Unsupervised interpolation recovery method for spectrum anomaly detection and localization

First, authors elaborate the proposed unsupervised spectrum interpolation recovery method in aspect of principles and implementation.

The received signals by spectrum managers contain several components, including normal signals s(t), abnormal (interference) signals i(t), and noise n(t). After receiving the data, the short-time Fourier transform (STFT) transformation is performed to generate the spectrogram S_normal or S_anomaly. The task of anomaly detection is to distinguish atypical spectrogram containing i(t) convolution item. The output is a Boolean value, with anomaly and normal samples corresponding to 1 and 0, respectively. The task of anomaly localization is to indicate the corresponding position of this anomaly item i(t), in S_anomaly. The output is a Boolean matrix, with pixel values corresponding to anomaly and normal signals being 1 and 0, respectively.

The spectrum interpolation recovery method (as depicted in Fig. 1) employs a masked AE model which follows an overall encoder–decoder architecture. The model’s encoder takes the visible portion S_visible of the spectrogram S as input and produces a representation Z_visible of the visible portion. The model's decoder takes the sequentially arranged representations Z_mask and Z_visible corresponding to the original spectrogram as input and generates the restoration results Ŝ_mask for the masked portion. The key to implementing spectrum interpolation recovery lies in establishing the relevant patterns, or interpolation weights, between features Z_visible and Z_mask.

The anomaly score function serves as a bridge between the generation model and the anomaly detection or anomaly localization tasks. The spectrogram is partitioned into n regions using a fixed-shaped mask for separate interpolation recovery. The obtained interpolation recovery result of the i th region is Ŝ_mask⁽ⁱ⁾. The differences between Ŝ_mask⁽ⁱ⁾ and S_mask⁽ⁱ⁾, denoted as D_d⁽ⁱ⁾ and D_l⁽ⁱ⁾ via their anomaly detection and anomaly localization score functions, then are summed up as ∑D_d⁽ⁱ⁾ and ∑D_l⁽ⁱ⁾. Classification is performed based on ∑D_d⁽ⁱ⁾ and ∑D_l⁽ⁱ⁾, yielding the final abnormality detection and localization results.

A dataset for anomaly detection and localization in the 5-GHz ISM band was developed. The normal signals consisted of real-world Wi-Fi signals, whereas the anomalous signals were artificially added to the baseband signals after down-conversion in the universal software radio peripheral (USRP). The method is implemented in PyTorch and trained on NVIDIA Tesla V100 GPU.

Fig. 1. Overview of the MAE model structure.

Then, authors present the experimental results.

The anomaly detection and localization performance of the spectrum interpolation method were evaluated on the 5.2-GHz ISM dataset under varying SNR, ISR, and abnormal types using a diagonal mask shape with a mask ratio of 25% (Fig. 4). The overall abnormal detection performance AUC = 0.9736 (Area Under receiver operating characteristic Curve) and abnormal localization performance AUPRC = 0.4883 (Area Under the Precision-Recall Curve) over the entire dataset were calculated. Both anomaly detection and localization performance were positively correlated with ISR. Among the 3 variables, ISR had the most significant impact on performance, followed by the shape of the abnormal signal, while the influence of SNR was inconspicuous (Fig. 4). Ignoring the label imbalance in anomaly localization, if the over the entire dataset performance of abnormality localization is evaluated using AUC, which is AUC = 0.8336 and lower than the abnormality detection performance indicated by AUC = 0.9736, suggesting that the abnormality localization performance is poorer compared to abnormality detection.

To demonstrate the performance improvement of the spectrum interpolation method, we designed the ViT-AE model and compared the sample-level and pixel-level accuracy of the 2 methods on normal and abnormal samples for both anomaly detection and localization tasks. In comparison with a generation model with higher accuracy, the precision in generating distinguishable out-of-distribution and in-distribution data is of greater importance. From the increase in discrimination resulting from the decrease in precision on anomalous samples, it is believed that the spectral interpolation recovery method avoids the over-recovery of anomalous samples. Besides, large-scale reconstruction errors caused by anomalous signals are diluted, equivalent to a reduction in the scope of reconstruction errors, thus improving the performance of anomaly localization. The results listed in Table 2 indicate that the spectrum interpolation recovery method can improve the performance of anomaly detection and localization.

In addition, the influence of different mask ratios on performance was tested on the 2.4-GHz ISM dataset. The performance showed a positive correlation with the mask ratio, with the best performance achieved with a 75% mask ratio.

Fig. 4. Anomaly detection and localization performance under different ISR, SNR, and anomaly types.

Finally, authors conclude the paper. (1) The proposed Unsupervised Interpolation Recovery Method and established data set effectively address the issues of over-recovery and large-scale reconstruction error, and improve the anomaly detection performance AUC 0.0382 (3.68%) and localization performance AUPRC 0.1992 (68.90%), respectively. Moreover, by leveraging visible spectrum sub-intervals as input, the proposed method can capture more temporal information, which is beneficial for anomaly detection and localization. (2) The SSIM (Structure Similarity Index Measure) and Mae (Mean Absolute Error) anomaly scores yield the best results in anomaly detection and localization, respectively. When the false-positive rate is 0.05, the proposed method achieves total recall rates of 0.8799 and 0.5536 for anomaly detection and localization, respectively. (3) Comparative studies on 2 datasets verify the effectiveness of the proposed method under different conditions. However, the performance improvement of the proposed method comes at the cost of increased computational complexity, which limits its practical deployment and further enhancement in scenarios with limited computational resources. It also hinders the ability to increase the bandwidth or frequency resolution of the spectrogram input.