Previous Abstract
Return to Session B4
### Session B4: Spectrum: Protection and Optimization

Previous Abstract Return to Session B4

**An FD-DEFLATE Data Compression Scheme for C/N0 Estimation in GNSS Interference Monitoring**

*Wenhao Li, Lingtao Wang, Minghan Zhong, Mingquan Lu, Hong Li Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University*

Alternate Number 4

Interference monitoring is becoming increasingly crucial, as detecting interference of GNSS signals in time is the key to ensure the stability of GNSS. Common methods for GNSS interference monitoring include the analysis of changes in the GNSS signal carrier-to-noise ratio (C/N0)[1], [2], [3]. However, monitoring GNSS interference may exceed the computational abilities of local hardware due to the large amount of raw GNSS data. One solution is to receive and monitor the GNSS signals separately: GNSS signals are received by remote devices, then transmitted to a centralized monitor station for further signal analysis and extraction of critical parameters such as the signal power for each individual satellite[4], [5]. Due to the amount of data required to monitor GNSS interference being too large compared with common transmission bandwidth[6], transmitting all of the GNSS data without further compression would be too costly and inefficient. Therefore, it is necessary to compress GNSS data before its transmission.

There are several compression methods for GNSS data[7]. Considering the complexity and application conditions, such as prior knowledge of data, available computational resources, and real-time processing requirfements, etc., we have tested four widely used compression methods for their performance on GNSS data, including Huffman, LZ77 (Lempel-Ziv), DEFLATE, and DCT-Huffman. The first three methods are lossless compression methods, while the last one is a lossy one. The compression ratios obtained from the tests are 1.15, 1.28, 2.5, and 2.54, respectively. Although the compression effect is not particularly ideal, lossy compression offers a relatively better compression ratio. However, even with the most efficient compression method (DCT-Huffman), the compression ratio for GNSS signals does not exceed 3, which is insufficiently effective for reducing the amount of transmitted data. Therefore, there is a need to design a more effective compression scheme tailored specifically for GNSS data.

To this end, we have adopted lossy compression approaches for GNSS data. Unlike signals from conventional communication systems, GNSS signals utilize the autocorrelation properties of pseudorandom codes for power estimation, and it presents no strict requirements for bit error rates[8], [9]. As long as the signal degradation remains within an acceptable threshold and does not cause aliasing, the power estimation of the compressed signal would reflect the power of received signals. Consequently, lossy compression methods are applicable. As data compression ratio increases, there is a more serious signal degradation[10]. Therefore, a compromise must be struck between compression ratio and signal degradation.

To address this issue, focusing on C/N0 as primary indicator of interference monitoring, this paper proposed an FD (Frequency Division)-DEFLATE data compression scheme, and it could achieve significant data compression while incurring a stable C/N0 loss, which means the original C/N0 could be reliably estimated based on received C/N0 estimation. Given the stochastic nature and low power level of GNSS data after down-conversion, the sampled GNSS data can be likened to random noise[11]. Compression methods that depend on the occurrence probability of symbols generally struggle to compress such random data effectively. Due to poor compression performance in the time domain and the inherent spectral information carried by GNSS signals after modulation, it is considered to transform the raw data into frequency domain for compression. In frequency domain, lossy compression is feasible through the removal of peripheral frequency components. Meanwhile, inverse transformation to the time domain retains the essential frequency domain structure, thus preserving the signal's autocorrelation properties and enabling standard GNSS acquisition and tracking procedures and C/N0 estimation of signals. Therefore, the frequency domain is more suitable for GNSS data compression compared to the time domain.

The proposed FD-DEFLATE scheme is composed of three parts, including spectral transformation, frequency division, and data compression.

1. Spectral transformation. Various methods, including the Fourier Transform (FT), Short-Time Fourier Transform (STFT), Wavelet Transform and Discrete Cosine Transform (DCT), are available for converting time-domain signals to transform domains. The first three transformation methods are useful for analyzing frequency content, but they have limitations such as high storage cost, limited benefits and high complexity for GNSS signals, hence not suitable for compressing GNSS data. DCT offers the advantages of preserving real-valued signals post-transformation, possessing a straightforward transformation process, and representing only positive frequency components, thereby reducing data volume. Meanwhile, a large number of observations conclude that the transform coefficients obtained from the DCT transformation of the signal are predominantly concentrated within a relatively small range. Leveraging this property of the DCT technique, it is possible to discard small coefficients without affecting the recovery of original signals during inverse transformation, thereby retaining only the essential coefficients and achieving the goal of data compression. Based on the aforementioned analysis, the DCT emerges as the optimal choice for transforming GNSS signals to the frequency domain, facilitating effective compression.

2. Frequency division. The frequency domain signal is processed by the frequency division module, which primarily aims to retain sub-bands with significant energy proportions while discarding those with minimal energy. The approach introduced in this study employs an adaptive threshold mechanism based on the power spectrum of the modulated signal to facilitate frequency selection. By analyzing the main lobe width and contour of the power spectrum for various modulated signals, the method generates a tailored adaptive threshold. This strategic threshold not only enhances the efficiency of data encoding but also reduces reconstruction distortion errors in the compressed signal compared with single fixed threshold, thereby advancing the precision of the reconstruction process. A parameter ? which is defined over the interval 0 to 1, is utilized to define the range of threshold values, facilitating the adjustment of the adaptive threshold. The greater ? is, the more coefficients of frequency are reserved.

3. Data compression. Data compression techniques can be categorized into five types based on their underlying principles[12], including variable length coding (VLC), statistical compression, dictionary encoding, context modeling, and multi-context modeling. Statistical encoding methods like Huffman coding are simple and fast but less effective for low-bitrate frequency domain signals. Context modeling techniques, such as the Burrows-Wheeler Transform (BWT), are powerful but complex and require significant space for large symbol matrices, making them less suitable for high sample rate GNSS signals. Dictionary compression, on the other hand, leverages the repetitive sequences within the data and is advantageous due to its high compression efficiency for highly repetitive signals, low resource consumption, and suitability for low bitrate quantized GNSS signals. The dictionary compression method chosen for this scheme is the DEFLATE, which offers moderate complexity, fast compression speed, efficient flexibility and adaptability to different data types. In addition, it has shown superior performance in direct compression of GNSS data. Therefore, it is selected as the redundancy compression module for the frequency domain.

The decompression process is relatively straightforward, involving DEFLATE decompression of the transmitted signal followed by the application of the inverse DCT, which yields the decompressed GNSS signal.

The compression scheme was tested based on real-world GPS L1 C/A signal. The evaluation metrics include data compression ratio and the stability of C/N0 loss induced by compression. The sampling rate was set as 20MHz, with an intermediate frequency of 46.42MHz, and a quantization bit width of 3-bit.

Firstly, the compression ratio of the GNSS data utilizing the proposed scheme was tested. A comprehensive dataset was compressed, focusing on a 20ms segment of continuous data to illustrate the compression rate. Each 1ms data of 20ms was compressed independently to calculate the compression rate, thus there are 20 points in 20ms compression test. To maintain consistency, the method parameter ? was kept at a fixed value of 0.6. Since the noise was deemed random for each 1ms segment of the signal, the compression of these segments was considered as independent processes. To ascertain the consistency of the compression performance, a Monte Carlo test of 20,000 iterations was conducted for the compression of each original C/N0 signal. The resulting distribution indicates that the distribution of compression rate for the antenna signals is notably consistent, with an average around 9.5. Furthermore, the compression rate exhibit stability across various time intervals, suggesting robust performance of the method.

Then, C/N0 loss induced by the compression was tested. Narrowband-wideband power ratio estimation (NWPR) method[13] was utilized to estimate the C/N0 of both original and compressed data, and comparisons of them were performed to evaluate the loss. The results reveal the mean and standard deviation of the C/N0 loss for the compressed signals. The data indicates that the average loss in C/N0 for the antenna signals is 4.5 dB, with a distribution that demonstrates considerable stability. Importantly, for signals that originally had varying C/N0 values, the estimated C/N0 of the compressed signals accurately reflects the quality of the original signals, which is crucial for the detection of potential interference. In full paper, we will conduct more multi-level tests about C/N0 loss.

By fixing the test signal and adjusting the values of different parameters ?, the proposed method can achieve various compression rates for signal compression. It can be observed that higher compression ratios lead to greater signal loss, consequently resulting in a more significant decrease in C/N0. Within a certain range, the compression performance and loss of the method can be flexibly controlled by adjusting the value of the parameter ?, thereby addressing diverse signal environments.

Four existing compression methods, Huffman, LZ77, DEFLATE, and DCT-Huffman, were selected to compress the same test data for comparative performance evaluation. It is observed that the compression rate of each of the four existing methods is less than 3, while the compression rate of the proposed FD-DEFLATE method is 9.5. Therefore, this proposed method is effective in reducing the cost of data transmission for GNSS signal interference monitoring compared with the four existing methods. More detailed tests will be conducted in full paper.

In summary, the primary contributions of this paper can be attributed to the following aspects:

1. Focusing on the issue of large data transmission volume in GNSS interference monitoring, this paper proposed an FD-DEFLATE GNSS data compression scheme.

2. This proposed method achieves a compression rate of 9.5 for GNSS data with C/N0 loss of 4.5 dBHz, and exhibits stable C/N0 loss for different original C/N0 signals after compression, which could evaluate the original signal’s C/N0 based on the compressed signals. Therefore, this method is effective in reducing the transmission volume of GNSS interference monitoring.

3. The principle behind the proposed method is the transformation of GNSS data into spectral domain and adaptive threshold filtering, which increase the compression rate of the followed DEFLATE algorithm.

4. This method can be implemented on hardware platforms in the future and tested its performance in practical scenarios.

REFERENCE

[1] P. Wang, E. Cetin, A. G. Dempster, Y. Wang, and S. Wu, “Time Frequency and Statistical Inference Based Interference Detection Technique for GNSS Receivers,” IEEE Trans. Aerosp. Electron. Syst., vol. 53, no. 6, Dec. 2017, pp. 2865–2876.

[2] P. Craven, R. Wong, N. Fedora, and P. Crampton, “Studying the Effects of Interference on GNSS Signals,” presented at the Proceedings of the 2013 International Technical Meeting of The Institute of Navigation, Jan. 2013, pp. 893–186.

[3] A. T. Balaei and E. Aboutanios, “Characterization of Interference Effects in Multiple Antenna GNSS Receivers,” in 2010 3rd International Congress on Image and Signal Processing, Oct. 2010, pp. 3930–3934.

[4] E. D. Kaplan and C. Hegarty, Understanding GPS/GNSS: Principles and Applications, Third Edition. Artech House, 2017.

[5] R. Perez, V. R. Q. Leithardt, and S. D. Correia, “Lossless Compression Scheme for Efficient GNSS Data Transmission on IoT Devices,” in 2021 International Conference on Electrical, Computer and Energy Technologies (ICECET), Dec. 2021, pp. 1–6.

[6] L. R. Weill, “Theory and Applications of Signal Compression in GNSS Receivers,” presented at the Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Sep. 2007, pp. 708–719. Accessed: Jun. 18, 2023.

[7] X. Ma, C. Xu, P. Zhang, and C. Hu, “The Application of the Improved LZW Algorithm in the Data Processing of GNSS Simulation,” in 2012 Fourth International Conference on Computational and Information Sciences, Aug. 2012, pp. 160–163.

[8] R. B. Langley, P. J. G. Teunissen, and O. Montenbruck, “Introduction to GNSS,” in Springer Handbook of Global Navigation Satellite Systems, P. J. G. Teunissen and O. Montenbruck, Eds., in Springer Handbooks. , Cham: Springer International Publishing, 2017, pp. 3–23.

[9] A. Kumar, S. Kumar, P. Lal, P. Saikia, P. K. Srivastava, and G. P. Petropoulos, “Chapter 1 - Introduction to GPS/GNSS technology,” in GPS and GNSS Technology in Geosciences, G. p. Petropoulos and P. K. Srivastava, Eds., Elsevier, 2021, pp. 3–20.

[10] W. A. Pearlman and A. Said, Digital Signal Compression: Principles and Practice. Cambridge University Press, 2011.

[11] C. J. Hegarty, “GNSS signals — An overview,” in 2012 IEEE International Frequency Control Symposium Proceedings, May 2012, pp. 1–7.

[12] C. McAnlis and A. Haecky, Understanding Compression: Data Compression for Modern Developers. O’Reilly Media, Inc., 2016.

[13] M. Pini, E. Falletti, and M. Fantino, “Performance Evaluation of C/N0 Estimators Using a Real Time GNSS Software Receiver,” in 2008 IEEE 10th International Symposium on Spread Spectrum Techniques and Applications, Aug. 2008, pp. 32–36.

Previous Abstract Return to Session B4

For Attendees * *Technical Program * *Registration * *CGSIC * *Hotel * *Travel and Visas * *Smartphone Decimeter Challenge * *Exhibits * *Submit Kepler Nomination For Authors and Chairs * *Abstract Management * *Author Resource Center * *Session Chair Resources * *Panel Moderator Resources * *Student Paper Awards * *Editorial Review Policies * *Publication Ethics Policies For Exhibitors * *Exhibitor Resource Center * *Marketing Resources Other Years * *Future Meetings * *Past Meetings