An Approach for SAR Feature Reconfiguring Based on Periodic Phase Modulation with Inter-Pulse Time Bias

Abstract

Artificial metasurfaces can rapidly modulate their electromagnetic scattering properties and the characteristics of echo signals, which can lead to different imaging features in synthetic aperture radar (SAR) imaging results. Based on this, for the first time, this paper proposes an approach for SAR feature reconfiguring based on periodic phase modulation with inter-pulse time bias. Considering the position and energy requirements of the expected reconfigured imaging target, this approach optimizes the metasurface modulation parameters via a dual algorithm collaborative optimization system, i.e., a modulation parameter generation algorithm (MPGA) and a parameter mapping matching algorithm (PMMA). Time-modulated metasurface targets can reconfigure imaging features of different targets at SAR reconnaissance moments under the guidance of optimized modulation parameters obtained using this approach. Compared with the previous single-point target research on the combination of SAR and metasurfaces, this method is expanded to include the combined analysis of multi-point targets and the reconfigurability of SAR features. Experiments have proved that the programmable reconfigurability of different target features (such as passenger plane targets and truck targets) can be achieved in SAR imaging results through dynamic adjustment of the modulation parameter set. The reconfigured imaging features maintain geometric consistency within the resolution error range, and the size and position of the target can be set as required.

1. Introduction

Synthetic aperture radar (SAR) can perform high-resolution imaging of targets around the clock in complex terrain and adverse weather conditions, and is widely used in intelligence reconnaissance, situational awareness, target identification, and other fields [1,2]. The SAR feature modulation method uses radar target feature modulation to modulate the target echo signals to hide, disrupt, and reconfigure the real target features, affecting radar imaging and recognition. The existing technical routes mainly include active modulation technology and passive modulation technology [3]. Active modulation technology simulates false echoes to create the desired effect through coherent modulation and forwarding of radar signals, but its system is usually complex, costly, and easily exposed, making it difficult to respond in a timely manner [4]. Passive modulation technology changes the radar target echo characteristics by deploying passive equipment around the protected target or on the target object, which is used to simulate, disrupt, or reshape the characteristics of false targets, forming a realistic false target deception effect in the radar image, thereby destroying the radar’s target recognition [5]. Currently, most of the passive devices used are fixed corner reflectors, foil strips, camouflage nets, absorbing materials, etc. [3], but their imaging characteristics are obvious, the effect is single, they cannot achieve complex modulation, and they are very easily identified. The target feature modulation technology based on electromagnetic modulation materials can simply modulate the signals irradiated on it and then reflect them back to achieve richer effects. It exhibits characteristics of strong concealment, rapid response, flexible modulation, etc.

Electromagnetic metasurfaces are composed of subwavelength-scale units arranged in a periodic or non-periodic manner [6], displaying unique modulation capabilities for electromagnetic waves. Actively tunable metasurface technology that integrates lumped elements or active modulation materials in the metasurface exhibits the ability to be reconfigured and can achieve real-time modulation of electromagnetic waves under external stimuli such as bias voltage or light field to achieve its reconfigurable characteristics [7,8,9]. Researchers have developed electromagnetic metasurfaces that can achieve amplitude [10,11,12,13,14], phase [15,16], polarization [17,18], and multi-dimensional joint modulation functions, which can quickly modulate the electromagnetic properties of the incident electromagnetic waves.

SAR feature modulation technology combined with electromagnetic metasurface is a passive intermittent technology based on the intermittent modulation principle [19]. It can quickly and dynamically manipulate the electromagnetic metamaterial attached or placed on the target surface through a time-varying coding modulation strategy to change the electromagnetic characteristics of the SAR target echo signals to achieve complex and effective feature reconfigurability effects. This electromagnetic modulation method does not actively transmit signals; instead, it can directly modulate the target echoes. It offers numerous advantages, including good concealment, strong real-time performance, and diverse modulation methods. This provides this SAR passive modulation technology, combined with an electromagnetic modulation metasurface, with great development potential in the field of radar target feature modulation [20,21]. In recent years, many research teams have used metasurface technology to adjust single or combined amplitude, phase, polarization, and other features to achieve deceptive effects on radar systems [22,23,24,25,26,27]. In applications for imaging radars, References [28,29] studied the intermittent modulation of imaging radar target features based on phase switched screen and active frequency selective surface absorbers, which can form a multi-false target deception effect in radar images. References [30,31] further studied the electromagnetic modulation technology of imaging radar target characteristics and proposed imaging radar image modulation methods based on a time-modulated reflector by using periodic and random coding modulation. Reference [32] provided multi-mode protection for key targets and generated multiple false targets by changing the amplitude and phase of the incident electromagnetic wave. Reference [33] proposes a passive SAR deception method based on diversified frequency time modulation, achieving high-fidelity SAR deception capabilities. Reference [34] proposes a subsection-shift-Doppler-frequency jamming method based on a phase-tunable metasurface for SAR jamming applications.

Radar target feature modulation technology based on electromagnetic metasurfaces has demonstrated substantial advancements in the fields of radar imaging, detection, tracking, and target recognition. However, there are still some problems in existing studies that need to be further explored. For example, the accuracy of radar target feature modulation is still insufficient, and the regularity of symmetric distribution is relatively obvious. In view of this, there is an urgent need to deepen the radar target feature transformation method based on electromagnetic metamaterials and expand diversified and refined pseudo target generation technology to effectively enhance the information protection capabilities of high-value targets.

In order to better cope with target detection and recognition and achieve more realistic scene target feature effects, this paper proposes a target SAR feature reconfigurability method, based on metasurfaces, to meet the needs of generating high-precision false target scenes. This method can realize the optimization analysis of the modulation parameters of the metasurface based on the position and energy requirements of the target to be generated, providing new ideas for the precision and diversification of SAR feature reconfigurability via metasurfaces.

The main contents of this paper are as follows:

• First, the imaging analysis of the electromagnetic periodic modulation method with inter-pulse time bias based on the metasurface is proposed and studied, which is the theoretical basis for the subsequent target reconfigurability method.
• Then, an optimization method for target SAR feature reconfigurability based on the metasurface is proposed. This method enables the generation of corresponding modulation parameter schemes according to the desired characteristics, simultaneously fulfilling the requirements of airspace and energy distribution.
• To verify the effectiveness of the proposed method, parameter modulation schemes are obtained for configuring the interesting truck and passenger plane target features, respectively, and the corresponding imaging results are obtained, meeting the requirements within the allowable error range.

After the introduction, in the second and third sections, this paper introduces the basic theory of metasurface modulation and the imaging analysis of the electromagnetic periodic modulation method, based on metasurfaces. The fourth section comprises detailed introduction to the optimization method of target SAR feature reconfigurability based on metasurfaces. Finally, the target feature reconfigurability experiments are provided, along with the results and a concluding summary.

2. Materials and Methods

2.1. Basic Theory of Metasurface Modulation

The target surface is attached with a special artificial electromagnetically adjustable metasurface, and excitation is applied to the metasurface. When electromagnetic waves are incident on the metasurface, the electromagnetic characteristics of the reflected echo signals will change. In terms of signal processing and analysis, the modulated echoes can be considered as a process of adding the modulation of the echo signals after the original echo signals. However, it should be clear that in the actual working process, reflecting and modulating electromagnetic waves comprises a simultaneous process, i.e., electromagnetic waves reflected by the metasurface will directly obtain modulated echoes.

Different types of metasurfaces can realize different electromagnetic characteristic modulation models. The common type of phase-switched screen (PSS) can realize the phase modulation model. The metasurface changes its own electromagnetic scattering characteristics according to the electromagnetic characteristic modulation model to modulate the radar signal echoes, as shown in Figure 1.

The switching speed of the metasurface characteristics is extremely fast, and its switching period is much shorter than the width of the radar transmission signal. Therefore, the echo coefficient modulation model $p(t)$ within a radar pulse time can be represented by a rectangular sub-pulse with $M$ periods, and the period of the sub-pulse is $T=T_p/M$. The modulation frequency $f_s$ of the metasurface can be calculated from $f_s=1/T$, and $\tau /T$ is defined as the duty ratio of the periodic modulation signal. If it is an ideal phase-modulated model, the phase of the echo signal and the phase of the incident signal are the same during the time period, and the echo signal shows the same reflection amplitude as that of the incident signal, then the phase-modulated echo coefficient $x$ is +1 currently. If the phase of the echo signal and the phase of the incident signal are reversed during the remaining time, the phase difference is $\pi$, and the echo signal shows the reflection amplitude opposite to the incident signal, then the phase-modulated echo coefficient $x$ is −1 currently. The phase-modulated echo coefficient switches between ±1 with time $t$, and the model of the phase-modulated echo coefficient is shown in the time domain signal, as seen in Figure 2.

The time domain signal of the periodic modulation model is represented by $p(t)$, its pulse width is $\tau$, and the switching period is $T_s$. Then, the time domain signal can be expressed as follows:

$$p(t)=\left(1-x\right)\mathrm{rect}\left({\displaystyle \frac{t}{\tau }}\right)\otimes {\displaystyle \sum _{n=-\infty }^{+\infty }\delta \left(t-n{T}_s\right)}+x,$$

(1)

where $x$ is the phase-modulated echo coefficient, $\mathrm{rect}(\cdot )$ is a rectangular pulse signal, and when $|t/\tau |<0.5$, its value is 1; otherwise, it is equal to 0. $\otimes$ represents the convolution operation, $\delta (\cdot )$ is the impulse pulse function, and $n$ takes integer values.

The spectrum of the periodic modulation model signal can be expressed as follows:

$$\begin{array}{cc}P(f)\hfill & =(1-x){\displaystyle \frac{\tau }{T_s}}\cdot {\displaystyle \sum _{n=-\infty }^{\infty }\sin c(n{f}_s\tau )\cdot \delta (f-n{f}_s)}+x\cdot \delta (f)\hfill \\ & =A_0\delta \left(f\right)+{\displaystyle \sum _{\begin{array}{l}n=-\infty \\ n\ne 0\end{array}}^{+\infty }{A}_n\delta \left(f-n{f}_s\right)}\hfill \end{array},$$

(2)

the amplitude coefficients $A_0=\left(1-x\right)\tau /T_s-1$, $A_n=\left(1-x\right)(\sin (n{f}_s\pi \tau ))/n\pi$, and $f_s=1/T_s$ are the modulation frequencies, and the sinc function is $\sin c(x)=\sin (\pi x)/\pi x$. The spectrum $P\left(f\right)$ of the periodic modulation model signal is discretely distributed, containing impulse frequency components and many discrete sidebands. The impulse frequency component is generated by the DC component of the modulation signal in the time domain. The discrete sideband envelope obeys the sinc function distribution, and the envelope is centered on integer multiples of $f_s$.

At this time, if the duty ratio of the modulation signal is 0.5, when $n$ is an even number, $A_n=0$, and the discrete sideband will only appear at odd multiples of the modulation frequency $f_s$, providing a significant benefit, i.e., it can effectively reduce the characteristics of the metasurface target itself. Therefore, the duty ratio $\tau /T$ is usually set to 0.5, and the following experiments are also based on this setting.

Performing inverse Fourier transform on the signal spectrum, another clearer expression of the time domain signal is obtained as follows:

$$p(t)=A_0+{\displaystyle \sum _{\begin{array}{l}n=-\infty \\ n\ne 0\end{array}}^{+\infty }{A}_n\exp (j2\pi n{f}_{s}t)}.$$

(3)

The echo signal after metasurface modulation can be regarded as the result of multiplying the radar incident signal $s_t\left(t\right)$ and the reflection coefficient modulation model $p(t)$. Therefore, the modulated echo can be expressed in the time domain as follows:

$$s_r\left(t\right)=s_t\left(t\right)\cdot p(t).$$

(4)

Correspondingly, the spectrum of the echo signal can be expressed as follows:

$$S_r\left(f\right)=S_t\left(f\right)\otimes P(f),$$

(5)

where $\otimes$ represents the convolution calculation.

2.2. Modulated Echo Model

Imaging radar usually uses the LFM signal as the transmission waveform. It can be assumed that the transmission pulse width is $T_p$, the signal bandwidth is $B$, the signal carrier frequency is $f_c$, and the frequency modulation slope is $K_r$. Then, the transmission signal can be expressed as follows:

$$s_t(t)=\mathrm{rect}\left({\displaystyle \frac{t}{T_p}}\right)\exp \left(j2\pi \left(f_{\mathrm{c}}t+{\displaystyle \frac{1}{2}}{K}_{\mathrm{r}}{t}^2\right)\right),$$

(6)

where, $t$ represents the fast time variable; $\mathrm{rect}(\cdot )$ represents the rectangular window function, when $\left|(t/T_p)\right|<0.5$, $\mathrm{rect}(t/T_p)=1$; otherwise, $\mathrm{rect}(t/T_p)=0$. The signal bandwidth $B$ is equal to the product of the pulse width $T_p$ and the frequency modulation slope $K_r$, i.e., $B=K_r{T}_p$.

When the transmitted LFM signal is modulated by the metasurface modulation model, the reflected signal is recorded as $s_r(t)$, and its expression is as follows:

$$s_r(t)=s_t(t)\cdot p(t)=\mathrm{rect}\left({\displaystyle \frac{t}{T_{\mathrm{p}}}}\right)\exp \left(j\pi K_{\mathrm{r}}{t}^2\right)\left[A_0\exp \left(j2\pi f_{\mathrm{c}}t\right)+{\displaystyle \sum _{\begin{array}{l}n=-\infty \\ n\ne 0\end{array}}^{+\infty }{A}_n}\exp \left(j2\pi \left(f_{\mathrm{c}}+n{f}_{\mathrm{s}}\right)t\right)\right]$$

(7)

It can be seen from Formula (7) that the phase modulation model-reflected signal received by the radar can be regarded as the sum of multiple echoes with different Doppler frequency shifts $n{f}_s$. Since the original signal energy is distributed to several sidebands, the signal energy at the original frequency point is greatly reduced. When the modulation method is based on the phase modulation model with a duty cycle of 0.5, the signals at the original frequency point and the even frequency shift point are zero.

3. A Periodic Phase Modulation Method with Inter-Pulse Time Bias

3.1. SAR Imaging Processing

Synthetic aperture radar works in a “stop-and-go” mode, receiving time-modulated echoes at different times. When storing signals, SAR stores the data of each pulse in a row, so the storage form of the echo in the radar processor can be regarded as two-dimensional echo signals, with the fast time $t_r$ in the range and the slow time $t_a$ in the azimuth as coordinates, which is shown in Figure 3. After the echo signals are mixed by the receiver, they can be expressed as follows:

$$\begin{array}{cc}{s}_r\left(t_r,t_a\right)\hfill & =\mathrm{rect}\left({\displaystyle \frac{t_r-\frac{2R\left(t_a\right)}{c}}{T_p}}\right)\cdot \exp \left(-j{\displaystyle \frac{4\pi R\left(t_a\right)}{\lambda }}\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot \left[A_0+{\displaystyle \sum _{\begin{array}{c}n=-N\\ n\ne 0\end{array}}^{+N}{A}_n}\exp \left(j2\pi n{f}_s\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\right]\hfill \end{array}$$

(8)

In Formula (8), $R\left(t_a\right)$ is the distance between the radar and the target at time $t_a$, $c$ is the propagation speed of electromagnetic waves in the air, and $\lambda$ is the wavelength corresponding to the radar operating frequency band. Due to the modulation operation, some false targets will appear in the processing result. $n=\pm 1,\pm 2,\dots ,\pm N$. is the order of these false targets. The receiver passband determines the value range $N=⌊B/f_s⌋$ of the false targets, where $⌊\cdot ⌋$ is the rounding down operation. The rest of the symbols have been provided and defined previously.

For two-dimensional imaging radar, after the echo signals pass through the range matching filter, it is necessary to perform pulse compression in the azimuth domain. The first term on the right side of the equal sign in Formula (8) is the signal window function. The second term is the slow time quadratic term in the azimuth domain, which is the basis of pulse compression in the azimuth domain. The third term is the fast time quadratic term in the range domain, which is the basis of pulse compression in the range domain. The fourth term is the fast time linear term in the range domain, which represents the frequency modulation of the echo signals by the phase modulation model. Obviously, there is no coupling phenomenon between the range and azimuth domains of the modulated echo signals. This feature will cause the radar image of the modulated echoes to maintain the characteristics the distribution of multiple false targets only in the range domain, as shown in Figure 4.

3.2. Imaging Effects of Inter-Pulse Time Bias

The above analysis is based on the assumption that the pulse repetition period $T_{PRI}$ is an integer multiple of the modulation period $T_s$, and the modulation of the stored pulse signals are synchronized within each pulse repetition period. When the pulse repetition period $T_{PRI}$ emitted by the radar is not an integer multiple of the modulation period $T_s$, there is a fixed inter-pulse time bias $t_{bias}$ in the modulation of the incident signals via the metasurface within each pulse repetition period, which is shown in Figure 5. The inter-pulse time bias can be expressed as follows:

$$t_{bias}=T_{PRI}-T_s\cdot ⌊{\displaystyle \frac{T_{PRI}}{T_s}}⌋,$$

(9)

where $⌊\cdot ⌋$ is the rounding symbol. If the inter-pulse time bias of the first pulse is set to 0, the time difference of the i-th pulse can be expressed as $(i-1)t_{bias}$.

When the inter-pulse time bias $t_{bias}$ exists, the modulated signals should be rewritten as

$$\begin{array}{cc}{s}_r\left(t_r,t_a\right)\hfill & =\mathrm{rect}\left({\displaystyle \frac{t_r-\frac{2R\left(t_a\right)}{c}}{T_p}}\right)\cdot \exp \left(-j{\displaystyle \frac{4\pi R\left(t_a\right)}{\lambda }}\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot \left[A_0+{\displaystyle \sum _{\begin{array}{l}n=-N\\ n\ne 0\end{array}}^{+N}{A}_n}\exp \left(j2\pi n{f}_s\left(t_r-(i-1)t_{bias}-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\right]\hfill \end{array}$$

(10)

The existence of $(i-1)t_{bias}$ in the formula changes the linear term of the slow time so that the false target generated in the range domain has an azimuth displacement, making the false target distribution of the imaging output tilted.

For the n-th order false target, by expanding the exponential term containing ${\mathrm{t}}_{bias}$, it can be expressed as

$$\begin{array}{cc}{s}_n\left(t_r,t_a\right)\hfill & =\mathrm{rect}\left({\displaystyle \frac{t_r-\frac{2R\left(t_a\right)}{c}}{T_p}}\right)\cdot \exp \left(-j{\displaystyle \frac{4\pi R\left(t_a\right)}{\lambda }}\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot A_n\cdot \exp \left(-j2\pi n{f}_{\mathrm{s}}(i-1)t_{bias}\right)\cdot \exp \left(j2\pi n{f}_s\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\hfill \end{array}$$

(11)

Since the approximate condition $R_0\gg V\cdot t_a$ is satisfied at a low oblique angle, $R_0$ is the closest distance between the radar and the target, and $V$ is the moving speed of the SAR platform. Then, the distance equation for the instantaneous slant distance $R(t_a)$ from the synthetic aperture radar carrier to the observed target is expressed as

$$R(t_a)=\sqrt{{R_0}^2+V^2{t_a}^2}\approx R_0+{\displaystyle \frac{V^2{t_a}^2}{2R_0}}$$

(12)

Substituting Formula (12) into Formula (11), it can be expressed as

$$\begin{array}{cc}{s}_n\left(t_r,t_a\right)\hfill & =\mathrm{rect}\left({\displaystyle \frac{t_r-\frac{2R\left(t_a\right)}{c}}{T_p}}\right)\cdot \exp \left(-j{\displaystyle \frac{4\pi }{\lambda }}{R}_0\right)\cdot \exp \left(-j\pi {\displaystyle \frac{2V^2}{\lambda R_0}}{t_a}^2\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot A_n\cdot \exp \left(-j2\pi n{f}_{\mathrm{s}}(i-1)t_{bias}\right)\cdot \exp \left(j2\pi n{f}_s\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\hfill \end{array}$$

(13)

Ignoring the amplitude envelope and constant term in the above equation, it can be expressed as

$$\begin{array}{cc}{s}_n\left(t_r,t_a\right)\hfill & =\exp \left(-j\pi K_a{t}_a^2\right)\cdot \exp \left(-j2\pi n{f}_{\mathrm{s}}(i-1)t_{bias}\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot A_n\exp \left(j2\pi n{f}_s\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\hfill \end{array}.$$

(14)

where $K_a=2V^2/\lambda R_0$ represents the frequency modulation in the azimuth. The last two exponential terms are the basis for the formation of multiple false targets in range and are not affected by the inter-pulse time bias.

Substituting the $t_a=(i-1)T_{PRI}$ into Formula (14) yields the corresponding outcome:

$$\begin{array}{cc}{s}_n\left(t_r,t_a\right)\hfill & =\exp \left(-j\pi K_a{t}_a^2\right)\cdot \exp \left(-j2\pi n{f}_{\mathrm{s}}{\displaystyle \frac{t_{bias}}{T_{PRI}}}{t}_a\right)\cdot \exp \left(j\pi K_{\mathrm{r}}{\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)}^2\right)\hfill \\ & \cdot A_n\exp \left(j2\pi n{f}_s\left(t_r-{\displaystyle \frac{2R\left(t_a\right)}{c}}\right)\right)\hfill \end{array}$$

(15)

The target echo signals modulated by the metasurface will generate a series of false target points after imaging processing, which will disturb the imaging results. At the same time, due to the existence of inter-pulse time bias $t_{bias}$, the modulated echo signals add a modulation frequency $n{f}_s{t}_{bias}/T_{PRI}$ in the azimuth, which is equivalent to changing the Doppler center of the n-th order false target, causing the false target azimuth position to shift.

The positions of these false target points are displaced from the position of the original metasurface in both the range and azimuth domains, as shown in Figure 6. It can be assumed that the range displacement component is $dx$ and the azimuth displacement component is $dy$, as shown in Figure 2. Then, $dx$ and $dy$ can be calculated, respectively, as follows:

$$\left\{\begin{array}{c}dx={\displaystyle \frac{cn{f}_s}{2K_r}}\\ dy={\displaystyle \frac{t_{bias}}{T_{PRI}}}\cdot {\displaystyle \frac{n{f}_s}{K_a}}V\end{array}\right.$$

(16)

Among these, $f_s=1/T_s$ is the modulation frequency, n is the order of the false target, $K_r$ is the fast-time frequency modulation slope, $K_a$ is the slow-time frequency modulation slope, and $V$ is the movement speed of the radar platform.

4. A Method of Target SAR Feature Reconfigurability Based on Periodic Phase Modulation with Inter-Pulse Time Bias

According to high-frequency electromagnetic scattering theory, the main electromagnetic scattering energy of radar targets in the high-frequency region can be equivalent to the superposition of several scattering centers. Then, for targets larger than the radar resolution unit, they can be regarded as composed of multiple point targets. Therefore, using different modulation strategies to modulate a single metasurface individual will generate different target imaging effects. On the one hand, it can change the imaging characteristics of the original target, and on the other hand, it can generate false targets.

The target SAR feature reconfigurability method based on metasurfaces is shown in Figure 7. First, it is necessary to input the number and position relationship of the metasurface array points, as well as the position and important scattering point information of the expected reconfigurable targets, obtaining the modulation parameter sets through parameter generation and parameter matching algorithms. At this point, reconfigurable target features can be obtained after the metasurface-modulated echoes are processed.

4.1. Modulation Parameter Generation Algorithm (MPGA)

It is clear from the previous analysis that when the modulation frequency changes slightly, the phenomenon of tilted false target distribution can be achieved by simply changing the modulation frequency. Based on this, assuming that the metasurface target is placed at position $(x_i,y_i)$, a new target model is configured using the false target generated by the first-order peak generated by the metasurface modulation. The false target is located at position $(x_i+dx,y_i+dy)$; then, $dx$ and $dy$ are needed to determine the modulation frequency of the metasurface reflector, i.e., the inverse of the modulation period.

Assuming that the metasurface target is located at $(x_0,y_0)$, for a modulation period $T_s$ with a time bias $T_{bias}$ from the pulse repetition interval, the position of the generated false target can be expressed as

$$dx={\displaystyle \frac{cn{f}_s}{2K_r}}$$

(17)

Since the change rate of $dy$ near $T_s$ is much faster than that of $dx$, the determination of $T_s$ can be divided into two parts, $T_x$ and $T_{bias}$. The final determination of $T_s$ = $T_x$ + $T_{bias}$, where $T_x$ determines the displacement in the range domain.

$$T_x={\displaystyle \frac{c}{2K_r\cdot dx}}$$

(18)

Then, the Newton iteration method is used to find a suitable time bias $T_{bias}$ in the neighborhood of $T_x$, so that

$$\left\{\begin{array}{c}\left|dx(T_x\pm T_{bias})-dx\right|\le {\epsilon }_x\\ \left|dy(T_x\pm T_{bias})-dy\right|\le {\epsilon }_y\end{array}\right.$$

(19)

4.2. Parameter Mapping Matching Algorithm (PMMA)

When the set metasurface targets are arranged in an array, there is also the problem of the mapping relationship between the real array target points and the false array target points. For the target generated at the proposed position, in order to generate the desired target more realistically, its energy distribution needs to be optimized. The mapping matching algorithm is a directional matching generation technology based on the energy and imaging quality of the false target. Its purpose is to obtain the correspondence between the false target and the metasurface array points, i.e., to determine the mapping relationship between the input and the output to obtain the optimal false target.

For the false targets generated at the distances $dx$ and $dy$ from the original metasurface target position, it is necessary to calculate the energy and imaging quality value indicators of the false targets at that location based on the unmodulated target energy and imaging indicators.

• Energy indicators:

The false target energy retention coefficient $z_{e(dx,dy)}$ is defined as the ratio of the energy generated at $(x_0+dx,y_0+dy)$ to the energy of the reference target $(x_0,y_0)$, as follows:

$$z_{e(dx,dy)}={\displaystyle \frac{{\displaystyle \sum _{x_0+dx-M}^{x_0+dx+M}{\displaystyle \sum _{y_0+dy-N}^{y_0+dy+N}{\left|A_{(m,n)}\right|}^{2}dmdn}}}{{\displaystyle \sum _{x_0-M}^{x_0+M}{\displaystyle \sum _{y_0-N}^{y_0+N}{\left|A_{(m,n)}\right|}^{2}dmdn}}}}$$

(20)

where $M$ and $N$ determine the size of the slice to calculate the target energy, and it is necessary to ensure that the energy of the target imaging is within this slice as much as possible.

From the definition, we can see that the larger $z_{e(dx,dy)}$ is, the smaller the energy loss of the generated target compared to the energy loss of the real target.

2.

Image quality indicators:

Generally, the parameters related to the SAR point target imaging quality assessment are the peak sidelobe ratio and the integrated sidelobe ratio. The peak sidelobe ratio (PSLR) refers to the height ratio of the maximum sidelobe to the main lobe. The integral sidelobe ratio (ISLR) represents the ratio of the energy of the impulse response outside the main lobe to the energy inside the main lobe. In this paper, the latter is selected as the point target imaging quality standard and basis. According to the definition, the integral sidelobe ratio of a false target located at $(x_0+dx,y_0+dy)$ is defined as

$$ISL{R}_{(dx,dy)}=10\cdot \lg \left({\displaystyle \frac{{\displaystyle \sum _{(m,n)\in sidelobe}{\left|A_{(m,n)}\right|}^{2}dmdn}}{{\displaystyle \sum _{(m,n)\in mainlobe}{\left|A_{(m,n)}\right|}^{2}dmdn}}}\right).$$

(21)

For imaging targets, the greater the energy, the smaller the integrated sidelobe ratio, and the better the imaging effect. In order to obtain better false target points, the energy and quality analysis of the target should be integrated. This is also an important reference for the mapping relationship when considering the spatial distribution. Therefore, the false target energy-quality coefficient ${(E-Q)}_{(dx,dy)}$ is defined as the weighted sum of the false target energy retention coefficient $z_e$ and the inverse of the integrated sidelobe ratio at $(x_0+dx,y_0+dy)$.

$${(E-Q)}_{(dx,dy)}=\beta \cdot z_{e(dx,dy)}+(1-\beta )\cdot 1/ISL{R}_{(dx,dy)},$$

(22)

where $\beta$ is the weight coefficient.

After the input determines the metasurface target and the preset expected target, the energy and imaging quality indicators relative to the unmodulated reference point target are obtained. According to the modulation parameter mapping matching algorithm, the candidate mapping relationships are sorted according to the energy-quality coefficient indicators. Then, the breadth-first algorithm is used to ensure the main lobe energy requirements, thereby determining the matching mapping relationship between the metasurface target point and the preset target point and obtaining the mapping relationship matrix. Then, the modulation parameter generation algorithm is executed according to the positional relationship between the matching points to obtain a modulation parameter set that can guide the modulation model.

5. Experiments and Results

This section designs two sets of simulation experiments to verify the effectiveness of the metasurface-based target SAR feature reconfigurability method proposed in this paper.

5.1. Radar Parameters

The SAR and PSS metasurface both operate in the X-band. The radar emits linear frequency modulation (LFM) waveforms, with the radar parameters shown in

Table 1. Airborne SAR operating parameters.

Range Domain Parameters	Value	Azimuth Domain Parameters	Value
Scene center distance	20 km	Radar speed	150 m/s
Pulse duration	2.5 μs	Radar operating frequency	10 GHz
Range modulation frequency	20 MHz/μs	Azimuth modulation frequency	75 Hz/s
Signal bandwidth	1 MHz	Antenna length	3.3325 m
Range sampling rate	60 MHz	Azimuth sampling rate	200 Hz
		Slant angle	0°

.

The imaging quality matrix of the generated false target relative to the unmodulated reference point target is shown in Figure 8. The horizontal axis of the three figures is the distance of the false target relative to the metasurface target in the range direction, and the vertical axis is the distance in the azimuth direction. The results are shown within 250 m to 250 m in the azimuth direction and 250 m in the range direction of the unmodulated original target (it is symmetrical, so only the positive direction is shown). The amplitude coordinate scale represents the numerical value of the corresponding parameter of the coordinate of the point. The results will determine the matching relationship between the target points in PMMA, thereby determining the modulation parameters. Figure 8a shows the energy retention coefficient of the false target, Figure 8b shows the inverse of the integrated sidelobe ratio, and Figure 8c shows the energy-quality coefficient when the weight coefficient is 0.5.

5.2. Experimental Purpose

Metasurface points are arranged into an input array (as shown in Figure 9, the array is labeled 0–13 from left to right and from top to bottom). Different phase modulation models can be applied to the metasurface array to reconfigure different targets.

• Experiment 1: Reconfiguring the SAR signature array of a passenger plane

The common Boeing 737 model passenger plane target is selected as the reconfigured feature target. According to public information on the Internet, its wingspan is 28.45 m, and its length is 37.81 m. According to the structure of the plane, the nose, wing, and fuselage scattering points with high scattering intensity are selected as the locations of the desired modulation-generated false points. The reconfigured plane target is 65 m away from the input array in the azimuth and 70 m away in the range (as shown in Figure 10a, labeled from 0 to 11).

• Experiment 2: Reconfiguring the SAR signature array of a truck

The common Dongfeng EQ2102 truck target is selected as the reconfigured feature target. According to the public information on the Internet, its overall size is 7495 × 2470 × 2740 (mm). According to the structure of the truck, the body contour scattering points with high scattering intensity are selected as the locations of the false points generated by the desired modulation. The reconfigured truck target is 15 m away from the input array in the azimuth and 50 m away in the range (as shown in Figure 10b, with labels 0–13 from top to bottom and from left to right).

5.3. Results and Analysis

According to the experimental settings in Section 5.2, two groups of experiments were conducted using the target feature reconfigurability method based on the metasurface proposed in this paper. The mapping relationship results shown in Figure 11 and the modulation parameter sets under the two experimental settings are shown in

Table 2. Modulation period parameter sets for achieving two sets of reconfigurability effects.

Label	Experiment 1: Modulation Period (Seconds)	Experiment 2: Modulation Period (Seconds)
0	8.327539819376977 × 10−8	1.1355662578026702 × 10−7
1	8.327533920724061 × 10−8	1.1355659029373009 × 10−7
2	9.861594529025383 × 10−8	1.1186205053270461 × 10−7
3	8.817454217418264 × 10−8	1.1530323251511429 × 10−7
4	8.327533226764895 × 10−8	1.0706884305570732 × 10−7
5	9.029870475152497 × 10−8	1.1021728881224057 × 10−7
6	9.861588689878635 × 10−8	1.1186195974914579 × 10−7
7	7.973242777040326 × 10−8	1.2286553031218273 × 10−7
8	7.420629065134477 × 10−8	1.228654887697628 × 10−7
9	8.614643839673231 × 10−8	1.1355657093743721 × 10−7
10	8.614640126455485 × 10−8	1.135565677113884 × 10−7
11	8.614636413237739 × 10−8	1.1530319592828522 × 10−7
12	8.146543304691033 × 10−8	1.2088407857756882 × 10−7
13	7.420624932313623 × 10−8	1.1186195974914579 × 10−7

.

Figure 11a,b show the energy-quality coefficients of the candidate mapping matrices of the target points of the metasurface array and the expected target points of the two groups of experiments, respectively. The horizontal axis represents the label corresponding to the array points, and the vertical axis represents the label of the expected reconfigured points. Figure 11c,d show the mapping relationship between the two groups of hypersurface array target points and the expected target points obtained by optimization based on the maximum energy principle. In these figures, the horizontal and vertical coordinates of each red square represent the mapping relationship between the input and output points.

Each column of Figure 11a,b represents the ${(E-Q)}_{(dx,dy)}$ result of reconfiguring each key target point for the metasurface target. Next, the breadth-first algorithm is used to select the maximum value in the ${(E-Q)}_{(dx,dy)}$ matrix. The horizontal axis corresponding to this value is the metasurface target, and the vertical axis is the reconfigured key target point, thereby determining a mapping relationship. Then, in the same way, it is determined that all the target points to be configured have a corresponding metasurface target. If there are still extra metasurface target points at this time, they can be chosen to modulate the reconfigured key points with greater energy or to be removed from the metasurface target array in order to obtain a unique set of optimal modulated combinations, as shown in Figure 11c,d.

Figure 12a,b show the imaging results of two groups of reconfigured targets, respectively. The results show that the expected target imaging features can be generated. They also show that the same metasurface target point array can achieve different SAR feature reconfigurability effects. In addition, due to the advantage of the phase modulation method in hiding its own target features, it can destroy the pre-array imaging. Therefore, this method can achieve three goals at the same time: first, the same array arrangement can achieve the effect of reconfiguring different targets; second, it can destroy the imaging characteristics of the original array; and third, it can generate scattered targets with different offsets at the central symmetry of the original position.

Figure 13a,b show the errors of two groups of reconfigured target points generated according to modulation and the expected target point positions. The horizontal axis is the label of the set point, and the vertical axis is the different errors corresponding to each point. The yellow point represents the position error between the false point and the expected position along the range direction, and the green point represents the position error between the false point and the expected position along the azimuth direction. Positives and negatives indicate the relative relationship with the expected position. The blue point represents the Euclidean distance error between the false point and the expected position. The order of magnitude of the three distance errors is 0.001 m, which is much smaller than the resolution of the imaging radar under experimental conditions (the resolution in the range direction is about 2.9 m, and the resolution in the azimuth direction is about 1.6 m). Within the allowable error range, we can consider this method to be correct and effective.

6. Discussion

The experimental results in

Table 3. Comparison of experimental results.

Experiment	Imaging Results	Imaging Area	Imaging Center Position
0 1		3 m × 18 m	(19,981.5, −14)
1		28.45 m × 37.81 m	(20,085, 70)
2		7.495 m × 2.47 m	(20,047, 15)

¹ Metasurface target array without modulation.

and Figure 14 confirm the following:

• It can be seen from the imaging results in Table 3 that the same metasurface target array can reconfigure different SAR features by switching the modulation parameters, and both Experiments 1 and 2 can hide the original metasurface array.
• It can be seen from the imaging area in Table 3 that this method can achieve a reconfigured target with adjustable size. The size of the reconfigured plane target in Experiment 1 is greater than the original metasurface array area, and the reconfigured truck target in Experiment 2 is smaller than the original metasurface array area. Therefore, the target size that can be reconfigured in the metasurface array area under the modulation of the parameter sets obtained in this paper is adjustable, i.e., it can be “small to large” or “large to small”.
• It can be seen from the imaging center position in Table 3 and Figure 14a–d that this method can achieve a reconfigured target with adjustable positions. The target to be reconfigured is set as the input, and these position parameters of the expected targets are modifiable and adjustable. Through the reconfigurability algorithm, the modulation parameter set can be obtained, which can generate a reconfigured target within the error range. It can be seen from the imaging center position in Figure 14e–h that this method can achieve a reconfigured target with adjustable orientation, indicating that the proposed approach for modulated SAR features can meet the different spatial distribution requirements of the reconfigured target.

7. Conclusions

In this paper, for the first time, it is proposed to actively change the phase characteristics of the SAR echo signals via the periodic phase modulation method with inter-pulse time bias. This method realizes the active reconfigurability of SAR imaging features. Based on this method, an approach for SAR feature reconfiguring is implemented first. Compared with the previous single-point target research, this method is expanded to the combined analysis of multi-point targets. A dual algorithm collaborative optimization system is developed, in which the modulation parameter generation algorithm (MPGA) is responsible for parameter space search, and the parameter mapping matching algorithm (PMMA) realizes the precise correspondence between the target features and the modulation parameters. Experiments have proved that the programmable reconfigurability of different target SAR features (such as truck and passenger plane targets) can be achieved in the SAR imaging results through dynamic adjustment of the modulation parameter set. It is possible to destroy the SAR features of the metasurface target and reconfigure new SAR features. In summary, this paper establishes a technical closed loop of parameter optimization—electromagnetic modulation—feature reconfigurability. This paradigm provides a new technical path for the subsequent development of intelligent electromagnetic camouflage and active radar confrontation.