Dual-Stage Algorithm Boosts BeiDou Signal Interference Detection and Suppression in Simulations

In controlled navigation satellite simulations, researchers have demonstrated a two-stage signal processing framework that pairs time-frequency analysis with artificial intelligence to detect and eliminate radio frequency interference in BeiDou B1I positioning transmissions. Developed by an engineering research team led by Fang Yuan, Yao Zhao, Xiao Feng, and Yong Liu, the approach integrates a lightweight convolutional neural network for rapid interference identification with a multi-scale wavelet packet transform module designed to suppress corrupting noise and reconstruct compromised navigation waveforms. Across extensive evaluations on tens of thousands of independently synthesized signal samples, the dual-stage pipeline attained an average interference recognition accuracy of 94.01 percent alongside a false positive rate of 3.31 percent. Furthermore, the subsequent wavelet packet reconstruction stage achieved a 94.63 percent signal recovery rate, a mean square error of 2.54 percent, and an output signal-to-noise ratio of 28.44 decibels in a rapid calculation span of 0.18 seconds.

However, satellite radio signals face severe physical vulnerabilities during orbital propagation because they must traverse immense spatial distances before reaching Earth-based receiver hardware. By the time high-frequency downlink transmissions arrive at ground-level antennas, their received signal power has attenuated substantially, rendering them exceptionally delicate and vulnerable to terrestrial electromagnetic disturbances. When environmental background noise, industrial emissions, or intentional ground-based transmissions share matching spectral frequency bands with greater energy intensity, navigation receivers can easily misinterpret high-powered interference as genuine orbital broadcasts, precipitating severe tracking drift or positioning failure. Conventional signal defense mechanisms frequently struggle in these volatile operating environments because standard suppression filters typically depend on static interference assumptions and fail to extract deep, non-stationary temporal and spectral features when dynamic electromagnetic jamming fluctuates across diverse jamming-to-noise ratios.

To establish an exact analytical foundation for automated signal defense, the investigative team formulated mathematical models representing six distinct categories of radio frequency interference commonly encountered by satellite receivers operating on the BeiDou B1I public service frequency. These modeled profiles encompass single-tone continuous wave interference, which concentrates stable sinusoidal energy at an isolated carrier frequency point, and multi-tone surplus continuous wave interference, which combines multiple distinct single-tone components into a structured periodic disturbance. Beyond continuous waves, the team modeled wideband interference using Gaussian broadband profiles, frequency modulation interference characterized by rapidly shifting spectral paths across time, sharp pulse interference featuring high instantaneous amplitude spikes, and Gaussian narrowband interference. Each interference pattern exhibits unique mathematical properties governed by power levels, carrier frequencies, modulation functions, and random phase distributions uniformly dispersed across the zero to two-pi interval. Modeling these disturbance profiles allowed the investigators to establish precise parametric benchmarks for testing receiver resilience under controlled laboratory conditions.

Recognizing that raw time-domain waveforms often obscure subtle signal anomalies, the researchers applied transform-domain methodologies to expose diagnostic multi-dimensional signatures. The extraction framework relies centrally on the short-time Fourier transform, which partitions incoming non-stationary signals into discrete temporal segments before applying Fourier transformation, thereby tracking dynamic spectral evolution as localized window functions glide across the observation window. To augment these continuous time-frequency representations with distinct quantitative descriptors, the investigators calculated specific mathematical indicators tailored to individual waveform behaviors. For broadband disturbances and sharp bursts, the researchers extracted the time-domain kurtosis coefficient, which measures the ratio of peak signal amplitude to mean amplitude to isolate transient pulse phenomena. They also computed an audio interference coefficient measuring the quotient between primary and secondary spectral modulus peaks to evaluate signal steepness, alongside a wavelet coefficient peak-to-average ratio that synthesizes peak, minimum, mean, and standard deviation metrics to capture local structural mutations across multi-scale decompositions.

The resulting normalized time-frequency feature maps and handcrafted statistical descriptors serve as direct inputs for a purpose-built, lightweight convolutional neural network designed to deliver high classification accuracy without incurring excessive computational latency. The neural architecture incorporates two sequential convolution-pooling stages: the primary layer applies 32 spatial filters of dimension three by three, and the secondary layer applies 64 identical three-by-three filters, with each convolution block followed by non-linear rectified linear unit activations and two-by-two max-pooling downsampling operations. The downsampled multidimensional features are flattened into a dense fully connected layer comprising 128 hidden neurons, regularized by a 0.50 dropout probability to curtail overfitting, before feeding into a final six-neuron Softmax classification layer corresponding to the six targeted interference classes. Model optimization was executed using the Adam algorithm with an initial learning rate of 0.001, a batch size of 64, an L2 weight regularization penalty of one ten-thousandth, and an early-stopping monitor tracking cross-entropy validation loss across a maximum of 100 training epochs.

Systematic training and testing were executed on a massive synthetic dataset structured to evaluate classifier resilience across wide fluctuations in jamming-to-noise ratios. The training split incorporated 74,400 total synthesized samples spanning jamming-to-noise ratios from negative 15 decibels to positive 15 decibels at one-decibel increments, providing 400 unique samples per interference class at each step, while the testing evaluation utilized 18,600 independently generated samples evaluated between negative 10 decibels and positive 20 decibels. Experimental results demonstrated that the convolutional model’s classification accuracy climbed steadily as interference intensity rose relative to background noise, achieving near-flawless recognition approaching 100 percent once jamming-to-noise ratios reached or exceeded negative five decibels. Individual interference profiles achieved performance stabilization at specific thresholds, with frequency modulation reaching stability at negative four decibels, single-tone interference at negative two decibels, multi-tone and narrowband interference at zero decibels, wideband interference at two decibels, and pulse interference stabilizing at three decibels.

When benchmarked against classical machine learning baselines under identical simulated conditions, the convolutional neural network demonstrated decisive operational advantages across multiple evaluation metrics. Over five independent test iterations, the convolutional network maintained an average recognition accuracy of 94.01 percent, outperforming support vector machines by 7.38 percent, energy detection methods by 8.36 percent, decision trees by 8.48 percent, and backpropagation neural networks by 5.86 percent. Furthermore, the convolutional architecture exhibited a false positive rate of 3.31 percent, reflecting reductions between 1.58 and 7.57 percentage points compared to the baseline algorithms, while completing recognition processing in 3.25 seconds—several seconds faster than all classical counterparts. The network also required only 50 seconds of training time, undercutting the 70 to 120 seconds demanded by alternative baselines. Although deeper architectures like ResNet and Transformer achieved marginally higher mean accuracy scores, post-hoc statistical evaluations using two-sided Welch’s t-tests with Holm adjustments revealed no statistically significant accuracy disparity (p equals 0.364), reinforcing the practical efficiency advantages of the lightweight network.

Following automated interference classification, the incoming signal passes directly into the second operational phase, where wavelet packet transform technology performs targeted signal purification and restoration. Unlike standard wavelet decomposition, which recursively divides only low-frequency approximations, wavelet packet transform systematically decomposes both low-frequency and high-frequency sub-bands, granting flexible, high-resolution partitioning across the entire time-frequency spectrum. The engineering pipeline implements a three-level wavelet packet decomposition utilizing a Daubechies-4 wavelet basis, chosen specifically for its compact temporal support and localization when isolating sharp, transient signal corruptions. Within the wavelet domain, normal navigation transmissions and background noise generate modest coefficient amplitudes, whereas high-powered interference produces intense localized spikes. To selectively excise these corrupted coefficients without stripping authentic navigation data, the algorithm applies an adaptive universal threshold proportional to the product of the estimated noise standard deviation and the square root of twice the natural logarithm of sample length, zeroing coefficients that breach the threshold boundary.

The filtering protocol also integrates a variance-ratio criterion function to measure structural similarity between the wavelet basis and incoming disturbance sequences, ensuring selective suppression in interference-dominated nodes while preserving delicate satellite signal structures. Once the identified interference coefficients are set to zero, the purified sub-band representations are transformed back into the continuous time domain via inverse wavelet packet reconstruction. Across repeated experimental evaluations with five independent noise realizations, the wavelet packet processing module achieved an average mean square error of 2.54 percent with a narrow standard deviation of 0.16 percent, outperforming standard continuous wavelet transforms, short-time Fourier filtering, basic Fourier transforms, and classical Kalman, mean, and particle filtering algorithms by margins ranging from 1.34 to 5.42 percentage points. Additionally, the wavelet packet stage attained a signal recovery rate of 94.63 percent, an output signal-to-noise ratio of 28.44 decibels, and an execution time of merely 0.18 seconds, satisfying the demanding timing requirements of practical satellite receiver tracking loops.

Despite the compelling performance demonstrated across simulated BeiDou B1I test scenarios, the authors emphasize several notable technical constraints that delineate the boundary between laboratory modeling and practical deployment. Foremost among these considerations is that all experimental conclusions stem from mathematically synthesized signal environments, meaning empirical validation on field-collected BeiDou and global navigation satellite receiver data under genuine electromagnetic conditions remains an essential next step. Additionally, while the model exhibited preliminary robustness when evaluating two-component composite interference mixtures—achieving 89.14 percent accuracy for combined continuous and wideband jamming, 91.56 percent for continuous and pulse jamming, and 85.52 percent for frequency modulation combined with narrowband disturbances—more complex real-world environments frequently generate multi-source jamming involving three or more overlapping emitters that have yet to be tested.

Subject of Research: BeiDou positioning signal interference recognition and suppression using time-frequency analysis

Article Title: BeiDou positioning signal interference recognition and processing algorithm based on time-frequency analysis

Article References: Yuan, F., Zhao, Y., Feng, X., & Liu, Y. (2026). BeiDou positioning signal interference recognition and processing algorithm based on time-frequency analysis. Discover Computing, 29(1), Article 884. https://doi.org/10.1007/s10791-026-10717-6

Image Credits: AI Generated

DOI: 10.1007/s10791-026-10717-6

Keywords: BeiDou Navigation Satellite System, BeiDou B1I signal, interference recognition, interference suppression, time-frequency analysis, convolutional neural network, wavelet packet transform, continuous wave interference, surplus continuous wave interference, Gaussian wideband interference, frequency modulation interference, pulse interference, Gaussian narrowband interference, short-time Fourier transform, jamming-to-noise ratio, signal reconstruction, signal-to-noise ratio, satellite navigation receivers