Abstract
Radio frequency interference (RFI) poses challenges in the analysis of synthetic aperture radar (SAR) images. Existing RFI suppression systems rely on prior knowledge of the presence of RFI. This paper proposes a lightweight neural networkbased algorithm for detecting and segmenting RFI (LDNet) in the timefrequency domain. The network accurately delineates RFI pixel regions in timefrequency spectrograms. To mitigate the impact on the operational speed of the entire RFI suppression system, lightweight modules and pruning operations are introduced. Compared to thresholdbased RFI detection algorithms, deep learningbased segmentation networks, and ACUNet specifically designed for RFI detection, LDNet achieves improvements in mean intersection over union (MIoU) by 24.56%, 13.29%, and 7.54%, respectively.Furthermore, LDNet reduces model size by 99.03% and inference latency by 24.53% compared to ACUNet.
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Introduction
Synthetic aperture radar (SAR), as an allweather remote sensing radar, plays a crucial role in various fields such as remote sensing, reconnaissance, and space surveillance. SAR necessitates the reception of its echo signals, which are subsequently processed through algorithms for imaging^{1}. The purity of the echo signals significantly influences the subsequent imaging outcomes. However, during signal collection, SAR may inadvertently capture spurious signals in adjacent frequency bands, collectively referred to as radio frequency interference (RFI)^{2}. RFI has the potential to mask the scattering effects of weak signals, impeding the analysis of SAR imaging results. Consequently, suppressing RFI in SAR signals has become a pivotal research direction.
Currently, scholars have proposed various algorithms for the suppression of RFI^{3}. These algorithms encompass traditional parameterized algorithms^{4,5,6,7}, nonparameterized algorithms^{8,9,10}, and semiparameterized algorithms^{11,12}. With the accumulation of data, the application of deep learningrelated technologies for RFI suppression has witnessed rapid development^{13,14,15}. By leveraging various neural network architectures, requirements for RFI suppression can be effectively addressed across multiple domains including the time domain, timefrequency domain, and image domain^{16,17,18}.
The aforementioned algorithms for RFI suppression process signals containing RFI after determining whether the signal is affected by RFI . However, these algorithms do not consider the potential impact of RFI processing on data points that do not contain RFI across various domains. Chojka et al.^{19} employed a convolutional network as a classifier to preliminarily differentiate images with and without RFI in the image domain. Artiemjew et al.^{20} used a LeNettype convolutional neural network to identify various levels of RFI damage in SAR images. Nevertheless, these two algorithms can only indicate the presence of RFI in images and do not precisely mark RFI regions. Tao et al.^{21} proposed a timeseriesbased RFI extraction model using Sentinel1 data in the same area, involving matrix decomposition and hyperparameter settings that incur significant computational complexity. Li et al.^{22} achieved the construction of Sentinel1 ground range detected (GRD) products without RFI background. Subsequently, they analyzed the differences between the constructed background and the images to identify Sentinel1 GRD products containing RFI. While this algorithm is concise and capable of rapidly screening and detecting many GRD products, its robustness is relatively low. Despite the convenience and intuitiveness of imagedomain RFI processing algorithms, their accuracy falls short of algorithms applied in the signal and timefrequency domains.
Fan et al.^{16} addressed the RFI detection problem as a twoclass classification issue in the timefrequency domain, utilizing VGG16 as the primary network to screen timefrequency spectrograms containing RFI. This algorithm filters spectrograms that include RFI but does not provide precise localization of the RFI, limiting its assistance in subsequent RFI suppression. Li et al.^{23} introduced a timedomain detector for detecting and locating impulsive RFI based on high RFI energy and shortduration characteristics. However, this algorithm exhibits poor performance in detecting weak RFI. Subsequently, they proposed a timefrequency detector combining eigenvalue decomposition (EVD) and shorttime Fourier transform (STFT)^{24}, which, compared to the reference, demonstrates improved detection and localization of weak RFI but involves complex spectral analysis processes. Ding et al.^{25} conducted statistical analysis on SAR signals after STFT, treating them as Rayleighdistributed. They employed a constant false alarm rate (CFAR) algorithm to detect RFI, aiming to optimize the final suppression effect. However, this thresholdbased approach faces challenges in balancing falsenegative and falsepositive probabilities.
Most studies treat the detection and suppression of RFI as relatively independent issues. This paper proposes a lightweight algorithm based on deep learning that exhibits precise RFI detection capabilities (LDNet) in the timefrequency domain. This algorithm can be combined with timefrequency domain RFI suppression algorithms to enhance the suppression effects without altering the underlying suppression algorithm. The specific research contributions are summarized as follows:

(1)
The algorithm can effectively distinguish whether RFI exists in timefrequency spectrograms. It accurately labels the RFI positions for spectrograms containing RFI and generates the corresponding binary matrices.

(2)
To mitigate the impact of the RFI detection algorithm on the overall operational speed of the suppression system, we introduce lightweight modules in the neural network design. Further reduction in the size of the network model is achieved through pruning operations while maintaining accuracy.

(3)
Experimental results demonstrate excellent RFI detection performance of the algorithm on a lightweight basis.
The remaining structure of this paper is as follows: “Methods” provides a detailed introduction to the LDNet model. “Results” evaluates the specific detection performance of the network against RFI and the degree of model lightweight. “Discussion” discusses the detection and segmentation performance of LDNet, along with its limitations. Finally, “Conclusion” summarizes the content of this paper.
Methods
The detection of RFI plays a pivotal and foundational role in implementing RFI suppression. Current RFI detection algorithms primarily filter the presence or absence of RFI without delving into the correlation and integration with RFI suppression algorithms. In light of the shortcomings observed in previous research, this study introduces an RFI detection algorithm, termed LDNet, based on deep neural networks. Firstly, the algorithm accomplishes fundamental RFI filtering by effectively screening the signal in the timefrequency domain. Secondly, the algorithm accurately labels RFI regions and generates corresponding binary matrices for timefrequency spectrograms containing RFI. Utilizing the generated binary matrices, the regions with RFI in the timefrequency spectrograms obtained from the RFI suppression algorithm are suppressed, while the regions without RFI retain the original timefrequency spectrogram data. This strategy enhances the suppression effect without altering the RFI suppression algorithm. Finally, to mitigate the impact of the RFI detection step on the overall operational speed of the RFI suppression process, we employ deep separable convolutions and a “cheap” attention mechanism to construct the network structure. This design allows for obtaining local and global information simultaneously while reducing the computational complexity of the network. Additionally, network pruning is applied to remove redundant parameters, further diminishing the computational complexity of the network. The complete processing flow is shown in Fig. 1.
Network architecture
The objective of LDNet is to extract regions affected by RFI from input timefrequency spectrograms. The architecture of this network is illustrated in Fig. 2, with its input being the timefrequency spectrogram of SAR signals. The output consists of a binary matrix indicating whether RFI influences data points.
The input of LDNet is defined as \(\mathcal {S}\in \mathbb {R}^{3\times H\times W}\). The Stem module expands the input in both the channel and spatial dimensions to capture edge information of RFI regions in the timefrequency spectrogram, ensuring that the network does not lose any crucial information during feature extraction. Subsequently, the channel dimension is reduced, integrating the extracted channel information , while the spatial dimension is restored to its original size to reduce data volume. The output of the Stem module is denoted as \(\mathcal {S}_1\in \mathbb {R}^{8\times H\times W}\). The feature mapping of the Stem module can be represented as:
where \(Conv_\uparrow\) represents the convolutional and batch normalization operations that expand spatial dimensions, and \(Conv_\downarrow\) represents the convolutional and batch normalization operations that reduce spatial dimensions. \(Conv_{3 \times 3}\) represents a convolutional operation of size \(3 \times 3\) without adjusting spatial dimensions, and \(Conv_{1 \times 1}\) represents a convolutional operation of size \(1 \times 1\). \({f_R}\) represents the ReLU6 activation function. ReLU6 is a special type of ReLU function, calculated as follows:
Following this, the network integrates local and global information through multiple information extraction modules (IEM), generating the feature map \(\mathcal {S}_2\in \mathbb {R}^{C\times H\times W}\). The structure of the IEM will be detailed in the next subsection.
Finally, pointwise convolution is directly applied in the Head module to compress the channel information, reducing the channel dimension of \(\mathcal {S}_2\) to 2. This operation represents dividing the categorization of the overall feature map into two classes (presence or absence of RFI), denoted as \(\mathcal {S}_3\in \mathbb {R}^{2\times H\times W}\). Its feature mapping can be represented as:
In postprocessing, the values in different channels of \(\mathcal {S}_3\) are interpreted as probabilities indicating the presence or absence of RFI, where 0 represents the presence of RFI and 1 represents the absence of RFI, ultimately generating a binary matrix.
Information extraction module (IEM)
The input feature map is bifurcated into two branches in the information extraction module (IEM) to compute new feature maps. The mapping process of the IEM is illustrated in Fig. 3. For ease of analysis, the input feature map to the nth IEM is defined as \({\mathcal {S}}_{2n}\), and the output as \({\mathcal {S}}_{2n}^{\prime }\).
For local information extraction, we employ a structure akin to inverted residuals. Initially, pointwise convolution is conducted in the channeldepth direction to amalgamate information across channels within the same spatial dimension, generating a novel feature map. Concurrently, we widen the channel dimension to better represent more detailed information . Subsequently, depthwise convolution is applied in the spatial dimension to each input channel, reducing network parameters based on learning both channel and spatial information. Finally, pointwise convolution is again utilized to compress the channel numbers of the feature map that has acquired spatial information, diminishing the volume of data transferred. The mapping process for local information extraction can be represented as:
Regarding the use of the ReLU nonlinear activation function, we apply it in highchannel dimensions based on the “manifold of interest” theory^{26}.
For the timefrequency spectrogram of SAR signals, it is of low rank in the absence of RFI. Even in the presence of RFI, the timefrequency spectrogram can be decomposed into a lowrank matrix and a sparse matrix. Hence, there is no need to compute relationships between feature map data points densely. This aligns with the assumption of the decoupled fully connected attention mechanism (DFC)^{27}, which assumes a lowrank condition for images. Therefore, in terms of global information extraction, we employ DFC to compute cheap global attention. Initially, ordinary convolution is used to integrate the spatial and channel information of the feature map, followed by the aggregation of information from different positions along the horizontal and vertical directions to compute attention values for each point. Computing attention values at horizontal and vertical positions for one data point involves the corresponding attention values at its respective horizontal and vertical positions. Thus, this design can encompass all data points, extract global information, and reduce network parameters. The mapping process for global information extraction can be represented as:
where \(Conv_{1 \times k}\) and \(Conv_{k \times 1}\) represent convolution operations with \(1 \times k\) kernels in the horizontal and vertical directions, respectively. Since there is no significant increase in the channel dimension during the process of extracting global information, no activation function is applied. In the backend of the IEM, local and global information extraction results are fused through elementwise summation, completing the feature mapping process for this module. The final output feature mapping process for the IEM can be represented as:
Computational analysis
To achieve a lightweight architecture, we refrain from using common residual blocks and transformer attention mechanisms in the IEM. For the design of the local information extraction network, assuming the input feature map dimensions are \([C_{in},H,W]\), we retain its spatial dimensions, increase the channel dimension, and transform the feature map to \([C_{hid},H,W]\), followed by reducing the channel dimension to yield a feature map of dimensions \([C_{out},H,W]\). If using a standard \(3\times 3\) convolution operation, the computational cost is given by:
For the local information extraction mechanism in IEM, the computational cost is:
Assuming \(C_{hid}=4\cdot C_{in}\), when \(C_{out}=2\cdot C_{in}\), the computational cost ratio is \({9\cdot C_{in}}/{(C_{in}+3)}\), indicating that when \(C_{in}>3/8\), the computational cost of the local information extraction mechanism in IEM is less than that of ordinary convolution. Similarly, when \(C_{out}=1/{(2\cdot C_{in})}\), the computational cost ratio is \({9\cdot C_{in}}/{(C_{in}+6)}\), signifying that when \(C_{in}>3/4\), the computational cost of the local information extraction mechanism in IEM is less than that of ordinary convolution. In the network design, these assumptions are feasible, and the dimensions of the input mappings in the network are always greater than 1.
For global information extraction, assuming the input feature map is \([C_{in},H,W]\) and the output feature map is \([C_{out},H,W]\). In transformer^{28}, calculating the attention value for one data point requires simultaneous involvement of all data points, resulting in an excessively large network model. If the complete attention mechanism in transformer is used, the computational cost is given by:
For the global information extraction mechanism in IEM, assuming a \(3\times 3\) convolution is used, with convolution size \(1\times 5\) in the horizontal and vertical directions of the spatial dimension, the computational cost is:
The computational cost ratio between the two mechanisms is \({(2\cdot H\cdot W+3\cdot C_{in}+C_{out})}/{(10+9\cdot C_{in})}\). Given that the spatial dimensions of the feature map in IEM remain uncompressed, the large value of \(H\cdot W\) indicates that the computational cost of the global information extraction mechanism in IEM is significantly lower than that of the transformer attention mechanism.
Network pruning
In the initial stages of network design, a considerable amount of redundant data is often introduced into the structure to enhance the network’s learning capability. However, this design approach poses a clear contradiction to the original intention of lightweight the network. To address this issue, we employ a structured pruning approach that effectively reduces redundant information within the network.
Specifically, we use the weights of convolutional kernels as indicators of their importance, measuring it through the \(L_2\) norm. This metric effectively captures each kernel’s contribution to network learning, enabling precise identification of kernels that contribute less to improving network performance. Subsequently, we implement pruning by removing kernels with lower importance, thereby achieving lightweight network structure. To achieve optimal lightweight effects, we iteratively optimize the network structure through multiple rounds of pruning and finetuning. This cyclic process reduces the model’s parameter size while preserving network performance and ensures robust performance on both training and testing datasets. Table 1 presents the specific architecture of each layer in the network and the resulting structure after pruning. Table 2 presents the variations in channel dimensions across four IEMs.
Results
We incorporated simulated RFI into real SAR echoes to emulate disturbed scenarios. The simulated RFI considered parameters such as the signal’s frequency, bandwidth, chirp rate, modulation index, and quantity. Three types of signals were designed: narrowband interference (NBI), chirpmodulated wideband interference (\(\hbox {WBI}_{\text {CM}}\)), and sinusoidalmodulated WBI (\(\hbox {WBI}_{\text {SM}}\)). Additionally, the range of signaltointerference ratio (SIR) was set between \(1\) and \(10\) dB. In order to enhance the network’s ability to detect RFI, we devised scenarios involving the mixture of multiple instances of the same category of RFI within a single signal and the combination of diverse RFI within a single signal. To prepare the data for training and evaluation, we transformed the simulated signals into the timefrequency domain using STFT. The resulting spectrograms were resized to dimensions of 256 \(\times\) 256 pixels and saved as RGB images with dimensions of 256 \(\times\) 256 \(\times\) 3. During training and testing, the data values were scaled to a range of 0 to 1 by dividing by 255.
For the RFI detection task, we annotated the spectrograms such that regions containing RFI were marked with a value of 1, while nonRFI regions were labeled with 0.
During network training, the mean squared error (MSE) loss function guided learning, with dynamic learning rate adjustment using the adaptive moment estimation (Adam) optimizer.
To validate the RFI detection performance of LDNet, we conducted comparisons with thresholdbased CFAR, segmentation networks based on deep learning, and ACUNet^{29} dedicated to RFI detection. We compared LDNet with deep learningbased networks to affirm its lightweight characteristic.
Comparison of RFI detection results
RFI detection can be treated as a binary state detection problem with CFAR. Typically, the maximum false alarm probability (MFAP) is chosen within the range of \(\left[ 10^{3},10^{8}\right]\). We set the MFAP to \(10^{6}\), and tested under the SIR of \(6\) dB. As shown in Fig. 4, LDNet outperformed CFAR in RFI detection . CFAR mistakenly labels spectrogram points exceeding a threshold as RFI, disregarding their true nature.
We created a test dataset spanning SIR values from \(1\) to \(10\) dB and evaluated eight algorithms: CFAR, FCN, LRASPP, three algorithms based on DeepLabV3+ with MobileNetV2^{26}, ResNet101^{30}, and Xception^{31} backbones , JSLCNN^{32}, and ACUNet. We treated RFI data points as positive and nonRFI data points as negative, allowing us to obtain the false positive rate (FPR) and false negative rate (FNR) of each algorithm’s segmentation results.
Table 3 compares the mean intersection over union (MIoU) , FNR, and FPR of each algorithm with LDNet. CFAR outperformed FCN and LRASPP due to the data imbalance between nonRFI and RFI points. DeepLabV3+ , JSLCNN and ACUNet enhanced RFI detection by fusing features, but suffered from reduced pixel accuracy. Through multiple iterations of pruning and finetuning training, the pruned LDNet exhibits slightly superior RFI detection performance compared to the unpruned LDNet. LDNet’s FPR and FNR were not the lowest, but its overall misclassification rate was the lowest.
Utilization of confusion matrices for a detailed analysis of algorithmic classification performance. At SIR \(= 6\) dB, Figure 5 illustrates the detection results of various algorithms. CFAR exhibits high RFI precision but suffers from many nonRFI misclassifications. Deep learning algorithms frequently mislabel RFI. FCN and LRASPP had poor RFI classification. DeepLabV3+based algorithms and JSLCNN showed comparable effectiveness. ACUNet avoided nonRFI misclassifications but frequently mislabeled RFI. Such errors are more consequential than nonRFI misclassifications. LDNet had the lowest misclassification rate, demonstrating superior RFI detection accuracy.
Comparison of networks’ comprehensive performance
Rapid RFI detection algorithms can significantly enhance the operational speed of the entire RFI suppression system. Table 4 provides a detailed overview of all deep learning algorithms utilized in this study, including their parameters, floatingpoint operations (FLOPs), frames per second (FPS), and latency. LDNet has the smallest model size, but its parallel local and global information extraction results in higher FLOPs than LRASPP, yet lower than others. LDNet also shows the fastest prediction speed. Among all models, ACUNet and LDNet perform best. Compared to ACUNet, LDNet reduces parameters, FLOPs, and latency by 99.03%, 95.19%, and 24.53%, respectively, while increasing FPS by 32.59%, indicating its significant advantage.
We evaluated network scale using parameters, prediction speed using latency, and RFI detection quality using MIoU. Figure 6 shows a threedimensional scatter plot visualizing the networks’ performance. Points nearer to (1,0,0) indicate better overall performance. JSLCNN, ACUNet , and LDNet all outperform other algorithms significantly , with LDNet demonstrating higher accuracy, lower latency, and a smaller network scale.
Discussion
Segmentation performance of LDNet
A lower SIR indicates a greater distinction between RFI and SAR signals, theoretically facilitating detection. This is because, at lower SIR levels, the characteristics of the RFI are more pronounced, making them easier to identify and segment. We evaluated the segmentation performance of LDNet under the SIR conditions specified in our experimental environment, and the results are shown in Fig. 7. It can be observed that within the SIR range of the dataset, LDNet demonstrates effective and stable detection performance.
To further evaluate LDNet’s performance beyond the SIR range defined in the dataset, we conducted additional tests at 0 dB, 5 dB, and 10 dB, as illustrated in Fig. 8. At 0 dB, LDNet maintains robust segmentation performance, effectively identifying and segmenting RFI signals. However, at 5 dB, we observed instances where LDNet misclassifies some RFI points as nonRFI when the SAR signal is in a highamplitude region. This suggests a reduction in LDNet’s accuracy under specific conditions. At 10 dB, there is a noticeable decline in segmentation performance. Nevertheless, it is important to note that at 10 dB, the influence of RFI on SAR imaging is minimal. Thus, even with less precise segmentation, the overall imaging quality remains largely unaffected.
Impact of misclassification
Misclassification can occur in two scenarios: RFI data points misclassified as nonRFI, and nonRFI data points misclassified as RFI. Misclassifying RFI as nonRFI results in incomplete RFI suppression, potentially leaving residual RFI in the timefrequency spectrograms, which can compromise subsequent data processing accuracy. Conversely, misclassifying nonRFI as RFI alters nonRFI data during suppression, leading to integrity and authenticity issues.
Based on the FNR and FPR results in Table 3, LDNet does not achieve optimal performance in either type of misclassification. However, upon analyzing their impact on RFI suppression, similar misclassification rates highlight the greater influence of FNR over FPR. An exception is CFAR, which, being thresholdbased rather than semanticbased, may misclassify highamplitude nonRFI information as RFI, thereby failing to protect such data. In summary, LDNet demonstrates superior overall performance considering combined misclassification effects.
Limitations and future directions
One limitation of LDNet is that some of its channel numbers are not powers of two, potentially reducing the efficiency of hardware parallel computation. To overcome this limitation, future research could concentrate on designing specialized hardware accelerators optimized for handling nonpoweroftwo channel numbers. These accelerators would involve tailored designs in processor architecture, memory access patterns, and computational units, thereby enhancing support for such channels and improving hardware parallel computation efficiency.
RFI in realworld environments exhibit diverse and complex characteristics, which may differ significantly from the training data distribution. Addressing this challenge requires the development of adaptive and online learning mechanisms for LDNet. These mechanisms would enable dynamic adjustment based on realtime received signals, thereby enhancing robustness against previously unseen interference signals. Additionally, leveraging data augmentation and synthetic techniques to enrich the training dataset can further bolster LDNet’s ability to generalize across varied environments and scenarios, thereby enhancing its performance in managing complex and variable RFI.
The integration of LDNet into existing RFI suppression systems necessitates careful consideration of compatibility and interface issues with other system components. Future research should therefore prioritize integrating LDNet into practical systems, conducting extensive testing to resolve compatibility challenges, and validating its performance and reliability in realworld environments.
Conclusion
This paper introduces a lightweight neural network for detecting and segmenting RFI, providing a novel perspective for enhancing the suppression effectiveness of RFI suppression algorithms in the timefrequency domain. Unlike algorithms that separate detection and suppression algorithms, this approach can filter timefrequency spectrograms containing RFI and identify the pixel regions affected by RFI, thereby optimizing the suppression results of RFI suppression algorithms. Experimental validation demonstrates that the proposed algorithm is lightweight and capable of effectively identifying RFI regions in the timefrequency domain .
Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
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F.Z. was responsible for the main conceptualization, experimentation, and manuscript writing of this project. Z.Z. and D.Z. conducted figure editing and contributed to manuscript writing. All authors reviewed the manuscript.
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Zheng, F., Zhang, Z. & Zhang, D. Lightweight deep neural network for radio frequency interference detection and segmentation in synthetic aperture radar. Sci Rep 14, 20685 (2024). https://doi.org/10.1038/s41598024717758
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DOI: https://doi.org/10.1038/s41598024717758