MFE-STN: A Versatile Front-End Module for SAR Deception Jamming False Target Recognition

Highlights

What are the main findings?

• A versatile front-end Multi-Feature Extraction and Spatial Transformation Network module is proposed for SAR deception jamming target recognition, integrating wavelet decomposition, manifold transformation, and spatial transformation network.
• An analysis of seven typical parameter-mismatch effects was conducted, and a simulated high-fidelity false target dataset was constructed.

What are the implications of the main findings?

• The MFE-STN module effectively captures discriminative signatures, enabling robust distinction between genuine and deceptive SAR targets with strong cross-domain generalization capabilities.
• The research provides new ideas and theoretical support for SAR false target recognition and the development of anti-jamming systems in complex electromagnetic environments, while the parameter analysis offers guidance for developing jammer systems.

Abstract

Advanced deception countermeasures now enable adversaries to inject false targets into synthetic-aperture-radar (SAR) imagery, generating electromagnetic signatures virtually indistinguishable from genuine targets, thus destroying the separability essential for conventional recognition algorithms. To address this problem, we propose a versatile front-end Multi-Feature Extraction and Spatial Transformation Network (MFE-STN), specifically designed for the task of discriminating between true targets and deceptive false targets created by SAR jamming, which can be seamlessly integrated with existing CNN backbones without architecture modification. MFE-STN integrates three complementary operations: (i) wavelet decomposition to extract the overall geometric features and scattering distribution of the target, (ii) a manifold transformation module for non-linear alignment of heterogeneous feature spaces, and (iii) a lightweight deformable spatial transformer that compensates for local geometric distortions introduced by deceptive jamming. By analyzing seven typical parameter-mismatch effects, we construct a simulated dataset containing six representative classes—four known classes and two unseen classes. Experimental results demonstrate that inserting MFE-STN boosts the average F1-score of known targets by 12.19% and significantly improves identification accuracy for unseen targets. This confirms the module’s capability to capture discriminative signatures to distinguish genuine targets from deceptive ones while exhibiting strong cross-domain generalization capabilities.

1. Introduction

SAR has become a cornerstone of all-weather strategic surveillance due to its cloud-penetrating and night-operational capabilities [1,2,3,4]. Next-generation airborne/spaceborne SAR systems integrate ultra-wideband signal processing and multi-channel antenna arrays [5], achieving synergistic balance between centimeter-level resolution and hundred-kilometer coverage. However, these advancements exponentially increase electromagnetic exposure risks for high-value targets [6,7,8], driving rapid development of active countermeasure technologies. Since the 1990s, military powers including Norway [9], the UK, and the US [10,11,12] have pioneered SAR electronic warfare systems, marking the formal integration of electronic countermeasures into SAR operations.

The electromagnetic countermeasures against SAR serve dual objectives: protecting friendly high-value assets while detecting adversary targets [13]. From a defensive standpoint, this is achieved by generating interference signals targeting SAR, thereby disrupting its normal operational processes and preventing the extraction of critical intelligence from the final imaging results.

In the field of SAR jamming technologies, existing research primarily categorizes countermeasures into two types based on energy application: active jamming and passive jamming [14,15,16]. This study focuses on active jamming techniques. Technically, active jamming is divided into suppression jamming [17,18,19,20,21,22,23,24,25,26,27] and deceptive jamming [28,29,30]. Suppression jamming disrupts radar signals through noise injection but risks exposure due to high-power requirements, whereas deception jamming reconstructs electromagnetic signatures to generate false targets with superior covertness, demonstrating higher military value.

False targets generated by SAR deception jamming can severely compromise the accuracy of image interpretation and lead to erroneous classification decisions [31,32,33]. Consequently, the development of efficient techniques for detecting such deception jamming is of critical importance. Traditional detection methods typically follow a two-step process. First, feature transformation is applied to the SAR jamming signal to extract discriminative features from single or combined feature domains. These domains range from fundamental ones like the time, frequency, and time-frequency domains [34,35,36], to more advanced transform domains such as the bispectrum, wavelet, and Fractional Fourier Transform domains [37,38]. Feature extraction serves as the foundation for subsequent jammer classification. Once the features are extracted, they are fed into a classifier, often designed using machine learning algorithms, for identification and classification. The selection of an appropriate classifier is crucial for enhancing recognition accuracy. Widely-used traditional classifiers include Decision Trees and Support Vector Machines (SVM) [39]. In reference [39], seven typical SAR jamming types were modeled, and a corresponding set of features was extracted from the time, frequency, and time-frequency domains. These features were then fed into both a Decision Tree and an SVM classifier for evaluation. The results demonstrated that the classifiers exhibited varying applicability to different jamming types; the Decision Tree achieved higher recognition accuracy for noise frequency modulation jamming and smart noise jamming, whereas the SVM performed better in identifying pure noise environments and range deception jamming.

However, such traditional jammer detection algorithms suffer from significant limitations. Firstly, these methods rely heavily on manual feature engineering. Features designed based on expert knowledge are not only highly sensitive to variations in the Jamming-to-Noise Ratio (JNR) and jammer parameters, but their design and selection efficiency also struggles to meet the demands of modern, complex tasks. Secondly, traditional machine learning classifiers are constrained by these handcrafted features, leading to poor generalization capabilities when confronted with novel jamming techniques in complex electromagnetic environments. In recent years, the rapid advancement of deep learning has led to its increasingly widespread application in jammer detection, owing to its powerful adaptive learning and generalization capabilities [40]. For instance, reference [41] proposes JRSNet, a SAR jammer recognition model specifically designed to address the issue of imbalanced training samples. By incorporating a discriminative feature distance metric and a multi-dimensional attention module, JRSNet effectively extracts modulation differences from time-frequency diagrams, achieving high-precision recognition and suppression of various jamming types. In another study, reference [42] introduces a recognition method for composite deception jamming based on Fast-Slow Time-Frequency Distribution features and a lightweight MAM-YOLOv8n detection network. This approach leverages coherent integration and differences in Doppler frequency shifts to effectively separate aliased jamming signals, significantly enhancing recognition performance under low Jamming-to-Signal Ratio conditions. However, as jamming techniques continue to evolve, deep learning methods that rely on training with existing jammer databases are beginning to show their limitations.

Given that deception jamming manifests in the final SAR image as false targets highly similar to real ones, a new research paradigm is emerging: detecting deception jamming by directly analyzing and exploiting the discrepancies between true and false targets within the image domain. Existing false target identification methods predominantly exploit multi-angle and multi-channel information for detecting signal-domain simulated false targets [43,44,45]. In reference [46], a SAR deception target recognition method based on shadow features and a two-stage convolutional neural network (CNN) is proposed. By extracting prominent shadow features of true targets and using a two-stage CNN for classification, it first identifies the target type and then distinguishes between true and false targets, achieving a recognition accuracy of 98.89% for true targets. Although these image-domain recognition methods can achieve a high accuracy rate for identifying genuine targets, they predominantly rely on a straightforward combination of conventional feature extraction and CNN. Their core limitation often lies in applying general-purpose feature extractors that learn discriminative patterns from a dataset, rather than performing targeted feature extraction explicitly designed around the theoretically derived intrinsic differences between genuine and deceptive targets. While effective on known data, this data-driven approach may struggle with generalization because it is not directly guided by the underlying physical mechanisms—namely, the signal parameter mismatches—that generate these differences. Consequently, this can lead to a lower recognition rate for false targets with novel characteristics and demonstrates insufficient generalization capability. So two critical gaps remain: insufficient research on the characteristic differences between authentic and false targets in actual SAR imagery; poor robustness in discriminating authenticity for unknown target types.

To tackle the above problems, this paper proposes a two-stage solution. First, a general signal model for convolutional deception jamming is constructed, enabling a systematic analysis of the mechanisms through which mismatches in seven key parameters affect the perceived authenticity of false targets. Building upon this foundation, the MFE-STN module is designed. The structure of the MFE-STN module is shown in Figure 1. The module operates in a sequential manner; it first utilizes a multi-feature extraction block, leveraging wavelet transformation and Riemannian manifold learning to capture diverse target characteristics. These extracted features are then transformed from grayscale to a pseudo-RGB format, a crucial step designed to boost the feature expression capability. Finally, a spatial transformation network is applied to correct geometric distortions and normalize the target. By coupling these mechanisms, the module significantly enhances the recognition capability of baseline models. The main contributions of this work are as follows:

1.

Reveal the intrinsic relationship between parameter mismatch and the imaging quality of false targets, and construct a high-fidelity false target dataset.

2.

Propose the MFE-STN module, which integrates Riemannian manifold transformation, wavelet decomposition, and spatial transformations.

3.

Implement a multi-feature extraction framework that significantly improves recognition robustness in complex electromagnetic environments.

The remainder of this paper is organized as follows. Section 2 establishes a general signal model and analyzes the factors influencing the realism of false targets generated by convolutional interference. Section 3 presents the advanced MFE-STN module, which combines manifold space feature extraction, wavelet transform, and STN coupling mechanisms. In Section 4, we validate the proposed method using a false target dataset generated from a SAR dataset slice. Finally, Section 5 presents the conclusions of the paper.

2. Jamming Signal Model and Analysis of False Target Realism

The effectiveness of SAR deception jamming fundamentally depends on the matching accuracy between jamming signal parameters and the radar imaging chain. Although existing studies have confirmed that parameter mismatches (e.g., carrier frequency and pulse repetition frequency) can induce false target distortion, large-scale parameter analysis and comprehensive investigation of parameter mismatch impacts remain underexplored. This paper establishes a generalized convolutional deception jamming signal model and systematically analyzes the influence mechanisms of seven critical parameters on three key aspects: spatial localization accuracy, resolution characteristics, and geometric scaling properties of false targets. The proposed theoretical framework lays a foundation for generating high-fidelity deceptive targets in SAR systems.

2.1. Jamming Signal Model

In this section, we explain how the jammer modulates and retransmits intercepted SAR signals to conduct deceptive interference and generate false targets at designated locations. The geometric relationship among the SAR platform, jammer, and false targets can typically be illustrated as shown in Figure 2. A coordinate system is established with the radar platform’s motion direction as the x-axis, the radar beam pointing direction as the y-axis, and the jammer’s location as the origin $\mathit{O}$. The radar platform moves at a constant velocity $\mathit{v}$ along the x-axis, and at time t = 0, the beam center is directed at point O. The false target generated by the jammer is denoted as point P, with coordinates (x, y). The parameter d represents the shortest slant range between the radar platform and the jammer. The instantaneous slant ranges between the radar platform, the jammer, and the false target at time $t_m$ are denoted as $R_j\left(t_m\right)$ and $R_f\left(t_m\right)$, respectively. The backscattering coefficient of the false target is represented by ${\sigma }_f$. The term $\mathit{L}$ denotes the synthetic aperture length.

To analyze the false target formation, we first consider a single false target point. According to [14], the system response function of the jammer can be expressed as follows:

$$\begin{array}{c}H\left(\omega \right)={\sigma }_p·exp\left(-j\omega {\displaystyle \frac{2\left(R_P\left(t_m\right)-R_O\left(t_m\right)\right)}{c}}\right)\end{array}$$

(1)

The backscattering coefficient of the false target is denoted as ${\sigma }_p$. The instantaneous slant ranges $R_P\left(t_m\right)$ and $R_O\left(t_m\right)$ can be expressed as follows:

$$\begin{array}{c}{R}_p\left(t_m\right)=\sqrt{{\left(R_S+y\right)}^2+{\left(x-v{t}_m\right)}^2}\end{array}$$

(2)

$$\begin{array}{c}{R}_O\left(t_m\right)=\sqrt{{R_S}^2+v^2{t_m}^2}\end{array}$$

(3)

As shown in (1), by adjusting the value of $\mathit{H}$, that is, by modifying the system response function of the jammer, false targets can be generated at different locations in the SAR imaging result, thereby achieving the purpose of deceptive jamming.

The distances between the radar platform, the jammer, and the false target can be calculated by (2) and (3). $R_S$ denotes the shortest slant range between the radar platform and the jammer. Generally, it holds that $R_S\gg \mathit{v}{t}_m$, $\left|t_m\right|\le L/\left(2v\right)$. Additionally, it is typically assumed that $R_S\gg x$, $R_S\gg y$. Based on this assumption, a Taylor expansion is performed on (2). Considering that the actual jamming scene consists of multiple false target points, the expression can be written as follows:

$$\begin{array}{c}\begin{array}{c}{R}_{x,y}\left(t_m\right)\approx R_S+y+{\displaystyle \frac{x^2}{2R_s}}-{\displaystyle \frac{xv{t}_m}{R_s}}+{\displaystyle \frac{v^2{t_m}^2}{2R_s}}=R_O\left(t_m\right)+\Delta R_{x,y}\left(t_m\right)\end{array}\end{array}$$

(4)

$$\begin{array}{c}\begin{array}{c}\begin{array}{c}\Delta R_{x,y}\left(t_m\right)=R_{x,y}\left(t_m\right)-R_O\left(t_m\right)=y+{\displaystyle \frac{x^2}{2R_s}}-{\displaystyle \frac{xv{t}_m}{R_s}}\end{array}\end{array}\end{array}$$

(5)

The term represents the instantaneous slant range from an arbitrary false target point $(x,y)$ to the radar platform. Therefore, for any target point in the false scene, (1) can be rewritten as follows:

$$\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}H\left(\omega \right)={\displaystyle \sum _{x,y}}{\sigma }_{x,y}·exp\left(-j\omega {\displaystyle \frac{2\Delta R_{x,y}\left(t_m\right)}{c}}\right)\end{array}\end{array}\end{array}\end{array}$$

(6)

Expanding it yields:

$$\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}H\left(\omega \right)={\displaystyle \sum _{x,y}}{\sigma }_{x,y}·exp\left(-j\omega {\displaystyle \frac{2}{c}}\left(y+{\displaystyle \frac{x^2}{2R_s}}-{\displaystyle \frac{xv{t}_m}{R_s}}\right)\right)\end{array}\end{array}\end{array}\end{array}\end{array}$$

(7)

The above equation serves as the fundamental model for generating deceptive jamming signals.

2.2. Analysis of False Target Realism

The effectiveness of deceptive jamming primarily depends on the accuracy of radar parameters acquired by the reconnaissance system. The key to successful deception lies in obtaining the radar’s signal parameters, motion parameters, and other relevant information. By intercepting these parameters, the jammer modulates the radar signal and embeds false target information, generating deceptive signals that resemble real scene echoes. When the radar processes these signals, the resulting image contains both the real scene and the superimposed false targets.

To precisely implement deceptive jamming—ensuring that false targets appear at the desired locations with high realism—the jammer must acquire various parameters of the SAR platform. These parameters include radar platform velocity $\mathit{v}$, carrier frequency ${\mathit{f}}_{\mathit{c}}$, bandwidth (BW) $\mathit{B}$, pulse duration ${\mathit{T}}_{\mathit{r}}$, azimuth sampling rate ${\mathit{f}}_{\mathit{s},\mathit{az}}$, downward `, platform altitude $\mathit{H}$, and more.

2.2.1. Impact of Bandwidth and Pulse Duration Mismatch

Bandwidth can be expressed as $B=K{T}_r$; it can be concluded that, due to the invariance of K, the bandwidth is linearly related to the pulse duration, with an equivalent degree of variation. The missing pulse width intercepted by the jammer will affect the distance resolution of false targets. The SAR range resolution is inversely proportional to the bandwidth. Therefore, when the pulse width changes, the range resolution deteriorates. However, since SAR matched filtering exhibits a certain degree of adaptability, it allows partial compensation for bandwidth discrepancies. As a result, small bandwidth mismatches typically do not lead to severe target distortion. Nonetheless, bandwidth errors may affect the energy distribution along the range dimension, resulting in a reduced range resolution of the target in the final image, causing slight blurring. Overall, the impact of bandwidth and pulse duration mismatches on the realism of false targets is relatively minor.

The theoretical range resolution of a SAR system is given by ${\delta }_r=c/2B$, where ${\delta }_r$ is the range resolution, and $\mathit{B}$ is the signal bandwidth. If the deceptive signal suffers a bandwidth error $\Delta B$, the degraded resolution becomes ${{\delta }_r}^{\prime }=c/2\left(B+\left|\Delta B\right|\right)$. When $\Delta B\ne 0$, i.e., the bandwidth decreases, the range resolution deteriorates, causing range-domain blurring of the target.

2.2.2. Impact of Carrier Frequency Mismatch

Mismatching the carrier frequency severely affects the azimuth resolution of false targets, often leading to target scaling and defocusing. The center frequency directly impacts the azimuth linear frequency modulation rate. The mismatch in the azimuth chirp rate further causes issues during the azimuth compression phase, leading to problems with the matched filter. This weakens the filter’s response and results in incorrect coherent integration. Such mismatches alter the Doppler frequency distribution of the target, thereby reducing the azimuth resolution. At the same time, due to the center frequency mismatch, the Doppler center frequency shift is affected, resulting in the shift of the false target. The relationship between the azimuth modulation frequency and the center frequency can be expressed as $K_a=2V_r^2{f}_c/c{R}_0$.

2.2.3. Impact of Azimuth Sampling Rate Mismatch

Mismatch in the azimuthal sampling rate can lead to scaling and defocusing of false targets. According to (7), the first-order phase of $t_m$ in the jammer’s system response function is given by $xv{t}_m/R_s$, where the slow time $t_m$ can be expressed as $t_m=t_{m0}+PRT\ast n$, and PRT is the pulse repetition period, which is related to the azimuthal sampling rate as $PRT=1/f_{s,az}$. Therefore, when there is a mismatch in the azimuthal sampling rate, cumulative errors are introduced in the slow time, leading to the first-order phase of $t_m$ error in the jammer’s system response function. This, in turn, causes the false targets to undergo scaling and defocusing in the azimuth scaling. At the same time, the Doppler center shift will also lead to a shift in the false target.

2.2.4. Impact of Platform Velocity Mismatch

Velocity mismatch affects the azimuth scaling and defocusing of false targets. According to (7), the first phase in the jammer’s system response function is given by $xv{t}_m/R_s$. So velocity directly influences the appearance of the first-order phase of $t_m$ in the jammer’s system response function. Velocity mismatch introduces the first-order phase of $t_m$ errors, which in turn lead to scaling and defocusing of the generated false targets in the azimuthal direction. At the same time, the Doppler center shift will also lead to a shift in the false target.

2.2.5. Impact of Platform Height and Downward Angle Mismatch

Mismatch in platform height and downward angle mainly affects the spatial position, scaling, and defocusing of false targets. The geometric relationship between platform altitude, downward angle, $R_S$, and ground distance R can be simplified into a right triangle, as $R=R_{S}cos\left(\theta \right)$. Therefore, when platform altitude and downward angle change, $R_S$ will change. According to (7), the first-order phase and the zero-order phase of $t_m$ in the jammer’s system response function are given by $x^2/2R_s$ and $xv{t}_m/R_s$, and when errors occur in $R_S$, both the first-order phase and the zero-order phase of $t_m$ of the system response function will change. The zero-order phase of $t_m$ error will cause the spatial position of the false targets to shift. When the platform height $\mathit{H}$ increases or the downward angle $\theta$ decreases, the ground distance projection corresponding to the unit slant range becomes longer. Although the false target remains relatively consistent in the slant range domain, during the imaging projection process, the ground coordinates undergo scaling. In other words, the slant range width remains unchanged, but the ground distance width changes, causing the target on the ground to stretch or shrink.

All contributing factors are summarized in

Table 1. Contributing factors for SAR imaging performance degradation.

Factor	Symbol Meaning	Effect					Importance
		Defocus Azimuth	Defocus Range	Position Shift	Azimuth Scaling	Range Scaling
$\mathit{v}$	Platform velocity	✓		✓	✓		High
${\mathit{f}}_{\mathit{s},\mathit{az}}$	Azimuth sampling rate	✓		✓	✓		High
$\mathit{H}$	Platform Height	✓		✓	✓	✓	Medium
$\theta$	Downward Angle	✓		✓	✓	✓	Medium
${\mathit{f}}_{\mathit{c}}$	Carrier frequency	✓		✓	✓		Medium
$\mathit{B}$	Bandwidth		✓				Low
${\mathit{T}}_{\mathit{r}}$	Pulse duration		✓				Low

. The effectiveness of SAR deception jamming relies on the accurate replication of several critical radar parameters. Among these, mismatches in azimuth sampling rate and platform velocity have the greatest impact on the azimuthal scaling and defocusing of false targets. Errors in SAR geometric parameters, such as platform altitude and downward angle, result in target displacement, scaling, and defocusing. In contrast, the effects of bandwidth and pulse duration mismatches are relatively minor, as they are typically compensated by the inherent filtering capability of SAR systems. Therefore, particular attention must be paid to the azimuth sampling rate, carrier frequency, platform velocity, and SAR geometric parameters during the practical implementation of SAR deception to ensure correct positioning and high-fidelity rendering of false targets. Furthermore, due to Doppler centroid shifts and the non-overlapping positions between the jammer and the implanted false targets, mismatches in azimuth sampling rate, carrier frequency, and platform velocity will also cause azimuthal displacement of the false targets.

3. MFE-STN Module

The preceding analysis establishes that the distinguishing characteristics of deceptive SAR targets are direct consequences of parameter mismatches, which manifest as a combination of distinct artifacts at different scales. To formulate an effective solution, our core research question is how to design a feature extraction module that is specifically sensitive to both the macroscopic geometric distortions and the microscopic feature alterations caused by these mismatches.

To address this, we propose the MFE-STN, a specialized front-end module whose architecture is a targeted design rather than an arbitrary collection of techniques. The STN component is explicitly designed to counteract large-scale geometric transformations—such as scaling, rotation, and translation—that result from mismatches in platform velocity. By learning an adaptive affine transformation for each input image, the STN spatially normalizes the target to a canonical pose, removing gross geometric variations and allowing the subsequent network to focus on more subtle, intrinsic discriminative features. Complementing this, the Multi-Feature Extraction block is engineered to capture fine-grained, non-linear discrepancies introduced by mismatches in carrier frequency or bandwidth. It employs two synergistic approaches: the Wavelet Transform (WT), which addresses artifacts like defocusing and textural variations by providing a multi-scale representation highly sensitive to subtle changes in edges and local energy, and the Riemannian Manifold Transformation, which tackles non-linear statistical deviations in scattering characteristics by projecting features into a tangent space that better preserves their complex geometric structure.

By synergistically combining these three components, the MFE-STN module constructs a comprehensive and robust feature space that is invariant to large geometric shifts while remaining highly sensitive to subtle, microscopic artifacts. Figure 1 illustrates the overall architecture of the module, and the following subsections will detail the implementation of each component.

3.1. Multi-Feature Extraction Module

The multi-feature extraction module is designed; it includes wavelet transforms and Riemannian manifold transformations, which are used for extracting the overall geometric features and scattering distribution of the target and analyzing nonlinear scattering characteristics, in order to improve the recognition ability of SAR deception interference targets.

3.1.1. Wavelet Transforms

Wavelet transform is a time-frequency localized analysis method that can decompose signals into sub-bands at different scales, allowing the extraction of frequency information at various levels. The general form of wavelet transform can be expressed as:

$$\begin{array}{c}{W}_{\psi }\left(a,b\right)={\int }_{-\infty }^{+\infty }f\left(t\right){\displaystyle \frac{1}{\sqrt{a}}}\psi \left({\displaystyle \frac{t-b}{a}}\right)dt\end{array}$$

(8)

$f\left(t\right)$ is the original signal, $\psi \left(t\right)$ is the mother wavelet, $\mathit{a}$ is the scale parameter that controls the stretching and shrinking of the wavelet, and $\mathit{b}$ is the translation parameter that controls the position of the wavelet in the time domain.

In SAR deception target detection, we use Discrete Wavelet Transform (DWT) for multi-scale analysis. DWT uses finite-length wavelet filters to decompose the signal, typically based on Daubechies wavelets (Db) or Coiflet wavelets (Coif). The discrete wavelet transform recursively decomposes the signal using a filter bank. The decomposition process is as follows: Low-pass filter $\mathit{H}$ and high-pass filter $\mathit{G}$ are applied to the original signal $f\left(t\right)$:

$$\begin{array}{c}{Y}_{low}\left[n\right]={\displaystyle \sum _k}H\left[k\right]f\left[2n-k\right]\hfill \\ Y_{high}\left[n\right]={\displaystyle \sum _k}G\left[k\right]f\left[2n-k\right]\hfill \end{array}$$

(9)

The low-frequency part ${\mathit{Y}}_{\mathit{low}}$ is further decomposed in the next layer, forming a multi-scale pyramid structure.

For the target slices, we apply filtering and down-sampling using the fourth-order Daubechies wavelet or Coiflet wavelet basis, obtaining four different decomposition components. These components are as follows. Low-frequency sub-band $\mathit{LL}$ (Approximation coefficients): Contains the global structural information of the target. High-frequency horizontal sub-band $\mathit{LH}$ (Horizontal details): Contains horizontal edge information. High-frequency vertical sub-band $\mathit{HL}$ (Vertical details): Contains vertical edge information. High-frequency diagonal sub-band $\mathit{HH}$ (Diagonal details): Contains diagonal texture features. The transformation formula is as follows:

$$\begin{array}{c}{W}_{LL}\left(m,n\right)={\displaystyle \sum _i}{\displaystyle \sum _j}f\left(i,j\right){\varphi }_{m,n}\left(i,j\right)\hfill \\ W_{LH}\left(m,n\right)={\displaystyle \sum _i}{\displaystyle \sum _j}f\left(i,j\right){\psi }_{h,m,n}\left(i,j\right)\hfill \\ W_{HL}\left(m,n\right)={\displaystyle \sum _i}{\displaystyle \sum _j}f\left(i,j\right){\psi }_{v,m,n}\left(i,j\right)\hfill \\ W_{HH}\left(m,n\right)={\displaystyle \sum _i}{\displaystyle \sum _j}f\left(i,j\right){\psi }_{d,m,n}\left(i,j\right)\hfill \end{array}$$

(10)

where ${\varphi }_{m,n}$ is the scaling function, and ${\psi }_h$, ${\psi }_v$, ${\psi }_d$, are the wavelet functions in the horizontal, vertical, and diagonal directions, respectively.

Because SAR targets occupy only a few resolution cells and the imagery is typically corrupted by speckle, we retain solely the LL sub-band of a single-level DWT. The LL coefficients preserve the scene’s dominant structural information while suppressing high-frequency noise and compressing the feature dimension. This delivers greater discriminability and numerical stability compared to the detail bands (LH, HL, HH) or deeper decompositions. To substantiate this choice, we evaluated the structural similarity between genuine and deceptive targets after one- to four-level DWTs. As shown in

Table 2. Structural similarity scores at different wavelet decomposition levels.

Level	LL	LH	HL	HH
0	0.61171 –	–	–	–
1	0.54315 (−0.06856)	0.69064 (+0.07893)	0.56076 (−0.05095)	0.80258 (+0.19087)
2	0.67530 (+0.06359)	0.67680 (+0.06509)	0.56785 (−0.04386)	0.61076 (−0.00095)
3	0.83852 (+0.22681)	0.63796 (+0.02625)	0.63907 (+0.02736)	0.56866 (−0.04305)
4	0.87293 (+0.26122)	0.77608 (+0.16437)	0.65856 (+0.04685)	0.64054 (+0.02883)

Red and blue values denote increases and decreases, respectively, from the baseline (the 0-Level LL).

, the original images are highly similar, whereas the single-level LL representation achieves the lowest similarity score, maximizing the contrast between true and false targets and thus facilitating their separation. To achieve an optimal balance between performance and efficiency, we evaluated various wavelet bases on the first-level approximation component, with the results detailed in

Table 3. Performance comparison of wavelet bases (first-level approximation components).

Metric	HAAR	DB4	DB8	BIOR4.4	COIF2
OrigSSIM	0.61171 –	0.61171 –	0.61171 –	0.61171 –	0.61171 –
OrigPSNR	21.344 –	21.344 –	21.344 –	21.344 –	21.344 –
L1A_SSIM	0.56772 (−0.04399)	0.54315 (−0.06856)	0.54124 (−0.07047)	0.54513 (−0.06658)	0.54667 (−0.06504)
L1A_PSNR	16.607 (-4.737)	16.174 (−5.170)	16.130 (−5.214)	16.503 (−4.841)	16.335 (−5.009)

Blue values denote decreases from the baseline (the OrigPSNR or OrigSSIM).

. The experiment revealed that all tested wavelets caused a substantial reduction in both SSIM and PSNR. This reduction positively confirms that wavelet decomposition successfully captures and enhances the subtle differences between true and false targets. Among all candidates, DB4 and DB8 exhibited the most outstanding difference extraction capabilities. The primary trade-off between them is that DB8 offers slightly better numerical performance at the cost of significantly higher computational complexity due to its longer filter. Conversely, DB4 delivers nearly equivalent performance with a much lower computational cost. This makes DB4 a superior compromise between accuracy and efficiency. Consequently, we have selected DB4 as the optimal wavelet basis for our study.

3.1.2. Rectangular Transformation on Riemannian Manifolds

In SAR images, deceptive targets and true targets are typically distributed on high-dimensional nonlinear manifolds. Traditional linear transformation methods (such as principal component analysis (PCA) and linear discriminant analysis (LDA)) lose important geometric information in this case, resulting in decreased detection performance. To better capture the nonlinear features of SAR images, we need to employ manifold learning methods to process the data, especially when the geometric structure of the target cannot be fully expressed by traditional linear transformations. The Rectangular Transformation on Riemannian Manifolds (RT-RM) provides the ability to transform data in non-Euclidean spaces while preserving the geometric structure and local geometric features of the data [47].

When processing data embedded in a Riemannian manifold, we need to use the logarithmic map and exponential map to perform data transformations. These maps are core tools in manifold learning, as they help us map data from manifold space to the tangent space, perform the transformation, and then return the data to the manifold.

The logarithmic map maps a data point from the manifold to the tangent space, representing the “local coordinates” of the data point in the tangent space. Let the reference point on the manifold $\mathit{M}$ be $\mathit{p}$ and the data point be ${\mathit{X}}_{\mathit{i}}$, then the logarithmic map is defined as:

$$\begin{array}{c}lo{g}_p\left(X_i\right)=v_i\in T_{p}M\end{array}$$

(11)

where $T_{p}M$ is the tangent space at point $\mathit{p}$ and ${\mathit{v}}_{\mathit{i}}$ is the vector in the tangent space representing the data point ${\mathit{X}}_{\mathit{i}}$ in relation to $\mathit{p}$.

The exponential map maps a point in the tangent space back to the manifold. It is the inverse process of the logarithmic map.

$$\begin{array}{c}{exp}_p\left(v_i\right)=X\in M\end{array}$$

(12)

where ${\mathit{v}}_{\mathit{i}}$ is a vector in the tangent space, and ${exp}_p\left({v_i}_i\right)$ is the corresponding point on the manifold $\mathit{M}$.

RT-RM is a transformation that directly operates on the Symmetric Positive Definite (SPD) manifold. It uses the Log-spectral transform to enhance features. This method effectively preserves the geometric structure of the data while avoiding complex nonlinear optimization problems. In the process of SAR image processing, the gradient of each pixel can be described using a SPD matrix.

$$\begin{array}{c}M=\left[\begin{array}{cc}{G}_x^2& G_x{G}_y\\ G_x{G}_y& G_y^2\end{array}\right]\end{array}$$

(13)

where $G_x,G_y$ are the image gradients, and $\mathit{M}$ is a 2 × 2 SPD matrix. This matrix has the properties of symmetry and positive definiteness (i.e., all eigenvalues are positive). SPD matrices do not form a Euclidean space but rather a Riemannian manifold. Direct linear transformations in the SPD space might lead to information loss or matrix degradation. Therefore, the Rectangular Transformation on Riemannian Manifold is employed for feature extraction. First, the logarithmic map is used to project the SPD matrix onto the tangent space (Euclidean space):

$$\begin{array}{c}{log}_I\left(M\right)=Ulog\left(\Lambda \right)U^T\end{array}$$

(14)

where $\Lambda$ is the eigenvalue matrix, and $log\left(\Lambda \right)$ acts on each eigenvalue, with $log\left(\Lambda \right)=diag\left(log\left({\lambda }_1\right),log\left({\lambda }_2\right)\right)$. This map projects the SPD matrix onto its tangent space, allowing the transformation to occur in the Euclidean space. In the tangent space, a simple rectangular transformation can be performed on the data:

$$\begin{array}{c}f\left(M\right)={\displaystyle \sum _i}log\left(1+{\lambda }_i\right)\end{array}$$

(15)

Here, ${\lambda }_i$ represents the eigenvalues of the SPD matrix. This transformation can be seen as a Log-Spectral Transformation, which enhances the data’s contrast and suppresses noise. A simple physical intuition for this process is to think of the Riemannian manifold as the curved surface of the Earth, and the tangent space as a flat local map. Direct calculations on the curved surface are complex. By projecting the data onto this ‘flat map’ (the tangent space), we can apply simpler and more powerful Euclidean operations to the features, effectively analyzing their non-linear structure without the complexity of curved-space geometry. The physical meaning of the transformation is as follows. Smoothing Eigenvalues: The logarithmic transformation reduces the impact of large eigenvalues, preventing numerical instability. Enhancing Discriminatory Power: The low-eigenvalue parts are stretched, while the high-eigenvalue parts grow more slowly, which enhances the distinctiveness between features. Feature Representation: The transformation relies on the eigenvalues directly, not the matrix itself, making it suitable for SAR target detection.

The rectangular transformation uses Log-Spectral Transformation, which only affects the eigenvalues and does not project the data back onto the manifold. Therefore, it does not require an Exponential Map, resulting in lower computational complexity. The feature extraction is completed directly in the tangent space shown in Figure 3, avoiding nonlinear optimization problems.

The feature extraction module combines wavelet transforms and RT-RM. This fusion step capitalizes on the single-level wavelet’s feature-extracting power, distilling the primary structural cues of SAR targets and sharply boosting the system’s ability to tell true from false. At the same time, by combining Riemannian manifold rectangular transformations, the non-Euclidean geometric structure of SPD matrix data in SAR images is well-considered. This allows high-dimensional features to be effectively processed in the tangent space of the Riemannian manifold, avoiding information loss that might occur with traditional linear transformations.The results of WT and RT-RM for true and false targets are shown in

Table 4. Feature transformations of true and false target slices using gray, RT-RM, and WT.

Group	Transform Type
	Gray	RT-RM	WT
True
False

. To quantitatively validate the primary function of the RT-RM module—to enhance the dissimilarity between genuine and deceptive targets—we conducted an analysis of image similarity metrics. We measured the average SSIM and PSNR between pairs of genuine targets and their corresponding deceptive counterparts before and after the RT-RM transformation. The results are presented in

Table 5. Performance comparison before and after RT-RM transformation.

Metric	Original	RT-RM Transformed
SSIM	0.61171 –	0.41750 (−0.19421)
PSNR	21.344 –	18.009 (−3.335)

Blue values denote decreases from the baseline (original).

. As demonstrated in Table 5, the RT-RM transformation leads to a substantial reduction in both SSIM and PSNR. This result provides direct quantitative evidence that the module successfully fulfills its intended role; it makes deceptive targets structurally less similar to genuine ones in the feature domain, thereby amplifying the discriminative cues and increasing their separability for subsequent network stages.

While visual inspection in Table 4 may suggest continued similarity, particularly for RT-RM, the quantitative analyses in Table 2, Table 3 and Table 5 demonstrate that both WT and RT-RM significantly increase the statistical dissimilarity between genuine and deceptive targets, which is the crucial factor for improving classification performance.

3.2. Spatial Transformation Network Module

STN is a differentiable geometric transformation module [48]. It is used in deep learning networks to perform adaptive adjustments to input data, such as scaling, rotation, affine transformations, etc. The core idea is to use a learned transformation matrix $\theta$ to adjust the input image, allowing the network to automatically focus on key target areas and improve classification and detection accuracy. In this study, STN is applied to SAR deception jamming target detection, addressing the issue of decreased detection performance caused by target rotation, scaling, or displacement. Specifically, STN consists of three main components. Localization Network: This component learns the transformation parameters $\theta$. Grid Generator: This generates transformed coordinates based on the transformation matrix $\theta$. Sampler: It performs bilinear interpolation on the input image to generate a normalized target region.

Given an input image $I\in R^{H\times W\times C}$, STN predicts a transformation matrix $\theta$ through a Localization Network:

$$\begin{array}{c}\theta =f_{loc}\left(I,W_{loc}\right)\end{array}$$

(16)

where $f_{loc}$ can be a convolutional neural network (CNN) or a fully connected neural network (FCN) that extracts transformation parameters from the input image, and $W_{loc}$ are the trainable weights of the network. The transformation matrix $\theta$ is typically an affine transformation matrix:

$$\begin{array}{c}\theta =\left[\begin{array}{ccc}{a}_{11}& a_{12}& t_x\\ a_{21}& a_{22}& t_y\end{array}\right]\end{array}$$

(17)

Here, $a_{ij}$ controls the scaling, rotation, and shearing, and $t_x$, $t_y$ control the translation.

STN applies an affine transformation to map the input image coordinates $(x_i,y_i)$ to normalized coordinates $({x^{\prime }}_i,{y^{\prime }}_i)$:

$$\left[\begin{array}{c}{x^{\prime }}_i\\ {y^{\prime }}_i\end{array}\right]=\theta \left[\begin{array}{c}{x}_i\\ y_i\\ 1\end{array}\right]=\left[\begin{array}{ccc}{a}_{11}& a_{12}& t_x\\ a_{21}& a_{22}& t_y\end{array}\right]\left[\begin{array}{c}{x}_i\\ y_i\\ 1\end{array}\right]$$

(18)

In SAR deception target detection, targets might undergo deformation due to viewpoint changes or interference mechanisms. This transformation adjusts the target’s position, scale, and orientation, making it easier for the network to learn to distinguish between deceptive and true targets.

The Grid Generator calculates the coordinates $({x^{\prime }}_i,{y^{\prime }}_i)$ for each pixel in the output image using the transformation matrix $\theta$. Bilinear interpolation is then applied to sample the input image and generate the transformed output image $I^{\prime }$:

$$\begin{array}{c}{I}^{\prime }\left(x^{\prime },y^{\prime }\right)={\displaystyle \sum _{i,j}}I\left(x_i,y_j\right)·\left(1-\left|x_i-x^{\prime }\right|\right)·\left(1-\left|y_j-y^{\prime }\right|\right)\end{array}$$

(19)

where $(x_j,y_j)$ are the coordinates of the nearest four pixels, and $I\left(x_i,y_j\right)$ is the pixel intensity (either grayscale or RGB value). Bilinear interpolation ensures that the transformed image retains important texture information without significant loss.

STN plays a critical role in the SAR deception target detection process in the following ways:

1.

Geometric Normalization: STN applies affine transformations to geometrically normalize the target, making it more stable for feature comparison in the feature space. This improves the contrast between deceptive and true targets.

2.

Handling Complex Background Clutter: SAR images typically contain complex background clutter. STN helps focus the network’s attention on the target region, reducing background interference and improving detection robustness.

3.

Dynamic Feature Extraction: Different types of deceptive targets may have subtle differences in their SAR representations. STN can dynamically adjust the feature extraction process, enhancing the model’s generalization ability.

A novel MFE-STN module, which integrates WT and RT-RM with STN, is proposed for SAR deception target detection. This module leverages the strengths of multi-feature extraction and spatial transformation to improve the representation of deceptive targets. Additionally, the Grayscale to RGB Transformation converts grayscale SAR images to pseudo-RGB images, boosting the feature expression capability of the neural network and providing more discriminative input data for the subsequent STN module. The STN Module is designed to adaptively apply spatial transformations to normalize the geometry of input targets, automatically correcting for variations in scale, rotation, and displacement of deceptive targets. By focusing the network’s attention on the target area and reducing background interference, the STN improves the separability between targets, enhancing the model’s ability to distinguish between deceptive and true targets. This results in increased robustness, making the detection system more adaptable to the challenging and dynamic nature of SAR images, particularly under deceptive interference.

4. Experiment Results

This section is divided into two parts. False target experiments validates the correctness of the theoretical analysis presented in Section 2, as well as the effectiveness of generating deceptive targets. The MFE-STN Module Experiment focuses on verifying the effectiveness of the proposed MFE-STN module in recognizing deceptive targets. Our experimental validation primarily leverages a high-fidelity simulated dataset. This approach is necessitated by the scarcity of labeled real SAR deception jamming data, which is often classified and unavailable for academic research. To overcome these limitations and ensure the relevance of our findings, our simulated dataset is rigorously designed to reflect real-world complexities and theoretically predicted jamming effects. This methodology provides a challenging and diverse testbed for evaluating the MFE-STN module’s robustness against real-world jamming false targets. Crucially, to provide comprehensive validation, our module was also tested and verified using actual real data.

In this section, the evaluation metrics used are listed in

Table 6. Evaluation metrics for SAR false target recognition experiments.

Evaluation Metrics	Equation
Accuracy	$\mathrm{Accuracy}={\displaystyle \frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}}$
Precision	$\mathrm{Precision}={\displaystyle \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}}$
Recall	$\mathrm{Recall}={\displaystyle \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}}$
F1 Score	$\mathrm{F}1=2\times {\displaystyle \frac{\mathrm{Precision}\times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$

. Specifically, True Positive (TP) refers to the number of positive samples correctly predicted; True Negative (TN) denotes the number of negative samples correctly predicted; False Positive (FP) represents the number of negative samples incorrectly predicted as positive; and False Negative (FN) refers to the number of positive samples incorrectly predicted as negative.

4.1. False Target Experiments

To begin, we verify the correctness of the influence factor analysis in Section 2. The experiment continues by superimposing jamming signals onto real SAR echo data. Relevant data parameters are shown in

Table 7. SAR and jamming signal parameter settings.

Parameter	Value	Unit
H	796	km
v	7062	m/s
$t_{start}$	6595.9	μs
$N_{az}$	1536	/
$N_{rg}$	2048	/
$T_0$	41.75	μs
K	−0.72135	MHz/μs
$f_c$	5300	MHz
$f_{s,r}$	32.317	MHz
$PRF$	1257	Hz
$\theta$	−1.5814	deg

, and Figure 4 displays the image without jamming.

In practical jamming scenarios, the jammer needs to preset reconnaissance parameters in advance based on empirical values, which often leads to significant deviations in the reconnaissance parameters. Following the principle of single-variable control, we investigate the effects of the following parameters by introducing relative errors of 0.5%, 1%, 2%, 5% and 10%, respectively: radar platform velocity $\mathit{v}$, carrier frequency ${\mathit{f}}_{\mathit{c}}$, bandwidth $\mathit{B}$, pulse duration $T_0$, azimuth sampling rate ${\mathit{f}}_{\mathit{s},\mathit{az}}$, squint angle θ, platform altitude $\mathit{H}$. The results of the experiment are shown in Figure 5. Given the linear relationship $B=K{T}_r$ between bandwidth and pulse duration, and the triangular geometric relationship between platform height and downward angle, their variation trends are largely consistent. Therefore, we present only the analysis for bandwidth and platform height here.

The results show that mismatches in bandwidth and pulse duration mainly affect the range resolution, causing slight blurring of the target in the range direction, although the overall impact is small. Mismatches in the center frequency affect the azimuth resolution, leading to target scaling or defocusing. Mismatches in the azimuth sampling rate directly affect Doppler resolution, potentially causing scaling or blurring of the deceptive target in the azimuth direction. Mismatches in platform speed lead to azimuthal scaling and defocusing, distorting the target shape, which is particularly important in high-resolution SAR imaging. Additionally, due to the offset of the Doppler center frequency and the non-overlapping positions of the jammer and false target implantation, azimuth sampling rate, carrier frequency, and platform speed mismatches will result in a position shift of the false target in the azimuth direction. Errors in SAR altitude and downward angle alter the spatial position of the target, resulting in positional shifts and potential defocusing. Therefore, during the implementation of deception jamming, key parameters such as azimuth sampling rate and platform speed must be strictly controlled to ensure that deceptive targets are accurately and faithfully embedded into the SAR image. It is also evident that within an acceptable small range of parameter errors, the most direct impacts on false targets are deformation and blurring, which is highly valuable for creating false target datasets.

Table 8. Comparison of image quality metrics by error level.

Error	$\mathit{v}$		${\mathit{f}}_{\mathit{s},\mathit{az}}$		$\mathit{H}$		${\mathit{f}}_{\mathit{c}}$		$\mathit{B}$
	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR
0	1.0000	/	1.0000	/	1.0000	/	1.0000	/	1.0000	/
0.5	0.8619	24.29	0.8696	24.08	0.8919	27.12	0.8965	27.33	0.9140	27.33
1.0	0.8372	22.96	0.8431	22.20	0.8672	26.69	0.8701	26.70	0.9138	26.70
2.0	0.8348	22.04	0.7959	21.58	0.8648	24.95	0.8654	25.54	0.9101	25.54
5.0	0.7923	20.11	0.7645	20.17	0.7519	20.39	0.8109	21.98	0.8955	24.70
10.0	0.6799	17.68	0.6774	17.77	0.7436	19.81	0.7903	21.02	0.8343	22.59

presents the image quality metrics for various variables under different error levels. The overall trend indicates that as the error increases, both the SSIM and PSNR values for all variables exhibit a downward trend, demonstrating that error accumulation significantly degrades the structural integrity and signal-to-noise ratio of the images. Specifically, the variables show distinct sensitivities to error. Variable $\mathit{B}$ is the most robust against errors. Even at the maximum error level (Error = 10.0%), its SSIM remains above 0.83 and its PSNR is maintained at 22.59 dB, showing the smallest performance decline compared to other variables. Variable ${\mathit{f}}_{\mathit{c}}$ follows in performance, managing to preserve relatively good image quality even under high-error conditions. In contrast, variables $\mathit{v}$ and ${\mathit{f}}_{\mathit{s},\mathit{az}}$ are the most sensitive to errors. When Error ≥ 5.0, their SSIM and PSNR values deteriorate sharply, with ${\mathit{f}}_{\mathit{s},\mathit{az}}$ experiencing the most severe degradation in structural similarity under medium-to-high errors. The stability of variable $\mathit{H}$ is intermediate. Although it maintains a high SSIM in the low-to-medium error range, its PSNR drops markedly under high-error conditions. In summary, different variables exhibit varying levels of robustness to error perturbations. Therefore, when generating false targets or implementing jamming techniques, close attention must be paid to these highly sensitive parameters to ensure the stability and effectiveness of the outcome.

To further investigate the impact of parameter mismatches on defocusing, a point target slicing method was employed. False point targets were embedded into the original SAR image, and point target slicing analysis was performed. The results are shown in

Table 9. Point-target IRW variation under parameter mismatch.

Error Factor	Range IRW (m)	Azimuth IRW (m)
No error (Baseline)	11.4179	9.8539
${\mathit{f}}_{\mathit{s},\mathit{az}}$	11.4179 (0.0000)	11.6158 (+1.7619)
$\mathit{v}$	11.4179 (0.0000)	11.6158 (+1.7619)
$\mathit{H}$	11.4179 (0.0000)	11.4853 (+0.6314)
${\mathit{f}}_{\mathit{c}}$	11.4179 (0.0000)	11.5506 (+0.6967)
$\mathit{B}$	12.3938 (+0.9759)	9.8539 (0.0000)

Red values denote increases from the baseline (no error).

. It is evident that, under a uniform 10% mismatch in each parameter, azimuth sampling rate and platform velocity have the most significant and comparable impact, leading to severe mainlobe broadening. The effects of carrier frequency and platform altitude on mainlobe broadening are progressively weaker. In contrast, a mismatch in bandwidth primarily causes mainlobe broadening in the range direction. In summary, aside from positional displacement caused by implantation errors, the primary effects of parameter mismatches are manifested as defocusing in both the azimuth and range directions.

After validating the analysis, we proceed to conduct slicing experiments using the SAR-aircraft-1.0 dataset [49] to further evaluate the effectiveness of the generated deceptive targets.

This experiment mainly includes the generation of deceptive targets and the verification of their effectiveness.

The SAR-AIRcraft-1.0 dataset includes four different sizes: 800 × 800, 1000 × 1000, 1200 × 1200, and 1500 × 1500, with a total of 4368 images and 16,463 airplane target instances. The specific airplane categories include seven types: A220, A320/321, A330, ARJ21, Boeing 737, Boeing 787, and “other”, where “other” represents aircraft instances that do not belong to the remaining six categories. In addition, this dataset features complex scenes, rich categories, dense targets, and diverse scales. For each scene in the dataset, we extract each target according to the standard file, creating the real target dataset. Based on the research in Section 2, in the case of small errors, parameter mismatches result in slight deformation and defocusing of deceptive targets in the final image domain. Therefore, the real target dataset is re-generated using the RD imaging method. Since the imaging parameters of SAR-AIRcraft-1.0 are unknown, the generated targets will have some defocus compared to the real target slices. To simulate the complex geometric artifacts predicted by our signal-level analysis, we introduced an image-domain augmentation step to enhance the realism and diversity of deceptive targets. This process, termed “stretching and folding deformations”, was a randomized pipeline applied uniquely to each target slice. It combined random affine transformations (scaling: 0.98–1.02, rotation: ±2 degrees, shear: ±2 degrees) for first-order geometric distortions, and random elastic deformations for complex non-linear warping and “folding” effects. The latter involved applying displacement vectors to a coarse 2 × 2 grid and smoothly interpolating them. This randomization is crucial; it prevents the module from merely learning to invert specific artificial transformations. Instead, it compels the network to learn fundamental, invariant jamming signatures that persist across diverse geometric perturbations, thereby mitigating confounding variables and promoting robust generalization. The specific process is shown in Figure 6.

The following figure shows a partial demonstration; the first row represents the true target slices, while the second row represents the true targets prepared in this experiment. From

Table 10. Visual comparison between true and deceptive SAR targets across aircraft categories.

Group	Target Type
	A220	A330	A320321	ARJ21
True
False

, it can be seen that the deceptive targets prepared in this experiment look almost identical to the false targets visually, making it difficult for image interpreters to distinguish between them. This indicates that the deceptive targets have high realism.

To further verify the effectiveness of the deceptive targets, we use an interpretation network for evaluation. The interpretation network used in this experiment is TPH-YOLOv5 [50]. TPH-YOLOv5, based on the traditional YOLOv5 framework, introduces the Transformer Prediction Head (TPH) mechanism, which enhances feature expression and target focusing capabilities, particularly in small target detection tasks. We must emphasize that TPH-YOLOv5 is used here only as an external validation instrument and is not a component of our contribution. SAR image targets typically have small sizes, complex backgrounds, and various interferences, but the TPH structure can more effectively extract global information, improving the network’s ability to distinguish subtle differences between deceptive and true targets. Additionally, YOLOv5 is known for its efficient inference speed, strong real-time performance, and end-to-end detection capability, making it suitable for analyzing large-scale SAR data.

In the experiment, we split the SAR-AIRcraft-1.0 dataset into training, validation, and testing sets at a ratio of 7:1:2. Due to the relatively small scale of the dataset, YOLOv5s was chosen as the model configuration. The number of epochs was set to 150, and the batch size was set to 32. The experimental results are shown in

Table 11. Interpretation network performance comparison.

Method	P	R	F1	${\mathit{AP}}_{0.5}$	${\mathit{AP}}_{0.75}$
Faster R-CNN [49]	77.6%	78.1%	77.8%	71.6%	53.6%
Cascade R-CNN [49]	89.0%	79.5%	84.0%	77.8%	59.1%
Reppoints [49]	62.7%	88.7%	81.2%	80.3%	52.9%
SKG-Net [49]	57.6%	88.8%	69.9%	79.8%	51.0%
SA-Net [49]	87.5%	82.2%	84.8%	80.4%	61.4%
YOLOv5 [50]	90.3%	90.3%	90.5%	84.5%	50.5%
TPH-YOLOv5 [50]	92.4%	95.6%	91.6%	96.4%	68.9%

. From the results, it can be seen that TPH-YOLOv5 outperforms other networks in all metrics, demonstrating superior interpretation performance, making it suitable for use as a verification network.

To comprehensively validate the effectiveness and impact of our simulated deceptive targets, we conducted a two-stage evaluation. First, to verify the deception efficacy, we trained a TPH-YOLOv5 model exclusively on the genuine SAR-AIRcraft-1.0 dataset. This model was then used to test images where our high-fidelity deceptive targets were manually injected. The results, shown in Figure 7a–c, demonstrate that the network, having never been exposed to deceptive examples, consistently misclassified the fake targets as their genuine counterparts. This outcome confirms the high realism of our simulation pipeline and establishes the critical vulnerability of standard recognition models to such attacks.

Given this vulnerability, we then investigated whether a naive data augmentation approach could serve as a simple solution. In a second experiment, we retrained the TPH-YOLOv5 network on a mixed dataset composed of both genuine and deceptive targets. The results of this retraining, presented in Figure 8, reveal a critical and counterintuitive finding. Although the network learns to identify the deceptive class, its performance on the primary task of recognizing genuine targets was significantly impaired, with the average accuracy dropping by 16% (e.g., A220 accuracy fell from 98% to 83%). We identify this phenomenon as ’feature confusion.’ In its effort to learn the subtle discriminative cues separating genuine from high-fidelity deceptive targets, the network develops new feature representations that inadvertently conflict with the features it relies on for robust inter-class classification of genuine targets. This finding is crucial; it demonstrates that a naive retraining strategy is not a viable solution and can lead to a detrimental performance trade-off. It is this fundamental challenge of feature confusion that provides the primary motivation for our proposed MFE-STN module, which is architecturally designed to create a more robust and separable feature space to mitigate this very issue.

4.2. MFE-STN Module Experiments

In the previous section, we successfully verified the effectiveness of the deceptive targets, demonstrating that they could successfully deceive the interpretation system. In this section, we validate the improvement in deceptive target recognition provided by the proposed MFE-STN module.

To ensure the reproducibility and rigor of our evaluation, we constructed a dataset of 3400 images, including 1900 genuine and 1500 deceptive SAR targets. The genuine images were sourced from public datasets, while the deceptive counterparts were generated via a high-fidelity simulation process incorporating realistic parameter-mismatch effects. To rigorously evaluate generalization, the dataset was strategically structured into a “Known-Type” set (3000 images, e.g., A220, A320) and an “Unknown-Type” set (400 images, e.g., Boeing 737, Boeing 787), with the latter reserved exclusively for testing. This structure facilitates a two-tiered evaluation strategy; the “Known-Type” set was partitioned into a training set (70%, or 2100 images) and “Test Set 1” (30%, or 900 images) to assess performance on familiar target types. The entire “Unknown-Type” set served as “Test Set 2” to critically evaluate the model’s cross-domain generalization ability on entirely novel object classes. All models were implemented using the PyTorch 2.1.1 framework and trained for 150 epochs on a single NVIDIA A40 GPU with a batch size of 32. We employed the Adam optimizer with an initial learning rate of $1\times {10}^{-4}$ and a weight decay of $1\times {10}^{-5}$.

The baseline networks used in this experiment included Convnext [51] and GoogLeNet [52]. Additionally, a Support Vector Machine (SVM) was included as a traditional machine learning baseline to provide context for the problem’s complexity. This setup represents a standard and robust approach for image classification using classical methods. The proposed MFE-STN module was added to the very front of each of these baseline networks. To evaluate the robustness of the proposed MFE-STN module, we selected four categories from the target slice dataset: A220, A320/321, A330, and ARJ21. These categories were split into 70% training and 30% validation sets. The results of the training are shown in

Table 12. Classification performance of different networks with and without MFE-STN module.

Model	Train_Acc	Val_Acc	Precision	Recall	F1
ConvNext	82.76%	91.43%	91.45%	91.43%	91.44%
ConvNext_MFE-STN	99.95% (+17.19)	99.98% (+8.55)	99.98% (+8.53)	99.87% (+8.44)	99.93% (+8.49)
GoogLeNet	92.44%	86.02%	83.40%	92.58%	87.75%
GoogLeNet_MFE-STN	99.94% (+7.50)	99.94% (+13.92)	99.94% (+16.54)	99.94% (+7.36)	99.94% (+12.19)

Red values denote increases from the baseline (ConvNext or GoogLeNet).

and Figure 9.

As seen in the results, the MFE-STN module led to improvements in all metrics for the baseline networks. The accuracy on the validation set improved by an average of 11.2%, and other metrics saw improvements ranging from 7.4% to 16.5%. Additionally, convergence was faster. For the test set, Boeing737 and Boeing787 categories were used. The trained models were tested to validate the enhancement in robustness brought by the MFE-STN module. As shown in the group of unknown in

Table 13. Comparative evaluation of algorithm variants on known and unknown SAR target sets.

ID	Backbone/Variant	Modules			Performance (%)
		MFE		STN	Val_Acc	Precision	Recall	F1
		WT	RT–RM
Known set
1	SVM				78.75	83.23	71.25	76.78
2	VIT				78.68	79.84	78.68	79.26
3	GoogLeNet (Baseline)				86.02	83.40	92.58	87.75
4	+ WT	✓			88.61 (+2.59)	86.26 (+2.86)	94.55 (+1.97)	90.21 (+2.46)
5	+ RT–RM		✓		83.31 (−2.71)	85.61 (+2.21)	83.80 (−8.78)	84.70 (−3.05)
6	+ STN			✓	93.01 (+6.99)	91.82 (+8.42)	95.38 (+2.80)	93.57 (+5.82)
7	+ WT + RT–RM + STN	✓	✓	✓	99.94 (+13.92)	99.94 (+16.54)	99.94 (+7.36)	99.94 (+12.19)
8	ConvNext (Baseline)				91.43	91.45	91.43	91.44
9	+ WT + RT–RM + STN	✓	✓	✓	99.98 (+8.55)	99.98 (+8.53)	99.87 (+8.44)	99.93 (+8.49)
Unknown set (SAR-AIRcraft-1.0 dataset)
10	SVM				73.42	72.38	72.38	72.38
11	VIT				75.90	76.71	78.13	77.41
12	GoogLeNet (Baseline)				90.61	90.70	90.55	90.62
13	+ WT + RT–RM + STN	✓	✓	✓	100.00 (+9.39)	100.00 (+9.30)	100.00 (+9.45)	100.00 (+9.38)
14	ConvNext (Baseline)				86.08	86.10	86.05	86.07
15	+ WT + RT–RM + STN	✓	✓	✓	100.00 (+13.92)	100.00 (+13.90)	100.00 (+13.95)	100.00 (+13.93)

Red and blue values denote increases and decreases, respectively, from the baseline. The bolded parts represent the outstanding experimental results.

, the module was still able to help the baseline network improve recognition accuracy on unknown categories by more than 9.39 %, thereby enhancing the network’s robustness.

The experimental results shown in Table 13 demonstrate that after integrating the module into the baseline network, significant improvements are observed in both the discrimination of true/false targets across four known categories and two previously unseen target types. This strongly validates the module’s enhanced capability to capture critical discrepancies between genuine and deceptive targets, thereby substantially boosting the baseline network’s recognition performance.

For a comprehensive comparative analysis, we also benchmarked against the Vision Transformer (ViT) model. As shown in Table 13, the results are revealing; despite its formidable capabilities in many domains, ViT delivers suboptimal performance on this specific task of distinguishing between genuine and deceptive targets. Its precision is merely on par with the traditional SVM baseline and lags significantly behind our proposed model. This finding strongly suggests that CNN-based architectures are inherently more effective for this type of task, which in turn underscores the significance of our proposed module.

To further validate the contribution of the MFE-STN module, we conducted ablation studies using GoogLeNet as the baseline network. The experimental results, as shown in the GoogLeNet variants of the known group in Table 13, reveal the critical synergy between our proposed components. A particularly insightful result is that appending the RT-RM block in isolation (ID 5) leads to a decrease in validation accuracy (83.31%) relative to the baseline (86.02%). This is not an indication of the module’s failure but a confirmation of its specialized role. As quantitatively demonstrated in Table 5, RT-RM’s function is to amplify non-linear feature dissimilarities, a process that does not correct for the geometric misalignments that also challenge the network. The true efficacy of RT-RM is unlocked only when it operates in synergy with the STN module. The STN corrects the geometric distortions, allowing the classifier to effectively leverage the rich, discriminative feature space curated by RT-RM. This powerful interplay is evidenced by the performance of the full MFE-STN model (ID 7), where accuracy surges to 99.94%. While the other ablated variants (ID 4 and 6) show improvements over the baseline, their gains remain less pronounced than those of the complete module. This confirms that while each component contributes, it is their synergistic integration that provides the most substantial overall enhancement to the baseline network.

In the unknown set of Table 13—corresponding to the Boeing 737 and Boeing 787 categories that were entirely excluded from training—the results further highlight the generalization capability of the proposed MFE-STN module. Although these targets differ from the four known aircraft types used during training, the baseline networks still exhibit reasonably high accuracy. However, their performance plateaus due to their limited ability to capture intrinsic, target-agnostic deception signatures. In contrast, integrating the MFE-STN module yields a substantial improvement, achieving a perfect 100% accuracy across all evaluation metrics and delivering gains exceeding 9.39% over the baseline models. This performance boost demonstrates that the MFE-STN module does not simply learn class-dependent patterns. Instead, it extracts deeper, universal cues associated with deception jamming and allows the model to identify deceptive targets even when encountering previously unseen aircraft types. The unknown-set evaluation thus serves as a stringent cross-domain generalization test, verifying that the proposed module effectively mitigates overfitting and equips the network with robust, transferable discriminative capability.

To rigorously assess the real-world applicability of our proposed method and bridge the simulation-to-reality gap, we performed an empirical validation. The validation utilized a high-fidelity dataset of deceptive targets generated and acquired through our jammer. Given the constraints about the scarcity of real data, this validation is not intended as a large-scale statistical evaluation but rather as a decisive proof-of-concept. Its primary objective is to ascertain the model’s robustness and generalization capabilities. The validation set comprises a limited yet representative collection of measured samples, including deceptive aircraft targets and deceptive vehicle targets. The aircraft targets are considered in-distribution, as they belong to the class on which the model was trained. Critically, the vehicle targets represent an out-of-distribution (OOD) scenario, providing a stringent test for the model’s generalization capacity. This OOD evaluation is designed to determine whether the MFE-STN module has learned to identify universal, target-agnostic signatures of deception jamming, rather than merely memorizing class-specific artifacts. Both the baseline (GoogLeNet) and our proposed model (GoogLeNet_MFE-STN) were deployed for inference on these measured samples directly, without any fine-tuning.

The results, as presented in

Table 14. Comparative performance of GoogLeNet and GoogLeNet_MFE-STN on real data.

Property	M-01	M-02	M-03	M-04	M-05	M-06
SAR Image
Description	Aircraft	Aircraft	Aircraft	Aircraft	Vehicle	Vehicle
GoogLeNet	True	True	True	True	True	True
GoogLeNet_MFE-STN	False	False	False	False	False	False

Note: All six targets (M-01 to M-06) are physically measured deceptive targets, for which the ground truth is “False”. Bold text indicates a correct classification.

, are highly encouraging. The baseline GoogLeNet model was completely deceived in all six cases, erroneously classifying every deceptive target as genuine. In stark contrast, the GoogLeNet_MFE-STN model achieved perfect accuracy, correctly identifying all six deceptive targets. Furthermore, a noteworthy observation is that the baseline GoogLeNet model exhibited low confidence when making incorrect judgments, typically around 0.67. Conversely, all correct classifications by our proposed module were consistently accompanied by high confidence scores. This, on one hand, indicates the robustness of our proposed module’s decision-making process. On the other hand, it also suggests a high degree of similarity between our synthetic deceptive target dataset, used during training, and real-world deceptive targets. Moreover, during testing with actual targets, which included vehicle models, our proposed module consistently performed accurate discrimination. This remarkable success, particularly with OOD vehicle targets, provides strong empirical evidence that the MFE-STN module significantly enhances generalization to real-world signals and effectively mitigates overfitting to simulation artifact.

As shown in

Table 15. Comparison of computational overhead and throughput for baseline models with and without MFE-STN module integration.

Model	Params (M)	Thr. (FPS)	Time (ms)
ConvNext	0.61 –	1443.8 –	5.58 –
ConvNext_MFE-STN	1.62 (+1.01)	1373.8 (−70.0)	5.82 (+0.24)
GoogLeNet	0.41 –	896.7 –	8.92 –
GoogLeNet_MFE-STN	1.28 (+0.87)	776.0 (−120.7)	10.31 (+1.39)

Red and blue values denote increases and decreases, respectively, from the baseline (ConvNext or GoogLeNet).

, the integration of the MFE-STN module into both architectures leads to an increase in model parameters and inference time, accompanied by a decrease in throughput. Specifically, ConvNext_MFE-STN’s parameters increased by 1.01 M and its inference time by 0.24 ms, while GoogLeNet_MFE-STN saw an 0.87M increase in parameters and a 1.39 ms extension in inference time. Despite this evident computational overhead, it is crucial to emphasize that this represents a necessary trade-off for the MFE-STN module to achieve its intended significant performance improvements. The enhanced representational and spatial transformation capabilities endowed by MFE-STN ultimately lead to a substantial gain in overall performance, with its benefits far outweighing the incurred computational cost. Consequently, the MFE-STN module proves to be an effective and valuable component, representing a worthwhile investment for achieving superior results.

5. Discussion

5.1. Interpretation of Experiment Results

The experimental results indicate the effectiveness and robustness of the MFE-STN module. In evaluations on known target types, the integration of MFE-STN increased the F1-score of the baseline GoogLeNet by 12.19% and resulted in a validation accuracy exceeding 99.9%, outperforming the baseline models. Furthermore, the module exhibited strong generalization capabilities on previously unseen target types, achieving a score of 100% across all evaluation metrics, which represents an accuracy gain of over 9.39%. In the proof-of-concept validation using physically measured data, the baseline model misclassified all deceptive targets as true. In contrast, the MFE-STN-enhanced model achieved 100% correct identification, demonstrating its potential to bridge the simulation-to-reality gap. Ablation studies further suggest that the module’s performance stems from the synergistic interplay of its components, rather than a simple summation of individual parts.

These findings show that the proposed MFE-STN module can substantially enhance the capability of baseline CNN architectures to recognize deceptive false targets in SAR imagery. By integrating MFE-STN as a front-end, models such as ConvNext and GoogLeNet achieved significant improvements across all key performance metrics for both known and previously unseen target types. This outcome supports our central hypothesis; a feature extraction module engineered based on the physical generation mechanisms of deceptive jamming can outperform general-purpose, data-driven feature extractors.

5.2. Methodological Innovation and Strengths

In contrast to previous research [43,44,45,46], which often relied on handcrafted features with limited generalization in complex electromagnetic environments, our approach addresses certain deficiencies of existing methods. While recent studies have adopted deep learning, they typically employ standard CNNs in an end-to-end, “black-box” fashion. Although effective on known datasets, these models may lack a deep understanding of the intrinsic discrepancies between true and false targets, leading to diminished performance when encountering novel jamming techniques. The innovation of the MFE-STN module lies in its targeted design, which is a direct response to the two primary artifacts induced by parameter mismatches in SAR deception jamming: macroscopic geometric distortions and microscopic feature alterations. The STN component is designed to correct for macroscopic geometric shifts, such as scaling and rotation. Concurrently, the MFE block is engineered to capture subtle, microscopic variations in texture and scattering characteristics. This physics-informed modular design enables the network to learn from the root causes of the discrepancies, thereby achieving improved robustness and generalization.

A strength of this work is its systematic methodology. We first established a general signal model for convolutional deceptive jamming and analyzed the impact of seven key parameter mismatches on the fidelity of false targets. This foundational analysis provided a theoretical underpinning for the MFE-STN module’s design and guided the construction of a high-fidelity simulated dataset. Furthermore, our experimental validation was rigorous. Beyond testing on simulated data, the module’s efficacy was confirmed using physically measured real-world data. This result provides evidence of the model’s ability to bridge the “simulation-to-reality” gap, highlighting its potential for real-world application.

5.3. Limitations and Future Work

Despite these positive results, this study has certain limitations. The primary constraint is the reliance on simulated data for large-scale training, even though the dataset is high-fidelity and validated against real measurements. The difficulty in collecting and accurately labeling large volumes of diverse, real-world SAR deception jamming data remains a challenge in the field. Consequently, future work should prioritize validating and refining the model against a more extensive set of real-world data. Additionally, the integration of the MFE-STN module increases the parameter count and computational overhead of the baseline networks. While this trade-off may be justifiable for a critical task where accuracy is paramount, future research could explore model compression or knowledge distillation techniques to develop a more lightweight yet comparably performant version of the module.

Future research could proceed in several potential directions. First, the false target dataset could be expanded to include a wider variety of target classes and more complex background clutter to continually improve the model’s robustness. Second, the MFE-STN front-end could be paired with other state-of-the-art network backbones to explore the upper bounds of recognition performance. Finally, the functionality of the module could be extended from a classification task to an end-to-end detection and localization framework, enabling the automatic identification and pinpointing of false targets within broader SAR scenes.

6. Conclusions

This study proposes a versatile front-end module for SAR deception jamming target recognition to enhance the baseline network’s ability to identify deceptive targets. Experimental results show that the MFE-STN module significantly improves the performance of the baseline network, enhancing both the identification accuracy of false targets and the robustness of identifying unknown types of deceptive targets. Furthermore, a validation was performed using physically measured data. This study not only provides new ideas for the development of SAR false target recognition, but also offers theoretical support and technical approaches for the development of anti-jamming systems in complex electromagnetic environments.

Furthermore, the analysis of various parameters’ impact on the authenticity of false targets provides theoretical guidance for the development of jammer systems in modern battlefield environments. Although satisfactory results have been achieved, challenges remain. As candidly discussed in Section 4, a primary limitation is the reliance on simulated data. While our simulation is high-fidelity and physics-based and uses physically measured data to validate, future research must prioritize validating these methods against real-world measurements. Additionally, further work is needed to expand the dataset scale and conduct more granular parameter analysis to meet the practical needs of complex battlefield scenarios. Future research should continue to optimize false target datasets and improve the generalization of all modules to meet the practical needs of complex battlefield scenarios. With ongoing technological innovations, synthetic aperture radar deception countermeasures will play an increasingly important role in future electronic warfare.