Radar target distance-Doppler feature high-degree-of-freedom modulation method based on optimized pseudo-random coding metasurface

Abstract

The invention provides a radar target distance-Doppler feature high-degree-of-freedom modulation method based on an optimized pseudo-random coding metasurface, and aims at solving the problem that system complexity and modulation flexibility are difficult to consider in an existing metasurface-based RTFM technology. The core mechanism of the method is to destroy the intra-pulse and inter-pulse phase characteristics of the radar by using the phase coding modulation capability of the PMM, and perform high-degree-of-freedom control on the energy of the harmonic wave generated by the reflection of the PMM through the established false target RD grid distribution model and optimization algorithm, thereby realizing the flexible distribution of the original target energy in the RD domain, and improving the reliability of the target. And thus, high-degree-of-freedom modulation of the target RD features is realized. Compared with a widely used PD radar active characteristic modulation method, the new method provided by the invention has the advantages of lower cost, lower system complexity and stronger electromagnetic concealment.

Description

[Technical Field]

[0001] This invention discloses a high-degree-of-freedom modulation method for radar target range-Doppler characteristics based on an optimized pseudo-random coded metasurface, belonging to the field of metasurface electromagnetic control and radar target feature modulation. Specifically, it relates to the modulation of radar target range and velocity characteristics. More specifically, it actively encodes and modulates the phase of the radar echo signal through the phase modulation effect of the metasurface. This allows the controlled echo signal, after passing through the radar signal processing system, to achieve highly controllable distribution of the radar target in the range-Doppler characteristic space, forming a "customized" false electromagnetic situation. This prevents the radar from accurately perceiving the actual target situation in the detected environment. [Background Technology]

[0002] Radar acquires range and velocity information of targets by transmitting and receiving electromagnetic waves; these two parameters are core characteristics for target detection, identification, and tracking. Modern radars widely employ pulse systems, accurately estimating these parameters through time delay and phase difference. Pulse Doppler (PD) radar integrates ranging and velocity measurement capabilities, possesses excellent clutter suppression performance, and is widely used in advanced modern radar systems. These key capabilities form the foundation of radar detection systems and have also prompted researchers to explore further methods for manipulating the multidimensional characteristics of targets.

[0003] In recent years, reconfigurable electromagnetic (EM) metamaterials and metasurfaces have demonstrated remarkable manipulation capabilities of EM waves. By applying external excitation to the active devices integrated within them, metasurfaces can flexibly alter their scattering characteristics, thereby achieving precise control over key attributes such as amplitude, phase, and polarization of reflected waves. This capability has led to the widespread application of reconfigurable metasurfaces not only in wireless communication and holographic imaging but also as a highly promising radar target feature modulation (RTFM) technique. Numerous studies have shown that metasurfaces can embed pre-defined artificial electromagnetic features into radar echoes, influencing the radar signal processing system's calculation of the original real target features, thus indirectly achieving control over the multi-dimensional features of radar targets. Some studies have designed metasurfaces with excellent absorption or polarization conversion properties, which can attenuate the target's radar cross-section (RCS) by tens of becquerels, thereby achieving target stealth. With the introduction of concepts such as Time-coding Metasurfaces (TCMs) and Space-time-coding Metasurfaces (STCMs), the harmonic generation capability of metasurfaces has been greatly enhanced, and their modulation degrees of freedom in RTFM have been further expanded, including range characteristics, velocity characteristics, micro-motion characteristics, imaging characteristics, and azimuth characteristics. Furthermore, besides applications in radar countermeasures, some studies utilize the RTFM effect of metasurfaces as a "feature QR code" recognizable by radar systems for information transmission or to assist in the identification of cooperative targets.

[0004] Among numerous coded waveforms, 1-bit periodic TCM (Transient Coding Mechanism) is widely used because it can achieve good harmonic generation capabilities in low-complexity, easily implemented systems, and each harmonic component has a precise analytical expression model. Researchers use a coding controller with two periodically switching level states as the external excitation source of TCM, causing the TCM to switch intermittently between different scattering states, thereby causing corresponding periodic changes in the electromagnetic properties of radar echoes, such as amplitude and phase, ultimately modulating a large number of spurious scattering peaks in the range dimension or imaging results. However, the harmonics generated by 1-bit periodic TCM always exhibit a linear distribution following the standard Sinc envelope in the frequency domain, resulting in strong regularity in the spurious scattering peaks synthesized from each order of harmonic components in the radar target feature space. Therefore, this limitation greatly restricts the practical application of 1-bit periodic coding schemes in the field of RTFM (Real-Time Frequency Modulation). To improve the flexibility of metasurfaces in RTFM, researchers have further proposed multi-bit coding, time-frequency coding, space-time coding, combined coding, and continuous modulation schemes that differ from discrete coding, based on 1-bit periodic coding. These modulation techniques break the strong regularity of harmonics generated by 1-bit periodic TCM, enabling metasurfaces to achieve new heights in harmonic generation and manipulation capabilities, thus allowing for more flexible and precise modulation of radar target characteristics.

[0005] However, while the aforementioned modulation methods enhance the RTFM capability of metasurfaces, they come at the cost of increased metasurface design and manufacturing costs, as well as a significant increase in overall system complexity, which negatively impacts system stability in practice. Therefore, exploring a metasurface-based RTFM scheme that balances good harmonic manipulation capabilities with low system complexity is currently a research hotspot and a major requirement. On the other hand, most current research on metasurface-based RTFM focuses only on modulation of a single feature dimension of radar targets, lacking research on joint modulation methods for two-dimensional and higher-dimensional features. At present, fully leveraging the potential of TCM to achieve flexible multi-dimensional joint RTFM remains a challenging task. Furthermore, some advanced radar systems are already able to simultaneously correlate target range and velocity characteristics to identify and eliminate insufficiently realistic modulated false targets; therefore, researching synchronous modulation methods for the range and velocity characteristics of targets using metasurfaces is of great significance.

[0006] To this end, combining the principles of radar target range and Doppler feature extraction, this invention first proposes a pseudo-target range-Doppler (RD) domain grid distribution model applicable to periodic modulation schemes. Inspired by the high coding freedom of pseudo-random codes and the multiple reflections and backtracking characteristics of corner reflectors, this invention further proposes a reflection system based on phase-modulated metasurfaces (PMMs). By periodically loading pre-optimized pseudo-random coding excitations onto the PMM using a programmable gate array (FPGA), this system can achieve extremely strong harmonic "customization" generation capabilities at a low system complexity level comparable to 1-bit TCM, thereby realizing high-degree-of-freedom joint modulation of radar target range-velocity characteristics based on the proposed grid model. [Summary of the Invention]

[0007] This invention addresses the challenge of balancing system complexity and modulation flexibility in current metasurface-based RTFM technology. It proposes a high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface. The core mechanism utilizes the phase-coded modulation capability of the PMM to disrupt intra- and inter-pulse phase characteristics of the radar. Through an established pseudo-target RD grid distribution model and optimization algorithm, the energy of harmonics generated by PMM reflections is controlled with high degrees of freedom, enabling flexible allocation of the original target energy within the RD domain, thereby achieving high-degree-of-freedom modulation of the target's RD features. The method employs the following steps to achieve the aforementioned radar target RD feature modulation:

[0008] Step 1: Radar signal parameter estimation

[0009] By utilizing the electronic reconnaissance device integrated into the modulation system, radar transmission signals are intercepted, the location of the enemy radar is determined, and basic parameters of the signal waveform are estimated, including: carrier frequency f. c Signal wavelength λ, pulse width T p Signal bandwidth B, pulse repetition frequency f r , frequency modulation slope K.

[0010] Step 2: Pre-construct a distance-Doppler feature space grid model

[0011] When the PMM accompanying the real target's motion (with the radar radial distance set to R0 and the relative radial velocity set to v0) is not modulated, according to the radar's principle of extracting target range-Doppler features, the real target's RD spectrum Y0(t,f) can be expressed as:

[0012]

[0013] Where t is the time variable, f is the frequency variable, and f d For the Doppler frequency shift of the real target, satisfying f d = 2v0 / λ. M is the number of pulses required for a single phase coherent accumulation by the radar, T r The radar pulse repetition period is t, where j is the imaginary unit. m For a slow-time variable, satisfying t m =2(R0-v0mT) r ) / c, 0≤m≤M-1, where c is the speed of light.

[0014] When the PMM performs periodic phase modulation, based on the correspondence between time-domain periodicity and frequency-domain discreteness, and combined with the multiplicative modulation effect on the incident signal r(t), the periodic phase modulation effect of the PMM causes the original radar signal to expand with 2N new harmonic components, and the interval between each harmonic is equivalent to the modulation frequency f. s (modulation period T) s (the reciprocal of), where, This indicates the number of harmonics entering the half-passband of the receiver's bandpass filter, i.e., the modulated echo.

[0015] Where R(f) is the spectrum of the original echo signal, R(f-nf) s ) represents the spectrum of the generated nth harmonic component, k n Let be the amplitude coefficient, and k0 be the amplitude coefficient corresponding to the 0th harmonic without frequency offset. Since both pulse compression and moving target detection (MTD) are sensitive to phase changes in the echo, the new linear phase terms carried by each harmonic component will significantly impact the radar's RD feature extraction process. For the nth harmonic component, its RD spectrum Y... n (t,f) can be represented as:

[0016]

[0017] Where Y0(t,f) is the original RD spectrum of the target.

[0018] Based on the principle of linear superposition and the linear relationships between distance r and time, velocity v and Doppler, the modulated target RD spectrum Y′(r,v) can be further written as:

[0019]

[0020] Where mod(·) is the modulo operation, reflecting the Doppler ambiguity that may be introduced by the harmonic frequency shift, k nThe amplitude coefficient is denoted by . The harmonic generation effect of PMM significantly alters the RD characteristics of the original target, specifically by discretely redistributing the RD spectrum peak energy of the original target to other locations. For radar, this is equivalent to generating 2N false targets, each with distinct RD characteristics.

[0021] Considering the correspondence between the periodicity in the time domain and the discreteness in the frequency domain, all modulation waveforms with periodic properties will cause the incident wave to be expanded in the form of multi-order harmonic components. Furthermore, according to equation (3), the positional distribution of the false targets generated by each order harmonic in the RD domain depends entirely on the radar pulse repetition frequency f. r and modulation frequency f s Based on this principle, a grid distribution model of the RD domain of a false target under periodic modulation can be pre-constructed. In fact, the RD domain distribution of a false target under any periodic modulation scheme can be described by this grid model. For the modulator, when the radar pulse repetition frequency f... r Once determined, a suitable modulation frequency f is set. s This allows for arbitrary changes to the grid form, thereby determining the RD characteristics of all harmonic-corresponding pseudo-targets. This is crucial for the subsequent high-degree-of-freedom modulation of the pseudo-target RD characteristics in this invention.

[0022] Step 3: Optimization of Periodic Pseudo-Random Encoding Waveform

[0023] According to formula (3), including the zero-order harmonic without frequency shift (corresponding to the real target), the energy of the RD domain target synthesized from the above 2N+1 harmonic components is completely determined by the amplitude coefficient k. n Control. High-energy decoys are often referred to as primary decoys. In most scenarios, due to the generally low signal-to-noise ratio, other low-energy decoys besides the primary decoy may be submerged in noise. Therefore, the distribution of the primary decoy in the RD domain needs to be carefully monitored. According to step two, the pre-construction of the mesh model provides guidance for controlling the RD domain distribution of decoys under periodic modulation. The key to achieving flexible modulation of RD features is to achieve flexible control of the harmonic energy of each order. Furthermore, based on the high reconfigurability of periodic pseudo-random coding, this step introduces an optimization algorithm to enable the system to have high-degree-of-freedom harmonic control and generation capabilities.

[0024] By periodically inputting pseudo-random coded excitation into the PMM, the resulting phase modulation effect, its time-domain waveform p(t) and spectrum P(f), can be expressed as:

[0025]

[0026] Where δ(·) represents the unit impulse function, g represents the g-th period of the coded waveform p(t) in the time domain, K represents the number of pseudo-random symbols in a single period, τ is the duration of each symbol, and the modulation period T is... s Satisfy T s =Kτ. b k This represents the phase term corresponding to the k-th symbol within a single period. For a pseudo-random sequence in 1-bit mode, b is defined as... k ∈[e j0 ,e jπ For 2-bit mode, define b k ∈[e j0 ,e jπ / 2 ,e jπ ,e j3π / 2 ].

[0027] Since it is also a periodic signal, P(f) exhibits the spectral form of multiple discrete harmonics, and the frequency interval between the harmonics is also the modulation frequency f. s The amplitude coefficient k of each harmonic n The expression can be written as:

[0028]

[0029] The above formula means that by changing the pseudo-random coding sequence c = [b1, b2, ..., b] within a single period... K This allows for flexible control of harmonic energy at each order. Furthermore, the number of definable forms of the coded sequence c is exponentially positively correlated with the number of symbols K in a single period; in 1-bit mode, the number of definable forms of c is 2^k. K When K is 32, the number of definable forms of c is close to 4.3 billion.

[0030] By defining different periodic pseudo-random code sequences, PMM can flexibly distribute the incident wave energy to each harmonic component. Therefore, obtaining a coding sequence c that meets the requirements is the key to achieving artificial control of harmonic energy. Genetic algorithm (GA) is an intelligent optimization algorithm that uses genetic mechanism to simulate the law of natural selection. It is widely used to solve discrete optimization problems in finite solution space and is very suitable for this coding optimization problem. According to formula (6), the second half of the multiplication symbol is exactly equivalent to the K-point discrete Fourier transform (DFT) C(k) of c, 0≤k≤K-1, which is of great significance for the construction of the fitness function. In order to make the most of the high coding flexibility of pseudo-random codes, the fitness function is defined as:

[0031]

[0032] Among them, f i (c) is the fitness subfunction, w iGiven its corresponding weight factor, the total fitness function It consists of I sub-functions. According to the above analysis, these sub-functions are all related to the DFT result C(k). By setting appropriate function forms and weighting factors, the encoded sequence c will eventually converge to the optimal result that can simultaneously satisfy multiple optimization objectives, that is, to achieve the "customized" generation effect of harmonics.

[0033] Step 4: Energy Allocation of RD Feature Space Grid Points

[0034] The pseudo-random coding sequence c obtained in step three is sent to the FPGA. The FPGA periodically converts the coding sequence into an excitation voltage to drive the PMM to generate the corresponding phase state switching, thereby adding multiplicative phase modulation to the incident radar signal. After the modulated radar signal is processed by the radar system pulse compression and MTD, the grid points in the grid model pre-constructed in step two will generate corresponding RD pseudo-target spectral lines, and the energy of each order of pseudo-target satisfies formula (6), that is, effectively realizing the radar target range-Doppler feature high degree of freedom modulation proposed in this invention.

[0035] The beneficial effects of this invention are as follows:

[0036] First, an innovative RD domain false target grid distribution model is proposed, which serves as a generalized model and provides guidance for metasurface radar target feature modulation using periodic modulation schemes.

[0037] Second, compared with the widely used PD radar active feature modulation method, the new method proposed in this invention has lower cost, lower system complexity and stronger electromagnetic stealth.

[0038] Third, by introducing a genetic algorithm and designing a fitness function to control the optimization direction of the pseudo-random code, the flexibility and reconfigurability of TCM are fully utilized, enabling the system to have high degree of freedom in harmonic control and RD feature modulation while maintaining low system complexity. [Attached Image Description]

[0039] Figure 1 The flowchart shows a high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface.

[0040] Figure 2 This is a schematic diagram of the RD feature space pseudo-target grid distribution model.

[0041] Figure 3 This is the basic form of a periodic pseudo-random encoded time-domain waveform.

[0042] Figure 4 This is a schematic diagram of a pseudo-random coding optimization model based on a genetic algorithm.

[0043] Figure 5(a) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 16 and n0 = [3,5].

[0044] Figure 5(b) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 16 and n0 = [3,5,8].

[0045] Figure 5(c) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 16 and n0 = [3,5,8,11].

[0046] Figure 5(d) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 32 and n0 = [2,7].

[0047] Figure 5(e) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 32 and n0 = [2,7,8].

[0048] Figure 5(f) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 32 and n0 = [2,7,8,10].

[0049] Figure 5(g) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 64 and n0 = [6,9].

[0050] Figure 5(h) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 64 and n0 = [6,9,13].

[0051] Figure 5(i) shows the harmonic generation optimization effect of 1-bit PMM when the number of symbols K = 64 and n0 = [6,9,13,18].

[0052] Figure 5(j) shows the harmonic generation optimization effect of 2-bit PMM when the number of symbols K = 64 and n0 = [-21, -2].

[0053] Figure 5(k) shows the harmonic generation optimization effect of 2-bit PMM when the number of symbols K = 64 and n0 = [-21, -2, 9].

[0054] Figure 5(l) shows the harmonic generation optimization effect of 2-bit PMM when the number of symbols K = 64 and n0 = [-21, -2, 9, 13].

[0055] Figure 6(a) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =101kHz and n0=[3,5,8,11].

[0056] Figure 6(b) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =101kHz and n0=[2,7,8,10].

[0057] Figure 6(c) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =101kHz and n0=[6,9,13,18].

[0058] Figure 6(d) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =52kHz and n0=[3,5,8,11].

[0059] Figure 6(e) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =52kHz and n0=[2,7,8,10].

[0060] Figure 6(f) shows a 1-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =52kHz and n0=[6,9,13,18].

[0061] Figure 6(g) shows a 2-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =52kHz and n0=[-21,-2,9,13].

[0062] Figure 6(h) shows a 2-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when = 52kHz and n0 = [-8, -7, -6, 10].

[0063] Figure 6(i) shows a 2-bit PMM with symbol number K = 64 and modulation frequency f. s The modulation effect of radar target RD features when =52kHz and n0=[-16,4,7,9].

Detailed Implementation Methods

[0064] To better understand the method of the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0065] This invention applies to pulse Doppler radars employing linear frequency modulated (LFM) signals. Taking an X-band radar system as an example, the radar transmits a LFM pulse signal with a center frequency of 10.3 GHz, a bandwidth of 20 MHz, a pulse width of 50 μs, and a pulse repetition frequency of 10 kHz. The radar coherently accumulates 64 pulses in one pass. Assuming the real target is located 4 km from the radar, and for ease of velocity dimension analysis, it is assumed to be stationary relative to the radar, with the PMM mounted on the real target.

[0066] This invention relates to the following specific steps, the specific process of which is as follows: Figure 1 As shown.

[0067] Step 1: Radar signal parameter estimation

[0068] In practical applications, the joint assistance of electronic reconnaissance systems and intelligence reconnaissance systems is required to provide data support for the subsequent pre-construction of the grid model. Using electronic reconnaissance systems and intelligence reconnaissance, basic parameters of radar transmission signals and targets are obtained, including the carrier frequency f. c =10.3GHz, pulse width T p =50μs, signal bandwidth B=20MHz, pulse repetition frequency f r =10kHz, the signal wavelength λ = c / f is obtained through calculation. c = 2.92cm, frequency modulation slope K = B / T p =4×10 11 Hz / s, where c is the speed of light, c = 3 × 10⁻⁶ 8 m / s.

[0069] Step 2: Pre-construct a distance-Doppler feature space grid model

[0070] From the perspective of intra-pulse and inter-pulse considerations, the two-dimensional time-domain expression of the LFM pulse waveform used by PD radar can be given by the following formula:

[0071]

[0072] Where t is the time variable, j is the imaginary unit, and t m T represents a slow-time variable. r The pulse repetition frequency f r The reciprocal of , R0 is the true target distance, v0 is the true target velocity, and m represents the m-th pulse emitted by the PD radar, then t m It can be represented as:

[0073]

[0074] Echo r′(t,t) periodically modulated by PMM m This can be represented as:

[0075]

[0076] Where p(t,t) m f is the two-dimensional time-domain form of periodic modulation. s For modulation frequency, k represents the number of harmonics entering the half-passband of the receiver's bandpass filter. n This is the amplitude coefficient. Therefore, the echo signal r′(t,t) m The spectrum R′(f) of ) can be expressed as:

[0077]

[0078] Where R(f) is r(t,t) m The corresponding spectrum, P(f) is p(t,t) m The corresponding spectrum, This represents the convolution operation.

[0079] For the nth harmonic component, its RD spectrum can be expressed as:

[0080]

[0081] Based on the principle of linear superposition and the linear relationship between distance r-time and velocity v-Doppler, the modulated target RD spectrum can be further written as:

[0082]

[0083] Here, mod(·) represents the modulo operation, reflecting the Doppler blurring that may be introduced by the harmonic frequency shift. The harmonic generation effect of PMM significantly changes the RD characteristics of the original target, specifically by discretely redistributing the RD spectrum peak energy of the original target to other locations. For radar, this is equivalent to generating 2N false targets with different RD characteristics.

[0084] Formula (13) establishes the mapping relationship between the harmonic order and the false RD characteristics of the corresponding false targets. The positional distribution of the false targets generated by each harmonic order in the RD domain depends entirely on the radar pulse repetition frequency f. r and modulation frequency f s Based on this principle, this step involves pre-constructing a range-Doppler feature space grid model. Different modulation frequencies can directly affect the distribution of false targets in the RD feature space, such as... Figure 2 As shown. When the modulation frequency f s As the distance increases, the false target range interval increases linearly, corresponding to the grid lines gradually thinning in the range dimension. Furthermore, the false target velocity interval depends on f. s For f r The result of the modulo operation depends on f.s / f r The decimal part of the value is positively linearly correlated with this value. Based on this principle, a distance-Doppler feature space grid model for the false target is pre-constructed.

[0085] Step 3: Optimization of Periodic Pseudo-Random Encoding Waveform

[0086] The periodic pseudo-random code is the core of the proposed method. Taking 1-bit encoding as an example, its basic form in the time domain waveform is as follows: Figure 3 As shown. By periodically inputting pseudo-random coded excitation into the PMM, the resulting phase modulation can be expressed as:

[0087]

[0088] Where g represents the g-th period of the encoded waveform p(t) in the time domain, K represents the number of pseudo-random symbols in a single period, τ is the duration of each symbol, and T is the modulation period. s Satisfy T s =Kτ. b k This represents the phase term corresponding to the k-th symbol within a single period. For a pseudo-random sequence in 1-bit mode, b is defined as... k ∈[e j0 ,e jπ For 2-bit mode, define b k ∈[e j0 ,e j π / 2 ,e jπ ,e j3π / 2 ].

[0089] The amplitude coefficient of the nth harmonic component can then be expressed as:

[0090]

[0091] Figure 4 The specific process of solving the target coding sequence c using GA is demonstrated. c is regarded as the gene of the population, Z is the total number of the population, and the population is iteratively optimized through continuous selection, crossover and mutation. The fitness will continuously improve and gradually converge to the optimal result. Among them, the fitness evaluation step is the core of the whole algorithm, which directly determines the optimization direction of the coding sequence c. According to formula (15), the second half of the multiplication symbol is exactly equivalent to the K-point DFT C(k) of c, 0≤k≤K, which is of great significance for the construction of the fitness function. In order to make the most of the high coding flexibility of pseudo-random codes, the fitness function is defined as:

[0092]

[0093] Among them, f i(c) is the fitness subfunction, w i Given its corresponding weight factor, the total fitness function It consists of I sub-functions. According to the above analysis, these sub-functions are all related to the DFT result C(k). By setting appropriate function forms and weighting factors, the encoded sequence c will eventually converge to the optimal result that can simultaneously satisfy multiple optimization objectives, that is, to achieve the "customized" generation effect of harmonics.

[0094] The three sub-objective functions are defined as follows:

[0095]

[0096] Here, n0 is the set of target harmonic orders, and std(·) represents the standard deviation operation. Specifically, f1(c) is used to ensure that the target harmonics have a high total energy, f2(c) is used to suppress the energy of the remaining harmonics, and f3(c) is used to ensure that the energy of the target harmonics is relatively average. Therefore, the final optimization goal is to concentrate the main energy on the specified order harmonics and keep their amplitudes relatively consistent.

[0097] Set the weighting factors w1 to 0.5, and w2 and w3 to 1.5. Figures 5(a)-5(l) The optimization effect of PMM on harmonic generation is shown under different symbol numbers K, different target harmonics n0, and different bit modes. Figures 5(a), 5(d), 5(g), and 5(j) show that when the number of target harmonics is small, even with a low symbol number K, relatively ideal optimization results can be achieved. When the number of target harmonics increases further, good results can be maintained under high K values; however, for low symbol numbers K, large-energy unspecified order harmonics will appear. Therefore, in practical applications, ensuring that the value of K meets the optimization requirements is a key focus. Furthermore, Figures 5(a)-5(i) This reflects the optimization effect in 1-bit mode. Since p(t) is a real signal in this mode, the distribution of harmonics is always symmetrical about the 0th harmonic. Figures 5(j)-5(l) The results show that the 2-bit modulation mode can generate asymmetrically distributed harmonics, and even generate only the main harmonics at negative frequencies. This breaks the regularity of symmetrical harmonic distribution in the original 1-bit mode, further improving the flexibility of harmonic generation. Overall, Figures 5(a)-5(l) The results shown well reflect the potential of periodic pseudo-random coding in the generation of highly customizable harmonics with high degrees of freedom, and also demonstrate that... Figure 4 The effectiveness of the GA model shown in solving the optimization problem of coded sequences and harmonic generation is demonstrated.

[0098] Step 4: Energy Allocation of RD Feature Space Grid Points

[0099] The number of symbols K in a single cycle is fixed at 64. Figures 6(a)-6(i) The modulation effect of PMM on radar target RD features under different optimized coding excitations is demonstrated. The white squares indicate the main false targets generated by target harmonics, whose energy can be several to tens of times higher than that of other false targets. In 1-bit mode, the target harmonic order sequence n0 is set to [3 5 8 11], [27 8 10], and [6 9 13 18], respectively. When the PMM modulation frequency f is set... s 10.1f r =101kHz, Figures 6(a)-6(c) The effects of three corresponding RD feature modulation methods are demonstrated. Results show that, under the same grid pattern, PMM can control the energy distribution of the false target at each grid point by changing the target harmonic order sequence n0, thereby synthesizing a high-energy main false target at a specified location in the RD feature space. Keeping n0 constant, when the PMM modulation frequency f... s Change to 5.2f r =52kHz, Figures 6(c)-6(f) The corresponding RD feature modulation effect is shown. According to formula (13), when the modulation frequency f s The radar pulse repetition frequency f is 52kHz. r At 10kHz, the distance spacing of the RD dummy targets synthesized from adjacent harmonics is 19.5m, and the velocity spacing is 29.2m / s. When the modulation frequency f... s The radar pulse repetition frequency f is 101 kHz. r At 10kHz, the distance interval of the RD pseudo-target synthesized by adjacent harmonics is 37.875m, and the velocity interval is 14.6m / s. The simulation and experimental results are consistent with the theoretical analysis, reflecting the accuracy of the proposed mesh model.

[0100] In 2-bit mode, the target harmonic order sequence n0 is set to [-21 -2 9 13], [-8 -7 -6 10], and [-16 4 7 9], respectively. When the PMM modulation frequency f is set... s 5.2f r =52kHz, Figures 6(g)-6(i)The simulation results demonstrate the effects of three different RD feature modulation methods. Unlike the symmetrical distribution of the false targets centered on the real target under 1-bit phase modulation, it is foreseeable that, due to the asymmetric harmonic spectrum generated by 2-bit phase modulation, a high-energy main false target is synthesized only in the grid points corresponding to the target harmonics. This reflects the superior performance of 2-bit PMM in terms of feature modulation flexibility. Overall, the simulation results are consistent with the theoretical analysis, further verifying the universality of the false target RD domain grid distribution model for periodically modulated waveforms and fully reflecting the flexibility of the proposed RD feature modulation method. Furthermore, it is noteworthy that, after phase modulation by PMM, the energy of the real target is dispersed to a large number of false targets, resulting in a significant attenuation of its RD spectrum peaks, indicating a certain degree of electromagnetic stealth effect.

[0101] It is evident from the above experimental results that the position, velocity, number, and energy intensity of the PD radar false targets generated based on the optimized pseudo-random coding PMM can all be controlled by the parameters of the coded waveform. By setting an appropriate optimized coding waveform, the PD radar can achieve flexible target feature modulation effects to form diverse false electromagnetic situations, which is consistent with the theoretical analysis and also proves the effectiveness of the method proposed in this invention.

Claims

1. A high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface, characterized in that: Includes the following steps: Step 1: Radar signal parameter estimation; using the electronic reconnaissance device integrated in the modulation system, intercept the radar transmission signal, locate the azimuth of the enemy radar, and estimate the basic parameters of the signal waveform from it. Step 2: Utilize the phase coding and modulation capability of PMM to destroy the intra-pulse and inter-pulse phase characteristics of the radar, and pre-construct a range-Doppler feature space grid model; Step 3: Optimization of periodic pseudo-random coding waveform; Step 4: Energy allocation of grid points in the RD feature space.

2. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 1, characterized in that: In step one, the basic parameters include: carrier frequency f c Signal wavelength λ, pulse width T p Signal bandwidth B, pulse repetition frequency f r , frequency modulation slope K.

3. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 1, characterized in that: In step two, when the PMM accompanying the real target's motion is not modulated, according to the radar's principle of extracting target range-Doppler features, the real target's RD spectrum Y0(t,f) is expressed as: Where t is the time variable, f is the frequency variable, and f d For the Doppler frequency shift of the real target, satisfying f d = 2v0 / λ; M is the number of pulses required for a single phase coherent accumulation by the radar, T r The radar pulse repetition period is t, where j is the imaginary unit. m For a slow-time variable, satisfying t m =2(R0-v0mT) r ) / c, 0≤m≤M-1, where c is the speed of light.

4. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 3, characterized in that: When the PMM performs periodic phase modulation, based on the correspondence between time-domain periodicity and frequency-domain discreteness, and combined with the multiplicative modulation effect on the incident signal r(t), the periodic phase modulation effect of the PMM causes the original radar signal to expand with 2N new harmonic components, and the interval between each harmonic is equivalent to the modulation frequency f. s That is, the modulation period T s The reciprocal of, where, This indicates the number of harmonics entering the half-passband of the receiver's bandpass filter, i.e., the modulated echo. Where R(f) is the spectrum of the original echo signal, R(f-nf) s ) represents the spectrum of the generated nth harmonic component, k n is the amplitude coefficient, and k0 is the amplitude coefficient corresponding to the 0th harmonic without frequency offset.

5. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface according to claim 4, characterized in that: For the nth harmonic component, the RD spectrum Y n (t,f) is represented as: Where Y0(t,f) is the original RD spectrum of the target.

6. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 5, characterized in that: Based on the principle of linear superposition and the linear relationships between distance r and time, velocity v and Doppler, the modulated target RD spectrum Y′(r,v) can be further written as: Where mod(·) is the modulo operation, k n The amplitude coefficient; According to equation (3), the positional distribution of false targets generated by each harmonic in the RD domain depends entirely on the radar pulse repetition frequency f. r and modulation frequency f s A grid distribution model of the pseudo-target RD domain under periodic modulation is pre-constructed.

7. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 1, characterized in that: In step three, the time-domain waveform p(t) and spectrum P(f) of the phase modulation effect resulting from the periodic input of pseudo-random coded excitation to the PMM are expressed as follows: Where δ(·) represents the unit impulse function, g represents the g-th period of the coded waveform p(t) in the time domain, K represents the number of pseudo-random symbols in a single period, τ is the duration of each symbol, and the modulation period T is... s Satisfy T s =Kτ;b k This represents the phase term corresponding to the k-th symbol within a single period. For a pseudo-random sequence in 1-bit mode, b is defined as... k ∈[e j0 ,e jπ For 2-bit mode, define b k ∈[e j0 ,e jπ / 2 ,e jπ ,e j3π / 2 ].

8. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 7, characterized in that: P(f) is represented by the spectrum of multiple discrete harmonics, and the frequency interval between the harmonics is also the modulation frequency f. s The amplitude coefficient k of each harmonic n The expression is written as: By changing the pseudo-random coding sequence c = [b1, b2, ..., b] within a single period, K This allows for flexible control of harmonic energy at each order; furthermore, the number of definitional forms of the coded sequence c is exponentially positively correlated with the number of symbols K in a single period. In 1-bit mode, the number of definitional forms of c is 2. K .

9. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface as described in claim 8, characterized in that: According to formula (6), the latter half of the multiplication sign is exactly equivalent to the K-point discrete Fourier transform C(k) of c, 0≤k≤K-1. The fitness function is defined as: Among them, f i (c) is the fitness subfunction, w i Given its corresponding weight factor, the total fitness function It consists of I sub-functions; these sub-functions are all related to the DFT result C(k). By setting appropriate function forms and weight factors, the encoded sequence c will eventually converge to the optimal result that can simultaneously satisfy multiple optimization objectives.

10. The high-degree-of-freedom modulation method for radar target range-Doppler features based on an optimized pseudo-random coded metasurface according to claim 9, characterized in that: In step four, the pseudo-random coding sequence c obtained by optimization in step three is sent to the FPGA. The FPGA periodically converts the coding sequence into an excitation voltage to drive the PMM to generate the corresponding phase state switching, thereby adding multiplicative phase modulation to the incident radar signal. After the modulated radar signal is processed by the radar system pulse compression and MTD, the grid points in the grid model pre-constructed in step two will generate the corresponding RD false target spectral lines, and the energy of each order of false target satisfies formula (6).

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