Performance Assessment of GNSS Receivers Equipped with Jamming Detection and Mitigation Units Based on the S-Transform
Giacomo Pojani, Yazan Abdoush, and Giovanni Emanuele Corazza, University of Bologna, Italy
Global satellite navigation systems (GNSS) deliver precise positing and timing information with global coverage. The fact that an enormous number of applications, both civilian and military, relies on the GNSS service poses a significant concern about the vulnerabilities of these systems. Among them, the susceptibility to interference is arguably the main one. Indeed, GNSS signals have extremely low power levels, once they are received on the Earth’s surface. Thus, they are likely overpowered by any source of interference in the receiver surroundings, which threatens the integrity and the accuracy of the position, velocity, and time (PVT) solution of the receiver, and which can even disrupt the service availability .
Nowadays, in-car jammers are sources of malicious interference that are commercialized online as inexpensive personal privacy devices (PPD). As recognized through field investigations, their usage is popular across the road network despite being illegal. Typically, these jammers broadcast up to one watt of radio frequency interference (RFI), in order to corrupt or completely disrupt the GNSS signal reception nearby . According to recent surveys [3, 4, 5], the majority of these devices transmit periodic linear chirps, which are modulated with sawtooth-like functions and rapidly scan bandwidths up to tens of megahertz in a matter of tens of microseconds.
Although the direct sequence spread spectrum (DS-SS) scheme is intrinsically resilient to interference, commercial in-car jammers are experimentally proven to affect both acquisition and tracking of consumer-grade GNSS receivers within a range of several kilometers . Therefore, equipping receivers with anti-jamming modules is a crucial task in ensuring the reliability of GNSS services. This critical demand motivated the research on cost-effective digital signal processing techniques for jamming detection and mitigation. Generally speaking, these techniques process the raw samples at the output of the ADC/AGC in a domain where the powerful chirp-like interference exhibits distinguishable characteristics with respect to those of the GNSS signals, which in turn are dominated by noise. What is crucial but often neglected in the literature is the evaluation of the effectiveness of the designed techniques across all the stages of a GNSS receiver. Therefore, we pursue this approach for methods either recently proposed or newly presented in this paper, which follow the current research trend towards the application of time-frequency analysis into GNSS receivers.
State of the art
Based on the processing domain, interference mitigation techniques can be classified as follows.
1) Time-domain techniques need no transformed domain information. In this context, adaptive filtering that makes use of FIR or IIR filters are common [6, 7]. However, this approach is effective for interference mitigation as long as the jamming waveform is modulated with either constant or slowly time-varying instantaneous frequency (IF). Thus, they perform poorly against interfering signals of fast sawtooth-like modulations, such as those employed by in-car jammers. In this respect, the use of a Kalman filter was also proposed to track quick frequency variations . Besides being practically limited to mono-component interference, this addition, however, is sensitive to any possible mismatch between the received waveform and the model underlying the estimation. Another member of this category of techniques is pulse blanking (PB) , which was suggested to mitigate wideband interference for narrowband GNSS receivers (e.g., using a TV tuner with 1MHz at baseband as front end). This low-complexity countermeasure capitalizes on the fact that when only a fraction of the jammed spectrum is captured by the receiver front-end, it will be perceived as a sequence of pulses.
2) Frequency-domain techniques search for interference by analyzing the FFT of the received samples . They are effective only when a relatively small number of spectral components are contaminated by interference and so to be excised, namely if the interfering waveform has a sparse representation in frequency. Being only instantly narrowband, the frequency-swept waves radiated by in-car jammers, however, easily span the whole receiver bandwidth, thus saturating the visible spectrum.
3) Time-frequency representations (TFR) map nonstationary signals into a two-dimensional domain . By doing so, they have the potential to overcome the limitations of the aforementioned approaches. Indeed, they can reveal and extract the time-varying spectral content that characterizes the waveforms commonly emitted by in-car jammers. For anti-jamming countermeasures, this capability is exploited to estimate the IF of the interfering periodic chirp. The estimate is then used to suppress the interference either by adapting a time-varying notch filter  or by constructing the subspace orthogonal to the one of the jammer and then projecting the received samples onto it [13, 14]. Alternatively, the interference energy can be firstly discriminated by detecting the energy exceeding the noise floor in the TFR. At this point, while inverting the TFR multiplied to a detection mask provides a clean version of the signal [15, 16], a similar outcome is obtained by subtracting from the incoming signal the jamming waveform synthesized by estimating the respective amplitude and phase . The main downside of these techniques lies in their computational requirements, which are often significant and so prohibitive for mass-market GNSS receivers. Furthermore, the interference rejection performance is conditioned by the accuracy of the TFR. Various representations exist in the literature. The short-time Fourier transform (STFT), for example, is linear and has relatively low complexity. However, this TFR is subject to a constant trade-off between temporal and spectral resolution, which is conditioned by the choice of the localizing window and can be ideally optimized only to one specific linear chip. Thence, there is no window that can cope well with simultaneous waveforms of different characteristics. When it comes to interference mitigation, this shortcoming is a crucial issue, as shown in . Another well-established anti-jamming tool is one that employs the Wigner-Ville distribution (WVD) , which can grant superior time-frequency resolution without undergoing the aforementioned trade-off. Nevertheless, due to the quadratic nature, this TFR suffers from the presence of artificial cross terms, especially when analyzing signals of multiple components . These artifacts may hide important characteristics, which are necessary for estimating the jamming waveforms. In order to improve on the STFT and the WVD, we have recently proposed a technique based on the S-transform (ST)  for suppressing the interference at the GNSS receiver end . The ST may be regarded as a multi-resolution extension of the STFT and a phase correction of the Wavelet transform . It provides consistent representations of both amplitude and globally-reference phase information, which can be time-averaged into the Fourier spectrum. Despite these desirable features, computing this TFR usually comes at an excessive cost in terms of complexity . For this reason, it has never been applied to GNSS receivers, until we presented in  a design that computes the ST only for the spectral components concentrating most of the interference power. This was possible through a preliminary detection stage in the frequency domain, which could reduce the computational burden to an extent that ultimately depends on the jammers spectral characteristics. In another recent paper , we adopted another strategy to address complexity of the ST rigorously and a priori, alongside other issues related to analysis, modification and synthesis based on the ST. More specifically, we developed a novel generalized sampling scheme, in order to allow for arbitrarily scaling the amount of redundancy originally embedded in the ST. The presented complexity-scalable TFR enables time-frequency filtering in real time, by providing a controllable trade-off between computational efficiency and accuracy.
Added value of the present work
Given its advantageous properties, the ST clearly emerges as a linear time-frequency tool that alleviates the need of a-priori knowledge about the analyzed signal, as opposed to the STFT, and suitable to analyze simultaneously multiple signals, as opposed to the WVD. This makes it a promising TFR for an application like interference mitigation, in which neither the number nor the characteristics of the received jamming waveforms are known. In this work, we intend to show new results about the performance of interference detection and mitigation techniques based on different versions of the ST: the fully redundant ST [18, 15], a recent frequency-adaptive ST , and especially a novel time-selective ST. Their effectiveness is compared to that of the pulse blanking described by Borio in . We choose this simple technique as a benchmark due to its popularity in both the literature and reality, as well as effectiveness when applied to narrowband GNSS receivers that see the jamming waveform as a sequence of pulses. Nevertheless, our preliminary results demonstrate that PB is insufficient or even detrimental in many other realistic cases, namely whenever the jammer sawtooth-like modulation function is just ten to twenty microseconds slower than that in , or the receiver has a wider front-end bandwidth than that in , or there are simultaneous jamming attacks. Under these conditions, we prove that the ST can generally improve the performance in terms of interference excision with respect to the PB, because it is less sensitive to the characteristics of the jammers. Particularly, we propose the method employing the time-selective ST as a novel, effective, and moderate-complexity technique for rejecting the interference attempts carried out by multiple and diverse in-car jammers.
Our case study considers the reception of GPS L1 C/A samples, which are collected with a LEICA SR9500 by the GNSS reference station of the University of Bologna. We post-process this signal through the following steps:
1. we emulate realistic jamming attacks coherently with , by setting different timings, repetition periods, bandwidths and jammer-to-noise power ratios (JNR), which is swept between 0dB and 30dB (i.e., the 8-bit receiver front-end is close to saturation);
2. we test different anti-jamming units that blank the incoming interference by making use of either the PB or one of the proposed TFRs based on the ST with different detection statistics at constant false-alarm rates (CFAR);
3. we finally evaluate the impact of the interference rejection at all the stages of our GPS software receiver, namely acquisition, tracking, and PVT calculation.
Interestingly, our results show that the performance of interference mitigation techniques cannot be assessed by only evaluating their impact on the acquisition processing gain and on the channel signal to noise ratios. Therefore, we examine also the effects of the energy loss and the additional distortion due to blanking on the navigation message and the final PVT solution.
As suggested in [9, 21], each software channel is implemented as a finite state machine with standard mechanisms of re-acquisition and frequency estimation aiding, in order to provide robustness against possible losses of code and carrier lock. We assess the receiver’s performance through the acquisition metrics, the estimates of the carrier-to-noise power density ratio (CN0) and of the carrier phase at the output of the tracking loops, the additional error on the carrier and code estimates, the integrity of the navigation message, and the estimation error of the final East-North-Up (ENU) location computed.
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