The Karhunen-Loève Transform as a Future Instrument to Interference Mitigation

A. Szumski, B. Eissfeller

Abstract:	Interference is one of the biggest threats of radio-communication systems. For the positioning systems, interference in GNSS signals causes degradation of the positioning system performance including inability to determine a position. Recent case of the Light-Square electromagnetic compatibility (EMC) problem or interfering transmitters of terrestrial DVB-T networks are the examples how difficult is to use a dedicated bandwidth without harmfully interfere other systems. There is also a growing problem of jamming devices which are today very small, simple to produce, easy accessible and which can significantly degrade the GNSS signal in a distance of many kilometers. There is therefore a big interest to protect GNSS signal and one of the way to make it is filtering the signal coming out from a receiver front-end. There are many methods and algorithm already existing and well known, such as the Fast Fourier Transform (FFT) or the Short Time Fourier Transform (STFT), used for signal analysis and followed in an algorithm by excision of a detected interference. Mentioned analysis methods are mature and easy to use. They are however based on the Fourier Transform (FT) which has limitations and as a consequence have a reduced possibility to detect interference. One of the main limitations is that methods based on the FT analyses signal only in a deterministic way and uses for the analysis a limited number of functions determined in advance. Another mathematical tool can be used for decomposition of data, similarly to the FT, which is free of the FT limitations. This is the Karhunen-Loève Transform (KLT). The KLT analyses the processed data defining constantly a limited number of functions which are described by its stochastic contribution to the data. It is the reason that the KLT, if talking about radio signals, is able to analyze either, narrowband and wideband signals. The main disadvantage is there is no fast version of the KLT existing which could be a counterpart to the FFT. This makes the KLT challenging to use because of the computation power requirements and because of this reason it is not used in such implementation as GNSS signal receivers until now. Fortunately, with fast developing hardware technology, there is a chance to reach for this mathematical tool. It was proposed quite recently to take an advantage of the KLT in interference mitigation. Some first studies were already done and it was shown that the KLT performs better than the FFT in detection of a signal buried in strong noise. Using the KLT calculations in the same testing scenario as used for the FFT based methods, the carrier-to-noise ratio (C/No) was several dB smaller to obtain the same result. There are also first examples that the KLT can be applied for the GNSS signals bandwidths and can, with a great result, mitigate interference signals. However, until today, there are no tests done which could present a capability of the KLT in a context of wide variety of interfering signals. One of the objectives of this work is to test and check the performance of the KLT based mitigation methods in the realistic scenario for the L1 / E1 band. The GNSS signals will be interfered with such signal types as continues wave, narrowband and wideband signals (all of them in a time stationary and time varying version), pulsed signals and Light-Squared-like signals. Another goal of the work is to test in parallel and check the performance of the mitigation algorithms in a real-time basing on technology available today. It is one of the objectives to give a definition of reference hardware resources needed to obtain presented results of the real-time interference mitigation and therefore an FPGA Virtex-5 LX5 has be chosen to perform all the KLT processes. An assessment of the interference mitigation methods will be made and in particular two different performance metrics will be analyzed: the C/No telling about signal power spectrum correction, and code tracking error ?DLL showing the positioning degradation after interfering plus interference mitigation. The result of this work shall give an answer to the question how much the KLT is able to protect the GNSS signal against interferences. A wide spectrum of interfering signal types are chosen to the testing to build a consistent overview on the KLT based interference mitigation methods. The conclusion obtained for the GPS L1 band can be extended for the other frequency bands. Even if a fast implementation of the KLT has not yet been discovered, the computational capabilities of hardware devices are constantly increasing and they will be soon high enough to allow for the migration of the KLT base algorithms into real-time receivers. There will be the answers for the questions how heavy computation are needed to obtain satisfactory interference mitigation with minimized signal degradation and if it is possible to do in real-time today or in near future.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	3443 - 3449
Cite this article:	Szumski, A., Eissfeller, B., "The Karhunen-Loève Transform as a Future Instrument to Interference Mitigation," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 3443-3449.
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