Anti-radar based on metasurface

Abstract

In advanced multi-static radar (MSR), multidimensional information from target echo signals is collected by different receivers to enable precise localization using various algorithms. Owing to its efficient target localization and tracking capability, MSR has found wide applications in sensing, military operations, aviation, and aerospace. Multi-static nature of MSR also makes it difficult to counter. Here, we propose an anti-radar methodology based on space-time-coding metasurface (STCM) to counter MSR. By designing the physical characteristics of STCM and developing adaptive and robust electronic countermeasure (ECM) control strategies, we realize a cost-effective, miniaturized and low-complexity ECM system with the flexible controlling capabilities. Under non-cooperative and dynamic ECM scenarios, the proposed method shows exceptional concealment and deception performance. To validate the methodology, we develop a prototype of the STCM-based anti-MSR system and successfully demonstrate its ability to neutralize various MSR technologies. The proposed method is expected to find practical applications in the anti-MSR scenarios.

This study proposes an anti-radar methodology based on space-time-coding metasurface to counter multi-static radar, which enables a cost-effective, miniaturized, and low complexity electronic countermeasure system.

Introduction

Radar is one of the most important electronic devices, which can detect and track various targets by radiating electromagnetic (EM) waves and receiving echo signals of the targets, and thus it has been widely used in sensing, military, aviation, and navigation fields^{1, 2, 3–4}. The development and application of multi-static radar (MSR) in recent years has overcome many of the disadvantages of the traditional mono-static radar. Usually, MSR uses a transmitter to illuminate targets and multiple receivers to detect the reflected or backscattered signals from targets, in which the multiple receivers are spatially separated from the transmitter^{5, 6, 7, 8, 9–10}. Here, the multiple receivers are processed in concert to provide better target position and velocity estimation performance, and the decentralized layout provides robust anti-jamming capability and survivability. With its significant advantages, the MSR system has been widely used in the accurate localization of targets based on diverse localization algorithms. For example, the transmitter radiates signals, and multiple receivers resolve the position and velocity of the target through the arrival time difference and frequency difference of echo signals^{11, 12, 13, 14, 15, 16, 17, 18, 19, 20–21}; or multiple receivers are collaborated with each other in detecting and fusing data to achieve localization and tracking of the target^{22, 23, 24, 25, 26–27}.

In specific scenarios such as military tasks, security protection, and facility concealment, advanced radar localization methods make it extremely easy to expose the target, and hence, anti-radar and electromagnetic stealth are in urgent demand. In current anti-radar methods, active jammers are commonly used to emit false signals or noise to confuse the MSR systems^{28, 29, 30, 31–32}. However, traditional active jammers are usually unable to sense and acquire information from passive receivers of MSR, preventing them from achieving omnidirectional interference to multiple receivers. This results in the interference failure and makes them vulnerable to suppression^{33, 34–35}. Moreover, the active jammers usually require expensive and bulky hardware (e.g., oscillators, nonlinear mixers, and wideband power amplifiers), making them difficult to deploy on drones and prone to active exposure³⁶. On the other hand, microwave absorbers offer advantages such as lightweight, low power consumption, easy integration, and efficient signal absorption^37,38. Nevertheless, since their coverage over certain areas on target (e.g., motors, propellers, and GPS antennas) is limited, the platform remains susceptible to detection by MSR. Meanwhile, some studies have analyzed the range and speed deception effects of time-coding metasurfaces (TCMs) on mono-static radars^39,40. However, these studies are limited to the theoretical analysis and simulation stage, and the isotropic characteristics of TCM cannot counter the distribution characteristics of MSR. Currently, due to the distributed architecture, anti-jamming capability, and various precise localization features of MSR, effective electronic countermeasure (ECM) technology has not yet been developed against MSR. Considering the limitations of the existing countermeasure methods, it is urgent and necessary to propose an effective ECM method for MSR, which should be cost-effective, miniaturized, low complexity, and capable of flexible regulations in the space and frequency domains.

In recent years, the concept of space-time-coding metasurface (STCM) has been proposed based on programmable metasurface^41,42. STCMs allow for the dynamic switching of digital element states, enabling simultaneous manipulation of EM waves in both the space and frequency domains. These features have led to a range of exciting applications, including beam steering and shaping^{43, 44, 45–46}, multiplexed wireless communication⁴⁷, sensing⁴⁸, and time-varying vortex generation⁴⁹, among others^{50, 51, 52, 53, 54, 55, 56, 57–58}. The abilities of STCMs to simultaneously manipulate the EM waves in space and frequency domains offer promising potential for countering MSR. However, previous studies have mainly focused on applying STCMs to cooperative systems, whose functionality remains static and is limited to a single incident angle. To address the challenges posed by non-cooperative, dynamic, and complex environments in ECM application, some specific advancements to the existing STCM framework are required, e.g., maintaining stable amplitude and phase characteristics over a large angle range at the element level and designing a tailored ECM control strategy. With these advancements, STCM can retain robust ECM ability even under rapid movement and multi-angle incidence conditions.

To address the technical gap in effective countermeasures against MSR, here we propose a STCM-based countermeasure method for MSR (see Supplementary Note 1 for details). STCM is affixed to the target to modulate the echo signal. By carefully designing the element characteristics and ECM control strategy, the proposed method can simultaneously manipulate the target’s echo properties in both space and frequency domains. As a result, each receiver will capture the harmonics, rendering the MSR localization methods ineffective. To overcome the limitations of traditional STCM architectures, the STCM element must have better oblique incidence stability and higher phase degree of freedom, thereby ensuring the relatively stable and precise scattering control under non-cooperative, dynamic, and wide-angle incident ECM scenarios. Furthermore, we analyze the distributed architecture, anti-jamming characteristics, and various localization methods of MSR. Based on this analysis, we develop an efficient and flexible space-frequency joint countermeasure strategy to suppress the fundamental wave and ensure a dense distribution of harmonics. The strategy can achieve target stealth and effectively jam the MSR systems, even without the ability to sense the passive receivers. The proposed ECM strategy demonstrates excellent robustness, maintaining effective performance even in the presence of phase and amplitude errors or fluctuations within STCM’s elements, and in complex scenarios involving multiple transmitters and receivers. To validate the anti-MSR performance, we conduct indoor static and outdoor dynamic ECM experiments, demonstrating the superior performance of this approach. Compared to the existing jamming methods, the proposed approach offers unique advantages of cost-effectiveness, miniaturization, low complexity, and flexible space-frequency modulations (see Supplementary Note 2 for more details), which may find broad applications in fields such as military operations, security protection, and facility concealment.

Results

STCM space-frequency joint ECM control strategy

An MSR system usually consists of a transmitter and multiple receivers. The transmitter actively emits signals, which are scattered back to the receivers after reaching the target. The multiple receivers work together to locate the target using echo signals. Figure 1 conceptually illustrates a scenario of the STCM-based anti-MSR, in which STCM is composed of a 2D programmable array of meta-elements integrated with PIN diodes. By loading different control voltages to PIN diodes, the reflection phases of the meta-elements can be switched periodically at time $T_0=1/f_0$ according to a specially designed STC matrix. A set of discrete harmonic spectra with frequency interval f₀ can be generated. When a signal with carrier frequency f_c impinges on the metasurface, the discrete harmonic spectra will be shifted around the carrier central frequency f_c, and the harmonics have different spatial domain properties.

Fig. 1 Conceptual illustration of the space-time-coding metasurface (STCM)-based anti-multi-static radar (MSR). [Images not available. See PDF.]

In this scenario, STCMs are affixed to the target. By applying different control voltages from the FPGA to the STCM according to the designed STC matrix, the echo signals of the target arriving at the receivers will be changed. Hence, the multiple receivers have difficulty locking on the real target.

In non-cooperative, dynamic, and complex ECM scenarios, the STCM element should be specially designed, and a more flexible space-frequency joint ECM control strategy should be developed to achieve robust countermeasures against the MSR systems. To this end, we design and fabricate an STCM prototype comprising 16 × 16 programmable elements, as shown in Fig. 2a (see Supplementary Note 3 for more details). Each element consists of a hexagonal metal patch and two bias lines fixed to a grounded dielectric substrate. The power capacity of the element can meet most ECM scenarios (see Supplementary Note 4 for details). By optimizing the scattering characteristics of STCM, suppressing the fundamental wave, and ensuring a dense distribution of harmonics, we introduce frequency shifts on the distributed passive receivers, as shown in Supplementary Note 5 for more details. This ECM control strategy enables both stealth and blind jamming against the MSR systems, even without detection of the passive receivers. The optimized STC matrix is presented in Fig. 2b, and the corresponding measured scattering pattern under normal incidence is shown in Fig. 2c. Meanwhile, we must ensure relatively stable amplitude and phase characteristics of the STCM elements. As shown in Fig. 2d, e, the amplitude and phase remain relatively stable within the incident angle range of 45° relative to transmitter. Figure 2f–h presents simulated scattering patterns of STCM using the STC matrix shown in Fig. 2b, under dynamic target movement and oblique incidence angles of 15°, 30°, and 45°. We note that stable scattering characteristics are maintained at 15° and 30°. When the transmitter illuminates STCM at an angle of 45°, an increase in the energy of the fundamental wave is observed near 45°. Hence, this strategy enables either reduction of echo energy for concealment (Receiver 1 in Fig. 2g) or generation of false harmonics for deception (Receiver 2 in Fig. 2g). As the target dynamically moves, even with phase and amplitude fluctuations at element’s level, the dense harmonic distribution remains sufficient to confuse the multiple receivers under the proposed ECM control strategy. Consequently, this strategy demonstrates excellent robustness, maintaining effective countermeasure performance despite the phase and amplitude errors or fluctuations in the STCM elements, or in complex scenarios involving multiple transmitters and receivers.

Fig. 2 Space-time-coding metasurface (STCM) space-frequency joint electronic countermeasure (ECM) control strategy. [Images not available. See PDF.]

a Photograph of the 2-bit STCM prototype. b The optimized STC matrix, in which the four colors represent four phases. c The corresponding measured scattering patterns, in which the energy of the fundamental frequency is suppressed in all directions, and six harmonics are generated in multiple directions. d, e The phase and amplitude of the element for incident angles from 0° to 60° at the desired frequency, and remain relatively stable within the range from 0° to 45°. f–h Scattering patterns of STCM when the transmitter illuminates the target respectively at 15°, 30°, and 45°, considering the phase and amplitude deviations.

Based on the designed STCM and ECM control strategy, we affix STCM on the target, and change the distribution of echo signals in both the space- and frequency domains by the STC modulations. In Fig. 1, the transmitter emits a signal of frequency f_c, which arrives at Receivers 1, 2, and 3 at frequencies $f_{\mathrm{c}}+\mathrm{\Delta }{f}_1$ , $f_{\mathrm{c}}+\mathrm{\Delta }{f}_2$ and $f_{\mathrm{c}}+\mathrm{\Delta }{f}_3$ , superimposed with a frequency offset. Multiple false targets emerge in the space, and hence, the real target position is difficult to acquire.

Principles of MSR and STCM-based anti-MSR

Below, we analyze the principles of multiple methods of MSR, including frequency difference of arrival (FDOA), time difference of arrival (TDOA), multiple receivers detection fusion (MRDF), and the STCM-based anti-MSR. As shown in Fig. 3, we investigate the countermeasure effect of STCM on the MSR system using numerical simulations (see “Methods” section for more details). In Fig. 3, the positions of the transmitter and receivers are (0, 0) km, (2.5, 0) km, (5, 0) km, and (7, 0) km, respectively, with the receiving angles relative to STCM being −26.56°, 18.45°, and 45°, respectively. When the transmitter illuminates STCM, the far-field scattering pattern is presented in Supplementary Fig. 8. Therefore, the frequency offsets of Receiver 1, Receiver 2, and Receiver 3 in Fig. 3 are +3f₀, −2f₀ and -f₀, respectively (see Supplementary Note 6 for more details).

Fig. 3 Principles and simulation results of MSR and space-time-coding metasurface (STCM)-based anti-multi-static radar (MSR). [Images not available. See PDF.]

a–d The FDOA localization scheme and the simulated results. Signal arrival frequency (c) and FDOA localization results (a) without the STC modulation. Signal arrival frequency (d) and FDOA localization results (b) with the STC modulation. e–h The TDOA localization scheme and the simulated results. Signal cross-correlation results (g) and TDOA localization results (e) without the STC modulation. Signal cross-correlation results (h) and TDOA localization results (f) with the STC modulation.

The MSR FDOA localization scenario and principle are shown in Fig. 3a. When a target is moving, there is a Doppler frequency shift f_di in the echo signal compared to the transmitted signal. Due to different relative positions between the receivers and the target, the Doppler frequency shift of the echo signals received by the receivers varies. The target’s speed and position can be determined by jointly analyzing the frequency differences of signals received by multiple receivers. Let the coordinates of the i-th passive receiver be $\left(x_i,y_i,z_i\right)$ , the coordinates of the target be $\left(x,y,z\right)$ , and the speed of the target be $\left(\stackrel{°}{x},\stackrel{°}{y},\stackrel{°}{z}\right)$ . The frequency difference of the echo signals between the i-th receiver and receiver 1 is:

1

$$\mathrm{\Delta }{f}_{\mathrm{d}}^{i,1}=\frac{f_{\mathrm{c}}}{c}\left(v_i-v_1\right)$$

2

$$v_i=\frac{\left(x-x_i\right)\stackrel{°}{x}+\left(y-y_i\right)\stackrel{°}{y}+\left(z-z_i\right)\stackrel{°}{z}}{\sqrt{{\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2+{\left(z-z_i\right)}^2}}$$

By jointly solving the system of Eq. (1), the target’s speed and position can be determined. The system of equations can be understood as follows: the frequency difference between two receivers defines an FDOA line or surface, and multiple FDOA lines or FDOA surfaces intersecting at one point is the actual position and speed of the target. Figure 3c shows the signal spectra of three receivers when STCM is not applied. The localization results are shown in Fig. 3a, where multiple FDOA lines intersect at the target’s position. When STCM is modulated, the frequency of the signal received by each receiver includes both the harmonic frequency component of the STC modulation and the Doppler frequency component of the moving target. Therefore, Eq. (1) can be rewritten as (see Supplementary Note 7 for more details):

3

$$\mathrm{\Delta }{f}_{\mathrm{d}}^{i,1}=\frac{f_{\mathrm{c}}}{c}\left(v_i-v_1\right)+\mathrm{\Delta }{f}_i-\mathrm{\Delta }{f}_1$$ where $\mathrm{\Delta }{f}_i$ represents the frequency offset of the i-th receiver. When STCM is applied, the signal spectrum of each receiver is shown in Fig. 3d, and the localization results are presented in Fig. 3b, in which the FDOA lines do not intersect at the target location. In contrast to Eq. (1), Eq. (3) yields an erroneous solution.

The MSR TDOA localization scenario and principle are shown in Fig. 3e. Due to different relative distances between the target and the receivers, the echo signals arrive at the receivers with different delays. The target position is determined using the arrival time difference of the signals received by multiple receivers, according to the following relational equation.

4

$$\sqrt{{\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2+{\left(z-z_i\right)}^2}-\sqrt{{\left(x-x_1\right)}^2+{\left(y-y_1\right)}^2+{\left(z-z_1\right)}^2}={\tau }_{i,1}c$$ where ${\tau }_{i,1}$ is the signal delay difference between each receiver and receiver 1. By jointly solving Eq. (4), the target position can be obtained. Similarly, the difference in arrival time between two receivers can define a TDOA line or surface, and the intersection of multiple TDOA lines or surfaces at a single point yields the true position of the target. In TDOA localization, the peak point of the cross-correlation result is taken as the signal delay. If the echo signal and the reference signal are the same, the cross-correlation achieves the maximum value at the correct delay position. When STCM is applied, each receiver captures the harmonic component of the echo signal, and the cross-correlation generates peaks at the wrong delay position, leading to erroneous delay estimation (see Supplementary Note 8 for more details). When STCM is not applied, the cross-correlation results are shown in Fig. 3g, and the localization results are given in Fig. 3e, where the TDOA lines intersect at the target position. When STCM is affixed, the results of cross-correlation are shown in Fig. 3h, and the delay difference is unrealistic compared to Fig. 3g. The localization results are presented in Fig. 3f, where the TDOA lines do not intersect at a certain point.

The MSR MRDF localization scenario is illustrated in Supplementary Fig. 10a, in which the transmitter and receivers direct their beams towards the target, and the transmitter emits linear frequency modulation (LFM) pulse train signals. Each receiver processes the echo signal through pulse compression (PC) and moving target detection (MTD) to measure the target’s distance and speed (Supplementary Fig. 10c). Then, through data fusion and coordinate conversion, precise localization and tracking of the target are achieved. When STCM is affixed, the received signals contain various harmonics, resulting in inaccurate PC and MTD results, as presented in Supplementary Note 10, and each receiver is unable to obtain the target’s true distance and speed (Supplementary Fig. 10d). As shown in Supplementary Fig. 10b, false targets generated by each receiver are located on the line between the receiver and target. After fusing the measured results from all receivers, it becomes difficult to focus on the real target’s position. In Fig. 3, we analyze the STCM countermeasure effect at a specific modulation frequency. In Supplementary Note 11, we present the target camouflage zones as the modulation frequency varies in the same scenario. Additionally, Fig. 3 focuses on a single transmitter and a limited number of receivers. In Supplementary Notes 12 and 13, we increase the number of transmitters and receivers and demonstrate the STCM countermeasure effects.

Indoor static experiments of the STCM-based anti-MSR

To validate the above concepts and methods, we construct a prototype of the anti-MSR system and conduct experiments in an indoor scenario, as shown in Fig. 4a. In the experimental schematic shown in Fig. 4b, five horn antennas are placed in the scenario and connected to the signal processing system to simulate one transmitter and four receivers. The signal processing system performs FDOA, TDOA, and MRDF localization techniques, respectively. STCM is placed at a distance in the scenario to simulate the target by using the STC matrix of Fig. 2b. The STCM, transmitter and receivers are located in the same Z-plane, with the coordinates of STCM (2.5, 3.9, 0) m, Transmitter (1.45, 2.35, 0) m, Receiver 1 (5.5, 2.4, 0) m, Receiver 2 (5.2, 0.75, 0) m, Receiver 3 (2.35, 1.15, 0) m, and Receiver 4 (0.85, 3.05, 0) m. The angles of the transmitter and receivers with respect to STCM are θ_T = −34.11°, θ_R1 = 63.43°, θ_R2 = 40.60°, θ_R3 = −3.12° and θ_R4 = −62.74°, in which Receivers 1, 2, 3, and 4 mainly receive the +2nd harmonic, +1st harmonic, −2nd harmonic, and +3rd harmonic, respectively.

Fig. 4 Indoor static experiments of the space-time-coding metasurface (STCM)-based anti-multi-static radar (MSR). [Images not available. See PDF.]

a The experiment scenario of indoor static MSR localization. b Schematic diagram of the experimental setup and process, in which the signal processing system is connected to four horn analog receivers and one horn analog transmitter, respectively. f₀ is the modulation frequency of the STCM.

Due to the fact that the positions of the false targets during STCM interference extend well beyond the range of the indoor scenario, we expanded the scenario to a larger scale in order to enhance the visibility of the localization jamming effect when evaluating the effectiveness of STCM in counteracting MSR TDOA localization. Specifically, we scaled the scenario from the meter to the kilometer (see “Methods” section for details). Firstly, STCM is not operated to simulate a target without STCM. The transmitter emits a 10.3 GHz monochromatic wave, which is reflected by the target and scattered to the receivers. The receivers’ echo signals are shown in Fig. 5a, in which a delay between the signals is observed. The cross-correlation results of the receivers are illustrated in Fig. 5c, and the cross-correlation peaks determine the actual delay. Based on the delay difference of the signals, the 3D and 2D localization results are presented in Fig. 5e, g, where both TDOA surfaces and TDOA lines intersect near the target’s true position (2.5,3.9,0) km. We solve for the position of the target as (2.49,3.89,0.01) km based on the localization method (see “Methods” section).

Fig. 5 Experimental results of the multi-static radar (MSR) time difference of arrival (TDOA) localization. [Images not available. See PDF.]

a, c, e, g Experimental results of the target localization without the STC modulation. The time-domain echo signals of the target (a), the cross-correlation results of echo signals (c), the 3D localization results (e), and the 2D localization results (g). b, d, f, h Experimental results of the target localization with the STC modulation. The time-domain echo signals of the target (b), the cross-correlation results of echo signals (d), the 3D localization results (f), and the 2D localization results (h).

When the modulation frequency of STCM is 0.5 MHz, the echo signals from receivers are shown in Fig. 5b. Compared to the case without STC modulation, the time differences of the signals from the receivers (Fig. 5d) are not real. The signal time differences of arrival at receivers 2, 3, and 4 relative to receiver 1 are −2.046 μs (true −2.65 μs), 3.203 μs (true 2.00 μs), and 6.495 μs (true 4.9925 μs). The 3D and 2D localization results are shown in Fig. 5f, h, where both TDOA surfaces and TDOA lines do not intersect near the true position of the target. We solve for the position of the target as (2.26,3.53,0.1) km. To summarize the comparison, STCM has an excellent interference effect on the MSR TDOA localization.

Secondly, we assess the effectiveness of STCM for anti-MSR FDOA localization. Since FDOA can only localize moving targets while the metasurface target is stationary in the current scenario, we thereby assume that the target moves at a velocity of (340,0,0) m/s, in which each receiver superimposes an analog Doppler frequency onto the received signal. Then Receivers 1, 2, 3, and 4 have frequency shifts of −3.89, −1.05, 7.18, and 16.92 kHz, respectively (see “Methods” section for details). The intermediate frequency of the signal processing system is set to 2 MHz. Since the target’s position and velocity in the FDOA equation are coupled, we alternatively analyze the results of the FDOA by assuming that the position and velocity of the target are the true values, respectively. When STCM is not modulated, the spectra of receivers’ signals are shown in Fig. 6a. The result of the velocity measurement is illustrated in Fig. 6c, where the FDOA lines are intersected at the target’s true velocity (340,0,0) m/s. The 3D and 2D localization results are shown in Fig. 6e, g. We note that the FDOA surfaces and FDOA lines intersect near the true position (2.5,3.9,0) m of the target. We solve for the position and velocity of the target as (2.49,3.91,0) m and (340.48,0,0) m/s. When the modulation frequency of STCM is 0.005 MHz, the spectra of the receivers’ signals are presented in Fig. 6b. In addition to the main harmonics (which have the highest amplitude), there are other harmonics in the signal spectra of the receivers. For ease of analysis, we consider only the main harmonics. The signal frequency differences of receivers 2, 3, and 4 relative to receiver 1 are 2.15 kHz (true −2.84 kHz), 8.92 kHz (true −11.1 kHz), and −25.82 kHz (true −20.82 kHz). The result of the velocity measurement is shown in Fig. 6d, and the FDOA lines are difficult to intersect at the true velocity of the target, leading to a false target velocity. The 3D and 2D localization results are shown in Fig. 6f, h. The FDOA3 line and FDOA3 surface cannot be displayed because FDOA3 deviates significantly from the true value. Neither FDOA surfaces nor FDOA lines are intersected at the target’s true position. We solve for the position and velocity of the target as $\left(1.87,1.29,0\right)\mathrm{m}$ and $\left(486.60,54.85,0\right)\mathrm{m}/\mathrm{s}$ , and the results are far from the true values. Meanwhile, Fig. 6g shows the radial velocity of the target calculated by the receiver based on the signal frequency, while the STC modulation changes the radial velocity between the moving target and the receivers, as illustrated in Fig. 6h.

Fig. 6 Experimental results of the multi-static radar (MSR) frequency difference of arrival (FDOA) localization. [Images not available. See PDF.]

a, c, e, g Experimental results of localization without the STC modulation. The spectra of signals from receivers (a). The velocity estimation results. Given the target position, we plot the FDOA lines in the velocity dimension (c). The 3D localization results. Given the target velocity, we plot the FDOA lines and surfaces in the space dimension (e). The 2D localization results (g). b, d, f, h Experimental results of localization with the STC modulation. The spectra of signals from receivers (b). The velocity estimation results (d). The 3D localization results (f). The 2D localization results (h).

We finally assess the effectiveness of STCM for anti-MSR MRDF localization. In this case, the transmitter emits LFM pulse train signals with parameters: bandwidth of 5 MHz, pulse width of 15 μs, pulse repetition interval of 48 μs, and a total of 64 pulses. The signal has a negative modulation slope. When STCM is not modulated, the MTD results of four receivers are shown in Fig. 7a, and all receivers can successfully recognize the target’s true distance and speed. The fusion results of multiple receivers are shown in Fig. 7b, in which the detection results from the receivers are close to the true targets, and the fusion can achieve accurate target localization. When the modulation frequency of STCM is 0.1 MHz, the MTD results of four receivers are shown in Fig. 7c. It is evident that the radial distances and velocities measured by the receivers are incorrect. The brightest point in the MTD result is the primary false target, and other harmonics lead to secondary false targets. For simplicity, we focus on the primary false target. The detection and fusion results of multiple receivers are presented in Fig. 7d. STCM can manipulate multiple harmonics simultaneously, causing them to register different velocity and distance offsets, and the MSR MRDF localization fails. In our experiments, we deliberately place the receivers at spatial locations directed to different harmonics to facilitate the analysis and presentation. Additionally, we provide further analysis of anti-MSR performance under different STC modulation frequencies, and the experiments with more modulation frequencies are demonstrated in Supplementary Note 14. The signals used in experiments are monochromatic waves, and the results with modulated signals are shown in Supplementary Notes 15 and 16.

Fig. 7 Experimental results of the multi-static radar (MSR) multiple receivers detection fusion (MRDF) localization. [Images not available. See PDF.]

a The MTD results of receivers without the STC modulation. b The data fusion localization results without the STC modulation. c The MTD results of receivers with the STC modulation. d The data fusion localization results with the STC modulation.

Outdoor dynamic experiments of the STCM-based anti-MSR

To validate the effectiveness and practicality of the proposed STCM-based countermeasure system, we additionally conduct an outdoor experiment in a more realistic scenario. As illustrated in Fig. 8a, we equip a small drone with three metasurfaces to counter the MSR system. The STCM-based anti-MSR system is powered by a compact battery, and its low power consumption enables extended operations. The lightweight and compact design of the anti-MSR system meets the payload requirements of a small drone, ensuring stable flight during the countermeasure process. The impact of the STCM system on the drone’s endurance is shown in Supplementary Note 17. The experimental setup is depicted in Fig. 8b, where the signal processing system is connected to a transmitting horn antenna and four receiving horn antennas to serve as the transmitter and receivers of the MSR system. We select three flight points to observe the echo signal characteristics at each receiver (see Supplementary Movie for the full flight process). We compare the echo signal characteristics of the drone without and with the metasurfaces equipped. The spectra of the signals at each receiver for the drone without the metasurface at three flight points are shown in Fig. 8c–e, respectively. It is clearly observed that the received spectra contain only the fundamental frequency F₀ signal reflected by the drone, and the energy of the echo signal at each receiver dynamically changes with the drone’s movement. When the drone is equipped with STCM, the spectra of the signals at each receiver at the three flight points are shown in Fig. 8f–h, respectively. Compared to the echo signals from the drone alone, the echo spectra primarily consist of higher-order harmonics, while the fundamental frequency is effectively suppressed. The fundamental frequency that still exists is generated by the parts of the drone that are not covered by the STCM. As the drone moves, the spectra of the signals at each receiver also change dynamically. For example, during the movement, the signal frequency at Receiver 1 shifts from the −1st harmonic to the −2nd harmonic, and then to the −3rd harmonic. This phenomenon is consistent with the STCM scattering characteristics we designed. Both indoor experiments and theoretical analyses demonstrate that it becomes impossible to accurately localize the target using the conventional MSR localization methods when the receivers capture various harmonics. Therefore, we have validated the effectiveness and feasibility of the method through the outdoor flight experiments.

Fig. 8 Outdoor dynamic experiments of the space-time-coding metasurface (STCM)-based anti-multi-static radar (MSR). [Images not available. See PDF.]

a The drone is equipped with three STCMs and is powered by a small battery to supply energy to the entire system. b Outdoor dynamic experiment scenarios. The signal processing system is connected to a transmitting horn and four receiving horns to simulate the MSR system’s transmitters and receivers. There are three flight points to observe the echo signal characteristics at each receiver. c–e Frequency spectra of each receiver at the flight points for the drone without any STCMs. f–h Frequency spectrum of each receiver at the flight points for the drone with STCMs.

Discussion

We propose an STCM-based MSR countermeasure method, enabling simultaneous modulation in both space and frequency domains and filling the current technological gap in effectively countering the MSR systems. By overcoming the limitations of traditional STCM architectures, this method leverages non-cooperative, dynamic, and wide-angle scattering control capabilities to achieve robust countermeasure performance. The proposed method employs an efficient and flexible space-frequency joint ECM strategy, which enables the target stealth and effective jamming of MSR, achieving kilometer-level position deception and velocity camouflage at hundreds of meters per second. To validate the effectiveness of the method, we conduct, for the first time, a closed-loop evaluation comprising theoretical analysis, static concept verification, and dynamic real-world ECM experiments based on the specially designed STCM. Compared to the traditional jamming devices, this method significantly reduces the hardware cost, system complexity, and overall size, while offering enhanced stealth capabilities and control flexibility. Unlike the traditional microwave absorbing materials, this technology not only effectively conceals the target itself but also enables radar deception and confusion. Therefore, the flexible space-frequency-domain control countermeasure method represents a significant breakthrough in the field of ECM. It establishes a paradigm for the STCM-based ECM technologies, demonstrating strong potential against various radar systems, including mono-static radar, synthetic aperture radar, and networked radar.

Looking ahead, beyond the concept verification, the function and performance of STCM can be further expanded to meet the increasingly diverse application requirements. In terms of breakthroughs in metasurface technology, we will conduct research on conformal metasurface structures to accommodate the surface coverage for complex targets and explore designs for dual polarization and dynamic incident angle ranges to enhance the adaptability of STCM in complicated ECM scenarios. By integrating these key technologies, future comprehensive validations will be pursued on more complex experimental platforms, providing a solid foundation for the practical deployment of STCM technologies across a wide range of ECM applications.

Methods

Moving target simulation

Figure 4b shows the indoor static experimental scenario to simulate the moving target in a real environment and to verify the STCM-based anti-MSR FDOA localization. We process the target echoes of each receiver to realistically simulate the moving target. Based on the positions of target and receiver in the experimental scenario in Fig. 4b, the Doppler frequency of the simulated target velocity at the receiver is calculated as

5

$$f_{\mathrm{d}}=\frac{v_{\mathrm{T}}+v_{\mathrm{R}}}{c}{f}_{\mathrm{c}}$$ Where $v_{\mathrm{T}}$ is the velocity of the target relative to the transmitter, $v_{\mathrm{R}}$ is the velocity of the target relative to the receiver. Let the signals received by the four receivers be S₁(t), S₂(t), S₃(t), and S₄(t). We perform the digital frequency conversion operations on the signals of the receivers when simulating the moving target:

6

$$\begin{array}{c}{S}_1^{\prime }\left(t\right)=S_1\left(t\right)\exp \left(j2\pi f_{1}t\right)\hfill \\ S_2^{\prime }\left(t\right)=S_2\left(t\right)\exp \left(j2\pi f_{2}t\right)\hfill \\ S_3^{\prime }\left(t\right)=S_3\left(t\right)\exp \left(j2\pi f_{3}t\right)\hfill \\ S_4^{\prime }\left(t\right)=S_4\left(t\right)\exp \left(j2\pi f_{4}t\right)\hfill \end{array}$$ where $S_1^{\prime }\left(t\right)$ , $S_2^{\prime }\left(t\right)$ , $S_3^{\prime }\left(t\right)$ and $S_4^{\prime }\left(t\right)$ are the echo signals of the receivers after the motion simulation; while $f_1$ , $f_2$ , $f_3$ and $f_4$ are the Doppler frequencies of the receivers’ signals. In the scenario of Fig. 4b, $f_1=-3.89\mathrm{kHz}$ , $f_2=-1.05\mathrm{kHz}$ , $f_3=7.18\mathrm{kHz}$ , and $f_4=16.92\mathrm{kHz}$ when the simulated target speed is $\left(340,0,0\right)\mathrm{m/s}$ . The above moving target simulation can better present the MSR FDOA localization results with and without the STC modulations.

Experimental scenario expansion

Figure 4b shows the indoor static experimental scenario, in which the baseline length between receivers is small. To reflect the TDOA localization effect of the system and the STCM-based anti-TDOA localization more intuitively. We reasonably extend the scenario based on the original data: extend the original meter level to the kilometer level. In this expansion, the original distances between the receivers and target in Fig. 4b, i.e., $d_1=3.35\mathrm{m}$ , $d_2=4.15\mathrm{m}$ , $d_3=2.75\mathrm{m}$ , and $d_4=1.86\mathrm{m}$ are extended to $d_1^{\prime }=3.35\mathrm{km}$ , $d_2^{\prime }=4.15\mathrm{km}$ , $d_3^{\prime }=2.75\mathrm{km}$ , and $d_4^{\prime }=1.86\mathrm{km}$ , respectively. Let the signals received by the four receivers be $S_1\left(t\right)$ , $S_2\left(t\right)$ , $S_3\left(t\right)$ , and $S_4\left(t\right)$ . We delay the signals from the receivers separately, and the signals from the four receivers are delayed as: $S_1\left(t-T_1\right)$ , $S_2\left(t-T_2\right)$ , $S_3\left(t-T_3\right)$ , $S_4\left(t-T_4\right)$ , where $T_1=\frac{d_1^{\prime }-d_1}{c}$ , $T_2=\frac{d_2^{\prime }-d_2}{c}$ , $T_3=\frac{d_3^{\prime }-d_3}{c}$ , $T_4=\frac{d_4^{\prime }-d_4}{c}$ . In the scenario of Fig. 4b, we have $T_1=11.17$ μs, $T_2=13.81$ μs, $T_3=9.17$ μs, and $T_4=6.18$ μs.

Localization solution methods

In the FDOA and TDOA localization methods, Eqs. (1) and (4) usually cannot be directly solved analytically when there are estimation errors in the parameters (arrival time of signal and frequency). In the current research, the least squares and parameter optimization have been used to solve for the target position and velocity. In this work, to verify the target localization and anti-localization results, we formulate the target parameter solutions of FDOA and TDOA, respectivel, to the optimization problems shown below:

7

$$\underset{x,y,z,\stackrel{°}{x},\stackrel{°}{y},\stackrel{°}{z}}{\mathrm{argmin}}\sqrt{\sum _{i=2}^M{\left(\mathrm{\Delta }{f}_d^{i,1}-\frac{f_c}{c}\left(v_i-v_1\right)\right)}^2}$$

8

$$\underset{x,y,z}{\mathrm{argmin}}\mathrm{}\sqrt{\sum _{i=2}^M{\left(\frac{\sqrt{{\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2+{\left(z-z_i\right)}^2}-\sqrt{{\left(x-x_1\right)}^2+{\left(y-y_1\right)}^2+{\left(z-z_1\right)}^2}}{c}-{\tau }_{i,1}\right)}^2}$$ where M represents the number of receivers. We solve the problems by invoking the optimization solver tool in MATLAB. Based on the parameters of receivers measured from experiments, the optimization method can get the target position and velocity iteratively. When STCM is not modulated, the target position and velocity are converged near the true values by the optimization method; with the STC modulation, however, the target position and velocity are difficult to converge to the true values.

Numerical simulation model of STCM

We conducted MATLAB numerical simulations to validate the impact of STCM’s scattering characteristics on the performance of various MSR localization techniques, such as strong suppression of the fundamental wave and the dense distribution of harmonics in space. Firstly, we construct the incident waveguide vector of the STCM, which can be expressed as:

9

$$\mathbf{a}\left(\theta \right)={\left[1,\exp \left(j2\pi \frac{d}{\lambda }\sin \left(\theta \right)\right),...,\exp \left(j2\pi \frac{\left(N-1\right)d}{\lambda }\sin \left(\theta \right)\right)\right]}_{1\times N}$$ where N is the number of STCM elements, L is the length of the time-coding. Here, we only consider the column coding of STCM with $N=16$ . d is the metasurface elements spacing, and λ is the wavelength. We assume that the signal transmitted by the transmitter is S, where K represents the total number of sampling points of the signal.

10

$$\mathbf{S}={\left[S\left(1\right),S\left(2\right),...,S\left(K\right)\right]}_{1\times K}$$

The metasurface incident signal matrix X can be expressed as:

11

$$\mathbf{X}={\mathbf{S}}^{\mathrm{T}}\mathbf{a}\left({\theta }_{\mathrm{t}}\right)$$

θ_t is the incident angle, assuming that the modulation period of STCM is T, the sampling rate is F_s, and the phase matrix P and the amplitude matrix A are shown in the Supplementary Note 18. 1 represents a matrix where all elements are 1. The coding sequence matrix C can be expressed as:

12

$$\mathbf{C}={\mathbf{1}}_{\left(K/\left(T{F}_{\mathrm{s}}L\right)\right)\times 1}\otimes \left[\left(\mathbf{P}\circ \mathbf{A}\right)\otimes {\mathbf{1}}_{\left(T{F}_{\mathrm{s}}\right)\times 1}\right]$$ where ° denotes the Hadamard product and ⊗ denotes the Kronecker product. The reflected signal matrix after modulation of the incident signal on the metasurface can be expressed as:

13

$$\mathbf{Y}=\mathbf{X}\circ \mathbf{C}$$

The metasurface reflected steering vector can be expressed as:

14

$$\mathbf{b}\left(\theta \right)={\left[1,\exp \left(j2\pi \frac{d}{\lambda }\sin \left(\theta \right)\right),...,\exp \left(j2\pi \frac{\left(N-1\right)d}{\lambda }\sin \left(\theta \right)\right)\right]}_{1\times N}$$ where θ represents the angle of the receiver relative to STCM. The signal received by a given receiver can be expressed as R:

15

$$\mathbf{R}=\mathbf{Y}{\mathbf{b}}^{\mathrm{T}}\left(\theta \right)$$

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 62331019, Y.H.Q., 62288101, T.J.C., 62101123, L.Z.), the Jiangsu Province Frontier Leading Technology Basic Research Project (BK20212002, T.J.C.), and the Fundamental Research Funds for the Central Universities (2242023K5002, L.Z.).

Author contributions

Y.H.Q. and T.J.C. gave the research direction and contributed the basic framework and feasible technical route of the project. Z.Z.S., L.Z. conceived the idea, carried out the theoretical analysis and numerical simulations. Z.Z.S., L.Z., X.Q.C. and Y.N.Z. built up the system and performed the experimental measurements. H.X., G.Y.X., Y.J.W., Z.X.L., and H.S.F. performed the data analysis. X.Y.Z., Z.Y.C., and H.C. provided the standard experimental site and equipment. Z.Z.S., L.Z., Y.H.Q., and T.J.C. wrote the manuscript. All authors discussed the theoretical aspects and numerical simulations, interpreted the results, and reviewed the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data supporting the findings of this study are presented in the paper and in the Supplementary information, or can be made available upon request by contacting the corresponding authors.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-025-62633-w.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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