Time-Varying Reflectivity Modulation on Inverse Synthetic Aperture Radar Image Using Active Frequency Selective Surface

Abstract

Interrupted-sampling repeater modulation (ISRM) can generate multiple virtual target images by sampling and forwarding radar signals to confront the inverse synthetic aperture radar (ISAR). However, the repeating delay is unavoidable and the system is complex. Moreover, numerous works mainly discuss the ISAR image deception based on periodic modulation, and the modulation effect is relatively limited. Active frequency selective surface (AFSS) can perform intermittent amplitude modulation to the reflected signal by varying target reflectivity, thus, it can achieve the function of ISRM. In this paper, the possibility of AFSS applied in the multiple virtual target generation is discussed, and an ISAR image-modulation method is proposed. The radar signal is periodically modulated by varying target reflectivity, which is accomplished by the AFSS-loaded PIN diodes. On this basis, the AFSS modulating frequency is randomly varied in a slow time domain. When the modulation signal is processed by the ISAR system, the produced target image is unfocused and cannot be recognized by radar. Simulation results are utilized to demonstrate the effectiveness of the proposed method.

1. Introduction

Interrupted-sampling repeater modulation (ISRM) is a novel active modulation technology for linear frequency modulation (LFM) radar [1,2]. By the periodic sampling and forwarding of radar signals, a number of fake targets are generated after radar processing. ISRM techniques are extensively applied in inverse synthetic aperture radar (ISAR) image modulation to form false target deception images. However, the repeating delay is unavoidable since the repeating pulse lags behind the radar pulse. The modulation efficiency is susceptible to duty ratio, and the duty ratio is generally less than 0.5. Meanwhile, numerous works mainly discuss the ISAR image deception based on periodic modulation, and the modulation effect is relatively limited [3,4,5].

Active frequency selective surfaces (AFSS) have received great attention due to their adjustable features [6], which are applied in various domains including antennas, spatial filters, electromagnetic compatibility, absorbers and communication [7,8,9,10]. In the radar target stealth field, numerous studies about microwave reflectivity, absorption bandwidth, directionality and polarization characteristics have been done [11,12,13,14]. Researchers have mainly focused on the AFSS absorbers from the perspective of energy attenuation. However, AFSS can also perform intermittent amplitude modulation to the reflected signal by varying target reflectivity and achieve the function of ISRM. Thus, it offers the possibility of AFSS being applied in the target feature modulation because its essence is a passive modulation and can respond to radar without repeating delay. Moreover, the modulation effect is flexible and varied by changing the switching method of AFSS.

In this paper, a time-varying reflectivity modulation method based on the AFSS reflector is proposed for ISAR. The method uses AFSS to periodically modulate the radar-reflecting signal by switching AFSS reflectivity. Meanwhile, the switching frequency is randomly modulated in slow time. The modulated signal arrives at the radar receiver and the target feature is transformed after ISAR imaging processing.

This work is mainly divided into the following parts. In Section 2, the signal model of AFSS modulation is established. In Section 3, the time-varying reflectivity modulation method is described and the imaging characteristics of the ISAR image are discussed. The simulation results with the Yak-42 aircraft model are demonstrated in Section 4. Finally, the conclusions are carried out in Section 5.

2. Signal Model of AFSS Modulation

The AFSS structure is made up of the active impedance layer, conductor backplane and dielectric spacer. The active impedance layer consists of periodic unit patches, PIN diodes and substrate materials. The two electromagnetic waves reflected by the active impedance layer and the conductor backplane interfere with each other; thus, the AFSS presents excellent absorption properties in a specific frequency band.

In this paper, the bow-tie dipole patch proposed by A. Tennant and B. Chambers [12,13] is used as the unit structure of AFSS for simulation and analysis. As presented in Figure 1a, HFSS is utilized to obtain the electromagnetic properties of the bow-tie-shaped AFSS. The frequency range of the plane wave is set from 2 GHz to 18 GHz. Different resistor values are used to simulate the different equivalent resistance of the PIN diode.

In Figure 1b, the reflectivity results of the AFSS reflector are shown with the different resistance values. The reflectivity results of the AFSS reflector are different when the resistance value is varied. When the resistance value is 120 Ω, the AFSS reflector presents absorbing properties around 8 GHz and the absorbing bandwidth is approximately 1 GHz. On the contrary, the AFSS reflector shows strong reflection characteristics around 8 GHz when the resistance value is 1000 Ω. By setting different resistance values, the AFSS structure can achieve the flexible modulation between the high-reflectivity and the low-reflectivity, when the working frequency of electromagnetic waves is in the high–low reflectivity tuneable area of the AFSS structure. Thus, AFSS can achieve amplitude modulation to the reflected signal by varying target reflectivity, which is similar to the ISRM [1,2].

Figure 2 presents the modulation mechanism of the AFSS structure. When the AFSS reflector is a high reflection (1000 Ω), the amplitude of the modulation signal is set to 1. When the AFSS reflector is the strong absorbing (120 Ω), the amplitude of the modulation is set to L. Suppose that the amplitude coefficient is periodically switched between L and 1, and the modulation signal is expressed as

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

(1)

where τ is the pulse duration of the high reflection, T_s is the switching period. * denotes the convolution operation, δ(·) is the shock signal, rect (t/τ) equals to 1 when |t/τ| < 0.5, and equals to 0 otherwise.

The spectrum of signal p (t) can be obtained by making Fourier transform to (1). That is:

$$P(f)=(1-L){\displaystyle \sum _{-\infty }^{+\infty }\frac{\tau }{T_s}\mathrm{sinc}\left(\frac{n\tau }{T_s}\right)\delta (f-n{f}_s)}+L\delta (f)$$

(2)

where f_s represents switching frequency and satisfies f_s = 1/T_s, τ/T_s denotes the duty ratio. From (2), the frequency spectrum of the modulating signal contains multiple harmonic components. After the Fourier series expansion, the p (t) can be expressed as

$$p(t)=\frac{\left(1-L\right)\tau }{T_s}+L+\underset{n\ne 0}{\left(1-L\right){\displaystyle \sum _{-\infty }^{+\infty }\frac{1}{n\pi }}}\sin \left(\frac{n\pi \tau }{T_s}\right)\exp \left(2n\pi f_{s}t\right)$$

(3)

3. Modulation Method and Characteristic Analyses

The schematic diagram of ISAR image modulation is presented in Figure 3. There are two possible ways to realize ISAR image modulation. One is to attach the AFSS material to the surface of the protected target. The other is to use the target bait made of AFSS to dynamically control the radar-reflected signal.

The ISAR usually uses the LEM signal as the transmit signal. So, the LFM signal is adopted in the paper with the following parameters: the carrier frequency f₀, the wavelength λ₀, the chirp rate K_r, the pulse repeat interval (PRI) T_PRI, the pulse width T_P, and the signal bandwidth satisfies B_w = K_rT_P. The LFM signal can be expressed as

$$s\left(\widehat{t},t_m\right)=\mathrm{rect}\left(\frac{\widehat{t}}{T_P}\right)\exp \left[j2\pi \left(f_{0}t+\frac{1}{2}{K}_r{\widehat{t}}^2\right)\right]$$

(4)

where $\widehat{t}$ represents the fast time, t_m represents the slow time and satisfies t_m = kT_PRI, k represents the pulse number, so the full time is t = $\widehat{t}$ + t_m.

Suppose the target with AFSS loaded is composed of I scattering points. When the LFM signal s ($\widehat{t}$, t_m) reaches the target, it is modulated by the AFSS reflector. So the reflected signal r ($\widehat{t}$, t_m) can be written by

$$r\left(\widehat{t},t_m\right)=p(\widehat{t}){\displaystyle \sum _{i=1}^I{\sigma }_i}\mathrm{rect}\left(\frac{\widehat{t}-2R_i/c}{T_P}\right)\exp \left\{j2\pi \left[f_0\left(t-\frac{2R_i}{c}\right)+\frac{1}{2}{K}_r{\left(\widehat{t}-\frac{2R_i}{c}\right)}^2\right]\right\}$$

(5)

where σ_i is the reflection coefficient of the ith point, R_i is the distance between the radar and the ith point at the moment t_m, and c is the electromagnetic propagation speed.

After the ISAR receives the reflected signal, pulse compression and Doppler processing are performed to achieve imaging results in range and azimuth directions.

For pulse compression processing, the de-chirp method is adopted in this paper. Assume that the reference distance is R_ref, and the reference signal is

$$s_{ref}\left(\widehat{t},t_m\right)=\mathrm{rect}\left(\frac{\widehat{t}-2R_{ref}/c}{T_P}\right)\exp \left\{j2\pi \left[f_0\left(t-\frac{2R_{ref}}{c}\right)+\frac{1}{2}{K}_r{\left(\widehat{t}-\frac{2R_{ref}}{c}\right)}^2\right]\right\}$$

(6)

After the de-chirp processing, the reflected signal r ($\widehat{t}$, t_m) can be expressed by

$$\begin{array}{l} r_d\left(\widehat{t},t_m\right)={\displaystyle \sum _{i=1}^I{\sigma }_i}\mathrm{rect}\left(\frac{\widehat{t}-2R_i/c}{T_P}\right)\exp \left[\frac{j4\pi K_r}{c}\left(R_{ref}-R_i\right)\widehat{t}\right]\exp \left[\frac{j4\pi f_0}{c}\left(R_{ref}-R_i\right)\right]\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left[\frac{\left(1-L\right)\tau }{T_s}+L+\underset{n\ne 0}{\left(1-L\right){\displaystyle \sum _{-\infty }^{+\infty }\frac{1}{n\pi }}}\sin \left(\frac{n\pi \tau }{T_s}\right)\exp \left(2n\pi f_s\left(\widehat{t}-\frac{2R_i}{c}\right)\right)\right]\end{array}$$

(7)

Performing the Fourier transform in (7), the expression of imaging result in the range domain is written by

$$I_r\left(R_r,R_a\right)={\displaystyle \sum _{i=1}^I{\sigma }_i{T}_P{T}_L\mathrm{sinc}\left[\frac{2w{T}_L{f}_0}{c}\left(R_a-\frac{c{f}_i{}_d}{2w{f}_0}\right)\right]}\left[\frac{\left(1-L\right)\tau }{T_s}+L+\underset{n\ne 0}{\left(1-L\right){\displaystyle \sum _{-N}^{+N}\frac{1}{n\pi }}}\sin \left(\frac{n\pi \tau }{T_s}\right)\mathrm{sinc}\left(\frac{2B}{c}\left(R_r+\frac{cn{f}_s}{2K_r}+\frac{R_{ref}-R_i}{2}\right)\right)\right]$$

(8)

where T_L represents the imaging accumulation time, w represents the target angular rate, and f_id denotes the Doppler frequency of the ith point. n is the order in which fake targets appear and N = ⌊B/f_s⌋.

According to (8), a scattering point can generate many fake points along the range direction, and does not expand along the azimuth direction. When the target with AFSS loaded is modulated, the produced points are superimposed on the image. As a consequence, many fake targets are generated. The nth fake target locates at

$$R_r=-\left(\frac{cn{f}_s}{2K_r}+\frac{R_{ref}-R_i}{2}\right)$$

(9)

In order to realize the two-dimensional image modulation, the modulating frequency f_s is varied randomly in the slow time domain. The modulated jamming echo is mismatched after processing by azimuth matching filter. When the modulating frequency f_s exceeds the Doppler bandwidth B_m, part of the modulation signal will fall outside the Doppler bandwidth, and the energy of the signal after modulation will suffer losses. Thus, the modulating frequency f_s should satisfy

$$f_s\left(t_m\right)=\xi (t_m)\cdot B_m$$

(10)

where ξ (t_m) is a random number within (a, b) (−1 < a < b < 1), B_m is the Doppler bandwidth.

In (9), cnf_s (t_m)/2K_r is a random variation, that is, the location of the generated fake targets is randomly changed along the range direction, and effective range focus cannot be achieved. Meanwhile, the random phase term exp (2nπf_s(t_m)($\widehat{t}$ − 2R_i/c)) in (7) is varied with slow time. There is a certain mismatch in azimuth compression processing. Thus, the output forms a noise-like defocused line along the azimuth direction.

In practical application, the AFSS modulation system needs to judge, process and react according to the environmental conditions, and generate different modulation waveforms to change its function. As shown in Figure 4, the modulation system first obtains the radar parameter information according to the electronic reconnaissance system. The control system transmits the corresponding instruction to the modulation waveform generator to achieve the envisaged modulation mode. The modulation waveform generator produces the corresponding waveform similar to a rectangular pulse string. When the modulation voltage is at a high level, the AFSS shows low scattering. On the contrary, the circuit is cut off and the voltage is 0 V, and the AFSS shows high scattering. Thus, AFSS can realize the switching of the scattering state to act on the radar signal.

4. Simulation Results

To further verify the image modulation method proposed in the paper, the Yak-42 aircraft model was used for simulation analysis. The model is shown in Figure 5a. The simulation parameters are shown in

Table 1. Simulation Parameters.

Parameter	Value	Unit
Carrier frequency (f0)	10	GHz
Signal bandwidth (B)	500	MHz
Chirp rate (Kr)	5 × 1012	Hz/s
Imaging accumulation time (TL)	0.064	s
Pulse duration (TP)	100	μs
Target angular rate (w)	0.157	rad/s

. The Fourier transform algorithm is used in the azimuth direction, and the de-chirping algorithm is used in the range direction.

The original imaging result of the Yak-42 aircraft is presented in Figure 5b. The image is in accordance with the target model.

The AFSS material is applied to the surface of the Yak-42 aircraft so that it can modulate the reflectivity of the target. Through the regulation of the input voltage, the AFSS material can perform periodic or aperiodic modulation of the multiple scattering points of the target. Figure 6a presents the ISAR imaging result of one-dimensional periodic modulation with f_s = 1.25 MHz and τ/T_s = 0.5. According to (8) and (9), ±1 th false targets appear at ±37.5 m and ±2 th false targets are concealed along the range direction. Thus, the distribution and location of multiple false targets in Figure 6a are consistent with the theoretical analysis.

Figure 6b shows the ISAR imaging result with periodic modulation along the range direction and aperiodic modulation along the azimuth direction. The produced target image is defocused and the observation area is formed. The protected target cannot be detected and recognized by radar.

5. Conclusions

This paper proposes a time-varying reflectivity modulation method based on the AFSS reflector against ISAR. The method applies the AFSS reflector originally used for target stealth to the field of target feature modulation. The 1 and L modulation model based on the AFSS properties are established, and the relevant characteristics of the generated image are analyzed in detail. The effectiveness of the method is verified by the simulation results. At present, the feasibility of the proposed ISAR image modulation method has been preliminarily demonstrated. However, this paper only verifies that the time-varying reflectivity modulation method based on AFSS can perform characteristic modulation on ISAR images from the signal level. The discussion on the electromagnetic properties of time-varying AFSS materials has not been carried out in this paper, such as frequency bandwidth, polarization range, angular domain size, energy size, etc. Therefore, the radar characteristics of time-varying electromagnetic materials still have many mysteries worthy of further exploration in terms of theory, properties and applications. In future research programs, the electromagnetic properties of time-varying AFSS materials and the synergy between multiple materials will be investigated in depth, which have important guiding significance for the application of time-varying AFSS materials in practical scenarios.