation waveforms.

Detailed Implementation Methods

[0043] To better understand the method of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. Specific implementation steps are as follows:

[0044] Step 1: Construct a non-uniform double-pulse periodic modulation model

[0045] A Transducer Module (TCM) can dynamically alter the amplitude of an incident radar signal using an external excitation source, thereby generating artificially induced target characteristics. The TCM structure consists of a switchable impedance layer, a dielectric substrate, and a metal backplane. By integrating electronic components and corresponding feed networks into the switchable impedance layer, changes in the external power supply modulate the impedance characteristics of these components, enabling the TCM to switch between reflection and absorption states. Figure 1 This is the amplitude control schematic of TCM. The PIN diode is loaded in the switching impedance layer. The FPGA provides external excitation. By changing the external voltage applied to the PIN diode, its impedance characteristics are changed, thereby adjusting the amplitude of the incident signal and realizing the switching between reflection and absorption states.

[0046] Based on the uniform single-pulse periodic modulation model of TCM, this invention designs a non-uniform double-pulse periodic modulation waveform, the schematic diagram of which is shown below. Figure 2 As shown. This signal has two rectangular pulses within one period, and the pulse period is T. s Within the same period, the duty cycle of the first pulse is β, the duty cycle of the second pulse is α, and the time delay relative to the first pulse is γT. s Based on the aforementioned characteristics of non-uniform double-pulse periodic signals, a time delay factor γ is defined to control the phase of the spectrum. To prevent abrupt waveform changes, the signal pulse parameters in the time domain are constrained as follows:

[0047]

[0048] A non-uniform double-pulse periodic signal can be viewed as the sum of two uniform single-pulse periodic intermittent signals in the time domain. The time-domain expressions for two uniform single-pulse periodic intermittent signals p1(t) and p2(t) with different duty cycles and time delays are as follows:

[0049]

[0050] Where rect(·) is a rectangular pulse, This is a convolution operation, where δ(·) is the impulse pulse, and n represents the sequence of impulse functions δ(t-nT). s The nth period in ), where t represents the time variable. This indicates a time shift of the entire expression, with the shift amount being... Indicates time shift

[0051] The Fourier series in trigonometric form for signals p1(t) and p2(t) are as follows:

[0052]

[0053] Among them, a 10 Let a be the DC component of the signal p1(t). 1n a is the coefficient of the cosine term of the nth harmonic in the Fourier series of signal p1(t); 20 The DC component of signal p2(t) is equal to its duty cycle α; 2n Let be the cosine coefficient of the nth harmonic of the signal p2(t), and its spectral envelope is also a sinc function determined by α.

[0054] From equations (2) and (3), it can be seen that the time delay of signal p2(t) relative to signal p1(t) is γT. s Based on the time-shifting property of the Fourier transform, the corresponding phase factor is e. -j2nπγ Therefore, the Fourier transforms of signals p1(t) and p2(t) are respectively:

[0055]

[0056]

[0057] Where f is the frequency variable, δ(f) is the spectrum of the impulse function, and δ(f-nf) is the frequency response of the impulse function. s ) indicates at frequency nf s Spectral line at position j. j is the imaginary unit, e -jnπβ This indicates that p1(t) is shifted due to time. The resulting phase factor; e -jnπ(2γ+α) This indicates that p2(t) is due to its own translation. and relative delay γT s The resulting phase factor.

[0058] Non-uniform double-pulse periodic signal p based on TCM TCM (t) is represented in the time domain as:

[0059]

[0060] According to the linearity property of the Fourier transform, pTCM The Fourier transform of (t) is P TCM (f) = P1(f) + P2(f):

[0061]

[0062] As can be seen from the above equation, the spectrum of a non-uniform double-pulse periodic signal is discrete, containing both DC and harmonic components. The modulation frequency f... s The smaller the value, the smaller the interval between harmonic components; conversely, the larger the value, the larger the interval. When n = 0, the amplitude of the DC component is A0 = β + α, and the phase is zero (because γ does not affect the DC term). When n ≠ 0, the amplitude of each discrete peak in the spectrum is a. n The specific expression is as follows:

[0063]

[0064] Taking the modulus of the above formula, the amplitude coefficient can be obtained as follows:

[0065]

[0066] Here, sin(nπβ) reflects the relative amplitude characteristics of the first pulse p1(t) (duty cycle β) on the nth harmonic; sin(nπα) reflects the relative amplitude characteristics of the second pulse p2(t) (duty cycle α) on the nth harmonic.

[0067] The above equation shows that the spectral amplitude of a non-uniform double-pulse periodic signal is affected by the duty cycle β, α, and the delay factor γ. Specifically, by controlling the duty cycle β, α, and the delay factor γ to control the phase, the coherent superposition of the frequency domain components of p1(t) and p2(t) can enhance or cancel specific frequency components, thereby achieving diversity in the harmonic peak amplitude distribution. Figures 3(a)-3(c) show the spectrum of the non-uniform double-pulse signal under different modulation parameters. As the modulation frequency increases, the harmonic peak spacing increases; different combinations of duty cycle and delay factor will lead to changes in the spectral amplitude distribution. Figures 4(a) and 4(b) illustrate the variation of the amplitude distribution of discrete peaks of each order with the time delay factor. Figure 4(a) shows the case where β≠α, and the value of γ will affect the amplitude distribution of each harmonic component: when γ<0.6, the energy of the second-order discrete peak is higher than that of the first-order, which may result in higher-energy harmonic peaks over a longer distance; when γ=0.6, the energies of the first-order and second-order discrete peaks are almost the same, both lower than that of the third-order, achieving different effects in the amplitude distribution of harmonic peaks; when γ>0.6, the energy is mainly concentrated in the first order. Figure 4(b) shows the case where β=α. In this case, if γ=0.5, the amplitude of the odd-order discrete peaks is 0, that is, the odd-order harmonic peaks disappear.

[0068] Step 2: Radar Modulated Echo

[0069] The transmitted signal used in this paper is linear frequency modulation (LFM), which is widely used in radar systems due to its large time-bandwidth product. The time-domain expression of the LFM signal is:

[0070]

[0071] Among them, T p It is the pulse width, f c It is the carrier frequency, K r It is the frequency modulation slope, defined as the ratio of the signal bandwidth to the pulse width, i.e., K. r =B / T p .like Figure 5 As shown, the signal is incident on the TCM and undergoes periodic non-uniform double-pulse modulation. The time-domain expression of the echo signal is:

[0072] r(t)=s(t·p TCM (t) (13)

[0073] The spectrum of the echo signal is:

[0074]

[0075] Where S(f) is the spectrum of the transmitted signal s(t), and P TCM (f) represents a non-uniform double-pulse periodic signal based on TCM.

[0076] Step 3: Pulse Compression Result Analysis

[0077] After TCM non-uniform double-pulse periodic modulation, the echo baseband signal is obtained at the receiving end through mixing and filtering processes:

[0078]

[0079] Matched filtering is performed on the echo baseband signal to obtain the matched filter output of the LFM signal. The expression is as follows:

[0080]

[0081] in, It is the order. The expression indicates decimal rounding, and sinc(·) represents the Singer function. From the above equation, it can be seen that the output of the matched filter is a series of symmetrical discrete peaks. The spatial distribution of each order of discrete peak is determined by the modulation frequency of the modulating signal, and the amplitude distribution is determined by the duty cycle and the time delay factor γ. The interval between each order of discrete peak is:

[0082]

[0083] The spacing between adjacent discrete peaks varies with the modulation frequency f s The amplitude coefficient of the zero-order peak value increases with the increase of [something].

[0084] C0=A0=β+α (18)

[0085] The amplitude coefficient of the non-zero order discrete peak value is:

[0086]

[0087] It can be seen that the amplitude distribution of the matched filter output is determined by the duty cycle β, α, delay factor γ, and modulation frequency f. s Joint control. Based on the above analysis, compared with the uniform single-pulse periodic waveform, the non-uniform double-pulse modulation waveform achieves higher control freedom and flexibility by independently controlling the width and position of the double pulses. Figures 6(a)-6(c) show the pulse compression results of non-uniform double-pulse periodic modulation based on TCM under different time delay factors. Comparing Figures 6(a), 6(b), and 6(c), it is found that the change of γ leads to the change of pulse compression results, realizing flexible modulation of the harmonic peak amplitude distribution: when γ = 0.5, the highest energy harmonic peak is ±2nd order, breaking the law of gradual decrease of harmonic peak amplitude in single-pulse uniform modulation; when γ = 0.6, the energy distribution of harmonic peaks is relatively uniform; when γ = 0.7, the ±1st order harmonic peak has the highest energy. Figures 7(a)-7(d) show the pulse compression results of non-uniform double-pulse periodic modulation based on TCM under different modulation parameters. Figures 7(a) and 7(b) show the case where the duty cycle β = α. The measurement results show that when γ = 0.5 and the duty cycle β = α, the odd-order harmonic peaks disappear. When γ = 0.6, the harmonic peak energy distribution is uniform, and harmonic peaks of all orders exist. Comparing Figures 6(a) and 7(c), and Figures 6(b) and 7(d), respectively, when γ = 0.5, exchanging the values ​​of β and α does not affect the modulation effect, that is, β and α have symmetry. When γ ≠ 0.5, exchanging the values ​​of β and α affects the modulation effect, indicating that β and α do not have symmetry.

[0088] Step 4: Analysis of the Modulation Effect Based on the CFAR Detector

[0089] Subsequently, the modulation effect of the modulated waveform was analyzed based on CFAR detection. The modulation frequency f was set. s=1MHz, different modulation waveforms were used for modulation, and the results are shown in Figures 8(a)-8(d). As shown in Figures 8(a) and 8(b), when a uniform single-pulse periodic modulation waveform is used, regardless of the change in duty cycle, only ±1st order harmonic peaks pass through CFAR detection, and the modulation effect is limited; when a non-uniform double-pulse periodic modulation is used, as shown in Figures 8(c) and 8(d), the modulation effect is improved by adjusting the combination of delay factor and duty cycle, thereby increasing the number of harmonic peaks detected by CFAR.

[0090] Subsequently, a quantitative analysis was performed based on the principle of Constant False Alarm Rate (CA-CFAR) and the detection cost of CFAR. Assuming there are multiple false targets in the background cells of a real target cell, for a real target cell d, if the target is correctly detected, the detection cost is V. d TP If the target is incorrectly detected, the value is V. d TN For other background units c (c≠d), if the detection result indicates the presence of a target, then the detection cost is V. c FP If the detection result indicates that the target does not exist, the detection cost is V. c FN According to the minimum error probability criterion, it is usually V. c FN =V d TP =0, V c FP =V d TN =1, meaning that correct detection has no cost, and incorrect detection has a cost of 1. Therefore, the total cost of detection in one search cycle is:

[0091]

[0092] Where 2L is the total length of the background unit. Given the true target position, the detection cost can be calculated using the above equation. The detection costs for different modulation waveforms at equivalent duty cycles are as follows: Figure 9 As shown, the detection cost increases with increasing signal-to-noise ratio (SNR). This is because as the SNR decreases, more and more high-order, low-energy harmonic peaks are submerged in noise, leading to a reduction in the number of effective harmonic peaks. At the same modulation frequency and duty cycle, when the SNR is above 30 dB, the detection cost of dual-pulse modulation is higher than that of single-pulse modulation, validating the effectiveness of the proposed modulation waveform.

Claims

1. A non-uniform dual-pulse modulation method based on TCM, characterized in that: The steps are as follows: Step 1: Construct a non-uniform double-pulse periodic modulation model Define a periodic, non-uniform double-pulse modulated signal, where each modulation period T s It contains two rectangular pulses: the first pulse has a duty cycle of β, and the second pulse has a duty cycle of α. The second pulse has a time delay relative to the first pulse, which is determined by a delay factor γ, and the delay time is γT. s ; Step 2: Radar Echo Modulation Analysis A linear frequency modulated (LFM) signal is used as the radar transmission signal and incident on a time-domain coded metasurface (TCM) loaded with a non-uniform double-pulse periodic modulation signal to obtain a modulated reflected signal. After the reflected signal reaches the radar receiver, it passes through a bandpass filter to filter out out-of-band signals and obtain the echo baseband signal. Step 3: Pulse Compression Result Analysis The echo baseband signal is pulse-compressed by matched filtering. The time-domain expression of the matched filter output is analyzed to obtain the position, interval, and amplitude coefficient of each output peak, and the time delay factor parameter is obtained. The influence of the time delay factor parameter is then analyzed by simulation to verify whether it is consistent with the analysis results, and the mapping relationship between the modulation parameter and the control effect is obtained. Step 4: Analysis of the Modulation Effect Based on the CFAR Detector Under the non-uniform double-pulse periodic amplitude control of the time-domain encoded metasurface (TCM), the amplitude-modulated echoes, after radar signal processing in steps two and three, form a series of amplitude-controllable harmonic peaks.

2. The non-uniform dual-pulse modulation method based on TCM according to claim 1, characterized in that: In step one, the TCM dynamically changes the amplitude of the incident radar signal through an external excitation source to generate artificially induced target features. The TCM structure consists of a switchable impedance layer, a dielectric substrate, and a metal backplate. By integrating electronic components and corresponding feed networks into the switchable impedance layer, the TCM can switch between reflection and absorption states. A PIN diode is loaded in the switchable impedance layer, and the FPGA provides external excitation. By changing the external voltage applied to the PIN diode, its impedance characteristics are changed, thereby adjusting the amplitude of the incident signal and realizing the switching between reflection and absorption states.

3. A non-uniform dual-pulse modulation method based on TCM according to claim 1 or 2, characterized in that: Based on the uniform single-pulse periodic modulation model of TCM, a non-uniform double-pulse periodic modulation waveform was designed. The signal has two rectangular pulses within one period, and the pulse period is T. s Within the same period, the duty cycle of the first pulse is β, the duty cycle of the second pulse is α, and the time delay relative to the first pulse is γT. s Define a time delay factor γ to control the phase of the spectrum; to prevent abrupt waveform changes, the parameter constraints of the signal pulse in the time domain are as follows: A non-uniform double-pulse periodic signal can be considered as the sum of two uniform single-pulse periodic intermittent signals in the time domain; the time-domain expressions of two uniform single-pulse periodic intermittent signals p1(t) and p2(t) with different duty cycles and time delays are as follows: Where rect(·) is a rectangular pulse, This is a convolution operation, where δ(·) is the impulse pulse, and n represents the sequence of impulse functions δ(t-nT). s The nth period in ); t represents the time variable, This indicates a time shift of the entire expression, with the shift amount being... Indicates time translation 4. The non-uniform dual-pulse modulation method based on TCM according to claim 3, characterized in that: The Fourier series in trigonometric form for signals p1(t) and p2(t) are as follows: Among them, a 10 Let a be the DC component of the signal p1(t). 1n a is the coefficient of the cosine term of the nth harmonic in the Fourier series of signal p1(t); 20 The DC component of signal p2(t) is equal to its duty cycle α; 2n Let be the cosine coefficient of the nth harmonic of the signal p2(t), and its spectral envelope is also a sinc function determined by α.

5. The non-uniform dual-pulse modulation method based on TCM according to claim 4, characterized in that: The time delay of signal p2(t) relative to signal p1(t) is γT s Based on the time-shifting property of the Fourier transform, the corresponding phase factor is e. -j2nπγ Therefore, the Fourier transforms of signals p1(t) and p2(t) are respectively: Where f is the frequency variable, δ(f) is the spectrum of the impulse function, and δ(f-nf) is the frequency response of the impulse function. s ) indicates at frequency nf s Spectral line at; j is the imaginary unit, e -jnπβ This indicates that p1(t) is shifted due to time. The resulting phase factor; e -jnπ(2γ+α) This indicates that p2(t) is due to its own translation. and relative delay γT s The resulting phase factor.

6. The non-uniform dual-pulse modulation method based on TCM according to claim 5, characterized in that: Non-uniform double-pulse periodic signal p based on TCM TCM (t) is represented in the time domain as: p TCM (t)=p1(t)+p2(t) (8) According to the linearity property of the Fourier transform, p TCM The Fourier transform of (t) is P TCM (f) = P1(f) + P2(f): The spectrum of a non-uniform double-pulse periodic signal is discrete, containing DC and harmonic components; the modulation frequency f s The smaller the value, the smaller the interval between harmonic components, and vice versa; when n = 0, the amplitude of the DC component is A0 = β + α, and the phase is zero; when n ≠ 0, the amplitude of each discrete peak in the spectrum is a n The specific expression is as follows: Taking the modulus of the above formula, the amplitude coefficient is obtained as follows: Here, sin(nπβ) reflects the relative amplitude characteristics of the first pulse p1(t) on the nth harmonic; sin(nπα) reflects the relative amplitude characteristics of the second pulse p2(t) on the nth harmonic.

7. The non-uniform dual-pulse modulation method based on TCM according to claim 1, characterized in that: In step two, the transmitted signal used is a linear frequency modulated (LFM) signal, and the time-domain expression of the LFM signal is: Among them, T p It is the pulse width, f c It is the carrier frequency, K r It is the frequency modulation slope, defined as the ratio of the signal bandwidth to the pulse width, i.e., K. r =B / T p The signal is incident on the TCM and undergoes periodic non-uniform double-pulse modulation; the time-domain expression of the echo signal is: r(t)=s(t)·p TCM (t) (13) The spectrum of the echo signal is: Where S(f) is the spectrum of the transmitted signal s(t), and P TCM (f) represents a non-uniform double-pulse periodic signal based on TCM.

8. The non-uniform dual-pulse modulation method based on TCM according to claim 7, characterized in that: In step three, after TCM non-uniform double-pulse periodic modulation, the echo baseband signal is obtained at the receiving end through mixing and filtering processes: Matched filtering is performed on the echo baseband signal to obtain the matched filter output of the LFM signal. The expression is as follows: in, It is the order. This indicates rounding to the nearest whole number, and sinc(·) represents the Singer function.

9. The non-uniform dual-pulse modulation method based on TCM according to claim 8, characterized in that: The output of the matched filter is a series of symmetrical discrete peaks. The spatial distribution of each discrete peak is determined by the modulation frequency of the modulating signal, and the amplitude distribution is determined by the duty cycle and the time delay factor γ. The interval between each discrete peak is: The spacing between adjacent discrete peaks varies with the modulation frequency f s The amplitude coefficient of the zero-order peak value increases with the increase of the value; the amplitude coefficient of the zero-order peak value is: C0=A0=β+α (18) The amplitude coefficient of the non-zero order discrete peak value is: The amplitude distribution of the matched filter output is determined by the duty cycle β, α, delay factor γ, and modulation frequency f. s Joint control.

10. The non-uniform dual-pulse modulation method based on TCM according to claim 1, characterized in that: In step four, suppose there are multiple false targets in the background cells of the real target cell. For the real target cell d, if the target is correctly detected, the detection cost is V. d TP If the target is incorrectly detected, the value is V. d TN For other background units c, c≠d, if the detection result indicates the presence of a target, then the detection cost is V. c FP If the detection result indicates that the target does not exist, the detection cost is V. c FN According to the minimum error probability criterion, V is... c FN =V d TP =0, V c FP =V d TN =1, meaning that correct detection has no cost, and incorrect detection has a cost of 1; therefore, the total cost of detection in one search cycle is: Where 2L is the total length of the background unit.

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