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Use of the Wavelet Transform for Interference Detection and Mitigation in Global Navigation Satellite Systems

Use of the Wavelet Transform for Interference Detection and Mitigation in Global Navigation... Hindawi Publishing Corporation International Journal of Navigation and Observation Volume 2014, Article ID 262186, 14 pages http://dx.doi.org/10.1155/2014/262186 Research Article Use of the Wavelet Transform for Interference Detection and Mitigation in Global Navigation Satellite Systems Luciano Musumeci and Fabio Dovis Department of Electronics and Telecommunications, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Turin, Italy Correspondence should be addressed to Luciano Musumeci; luciano.musumeci@polito.it Received 9 October 2013; Revised 20 December 2013; Accepted 30 December 2013; Published 26 February 2014 Academic Editor: Sandro Radicella Copyright © 2014 L. Musumeci and F. Dovis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Radio frequency interference detection and mitigation are becoming of paramount importance due to the increasing number of services and applications based on the position obtained by means of Global Navigation Satellite Systems. A way to cope with such threats is the implementation in the receiver of advanced signal processing algorithm able to raise proper warning or improve the receiver performance. In this paper, we propose a method based on the Wavelet Transform able to split the useful signal from the interfering component in a transformed domain. The wavelet packet decomposition and proper statistical thresholds allow the algorithm to show very good performance in case of multiple pulse interference as well as in the case of narrowband interference, two scenarios in which traditional countermeasures might not be eeff ctive. 1. Introduction which broadcast strong signals on frequencies within or located near the GNSS frequency bands. As an example, Reliable positioning and navigation are becoming imperative the terrestrial Digital Video Broadcasting (DVB-T) system in a growing number of applications that are being devel- may represent a real threat for the GNSS receiver operation. oped for public services and safety critical purposes. As a In fact, nonlinearity distortion generated in the DVB-T consequence, satellite and radio navigation is evolving in an transmitterampliefi rmayleadtothegenerationofharmonics accelerating pace and it is becoming a pervasive technology in the GPS L1 (and thus Galileo E1) frequency band. in a large number of consumer and professional devices. In [2] a set of on-field experiments aiming at assessing For such a reason, parallel to the development of techniques the eeff ct of DVB-T and VHF/UHF signals on GNSS receiver able to improve the positioning accuracy, the research is are described. Figure 1(a) shows the possible interference becoming of paramount importance to improve the robust- sources that can have secondary harmonics within the GPS ness of the positioning methodologies in order to make sure L1, while Figure 1(b) specifies these potential interferers, that the navigation is trustworthy and the risks and threats with respect to the order of the harmonics. eTh DVB-T are properly accounted for. As far as Global Navigation is transmitted within the frequency range of 174–230 MHz Satellite Systems (GNSS) based techniques, intentional or (ultrahigh frequency, UHF band III) and 470–862 MHz (very unintentional interference represents one of the main threats high frequency, VHF bands IV and V). Additional details on to be considered. GNSS receiver operation can be easily DVB-T system impact on GNSS receiver performance can be disrupted by interfering signal due to the extreme weakness of found in [3]. the GNSS signals reaching the GNSS user antenna. In fact, the Another example of out-of-band RF interference risk for presence of undesired RFI and other channel impairments the GNSS systems has been provided by the LightSquared can result in degraded navigation accuracy or complete loss case in the United States. eTh company deployed a ground- of receiver tracking [1]. Furthermore, due to the lack of based 4G-LTE network that transmits on a frequency band frequency allocations, the majority of the interference issues right next to the primary GPS frequency (L1). Although come from the presence of other communication systems LightSquared would have operated in its own authorized 2 International Journal of Navigation and Observation 1559 1591 been shown that on-board GNSS receiver yfl ing at 40000 feet 1565.19 1585.65 over Frankfurt airport area might be seriously threatened by DME/TACAN interference which may cause complete loss of lock of the GNSS signal. Many other examples of communication systems which Frequency (MHz) may represent a possible in-band unintentional interference sources for the GNSS are described in [3]. Last but not least, also intentional interference is a threat 1525 1559 1660 to be considered for civil GNSS community. Portable devices, jamming the GNSS bandwidth, typically broadcast signals GPS L1 Galileo E1 frequency modulated where the instantaneous frequency Interference sweeps arange of severalMHz in afew microseconds affecting the entire GNSS band targeted by the device [ 7]. (a) These few examples of interference generated by other Mobile communication systems proved that interference is a real satellite DVB-T/TV secondary harmonics DAB applications issue in GNSS and that proper countermeasures have to be designed. In fact, the different interference sources may broadcast signals that are very different in terms of power, 1559 1591 modulation, and pulse shape, thus making it difficult to have 1565.19 1585.65 a universal countermeasure able to cope with all of them. In this paper, this issue is addressed working with a transformed domain approach that is able to deal with a large number of 8th VHF 10 2nd UHF 66 3rd UHF 23 9th VHF 7 different kind of interfering sources, thus being effective in a 3rd UHF 22 2nd UHF 67 wide range of scenarios. GPS L1 eTh paper is organized as follows. Section 2 provides a Galileo E1 model for the useful signal and the interference together Interference with a basic interference signal classification. Section 3 will (b) be devoted to a general description of the current state of the art of interference mitigation algorithms for GNSS. Figure 1: Possible in-band and out-of-band interferences (a). After introducing the Wavelet Transform in Section 4,an Secondary harmonics interference within the GPS L1 and Galileo innovative interference mitigation algorithm based on the E1 bands (b). use of the wavelet packet decomposition will be presented in Section 5. Such an algorithm will be fully described, and its band, the proximity to the GPS signals induced overload or performance in detecting and suppressing interference will saturation of the radio frequency front-ends of the GNSS be discussed in Section 6. receivers. eTh threat to GPS was so strong that, following extensive testing and analysis, the Federal Communication 2. Signal Model and Interference Classification Commission denied the LightSquared’s terrestrial operations [4]. The received interfered GNSS signal at the receiver antenna The interference issue is not only aeff cting the L1 band can be written as where the civil GPS signal and the Open Service of Galileo 𝐿−1 arebroadcast.Thefutureaidings forGNSSbased aviation 𝑠 (𝑡 )= ∑𝑦 (𝑡 )+𝑖 (𝑡 )+𝜂 (𝑡 ), (1) RF,𝑙 applications will be broadcastinthe GalileoE5and GPS 𝑙=0 L5 frequency bands which are shared with other Aero- nautic Radio Navigation Systems, as described in [5]. In where 𝐿 is the total number of GNSS useful signals, 𝑦 (𝑡) is RF,𝑙 fact, GNSS based aviation aids will be broadcasted by the the useful GNSS signal received by the 𝑙 th satelliteinlineof Space Based Augmentation Systems over the L5/E5 frequency sight, 𝑖(𝑡) is the additive interfering signal transmitted over band.However,suchfrequency bandsare shared with other a carrier frequency 𝑓 and characterized by a two-sided int Aeronautical Radio Navigation Systems (ARNS) such as the bandwidth 𝐵 ,and 𝜂(𝑡) is the additive white Gaussian noise. int Distance Measuring Equipment (DME) and the military one Before being fed to the acquisition and tracking block, the Tactical Air Navigation (TACAN). Both systems provide signal is first downconverted to an intermediate frequency, slant range information between an aircraft and a ground sampled, and quantized in the receiver front-end. us, Th the reference station, through the communication between two composite received signal at the ADC output according to [8] components, an interrogator installed on board of the aircraft can be written as andatransponder placed on theground, usuallywithinthe 𝐿−1 airport area. Such DME/TACAN ground stations broadcast 𝑠 [𝑛 ] =𝑠 [𝑛𝑇 ] =𝑄 [ ∑𝑦 [𝑛𝑇 ] +𝑖 [𝑛𝑇 ] +𝜂 [𝑛𝑇 ]] , powerful modulated double-pulse signals which may corrupt IF IF 𝑠 IF,𝑙 𝑠 𝑠 𝑠 𝑙=0 the GNSS on-board receiver operation. A detailed descrip- (2) tion of such aeronautical systems is presented in [6]. It has International Journal of Navigation and Observation 3 where the function 𝑄 denotes the quantization over 𝑘 bits, proposed show advantages and limitations depending on the and 𝑇 is the sampling frequency. Expanding the term 𝑦 , interfered scenario considered. In the following, a classifica- 𝑠 IF,𝑙 the expression for the single digitized GNSS signal aeff cted tion is provided in order to highlight the advantages and lim- by noise and interference components becomes (neglecting itations of the different methods. Interference detection and for the sake of simplicity the subscript 𝑙 ) mitigation techniques can be grouped in different families according to the point within the GNSS receiver chain they 𝑠 [𝑛 ] =𝑄 [ 2𝐶𝑑 (𝑛 − 𝑛 )𝑐(𝑛 − 𝑛 )×cos (2𝜋𝐹 𝑛+𝜙 ) IF 0 0 𝐷,0 0 𝑘 are applied on, as reported in Figure 2. +𝑖 [𝑛 ] +𝜂 [𝑛 ]], (i) Antenna level techniques which are based on the use (3) of antenna arrays capable of generating radiation pat- tern which attenuates the interference signal coming where 𝐶 is the received GNSS signal power from one satellite from a determined direction [9]. in view, 𝑑 and 𝑐 are, respectively, the navigation data message (ii) Automatic Gain Control (AGC) level where the content and the pseudorandom noise sequence, 𝐹 =(𝑓 + 𝐷,0 IF interference monitoring is performed detecting a 𝑓 )𝑇 is the Doppler aeff cted frequency, 𝑛 =𝜏 /𝑇 is the 0 𝑠 0 0 𝑠 persistent saturation status of the AGC (see, e.g., [10, digital code delay, and 𝜙 is the code delay. 11]). 𝑖[𝑛] and 𝜂[𝑛] are the digitized interference and the digital Gaussian noise component, respectively. Given 𝐵 the front- (iii) Postcorrelation techniques which are based on the IF end bandwidth, it can be shown that by sampling the signal at analysis of the shape of the correlation function, in the Nyquist frequency 𝑓 =2𝐵 , the noise variance becomes most cases exploiting a multicorrelator receiver [12]. 𝑠 IF (iv) Raw observable level techniques which are based on 𝑁 𝑓 2 2 0 𝑠 (4) 𝜎 =𝐸{𝜂 [𝑛 ]}= =𝑁 𝐵 , IF 0 IF the processing of the raw samples at the Analog to Digital Converter (ADC) output. where 𝑁 /2 is the power spectral density (PSD) of the noise. In particular, among the interference countermeasures A general classification of the interfering signals is based at raw observable level, it is possible to distinguish those on their spectral characteristics such as their carrier fre- which perform interference detection and cancellation in one quency 𝑓 or their bandwidth 𝐵 . int int single domain as the pulse blanking in the time domain or (i) Out-of-band interference refers to interfering signals thenotch filtering in thefrequency domain.Theinnovative whose carrier frequency is located near to the targeted interference mitigation based on the use of the Wavelet GNSS frequency band (𝑓 <𝑓 −𝐵 /2 or 𝑓 > int IF IF int Transform properties belongs to this latter family, since 𝑓 +𝐵 /2). IF IF it performs detection and mitigation of the interference (ii) In-band interference refers to interfering signals with processing thereceivedsignalinatransformeddomain. carrier frequency within the GNSS frequency band Pulse blanking is the most traditional countermeasure (𝑓 −𝐵 /2 < 𝑓 <𝑓 +𝐵 /2). suited for pulsed interference. Implemented by means of a IF IF int IF IF digital circuit in the digital part of the receiver front-end, Moreover, interference can be further classiefi d according to such technique performs an interference excision in the time its characteristics in the frequency domain. domain by thresholding sample by sample the output of the (i) Narrowband interference when the spectral occu- Analog to Digital Converter (ADC) converter, as it is shown pation is smaller with respect to the GNSS signal in Figure 3. Pulse detection in this case can be performed in bandwidth (𝐵 ≪𝐵 ). int IF either analog circuitry, through analog power measurement, or digital circuitry, looking at the histogram of the samples at (ii) Wide-band interference when the spectral occupa- the output of the ADC [13]. This simple mechanism performs tion is comparable with respect to the GNSS signal pulsed interference suppression in the time domain and it bandwidth (𝐵 ≈𝐵 ). int IF oer ff s good performance in the presence of pulsed interfering (iii) Continuous wave (CW) interference which appears as source characterized by a low Pulse Repetition Frequency a spike in the frequency domain (𝐵 →0). int (PRF). However, the technique shows limitation when highly Furthermore, in general, interference might have time- dense in-time and strong interfering pulses are present since frequency varying characteristics, for example, pulsed inter- they lead the pulse blanking circuitry suppressing a large ference or chirp signals. The former is mainly characterized portion of the composite received signal and thus worsening by on-off status of short duration (order of ), which alter- the GNSS receiver performance due to the degraded quality nates in the time domain, whilst the latter is characterized ofthereceivedsignal.In[6], it has been shown that, due to the by a linearly variation in time of the instantaneous frequency described strong DME/TACAN interference environment, thus resulting in a wide-band interference. More details on the pulse blanking of the receiver on-board suppresses about interference classification can be found in [ 1]. 56% of the incoming signal thus leading to the loss of lock of the weakest GNSS received signals. Furthermore, the drawbacks of such simple interference 3. Interference Countermeasures countermeasure come from the fact that its performance Several kinds of interference countermeasures have been is strongly dependent on the receiver front-end design. In developed since the early years of GNSS. The methods fact, strong and dense in-time pulsed signals can cause the 𝜇𝑠 4 International Journal of Navigation and Observation Antenna Tracking stage (DLL) Front-end PLL ∑ (·) ∑ (·) Discriminator AGC ADC BPF ∑ (·) NCO Filter Interference detection and mitigation Figure 2: GNSS receiver chain block scheme. Ideal blanking mitigation Nonideal blanking mitigation 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 −1 −1 15 20 25 30 35 40 15 20 25 30 35 40 Time (𝜇 s) Time (𝜇 s) Before blanking Before blanking After blanking After blanking Blanking threshold Blanking threshold (a) (b) Figure 3: Signal before and aeft r interference removal by means of ideal (a) and nonideal pulse blanking (b). saturation of the active components in the GNSS receivers input dynamics of the ADC is not properly set [14]. The fact chain (e.g., amplifiers), which may require a recovery time that the blanked samples should not be used for the AGC to resume their normal state. This saturation eect ff may tuning in order to avoid ADC overloading has to be taken lead the pulse blanking suppressing the received signal even in consideration. In Figure 3, DME/TACAN pulse pair before during the off-status of the pulse thus causing an increasing (blue line) and aeft r (red line) the application of both ideal (a) degradation on the received useful GNSS signal. In [14], it and nonideal (b) pulse blanking is shown. Nonideal blanking is mentioned that for a particular commercial receiver, an reveals a delay in pulse detection as well as a recovery interference pulsed signal with a peak power 15 dB above the time needed to the active components of the front-end to thermal noise is sufficient to saturate the last amplification recover their normal operation, which produce a different stage of the receiver front-end. Furthermore, careful design mitigated signal. Furthermore, due to the bell shaping of the of the Automatic Gain Control (AGC) is needed when a DME/TACANandtothepresenceofthemodulationoverthe pulse blanker circuitry is present. A slow AGC sets the A/D pulseduration, notall thesamples belongingtothe pulseare input levels averaging the input signal power over a large time suppressed leading to an increased noise floor [ 15, 16]. Unlike during which if too many pulses oscillations are present, the thepulse blanking,which worksinthe time domain,other Normalized amplitude Normalized amplitude International Journal of Navigation and Observation 5 interference countermeasures provide interference detection already extensively used; in fact, in literature, it is possible to and cancellation in the frequency domain. As an example, n fi d several research works in which the Wavelet Transform interference cancellation can be performed suppressing the has been adopted mainly to cope with the multipath issue. In particular, in [21], a new trend extraction technique for interference carrier frequency exploiting notch filtering. Such multipath mitigation in carrier phase measurements domain an interference countermeasure is well suited for CW or using wavelet multiresolution analysis is presented. More narrowband interference. In [16], notch filtering is proposed detailed descriptions of this algorithm can be found in for suppressing DME/TACAN interference which appears in [22–25]. Multipath mitigation is not the only framework the frequency domain as Narrowband interference. In such which Wavelet Transform has used. For instance, in [26], a a scenario the use of notch filters allows the suppression of singularity detection technique for GPS cycle slips based on the entire DME/TACAN pulse (tails included) but it reveals the wavelet decomposition is described. In [27], an Empirical several drawbacks in the presence of multitone interference Mode Decomposition (EMD) exploiting the Wavelets’ prop- sources. erties is described as a method to reduce the carrier phase As an example, in [7], adaptive notch filtering scheme is measurements error. Finally in [28], methodology based on described as interference countermeasure against jammers. Wavelet Transform to evaluate the terrain and extract features Another algorithm performing interference mitigation along the vehicle path is presented. o Th se features which can in frequency domain is the Frequency Domain Adaptive be hazardous to a following vehicles path are of particular Filtering introduced in [17]. Such technique is based on a Fast interest. Fourier Transform (FFT) of the samples at the ADC output. A different wavelet based mitigation algorithm approach Interference suppression is performed through a sample by for interference suppression will be presented and fully sample thresholding in the FFT domain. Basically, each FFT described in the next section. point is compared to a threshold, fixed according to a certain falsealarm probability, andzeroedwhenthe thresholdis 4. The Wavelet Transform exceeded. en Th an inverse FFT operation is performed on the manipulated incoming signal, in order to obtain back Wavelet Transform overcomes the common limit of those the signal in the time domain to feed to the acquisition and transformations based on Fast Fourier Transform (FFT) tracking blocks. as the Short Time Fourier Transform (STFT). The set of In most of the cases, interference is an unexpected and orthogonal basis functions which are employed for the STFT unpredictable event. Interference signal characteristics in computation can be seen as bandpass filters having equal time and frequency domain might be highly variable. For frequency bandwidths and thus representing a set of windows such a reason, research in this efi ld is moving towards in time with equal duration. This leads to a different reso- the investigation of innovative interference countermeasures lution in the characterization of high frequency phenomena able to represent the incoming signal in a two-dimensional with respect to the resolution achieved in characterizing domain, for example, the time-frequency domain, where low frequency phenomena. Exploiting fixed windows, many interference component can be better isolated and removed cycles of a high frequency signal can be captured, while for a without suppressing great portion of GNSS useful signal. low frequency signal very few cycles are within the windows. In [18], an interference mitigation algorithm based on the For such a reason, resolution of Fourier Transform is poor at time-frequency representation of the GNSS received signal is low frequency, while it improves as the frequency increases proposed. Here, an Orthogonal-Like Gabor Expansion of the [29]. Another drawback of using transformation based on samples at the ADC output is employed in order to perform fixed windows is revealed when considering the rising part of the time-frequency representation of the incoming interfered the signal. Very narrow window will help to localize the rising signal. Each value in the transformed domain is compared portion of the signal very well with respect to a wide window, to a mask, which is computed through an Orthogonal-Like at the expenses of a loss of information in the steady part of Gabor Expansion on the expected GNSS received signal the signal, which is better characterized by wider windows. that would be present in an interference-free environment. In order to overcome these issues, a set of functions which Such processallowstoidentify thosecoecffi ientsinthe could better match the frequency components of the signal time-frequency representation which represent interference to be characterized is needed. From such basis functions, a information and that can be used to generate a synthetic filters bank where the low-pass filters response has narrower reconstruction of the interfered signal. Interference suppres- bandwidths (so wider in the time domain) than the high-pass sion is performed subtracting a synthetic interference signal filters response can be derived. u Th s, a transformation based reconstruction from the original received signal. A drawback on windows which are functions of both time and frequency for this algorithm is that synchronization strategy is needed such that their bandwidths get narrower as the frequency to perform a correct subtraction between the original signal decreases is needed. eTh se requirements are accomplished by and the synthetic reconstruction. the basis functions used to perform the Wavelet Transform. In Recently, an innovative interference mitigation algorithm the STFT, all the bandpass filters are obtained by modulation basedontheuseoftheWaveletTransformhasbeenpresented of asinglefilter andthustheyhaveequal bandwidth[ 29]. in [19, 20], for pulsed interference mitigation. Here, Wavelet Concerning the Wavelet Transform, filters responses are Transform is employed to obtain time-scale representation obtained as of the incoming interfered signal. In the framework of the −𝑘/2 −𝑘 (5) navigation satellite systems, the Wavelet Transform has been ℎ (𝑡 )=𝑎 ℎ (𝑎 𝑡 ) 𝑘 6 International Journal of Navigation and Observation −8 4.1. Discrete Time Wavelet Transform. It can be shown that ×10 Discrete Meyer based filters bank 3.5 a digital implementation of the Wavelet Transform can be equivalently implemented by using digital filters. The equivalent expression of (6) for digital filters would be 2.5 𝑘 𝑘 𝑗2 𝜔 2 𝐻 (𝑒 )=𝐻(𝑒 )󳨀→𝐻 𝑧 =𝐻(𝑧 ), (10) ( ) 2 𝑘 𝑘 1.5 where 𝑘 is a nonnegative integer. In [29], it is shown that 𝐻 (𝑧) is a multiband (rather than passband) filter; thus, in 1 𝑘 order to obtain passband filters, a low pass filter 𝐺(𝑧) is 0.5 employed. In [30], 𝐺(𝑧) is defined as the mirror filter of 𝐻(𝑧) and together are called quadrature mirror filters. u Th s, 0 1 2 3 4 5 6 7 89 according to a dyadic scaling operation, the nonuniform Frequency (MHz) filters bank responses are obtained as follows: Figure 4: Meyer wavelet filters transfer functions. 2 2 4 𝐻 (𝑧 ),𝐺 (𝑧 )𝐻(𝑧 ),𝐺 (𝑧 )𝐺(𝑧 )𝐻(𝑧 )⋅⋅⋅ . (11) The Wavelet Transform can be extended to obtain the or equivalently in the frequency domain so-called Wavelet Packets Decomposition (WPD), where the discrete-time signal is passed through a uniform wavelet 𝑘/2 𝑘 𝐻 (𝑗Ω )=𝑎 𝐻 ( Ω), (6) based filter bank, as shown in Figure 5. eTh scaling and shifting process is also iterated at higher frequencies, thus where 𝑎>1 and 𝑘∈ Z. resulting in a uniform filter bank; the output of each is provid- As seen in (5)and (6), all the transfer functions are ing a set of coefficients (scales) each of which is representing a obtained by frequency-scaling operation of a prototype determined frequency portion of the incoming decomposed 𝐻(𝑗Ω) , the so-called mother wavelet, thus resulting in a signal. Each stage of the uniform filters bank is composed nonuniform filters bank. As an example, Figure 4 shows the by a filtering process through 𝐻(𝑧) and 𝐺(𝑧) ,respectively, transfer functions of each branch of the nonuniform filters thewavelet vector andthe scalingvectorindividuallyshift bank obtained by a dyadic scaling operation from the Meyer orthogonal and orthogonal to each other, which produce a −𝑘/2 wavelet function. The scale factor 𝑎 is introduced as a decomposition of the signal in high frequency component normalization factor in order to ensure constant energy inde- and low frequency component, followed by a downsampling pendent from 𝑘 as well as the ratio between the bandwidth operation. and the center-frequency Ω . Furthermore, since the filter bandwidth 𝐻 (𝑗Ω) is narrower for larger 𝑘 ,its output canbe 5. The Wavelet Based Mitigation Algorithm sampled at lower rate. Summarizing, given an arbitrary input 𝑥(𝑡) ,the output of thefilter ℎ (𝑡) is defined as The proposed wavelet based mitigation algorithm is com- pletely based on the WPD previously described. eTh algo- 𝑋 (𝑘, 𝑛 )= ∫ 𝑥 (𝑡 )ℎ (𝜏−𝑡 ) DWT 𝑘 rithm for interference detection and suppression is mainly −∞ (7) based on three steps. −𝑘/2 −𝑘 =𝑎 ∫ 𝑥 (𝑡 )ℎ(𝑎 (𝜏−𝑡 ))𝑑.𝑡 (i) Decomposition phase where the incoming GNSS −∞ interfered signal is passed through the uniform filter Replacing the continuous variable 𝜏 with 𝑛𝑎 𝑇 ,itfollows that bank thus achieving the time-scale representation. The number of wavelet stages to apply for the signal −𝑘/2 −𝑘 decomposition is a free parameter. Following in this 𝑋 (𝑘, 𝑛 )=𝑎 ∫ 𝑥 (𝑡 )ℎ(𝑛𝑇 − 𝑎 𝑡) DWT −∞ paper, the optimal number of wavelet decomposition (8) ∞ stages will be assessed with respect to the interference = ∫ 𝑥 (𝑡 )ℎ (𝑛𝑎 𝑇−𝑡).𝑡𝑑 spectral characteristics and with respect to the GNSS −∞ receiver performance at both acquisition and tracking The above integral represents the convolution between 𝑥(𝑡) levels. and ℎ (𝑡) evaluated at a discrete set of points 𝑛𝑎 𝑇 ;thatis, the (ii) Detection-mitigation phase is performed in each convolution output is sampled with a spacing 𝑎 𝑇 .Theset of scale obtained at the output of the filters bank. A coefficients obtained for each value of 𝑘 provides the discrete simple blanking operation will be adopted in order Wavelet Transform. u Th s, all the orthogonal basis functions to suppress those coecffi ients in each scale represent- −𝑘 ing interference components. For such a reason, a composing the filters bank are derived by dilation ( 𝑡→𝑎 𝑡 ) criterion for the blanking threshold determination and shifting ( 𝑡→𝑡−𝑛𝑎 𝑇 ) of a prototype function 𝜓(𝑡) ,the is needed. eTh adopted criterion is mainly based on mother wavelet; that is, a statistical characterization of the GNSS received −𝑘/2 −𝑘 (9) 𝜓 (𝑡 )=𝑎 𝜓 (𝑎 𝑡−𝑛𝑇 ). signal at the ADC output. It is well known that 𝑘𝑛 Power spectral density (dB/Hz) 𝑑𝑡 𝑑𝑡 𝑗𝑎 𝑗𝑤 International Journal of Navigation and Observation 7 ↓2 G(z) H(z) ↓2 G(z) ↓2 G(z) ↓2 H(z) ↓2 ↓2 G(z) H(z) ↓2 y [n] IF G(z) ↓2 ↓2 H(z) G(z) ↓2 H(z) ↓2 H(z) ↓2 G(z) ↓2 ↓2 H(z) Figure 5: Wavelet Packet Decomposition by means of 3-stage uniform filters bank. GNSS signal is completely buried in the noise at the interference will be assessed looking at the time-frequency user antenna level. Choosing a sampling frequency signal characteristics and comparing the signal quality before matching the Nyquist condition, the filtered digitized and aeft r mitigation. A full software GNSS receiver, N-GENE noise can be considered still uncorrelated; thus, it [31], capable of processing Galileo and GPS signals over all is allowed to assume that at the ADC output, the the GNSS frequency bands, has been employed in order to digitized GNSS signal in an interference-free envi- assess receiver performance at both acquisition and tracking ronment is still Gaussian distributed with zero mean level after the wavelet based interference suppression. Such and variance 𝜎 . Denoting the false alarm probability a software receiver is realized with FFT based acquisition IF 𝑝 as the probability of the event in absence of scheme parallel in the time domain and tracking loops based interference, a generic sample at the ADC output on 2nd order loop filters. Results in terms of separation crosses the blanking threshold 𝐵 ,itfollows that between the correct acquisition peak in the search space th and the noise floor ( 𝛼 )aswellaspseudorange tracking mean 2 2 −𝑥 /2𝜎 IF error and 𝐶/𝑁 aer ft the wavelet mitigation algorithm will be 𝑝 =2 ⋅ ∫ 𝑒 . (12) 𝐵 𝜎 2𝜋 provided and compared with the receiver performance in an th IF interference-free scenario. u Th s, for a required false alarm probability 𝑝 , Two macroscenarios have been considered. inverting (12), it follows that (i) Pulsed interference scenario which is representative 2 −1 √ of a realistic interference scenario experienced by a 𝐵 =𝜎 2⋅𝑒𝑐𝑓𝑟 (𝑝 ). (13) th IF GNSS receiver on board of an aircraft at 40000 feet over the central Europe region and the operation of This blanking threshold magnitude is applied in each whichmay be corruptedbythe strong pulsed signals scale, since the wavelet filtering stages are performed reaching the GNSS antenna and coming from the with unitary energy filters. different ground DME/TACAN beacons. (iii) Reconstruction phase achieved through an inverse (ii) Narrowband interference scenario generated with syn- Wavelet Packet transform applied on the wavelet thetic data at intermediate frequency. Dieff rent Nar- scales after the mitigation phase. eTh main advantage rowbandinterferencescenarios will be takeninto of this algorithm with respect to the Gabor expansion account considering different interference bandwidth based algorithm is that no signal storage for the and different off-set between the intermediate fre- signal decomposition as well as no synchronization quency and the interference carrier frequency. In this operation at signal reconstruction is needed. section, the best configuration of the parameters algo- rithm such as the number of wavelet decompositions 6. Experimental Results or the filters length will be assessed looking at the receiver performance. This section will entirely focus on the application of such wavelet based interference mitigation algorithm in realis- tic interference scenarios. Analysis is performed exploiting 6.1. Pulsed Interference. An extremely realistic DME/TACAN software simulations. Wavelet based algorithm has been interference scenario has been simulated through the software implemented and offline applied on different data use of the Interference Test Facility (ITF) available at sets generated at intermediate frequency and representative the radio-navigation laboratory of the European Space of specific interference scenarios. Benefits in suppressing Agency/European Space Research and Technology Centre 𝑓𝑎 𝑓𝑎 𝑓𝑎 𝑓𝑎 Fr requency bins (kHz) 8 International Journal of Navigation and Observation −30 (ESA/ESTEC). The ITF is a hardware software platform −40 capable of generating a wide range of realistic interference scenarios and it is mostly devoted to the testing of GNSS −50 hardware receiver performance under interference. More −60 details on the different capabilities and configurations of this −70 0 2 4 6 8 10 12 14 16 18 tool canbefound in [32]. Frequency (MHz) A realistic scenario of a GNSS receiver corrupted by the composite pulsed signal coming from up to 40 DME/TACAN stations broadcasting strong pulsed signals within the GPS L5 and Galileo E5a frequency bands has been simulated. Figure 6 shows 10 ms of data collected at intermediate −50 frequency (9 MHz) sampled at 36 MHz. Spectral character- −100 0 1 2 3 4 5 6 7 8 910 istics of thesingleDME/TACAN pulsed signal areshown Time (ms) in theplotontop.Itappears as anarrowbandinterference with approximately 300 kHz bandwidth. eTh entire spectrum Figure 6: 10 ms of Galileo E5a signal at intermediate frequency is jammed due to the fact that several ground beacons aec ff ted by DME/TACAN pulsed interference. have been simulated broadcasting pulses on different carrier frequency within the Galileo E5a and GPS L5 frequency bands. Under this condition, receiver operation is disrupted Galileo E5aQ PRN20 search space: 𝛼 = 24.8 dB mean as demonstrated in [6]. 1 ms of coherent integration time combined with 80 noncoherent accumulations has been adopted in order to ×10 acquire the Galileo E5a pilot channel (PRN 20) in presence of strong DME/TACAN interference and results are shown in Figure 7. In this scenario, a high number of noncoherent accumulationshavebeenemployedinorder to be able to 4 detect the correct acquisition peak from the noise floor, leading to an acquisition metric 𝛼 equal to 24.8 dB. mean Wavelet based mitigation algorithm has been applied to the interfered data-set. First, a time-scale representation of the 08 0.8 signal at the ADC output is achieved exploiting 5 stages of a 0.6 0.4 wavelet based filters bank, employing a Meyer wavelet family 0.2 −5 (see Figure 8). After 5 stages of WPD, 32 scales are obtained, each Figure 7: N-GENE acquisition search space in presence of of which represents a determined frequency component of DME/TACAN interference: Galileo E5a-Q channel, PRN 20. the interfered received Galileo E5a signal. As it is shown in Figure 8, composite DME/TACAN signal reaching the user antenna is spread all over the time-scale domain. The black floors represent the blanking threshold applied for the signal powerissaved,asconrfi medbythe absenceofdrops interference component detection within each wavelet scale in the spectrum shown in Figure 10. andcomputedaccordingtoafalsealarm probability 𝑝 Figure 11 shows the acquisition search space obtained −4 letting the software receiver acquire the data-set processed by of 10 as in (13). Once the time-scale representation of the wavelet based mitigation engine. It can be clearly seen that the incoming signal is achieved, an interference suppression acquisition of the Galileo E5a pilot channel (PRN 20) can be algorithm based on a simple blanking operation is performed achieved already exploiting only 10 noncoherent accumula- in each wavelet scale. Figure 9 shows the modified time-scale tions combined with 1 ms of coherent acquisition time, thus domain achieved aer ft the blanking operation. reducing the Mean Acquisition Time (MAT) needed to detect Such modified scales are fed to a wavelet based anti- thesatellite.Anexcellent interference suppressionisachieved transformation block which is in charge of the signal recon- as demonstrated by the high reduction of the noise floor in struction. Figure 10 provides a comparison between the the search space. In fact, the separation between the main time-spectral characteristics of the signal before and aer ft peak and the noise floor, denoted by 𝛼 ,isapproximately theinterferencesuppression throughthe WPDalgorithm, mean 30.2 dB (4 dB higher than the interfered case in Figure 7) showing the benefits of this algorithm when looking at the exploiting a considerably less number of noncoherent accu- spectrum achieved aer ft the mitigation (top plot). eTh eeff ct mulations (only 10). Furthermore, interference suppression of thepulsedinterferenceisstronglyattenuated. performed through this wavelet based method overperforms Furthermore, unlike a common interference mitigation the interference mitigation performance achieved aer ft apply- techniqueperformed in thetimedomain, as thepulse ing a simple pulse blanking operation on the IF-samples blanking, where useful signal components are suppressed of the collected data-set, as it can be seen in Figure 12, together with interference, the majority of the useful GNSS where, although correct Doppler and code delay acquisition Code delay (ms) Power spectral CAF ADC level density (dB/Hz) 𝑓𝑎 Frequency bins (kHz) W Wavelet scales Frequency bins (kHz) Wavelet scales International Journal of Navigation and Observation 9 Time-scale domain-N= 5 Galileo E5aQ PRN20 search space: 𝛼 = 30.2 dB mean ×10 3.5 2.5 1.5 −100 −200 0.5 −300 20 20 10000 10 0.8 8000 8000 0.6 10 0.4 0.2 2000 −5 Figure 11: N-GENE acquisition search space aer ft wavelet based Figure 8: Time-scale representation achieved by 5 stages of wavelet mitigation algorithm: Galileo E5a-Q channel, PRN 20. packet decomposition. Galileo E5aQ PRN20 search space: 𝛼 = 22.4 dB mean ×10 −100 −200 −300 20 1 0.8 6000 0 0.6 0.4 0.2 −5 Figure 9: Time-scale aer ft interference removal. Figure 12: N-GENE acquisition search space aer ft pulse blanking: Galileo E5a-Q channel, PRN 20. Signal reconstruction-N= 5 −30 is achieved, a noisier search space as well as a reduction of the correlation peak amplitude can be observed. −40 Concerning the software receiver tracking performance, −50 carrier to noise density ratio 𝐶/𝑁 and DLL jitter have been −60 assessed. Figure 13 shows 10 seconds of the estimated 𝐶/𝑁 during the Galileo E5a pilot channel tracking in presence of −70 0 2 4 6 8 10 12 14 16 18 suchastrongpulsedinterferenceforthreedieff rentscenarios: Frequency (MHz) (i) when no interference countermeasures are employed (red line), (ii) when a traditional pulse blanking is employed (black line), −50 (iii) when the wavelet based interference mitigation algo- rithm is adopted (cyan line). −100 0 1 2 3 4 5 6 7 8 910 By meansofthe waveletpacketdecomposition algorithm, a Time (ms) higher interference components suppression together with a Interfered negligible distortion of the useful GNSS signal components Mitigated with respecttothe case of thepulse blanking adoption is achieved, as demonstrated by higher average value of the Figure 10: Galileo E5a signal at intermediate frequency before (blue curve) and aeft r mitigation (red curve). estimated 𝐶/𝑁 trend. The same conclusions can be drawn Code delay (ms) Code delay (ms) Samples (n) Samples (n) Power spectral density Amplitude Amplitude ADC level (dB/Hz) CAF CAF 10 International Journal of Navigation and Observation Pulsed interference case −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 P correlator After pulse blanking excision −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 1 2 3 4 5 6 7 8 910 P Time (s) After WPD based excision Pulsed interference Aer b ft lanking mitigation After wavelet mitigation −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 Figure 13: Carrier to Noise density ratio in absence of interference P correlator countermeasures (red), after pulse blanking (black), and after WPD Figure 15: N-Gene data demodulation performance. based interference removal (blue). These results have been obtained setting a predetection integration time 𝑇 equal to 1 ms and choosing loops band- ×10 Pulsed interference case width equal to 5 and 15 Hz, respectively, for the DLL and PLL. Finally, data demodulation performance can be observed in Figure 15, where the prompt in-phase and quadrature correlations are plotted in the complex plane. As expected, 0123456789 0 1 2 3 4 5 6 7 8 9 1010 tracking and thus correct data demodulation can not be Ti Tim me (s) e (s) achieved if no interference countermeasures are employed ×1100 Aer p Aer pu ul ls se b e blan lanki kin ng: g: 𝜎𝜎 = = 76. 76.55 cm cm (top plot), while the data demodulation is noisier when DL DLL L employing the pulse blanking for interference suppression with respect to the case when the WPD algorithm is used. Such results at tracking level conrfi m the capability of this 0123456789 0 1 2 3 4 5 6 7 8 9 1100 wavelet based mitigation algorithm in eeff ctively suppressing Ti Tim me (s) e (s) interference and saving useful GNSS signal components. ×10 Aer WPD based excision: 𝜎 = 72.6 cm DLL 6.2. Narrowband Interference. This section is devoted to the performance analysis of the wavelet based mitigation algo- rithm in mitigating Narrowband interference. eTh analysis 0123456789 10 addresses the problem of ndin fi g the best trade-off between Time (s) thechoiceofthe waveletbased mitigation techniqueparam- eters such as number of wavelet decomposition stages 𝑁 and Prom Prompt pt c co or rr re el la at tor ors s its computational burden. Such trade-off analysis is correlated E Ea arly c rly co or rr rel ela at to or rs s with the Narrowband interference spectral characteristics. La Lat te e c co or rr re el la at to or rs s A digital GNSS signal generator [33] has been adopted in Figure 14: Early Prompt Late correlators during 10 seconds of order to generate synthetic GPS L1 data combined with Galileo E5a-Q channel PRN 20 tracking. Narrowband interference. Several Narrowband interference scenarios have been considered, and a parametric study with respect to interference bandwidth 𝐵 , interference carrier looking at the Early-Prompt-Late correlators values recorded int frequency 𝑓 , and number of wavelet decomposition stages int during the tracking period for the three considered scenarios 𝑁 has been performed. In order to find the best tuning and depicted in Figure 14. We can clearly observe how the of the WPD based algorithm parameters, its application on use of a traditional pulse blanking in presence of strong and synthetic interfered GNSS data has been performed and per- dense in-time pulsed interference would cut off large portion formance in suppressing interference has been assessed. eTh of received signal thus leading to a decrease of the correlations results which will be presented in the following paragraphs amplitude and a minor separation between the E-L corre- have been preliminarily discussed in [34]. lations amplitude with the prompt correlations amplitude andthusahigher DLLjitteroutput. Table 1 summarizes the N-Gene acquisition and tracking performance for the 6.2.1. Performance with respect to the Wavelet Decomposition considered scenarios. Depth 𝑁 . eTh rfi st analysis has been devoted to assess the Correlation Correlation Correlation C/N (dB-Hz) amplitude amplitude amplitude P P Q Q International Journal of Navigation and Observation 11 Table 1: Acquisition and tracking performance comparison. Scenario Noncoherent accumulations𝐾𝛼 (dB) 𝐶/𝑁 (dB-Hz) 𝜎 (cm) mean 0 DLL DME/TACAN interfered 80 24.8 —— After pulse blanking mitigation 10 22.4 36 76.5 After WPD based mitigation 10 30.2 40.2 72.6 Wavelet scale resolution (kHz) 10 1023 511.5 255.7 127.9 63.9 32 16 8 32.2 30.2 28.2 𝛼 26.2 24.2 22.2 1 3 4 5 6 7 8 910 Number of wavelet decomposition stages (N) −300 −200 −100 0 100 200 300 Δ (kHz) BW = 40 kHz BW = 80 kHz Biorthogonal Gaussian BW = 120 kHz Coiflets Meyer Daubechies Symlets Figure 16: Acquisition metric 𝛼 versus the WPD stages 𝑁 for mean different interference bandwidth. Figure 17: Acquisition metric 𝛼 with respect to the frequency max offset Δ between the interference carrier and the GNSS signal impact of thenumberofwavelet decompositionstagesonthe carrier for different wavelet families: 7 WPD stages. Narrowband interference suppression performance. Differ- ent interference scenarios have been considered, combining GPS L1 C/A code signals with Narrowband interference −8 ×10 200 kHz far from the intermediate frequency. Results are Modified Gaussian based filters bank 3.5 shown in Figure 16, where the trend of the acquisition metric 𝛼 is plot versus the number 𝑁 of decomposition stages. mean 3 Acquisition performance is achieved using 1 ms of coherent 2.5 integration time and 20 noncoherent accumulations. eTh three lines referred to three different interference scenar- ios characterized by the presence of Narrowband interfer- 1.5 ence with, respectively, 40, 80,and 120 kHz of bandwidth. Increasing the acquisition stage increases the wavelet scale resolution andthusits frequencyselectivity.Inall thethree 0.5 interference scenarios, for increasing values of 𝑁 ,the WPD based algorithm provides better performance in capturing 0 0 1 2 3 4 5 6 7 89 and isolating narrowband interference, thus leading to better Frequency (MHz) interference suppression with a limited removal of useful signal components, as demonstrated by the increasing trend Figure 18: Modified Gaussian wavelet filters transfer functions. of 𝛼 in Figure 16. However, a saturation effect can be mean observed for higher value of 𝑁 (greater than 7). In such a region, acquisition performance is not anymore improving the ADC output has been achieved through an iterative since wavelet scale resolution is already comparable or nar- filtering process exploiting filter response derived by the rower with respect to the interference bandwidth. Moreover, Meyer wavelet family. Several other wavelet functions exist, as expected, performance of such technique is limited by andmostofthemare discussedin[35]. Figure 17 shows interference bandwidth. At higher interference bandwidth, the acquisition metrics 𝛼 with respect to the frequency max lower acquisition metric values are achieved. offset between the signal carrier and the interference carrier. Removal of the interference has been achieved for each 6.2.2. Wavelet Families Comparison and Interference Carrier interfered scenario exploiting 7 WPD stages and interference Offset. So far, time-scale representation of the signal at suppression process has been repeated using different mother (dB) mean Power spectral density (dB/Hz) (dB) max 12 International Journal of Navigation and Observation Wavelet scale resolution (kHz) acquisition performance improves. This is due to the fact that 1023 511.5 255.7 127.9 63.9 32 16 8 by increasing the wavelet filter length, wavelet function side- 31.6 lobe is lowered resulting in a better orthogonality between the subbands. 29.6 6.2.4. Computational Complexity. Although Wavelet based 27.6 mitigation algorithm provides high capability in interfer- ence suppression, its implementation is characterized by a 25.6 non negligible complexity. Computational burden is mainly determined by the number of wavelet decomposition stages 23.6 𝑁 which determines the number of filtering operations according to the exponential law 2 .Furthermore,the 3 4 5 6 7 8 910 same number of filtering operations is employed for signal reconstruction purposes. All filtering operations are realized Number of wavelet decomposition stages (N) with FIR filters with length 𝐿 . Each output sample is obtained 30 70 with L products and 1 single sum; thus the total number of 40 90 performed operations for decomposition and reconstruction 50 102 of 𝑛 samples of incoming signal is (14) 𝑂 (𝑛, 𝑁, 𝐿 )= 2⋅2 × (𝑛𝐿 + 𝑛 ). Figure 19: Acquisition metric 𝛼 with respect to the number mean of WPD stages 𝑁 and for different filter lengths of the modified However, the filter bank implementation allows for the Gaussian wavelet. processing sample by sample of the incoming signal, without any signal buffering process, at the price of the delay of the wavelet from which the wavelet filters transfer functions decomposition stage and by the reconstruction filter bank characterizing the uniform filters bank are originated. operating on the thresholded samples. Furthermore, better It can be observed that, by increasing the carrier offset efficiency of the method might be achieved by the combina- between the interfering signal and the GNSS signal, the tion of the WPD with the introduction of a frequency domain acquisition metrics may not have an increasing trend. This based predetection especially in those cases where interfer- is due to the fact that, for determined values of Δ ,the ence components are not spread all over the GNSS received Narrowband interference may fall in two different subbands signal spectrum but in a determined frequency region. In and thus interference removal may be negatively aeff cted if such a case, a controlled dyadic scaling operation iterated the wavelet subbands are overlapped. For such a reason, it is on determined subbands could be implemented. It has to be importanttohavewavelet filterresponsewhich is selectivein remarked that wavelet decomposition is already implemented the frequency domain. This property is well accomplished by for multimedia images and audio data compression coding a wavelet function derived from an orthogonalization process scheme, and the availability of Field Programmable Gate of a Gaussian function: the so-called modiefi d Gaussian Array (FPGA) allows the WPD implementation for real- function, which is described in [35]. Figure 18 shows the time application. Furthermore, the wavelet based algorithm wavelet filters transfer functions obtained from the Gaussian can represent an efficient postprocessing technique for inter- wavelet function. It can be observed that such Gaussian ference detection and characterization which can be easily wavelet filters are characterized by a more selective frequency implemented in potential GNSS interference monitoring response with less overlap between the subbands. stations with the aim of investigating the harsh interference For such a reason, interference removal exploiting environment in sensitive areas. wavelet filters response derived from the modified wavelet Gaussian overperforms the interference process performed 7. Conclusions exploiting other wavelet function, as shown in Figure 17. In this paper, an innovative interference mitigation algorithm 6.2.3. Wavelet Filter Length. Final investigation has been exploiting the Wavelet Packet Decomposition has been pre- performed in order to analyse the impact of the filter length sented. Detection and interference suppression mechanism on the interference suppression. In fact, all the wavelet has been described. Simulation results showed its eeff ctive- impulse responses are characterized by a fast decreasing ness in different interference scenarios. In particular, the amplitude in the time domain, thus allowing a good approxi- method is demonstrated to be eeff ctive with respect to the mated implementation by means of Finite Impulse Response classical blanker in multiple pulse interference representing (FIR) filters. However, the truncation of the filter response the DME/TACAN interference scenario on the Galileo E5a causes a loss in the orthogonality of the subbands. eTh same and GPS L5 frequency bands. Application of this wavelet Narrowband interference scenario has been considered, the based method showed that high interference suppression modified Gaussian wavelet functions have been adopted for canbeachievedwithout distorting or suppressinguseful the WPD, and results are shown in Figure 19.Itcan be GNSS signal components, as proved by the performance at observed that by increasing the number of filter coefficients, acquisition and tracking stages. Furthermore, the method (dB) mean International Journal of Navigation and Observation 13 proved to be eecti ff ve also in several Narrowband interference [11] S. Savasta, F. Dovis, R. Lesca, D. Margaria, and B. Motella, “On the interference mitigation based on ADC parameters scenarios, since it allows a tuning of the parameters to match tuning,” in Proceedings of the IEEE/ION Position, Location and the operating scenario. 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Use of the Wavelet Transform for Interference Detection and Mitigation in Global Navigation Satellite Systems

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Hindawi Publishing Corporation
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Copyright © 2014 Luciano Musumeci and Fabio Dovis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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1687-5990
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10.1155/2014/262186
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Hindawi Publishing Corporation International Journal of Navigation and Observation Volume 2014, Article ID 262186, 14 pages http://dx.doi.org/10.1155/2014/262186 Research Article Use of the Wavelet Transform for Interference Detection and Mitigation in Global Navigation Satellite Systems Luciano Musumeci and Fabio Dovis Department of Electronics and Telecommunications, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Turin, Italy Correspondence should be addressed to Luciano Musumeci; luciano.musumeci@polito.it Received 9 October 2013; Revised 20 December 2013; Accepted 30 December 2013; Published 26 February 2014 Academic Editor: Sandro Radicella Copyright © 2014 L. Musumeci and F. Dovis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Radio frequency interference detection and mitigation are becoming of paramount importance due to the increasing number of services and applications based on the position obtained by means of Global Navigation Satellite Systems. A way to cope with such threats is the implementation in the receiver of advanced signal processing algorithm able to raise proper warning or improve the receiver performance. In this paper, we propose a method based on the Wavelet Transform able to split the useful signal from the interfering component in a transformed domain. The wavelet packet decomposition and proper statistical thresholds allow the algorithm to show very good performance in case of multiple pulse interference as well as in the case of narrowband interference, two scenarios in which traditional countermeasures might not be eeff ctive. 1. Introduction which broadcast strong signals on frequencies within or located near the GNSS frequency bands. As an example, Reliable positioning and navigation are becoming imperative the terrestrial Digital Video Broadcasting (DVB-T) system in a growing number of applications that are being devel- may represent a real threat for the GNSS receiver operation. oped for public services and safety critical purposes. As a In fact, nonlinearity distortion generated in the DVB-T consequence, satellite and radio navigation is evolving in an transmitterampliefi rmayleadtothegenerationofharmonics accelerating pace and it is becoming a pervasive technology in the GPS L1 (and thus Galileo E1) frequency band. in a large number of consumer and professional devices. In [2] a set of on-field experiments aiming at assessing For such a reason, parallel to the development of techniques the eeff ct of DVB-T and VHF/UHF signals on GNSS receiver able to improve the positioning accuracy, the research is are described. Figure 1(a) shows the possible interference becoming of paramount importance to improve the robust- sources that can have secondary harmonics within the GPS ness of the positioning methodologies in order to make sure L1, while Figure 1(b) specifies these potential interferers, that the navigation is trustworthy and the risks and threats with respect to the order of the harmonics. eTh DVB-T are properly accounted for. As far as Global Navigation is transmitted within the frequency range of 174–230 MHz Satellite Systems (GNSS) based techniques, intentional or (ultrahigh frequency, UHF band III) and 470–862 MHz (very unintentional interference represents one of the main threats high frequency, VHF bands IV and V). Additional details on to be considered. GNSS receiver operation can be easily DVB-T system impact on GNSS receiver performance can be disrupted by interfering signal due to the extreme weakness of found in [3]. the GNSS signals reaching the GNSS user antenna. In fact, the Another example of out-of-band RF interference risk for presence of undesired RFI and other channel impairments the GNSS systems has been provided by the LightSquared can result in degraded navigation accuracy or complete loss case in the United States. eTh company deployed a ground- of receiver tracking [1]. Furthermore, due to the lack of based 4G-LTE network that transmits on a frequency band frequency allocations, the majority of the interference issues right next to the primary GPS frequency (L1). Although come from the presence of other communication systems LightSquared would have operated in its own authorized 2 International Journal of Navigation and Observation 1559 1591 been shown that on-board GNSS receiver yfl ing at 40000 feet 1565.19 1585.65 over Frankfurt airport area might be seriously threatened by DME/TACAN interference which may cause complete loss of lock of the GNSS signal. Many other examples of communication systems which Frequency (MHz) may represent a possible in-band unintentional interference sources for the GNSS are described in [3]. Last but not least, also intentional interference is a threat 1525 1559 1660 to be considered for civil GNSS community. Portable devices, jamming the GNSS bandwidth, typically broadcast signals GPS L1 Galileo E1 frequency modulated where the instantaneous frequency Interference sweeps arange of severalMHz in afew microseconds affecting the entire GNSS band targeted by the device [ 7]. (a) These few examples of interference generated by other Mobile communication systems proved that interference is a real satellite DVB-T/TV secondary harmonics DAB applications issue in GNSS and that proper countermeasures have to be designed. In fact, the different interference sources may broadcast signals that are very different in terms of power, 1559 1591 modulation, and pulse shape, thus making it difficult to have 1565.19 1585.65 a universal countermeasure able to cope with all of them. In this paper, this issue is addressed working with a transformed domain approach that is able to deal with a large number of 8th VHF 10 2nd UHF 66 3rd UHF 23 9th VHF 7 different kind of interfering sources, thus being effective in a 3rd UHF 22 2nd UHF 67 wide range of scenarios. GPS L1 eTh paper is organized as follows. Section 2 provides a Galileo E1 model for the useful signal and the interference together Interference with a basic interference signal classification. Section 3 will (b) be devoted to a general description of the current state of the art of interference mitigation algorithms for GNSS. Figure 1: Possible in-band and out-of-band interferences (a). After introducing the Wavelet Transform in Section 4,an Secondary harmonics interference within the GPS L1 and Galileo innovative interference mitigation algorithm based on the E1 bands (b). use of the wavelet packet decomposition will be presented in Section 5. Such an algorithm will be fully described, and its band, the proximity to the GPS signals induced overload or performance in detecting and suppressing interference will saturation of the radio frequency front-ends of the GNSS be discussed in Section 6. receivers. eTh threat to GPS was so strong that, following extensive testing and analysis, the Federal Communication 2. Signal Model and Interference Classification Commission denied the LightSquared’s terrestrial operations [4]. The received interfered GNSS signal at the receiver antenna The interference issue is not only aeff cting the L1 band can be written as where the civil GPS signal and the Open Service of Galileo 𝐿−1 arebroadcast.Thefutureaidings forGNSSbased aviation 𝑠 (𝑡 )= ∑𝑦 (𝑡 )+𝑖 (𝑡 )+𝜂 (𝑡 ), (1) RF,𝑙 applications will be broadcastinthe GalileoE5and GPS 𝑙=0 L5 frequency bands which are shared with other Aero- nautic Radio Navigation Systems, as described in [5]. In where 𝐿 is the total number of GNSS useful signals, 𝑦 (𝑡) is RF,𝑙 fact, GNSS based aviation aids will be broadcasted by the the useful GNSS signal received by the 𝑙 th satelliteinlineof Space Based Augmentation Systems over the L5/E5 frequency sight, 𝑖(𝑡) is the additive interfering signal transmitted over band.However,suchfrequency bandsare shared with other a carrier frequency 𝑓 and characterized by a two-sided int Aeronautical Radio Navigation Systems (ARNS) such as the bandwidth 𝐵 ,and 𝜂(𝑡) is the additive white Gaussian noise. int Distance Measuring Equipment (DME) and the military one Before being fed to the acquisition and tracking block, the Tactical Air Navigation (TACAN). Both systems provide signal is first downconverted to an intermediate frequency, slant range information between an aircraft and a ground sampled, and quantized in the receiver front-end. us, Th the reference station, through the communication between two composite received signal at the ADC output according to [8] components, an interrogator installed on board of the aircraft can be written as andatransponder placed on theground, usuallywithinthe 𝐿−1 airport area. Such DME/TACAN ground stations broadcast 𝑠 [𝑛 ] =𝑠 [𝑛𝑇 ] =𝑄 [ ∑𝑦 [𝑛𝑇 ] +𝑖 [𝑛𝑇 ] +𝜂 [𝑛𝑇 ]] , powerful modulated double-pulse signals which may corrupt IF IF 𝑠 IF,𝑙 𝑠 𝑠 𝑠 𝑙=0 the GNSS on-board receiver operation. A detailed descrip- (2) tion of such aeronautical systems is presented in [6]. It has International Journal of Navigation and Observation 3 where the function 𝑄 denotes the quantization over 𝑘 bits, proposed show advantages and limitations depending on the and 𝑇 is the sampling frequency. Expanding the term 𝑦 , interfered scenario considered. In the following, a classifica- 𝑠 IF,𝑙 the expression for the single digitized GNSS signal aeff cted tion is provided in order to highlight the advantages and lim- by noise and interference components becomes (neglecting itations of the different methods. Interference detection and for the sake of simplicity the subscript 𝑙 ) mitigation techniques can be grouped in different families according to the point within the GNSS receiver chain they 𝑠 [𝑛 ] =𝑄 [ 2𝐶𝑑 (𝑛 − 𝑛 )𝑐(𝑛 − 𝑛 )×cos (2𝜋𝐹 𝑛+𝜙 ) IF 0 0 𝐷,0 0 𝑘 are applied on, as reported in Figure 2. +𝑖 [𝑛 ] +𝜂 [𝑛 ]], (i) Antenna level techniques which are based on the use (3) of antenna arrays capable of generating radiation pat- tern which attenuates the interference signal coming where 𝐶 is the received GNSS signal power from one satellite from a determined direction [9]. in view, 𝑑 and 𝑐 are, respectively, the navigation data message (ii) Automatic Gain Control (AGC) level where the content and the pseudorandom noise sequence, 𝐹 =(𝑓 + 𝐷,0 IF interference monitoring is performed detecting a 𝑓 )𝑇 is the Doppler aeff cted frequency, 𝑛 =𝜏 /𝑇 is the 0 𝑠 0 0 𝑠 persistent saturation status of the AGC (see, e.g., [10, digital code delay, and 𝜙 is the code delay. 11]). 𝑖[𝑛] and 𝜂[𝑛] are the digitized interference and the digital Gaussian noise component, respectively. Given 𝐵 the front- (iii) Postcorrelation techniques which are based on the IF end bandwidth, it can be shown that by sampling the signal at analysis of the shape of the correlation function, in the Nyquist frequency 𝑓 =2𝐵 , the noise variance becomes most cases exploiting a multicorrelator receiver [12]. 𝑠 IF (iv) Raw observable level techniques which are based on 𝑁 𝑓 2 2 0 𝑠 (4) 𝜎 =𝐸{𝜂 [𝑛 ]}= =𝑁 𝐵 , IF 0 IF the processing of the raw samples at the Analog to Digital Converter (ADC) output. where 𝑁 /2 is the power spectral density (PSD) of the noise. In particular, among the interference countermeasures A general classification of the interfering signals is based at raw observable level, it is possible to distinguish those on their spectral characteristics such as their carrier fre- which perform interference detection and cancellation in one quency 𝑓 or their bandwidth 𝐵 . int int single domain as the pulse blanking in the time domain or (i) Out-of-band interference refers to interfering signals thenotch filtering in thefrequency domain.Theinnovative whose carrier frequency is located near to the targeted interference mitigation based on the use of the Wavelet GNSS frequency band (𝑓 <𝑓 −𝐵 /2 or 𝑓 > int IF IF int Transform properties belongs to this latter family, since 𝑓 +𝐵 /2). IF IF it performs detection and mitigation of the interference (ii) In-band interference refers to interfering signals with processing thereceivedsignalinatransformeddomain. carrier frequency within the GNSS frequency band Pulse blanking is the most traditional countermeasure (𝑓 −𝐵 /2 < 𝑓 <𝑓 +𝐵 /2). suited for pulsed interference. Implemented by means of a IF IF int IF IF digital circuit in the digital part of the receiver front-end, Moreover, interference can be further classiefi d according to such technique performs an interference excision in the time its characteristics in the frequency domain. domain by thresholding sample by sample the output of the (i) Narrowband interference when the spectral occu- Analog to Digital Converter (ADC) converter, as it is shown pation is smaller with respect to the GNSS signal in Figure 3. Pulse detection in this case can be performed in bandwidth (𝐵 ≪𝐵 ). int IF either analog circuitry, through analog power measurement, or digital circuitry, looking at the histogram of the samples at (ii) Wide-band interference when the spectral occupa- the output of the ADC [13]. This simple mechanism performs tion is comparable with respect to the GNSS signal pulsed interference suppression in the time domain and it bandwidth (𝐵 ≈𝐵 ). int IF oer ff s good performance in the presence of pulsed interfering (iii) Continuous wave (CW) interference which appears as source characterized by a low Pulse Repetition Frequency a spike in the frequency domain (𝐵 →0). int (PRF). However, the technique shows limitation when highly Furthermore, in general, interference might have time- dense in-time and strong interfering pulses are present since frequency varying characteristics, for example, pulsed inter- they lead the pulse blanking circuitry suppressing a large ference or chirp signals. The former is mainly characterized portion of the composite received signal and thus worsening by on-off status of short duration (order of ), which alter- the GNSS receiver performance due to the degraded quality nates in the time domain, whilst the latter is characterized ofthereceivedsignal.In[6], it has been shown that, due to the by a linearly variation in time of the instantaneous frequency described strong DME/TACAN interference environment, thus resulting in a wide-band interference. More details on the pulse blanking of the receiver on-board suppresses about interference classification can be found in [ 1]. 56% of the incoming signal thus leading to the loss of lock of the weakest GNSS received signals. Furthermore, the drawbacks of such simple interference 3. Interference Countermeasures countermeasure come from the fact that its performance Several kinds of interference countermeasures have been is strongly dependent on the receiver front-end design. In developed since the early years of GNSS. The methods fact, strong and dense in-time pulsed signals can cause the 𝜇𝑠 4 International Journal of Navigation and Observation Antenna Tracking stage (DLL) Front-end PLL ∑ (·) ∑ (·) Discriminator AGC ADC BPF ∑ (·) NCO Filter Interference detection and mitigation Figure 2: GNSS receiver chain block scheme. Ideal blanking mitigation Nonideal blanking mitigation 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 −1 −1 15 20 25 30 35 40 15 20 25 30 35 40 Time (𝜇 s) Time (𝜇 s) Before blanking Before blanking After blanking After blanking Blanking threshold Blanking threshold (a) (b) Figure 3: Signal before and aeft r interference removal by means of ideal (a) and nonideal pulse blanking (b). saturation of the active components in the GNSS receivers input dynamics of the ADC is not properly set [14]. The fact chain (e.g., amplifiers), which may require a recovery time that the blanked samples should not be used for the AGC to resume their normal state. This saturation eect ff may tuning in order to avoid ADC overloading has to be taken lead the pulse blanking suppressing the received signal even in consideration. In Figure 3, DME/TACAN pulse pair before during the off-status of the pulse thus causing an increasing (blue line) and aeft r (red line) the application of both ideal (a) degradation on the received useful GNSS signal. In [14], it and nonideal (b) pulse blanking is shown. Nonideal blanking is mentioned that for a particular commercial receiver, an reveals a delay in pulse detection as well as a recovery interference pulsed signal with a peak power 15 dB above the time needed to the active components of the front-end to thermal noise is sufficient to saturate the last amplification recover their normal operation, which produce a different stage of the receiver front-end. Furthermore, careful design mitigated signal. Furthermore, due to the bell shaping of the of the Automatic Gain Control (AGC) is needed when a DME/TACANandtothepresenceofthemodulationoverthe pulse blanker circuitry is present. A slow AGC sets the A/D pulseduration, notall thesamples belongingtothe pulseare input levels averaging the input signal power over a large time suppressed leading to an increased noise floor [ 15, 16]. Unlike during which if too many pulses oscillations are present, the thepulse blanking,which worksinthe time domain,other Normalized amplitude Normalized amplitude International Journal of Navigation and Observation 5 interference countermeasures provide interference detection already extensively used; in fact, in literature, it is possible to and cancellation in the frequency domain. As an example, n fi d several research works in which the Wavelet Transform interference cancellation can be performed suppressing the has been adopted mainly to cope with the multipath issue. In particular, in [21], a new trend extraction technique for interference carrier frequency exploiting notch filtering. Such multipath mitigation in carrier phase measurements domain an interference countermeasure is well suited for CW or using wavelet multiresolution analysis is presented. More narrowband interference. In [16], notch filtering is proposed detailed descriptions of this algorithm can be found in for suppressing DME/TACAN interference which appears in [22–25]. Multipath mitigation is not the only framework the frequency domain as Narrowband interference. In such which Wavelet Transform has used. For instance, in [26], a a scenario the use of notch filters allows the suppression of singularity detection technique for GPS cycle slips based on the entire DME/TACAN pulse (tails included) but it reveals the wavelet decomposition is described. In [27], an Empirical several drawbacks in the presence of multitone interference Mode Decomposition (EMD) exploiting the Wavelets’ prop- sources. erties is described as a method to reduce the carrier phase As an example, in [7], adaptive notch filtering scheme is measurements error. Finally in [28], methodology based on described as interference countermeasure against jammers. Wavelet Transform to evaluate the terrain and extract features Another algorithm performing interference mitigation along the vehicle path is presented. o Th se features which can in frequency domain is the Frequency Domain Adaptive be hazardous to a following vehicles path are of particular Filtering introduced in [17]. Such technique is based on a Fast interest. Fourier Transform (FFT) of the samples at the ADC output. A different wavelet based mitigation algorithm approach Interference suppression is performed through a sample by for interference suppression will be presented and fully sample thresholding in the FFT domain. Basically, each FFT described in the next section. point is compared to a threshold, fixed according to a certain falsealarm probability, andzeroedwhenthe thresholdis 4. The Wavelet Transform exceeded. en Th an inverse FFT operation is performed on the manipulated incoming signal, in order to obtain back Wavelet Transform overcomes the common limit of those the signal in the time domain to feed to the acquisition and transformations based on Fast Fourier Transform (FFT) tracking blocks. as the Short Time Fourier Transform (STFT). The set of In most of the cases, interference is an unexpected and orthogonal basis functions which are employed for the STFT unpredictable event. Interference signal characteristics in computation can be seen as bandpass filters having equal time and frequency domain might be highly variable. For frequency bandwidths and thus representing a set of windows such a reason, research in this efi ld is moving towards in time with equal duration. This leads to a different reso- the investigation of innovative interference countermeasures lution in the characterization of high frequency phenomena able to represent the incoming signal in a two-dimensional with respect to the resolution achieved in characterizing domain, for example, the time-frequency domain, where low frequency phenomena. Exploiting fixed windows, many interference component can be better isolated and removed cycles of a high frequency signal can be captured, while for a without suppressing great portion of GNSS useful signal. low frequency signal very few cycles are within the windows. In [18], an interference mitigation algorithm based on the For such a reason, resolution of Fourier Transform is poor at time-frequency representation of the GNSS received signal is low frequency, while it improves as the frequency increases proposed. Here, an Orthogonal-Like Gabor Expansion of the [29]. Another drawback of using transformation based on samples at the ADC output is employed in order to perform fixed windows is revealed when considering the rising part of the time-frequency representation of the incoming interfered the signal. Very narrow window will help to localize the rising signal. Each value in the transformed domain is compared portion of the signal very well with respect to a wide window, to a mask, which is computed through an Orthogonal-Like at the expenses of a loss of information in the steady part of Gabor Expansion on the expected GNSS received signal the signal, which is better characterized by wider windows. that would be present in an interference-free environment. In order to overcome these issues, a set of functions which Such processallowstoidentify thosecoecffi ientsinthe could better match the frequency components of the signal time-frequency representation which represent interference to be characterized is needed. From such basis functions, a information and that can be used to generate a synthetic filters bank where the low-pass filters response has narrower reconstruction of the interfered signal. Interference suppres- bandwidths (so wider in the time domain) than the high-pass sion is performed subtracting a synthetic interference signal filters response can be derived. u Th s, a transformation based reconstruction from the original received signal. A drawback on windows which are functions of both time and frequency for this algorithm is that synchronization strategy is needed such that their bandwidths get narrower as the frequency to perform a correct subtraction between the original signal decreases is needed. eTh se requirements are accomplished by and the synthetic reconstruction. the basis functions used to perform the Wavelet Transform. In Recently, an innovative interference mitigation algorithm the STFT, all the bandpass filters are obtained by modulation basedontheuseoftheWaveletTransformhasbeenpresented of asinglefilter andthustheyhaveequal bandwidth[ 29]. in [19, 20], for pulsed interference mitigation. Here, Wavelet Concerning the Wavelet Transform, filters responses are Transform is employed to obtain time-scale representation obtained as of the incoming interfered signal. In the framework of the −𝑘/2 −𝑘 (5) navigation satellite systems, the Wavelet Transform has been ℎ (𝑡 )=𝑎 ℎ (𝑎 𝑡 ) 𝑘 6 International Journal of Navigation and Observation −8 4.1. Discrete Time Wavelet Transform. It can be shown that ×10 Discrete Meyer based filters bank 3.5 a digital implementation of the Wavelet Transform can be equivalently implemented by using digital filters. The equivalent expression of (6) for digital filters would be 2.5 𝑘 𝑘 𝑗2 𝜔 2 𝐻 (𝑒 )=𝐻(𝑒 )󳨀→𝐻 𝑧 =𝐻(𝑧 ), (10) ( ) 2 𝑘 𝑘 1.5 where 𝑘 is a nonnegative integer. In [29], it is shown that 𝐻 (𝑧) is a multiband (rather than passband) filter; thus, in 1 𝑘 order to obtain passband filters, a low pass filter 𝐺(𝑧) is 0.5 employed. In [30], 𝐺(𝑧) is defined as the mirror filter of 𝐻(𝑧) and together are called quadrature mirror filters. u Th s, 0 1 2 3 4 5 6 7 89 according to a dyadic scaling operation, the nonuniform Frequency (MHz) filters bank responses are obtained as follows: Figure 4: Meyer wavelet filters transfer functions. 2 2 4 𝐻 (𝑧 ),𝐺 (𝑧 )𝐻(𝑧 ),𝐺 (𝑧 )𝐺(𝑧 )𝐻(𝑧 )⋅⋅⋅ . (11) The Wavelet Transform can be extended to obtain the or equivalently in the frequency domain so-called Wavelet Packets Decomposition (WPD), where the discrete-time signal is passed through a uniform wavelet 𝑘/2 𝑘 𝐻 (𝑗Ω )=𝑎 𝐻 ( Ω), (6) based filter bank, as shown in Figure 5. eTh scaling and shifting process is also iterated at higher frequencies, thus where 𝑎>1 and 𝑘∈ Z. resulting in a uniform filter bank; the output of each is provid- As seen in (5)and (6), all the transfer functions are ing a set of coefficients (scales) each of which is representing a obtained by frequency-scaling operation of a prototype determined frequency portion of the incoming decomposed 𝐻(𝑗Ω) , the so-called mother wavelet, thus resulting in a signal. Each stage of the uniform filters bank is composed nonuniform filters bank. As an example, Figure 4 shows the by a filtering process through 𝐻(𝑧) and 𝐺(𝑧) ,respectively, transfer functions of each branch of the nonuniform filters thewavelet vector andthe scalingvectorindividuallyshift bank obtained by a dyadic scaling operation from the Meyer orthogonal and orthogonal to each other, which produce a −𝑘/2 wavelet function. The scale factor 𝑎 is introduced as a decomposition of the signal in high frequency component normalization factor in order to ensure constant energy inde- and low frequency component, followed by a downsampling pendent from 𝑘 as well as the ratio between the bandwidth operation. and the center-frequency Ω . Furthermore, since the filter bandwidth 𝐻 (𝑗Ω) is narrower for larger 𝑘 ,its output canbe 5. The Wavelet Based Mitigation Algorithm sampled at lower rate. Summarizing, given an arbitrary input 𝑥(𝑡) ,the output of thefilter ℎ (𝑡) is defined as The proposed wavelet based mitigation algorithm is com- pletely based on the WPD previously described. eTh algo- 𝑋 (𝑘, 𝑛 )= ∫ 𝑥 (𝑡 )ℎ (𝜏−𝑡 ) DWT 𝑘 rithm for interference detection and suppression is mainly −∞ (7) based on three steps. −𝑘/2 −𝑘 =𝑎 ∫ 𝑥 (𝑡 )ℎ(𝑎 (𝜏−𝑡 ))𝑑.𝑡 (i) Decomposition phase where the incoming GNSS −∞ interfered signal is passed through the uniform filter Replacing the continuous variable 𝜏 with 𝑛𝑎 𝑇 ,itfollows that bank thus achieving the time-scale representation. The number of wavelet stages to apply for the signal −𝑘/2 −𝑘 decomposition is a free parameter. Following in this 𝑋 (𝑘, 𝑛 )=𝑎 ∫ 𝑥 (𝑡 )ℎ(𝑛𝑇 − 𝑎 𝑡) DWT −∞ paper, the optimal number of wavelet decomposition (8) ∞ stages will be assessed with respect to the interference = ∫ 𝑥 (𝑡 )ℎ (𝑛𝑎 𝑇−𝑡).𝑡𝑑 spectral characteristics and with respect to the GNSS −∞ receiver performance at both acquisition and tracking The above integral represents the convolution between 𝑥(𝑡) levels. and ℎ (𝑡) evaluated at a discrete set of points 𝑛𝑎 𝑇 ;thatis, the (ii) Detection-mitigation phase is performed in each convolution output is sampled with a spacing 𝑎 𝑇 .Theset of scale obtained at the output of the filters bank. A coefficients obtained for each value of 𝑘 provides the discrete simple blanking operation will be adopted in order Wavelet Transform. u Th s, all the orthogonal basis functions to suppress those coecffi ients in each scale represent- −𝑘 ing interference components. For such a reason, a composing the filters bank are derived by dilation ( 𝑡→𝑎 𝑡 ) criterion for the blanking threshold determination and shifting ( 𝑡→𝑡−𝑛𝑎 𝑇 ) of a prototype function 𝜓(𝑡) ,the is needed. eTh adopted criterion is mainly based on mother wavelet; that is, a statistical characterization of the GNSS received −𝑘/2 −𝑘 (9) 𝜓 (𝑡 )=𝑎 𝜓 (𝑎 𝑡−𝑛𝑇 ). signal at the ADC output. It is well known that 𝑘𝑛 Power spectral density (dB/Hz) 𝑑𝑡 𝑑𝑡 𝑗𝑎 𝑗𝑤 International Journal of Navigation and Observation 7 ↓2 G(z) H(z) ↓2 G(z) ↓2 G(z) ↓2 H(z) ↓2 ↓2 G(z) H(z) ↓2 y [n] IF G(z) ↓2 ↓2 H(z) G(z) ↓2 H(z) ↓2 H(z) ↓2 G(z) ↓2 ↓2 H(z) Figure 5: Wavelet Packet Decomposition by means of 3-stage uniform filters bank. GNSS signal is completely buried in the noise at the interference will be assessed looking at the time-frequency user antenna level. Choosing a sampling frequency signal characteristics and comparing the signal quality before matching the Nyquist condition, the filtered digitized and aeft r mitigation. A full software GNSS receiver, N-GENE noise can be considered still uncorrelated; thus, it [31], capable of processing Galileo and GPS signals over all is allowed to assume that at the ADC output, the the GNSS frequency bands, has been employed in order to digitized GNSS signal in an interference-free envi- assess receiver performance at both acquisition and tracking ronment is still Gaussian distributed with zero mean level after the wavelet based interference suppression. Such and variance 𝜎 . Denoting the false alarm probability a software receiver is realized with FFT based acquisition IF 𝑝 as the probability of the event in absence of scheme parallel in the time domain and tracking loops based interference, a generic sample at the ADC output on 2nd order loop filters. Results in terms of separation crosses the blanking threshold 𝐵 ,itfollows that between the correct acquisition peak in the search space th and the noise floor ( 𝛼 )aswellaspseudorange tracking mean 2 2 −𝑥 /2𝜎 IF error and 𝐶/𝑁 aer ft the wavelet mitigation algorithm will be 𝑝 =2 ⋅ ∫ 𝑒 . (12) 𝐵 𝜎 2𝜋 provided and compared with the receiver performance in an th IF interference-free scenario. u Th s, for a required false alarm probability 𝑝 , Two macroscenarios have been considered. inverting (12), it follows that (i) Pulsed interference scenario which is representative 2 −1 √ of a realistic interference scenario experienced by a 𝐵 =𝜎 2⋅𝑒𝑐𝑓𝑟 (𝑝 ). (13) th IF GNSS receiver on board of an aircraft at 40000 feet over the central Europe region and the operation of This blanking threshold magnitude is applied in each whichmay be corruptedbythe strong pulsed signals scale, since the wavelet filtering stages are performed reaching the GNSS antenna and coming from the with unitary energy filters. different ground DME/TACAN beacons. (iii) Reconstruction phase achieved through an inverse (ii) Narrowband interference scenario generated with syn- Wavelet Packet transform applied on the wavelet thetic data at intermediate frequency. Dieff rent Nar- scales after the mitigation phase. eTh main advantage rowbandinterferencescenarios will be takeninto of this algorithm with respect to the Gabor expansion account considering different interference bandwidth based algorithm is that no signal storage for the and different off-set between the intermediate fre- signal decomposition as well as no synchronization quency and the interference carrier frequency. In this operation at signal reconstruction is needed. section, the best configuration of the parameters algo- rithm such as the number of wavelet decompositions 6. Experimental Results or the filters length will be assessed looking at the receiver performance. This section will entirely focus on the application of such wavelet based interference mitigation algorithm in realis- tic interference scenarios. Analysis is performed exploiting 6.1. Pulsed Interference. An extremely realistic DME/TACAN software simulations. Wavelet based algorithm has been interference scenario has been simulated through the software implemented and offline applied on different data use of the Interference Test Facility (ITF) available at sets generated at intermediate frequency and representative the radio-navigation laboratory of the European Space of specific interference scenarios. Benefits in suppressing Agency/European Space Research and Technology Centre 𝑓𝑎 𝑓𝑎 𝑓𝑎 𝑓𝑎 Fr requency bins (kHz) 8 International Journal of Navigation and Observation −30 (ESA/ESTEC). The ITF is a hardware software platform −40 capable of generating a wide range of realistic interference scenarios and it is mostly devoted to the testing of GNSS −50 hardware receiver performance under interference. More −60 details on the different capabilities and configurations of this −70 0 2 4 6 8 10 12 14 16 18 tool canbefound in [32]. Frequency (MHz) A realistic scenario of a GNSS receiver corrupted by the composite pulsed signal coming from up to 40 DME/TACAN stations broadcasting strong pulsed signals within the GPS L5 and Galileo E5a frequency bands has been simulated. Figure 6 shows 10 ms of data collected at intermediate −50 frequency (9 MHz) sampled at 36 MHz. Spectral character- −100 0 1 2 3 4 5 6 7 8 910 istics of thesingleDME/TACAN pulsed signal areshown Time (ms) in theplotontop.Itappears as anarrowbandinterference with approximately 300 kHz bandwidth. eTh entire spectrum Figure 6: 10 ms of Galileo E5a signal at intermediate frequency is jammed due to the fact that several ground beacons aec ff ted by DME/TACAN pulsed interference. have been simulated broadcasting pulses on different carrier frequency within the Galileo E5a and GPS L5 frequency bands. Under this condition, receiver operation is disrupted Galileo E5aQ PRN20 search space: 𝛼 = 24.8 dB mean as demonstrated in [6]. 1 ms of coherent integration time combined with 80 noncoherent accumulations has been adopted in order to ×10 acquire the Galileo E5a pilot channel (PRN 20) in presence of strong DME/TACAN interference and results are shown in Figure 7. In this scenario, a high number of noncoherent accumulationshavebeenemployedinorder to be able to 4 detect the correct acquisition peak from the noise floor, leading to an acquisition metric 𝛼 equal to 24.8 dB. mean Wavelet based mitigation algorithm has been applied to the interfered data-set. First, a time-scale representation of the 08 0.8 signal at the ADC output is achieved exploiting 5 stages of a 0.6 0.4 wavelet based filters bank, employing a Meyer wavelet family 0.2 −5 (see Figure 8). After 5 stages of WPD, 32 scales are obtained, each Figure 7: N-GENE acquisition search space in presence of of which represents a determined frequency component of DME/TACAN interference: Galileo E5a-Q channel, PRN 20. the interfered received Galileo E5a signal. As it is shown in Figure 8, composite DME/TACAN signal reaching the user antenna is spread all over the time-scale domain. The black floors represent the blanking threshold applied for the signal powerissaved,asconrfi medbythe absenceofdrops interference component detection within each wavelet scale in the spectrum shown in Figure 10. andcomputedaccordingtoafalsealarm probability 𝑝 Figure 11 shows the acquisition search space obtained −4 letting the software receiver acquire the data-set processed by of 10 as in (13). Once the time-scale representation of the wavelet based mitigation engine. It can be clearly seen that the incoming signal is achieved, an interference suppression acquisition of the Galileo E5a pilot channel (PRN 20) can be algorithm based on a simple blanking operation is performed achieved already exploiting only 10 noncoherent accumula- in each wavelet scale. Figure 9 shows the modified time-scale tions combined with 1 ms of coherent acquisition time, thus domain achieved aer ft the blanking operation. reducing the Mean Acquisition Time (MAT) needed to detect Such modified scales are fed to a wavelet based anti- thesatellite.Anexcellent interference suppressionisachieved transformation block which is in charge of the signal recon- as demonstrated by the high reduction of the noise floor in struction. Figure 10 provides a comparison between the the search space. In fact, the separation between the main time-spectral characteristics of the signal before and aer ft peak and the noise floor, denoted by 𝛼 ,isapproximately theinterferencesuppression throughthe WPDalgorithm, mean 30.2 dB (4 dB higher than the interfered case in Figure 7) showing the benefits of this algorithm when looking at the exploiting a considerably less number of noncoherent accu- spectrum achieved aer ft the mitigation (top plot). eTh eeff ct mulations (only 10). Furthermore, interference suppression of thepulsedinterferenceisstronglyattenuated. performed through this wavelet based method overperforms Furthermore, unlike a common interference mitigation the interference mitigation performance achieved aer ft apply- techniqueperformed in thetimedomain, as thepulse ing a simple pulse blanking operation on the IF-samples blanking, where useful signal components are suppressed of the collected data-set, as it can be seen in Figure 12, together with interference, the majority of the useful GNSS where, although correct Doppler and code delay acquisition Code delay (ms) Power spectral CAF ADC level density (dB/Hz) 𝑓𝑎 Frequency bins (kHz) W Wavelet scales Frequency bins (kHz) Wavelet scales International Journal of Navigation and Observation 9 Time-scale domain-N= 5 Galileo E5aQ PRN20 search space: 𝛼 = 30.2 dB mean ×10 3.5 2.5 1.5 −100 −200 0.5 −300 20 20 10000 10 0.8 8000 8000 0.6 10 0.4 0.2 2000 −5 Figure 11: N-GENE acquisition search space aer ft wavelet based Figure 8: Time-scale representation achieved by 5 stages of wavelet mitigation algorithm: Galileo E5a-Q channel, PRN 20. packet decomposition. Galileo E5aQ PRN20 search space: 𝛼 = 22.4 dB mean ×10 −100 −200 −300 20 1 0.8 6000 0 0.6 0.4 0.2 −5 Figure 9: Time-scale aer ft interference removal. Figure 12: N-GENE acquisition search space aer ft pulse blanking: Galileo E5a-Q channel, PRN 20. Signal reconstruction-N= 5 −30 is achieved, a noisier search space as well as a reduction of the correlation peak amplitude can be observed. −40 Concerning the software receiver tracking performance, −50 carrier to noise density ratio 𝐶/𝑁 and DLL jitter have been −60 assessed. Figure 13 shows 10 seconds of the estimated 𝐶/𝑁 during the Galileo E5a pilot channel tracking in presence of −70 0 2 4 6 8 10 12 14 16 18 suchastrongpulsedinterferenceforthreedieff rentscenarios: Frequency (MHz) (i) when no interference countermeasures are employed (red line), (ii) when a traditional pulse blanking is employed (black line), −50 (iii) when the wavelet based interference mitigation algo- rithm is adopted (cyan line). −100 0 1 2 3 4 5 6 7 8 910 By meansofthe waveletpacketdecomposition algorithm, a Time (ms) higher interference components suppression together with a Interfered negligible distortion of the useful GNSS signal components Mitigated with respecttothe case of thepulse blanking adoption is achieved, as demonstrated by higher average value of the Figure 10: Galileo E5a signal at intermediate frequency before (blue curve) and aeft r mitigation (red curve). estimated 𝐶/𝑁 trend. The same conclusions can be drawn Code delay (ms) Code delay (ms) Samples (n) Samples (n) Power spectral density Amplitude Amplitude ADC level (dB/Hz) CAF CAF 10 International Journal of Navigation and Observation Pulsed interference case −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 P correlator After pulse blanking excision −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 1 2 3 4 5 6 7 8 910 P Time (s) After WPD based excision Pulsed interference Aer b ft lanking mitigation After wavelet mitigation −4000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 Figure 13: Carrier to Noise density ratio in absence of interference P correlator countermeasures (red), after pulse blanking (black), and after WPD Figure 15: N-Gene data demodulation performance. based interference removal (blue). These results have been obtained setting a predetection integration time 𝑇 equal to 1 ms and choosing loops band- ×10 Pulsed interference case width equal to 5 and 15 Hz, respectively, for the DLL and PLL. Finally, data demodulation performance can be observed in Figure 15, where the prompt in-phase and quadrature correlations are plotted in the complex plane. As expected, 0123456789 0 1 2 3 4 5 6 7 8 9 1010 tracking and thus correct data demodulation can not be Ti Tim me (s) e (s) achieved if no interference countermeasures are employed ×1100 Aer p Aer pu ul ls se b e blan lanki kin ng: g: 𝜎𝜎 = = 76. 76.55 cm cm (top plot), while the data demodulation is noisier when DL DLL L employing the pulse blanking for interference suppression with respect to the case when the WPD algorithm is used. Such results at tracking level conrfi m the capability of this 0123456789 0 1 2 3 4 5 6 7 8 9 1100 wavelet based mitigation algorithm in eeff ctively suppressing Ti Tim me (s) e (s) interference and saving useful GNSS signal components. ×10 Aer WPD based excision: 𝜎 = 72.6 cm DLL 6.2. Narrowband Interference. This section is devoted to the performance analysis of the wavelet based mitigation algo- rithm in mitigating Narrowband interference. eTh analysis 0123456789 10 addresses the problem of ndin fi g the best trade-off between Time (s) thechoiceofthe waveletbased mitigation techniqueparam- eters such as number of wavelet decomposition stages 𝑁 and Prom Prompt pt c co or rr re el la at tor ors s its computational burden. Such trade-off analysis is correlated E Ea arly c rly co or rr rel ela at to or rs s with the Narrowband interference spectral characteristics. La Lat te e c co or rr re el la at to or rs s A digital GNSS signal generator [33] has been adopted in Figure 14: Early Prompt Late correlators during 10 seconds of order to generate synthetic GPS L1 data combined with Galileo E5a-Q channel PRN 20 tracking. Narrowband interference. Several Narrowband interference scenarios have been considered, and a parametric study with respect to interference bandwidth 𝐵 , interference carrier looking at the Early-Prompt-Late correlators values recorded int frequency 𝑓 , and number of wavelet decomposition stages int during the tracking period for the three considered scenarios 𝑁 has been performed. In order to find the best tuning and depicted in Figure 14. We can clearly observe how the of the WPD based algorithm parameters, its application on use of a traditional pulse blanking in presence of strong and synthetic interfered GNSS data has been performed and per- dense in-time pulsed interference would cut off large portion formance in suppressing interference has been assessed. eTh of received signal thus leading to a decrease of the correlations results which will be presented in the following paragraphs amplitude and a minor separation between the E-L corre- have been preliminarily discussed in [34]. lations amplitude with the prompt correlations amplitude andthusahigher DLLjitteroutput. Table 1 summarizes the N-Gene acquisition and tracking performance for the 6.2.1. Performance with respect to the Wavelet Decomposition considered scenarios. Depth 𝑁 . eTh rfi st analysis has been devoted to assess the Correlation Correlation Correlation C/N (dB-Hz) amplitude amplitude amplitude P P Q Q International Journal of Navigation and Observation 11 Table 1: Acquisition and tracking performance comparison. Scenario Noncoherent accumulations𝐾𝛼 (dB) 𝐶/𝑁 (dB-Hz) 𝜎 (cm) mean 0 DLL DME/TACAN interfered 80 24.8 —— After pulse blanking mitigation 10 22.4 36 76.5 After WPD based mitigation 10 30.2 40.2 72.6 Wavelet scale resolution (kHz) 10 1023 511.5 255.7 127.9 63.9 32 16 8 32.2 30.2 28.2 𝛼 26.2 24.2 22.2 1 3 4 5 6 7 8 910 Number of wavelet decomposition stages (N) −300 −200 −100 0 100 200 300 Δ (kHz) BW = 40 kHz BW = 80 kHz Biorthogonal Gaussian BW = 120 kHz Coiflets Meyer Daubechies Symlets Figure 16: Acquisition metric 𝛼 versus the WPD stages 𝑁 for mean different interference bandwidth. Figure 17: Acquisition metric 𝛼 with respect to the frequency max offset Δ between the interference carrier and the GNSS signal impact of thenumberofwavelet decompositionstagesonthe carrier for different wavelet families: 7 WPD stages. Narrowband interference suppression performance. Differ- ent interference scenarios have been considered, combining GPS L1 C/A code signals with Narrowband interference −8 ×10 200 kHz far from the intermediate frequency. Results are Modified Gaussian based filters bank 3.5 shown in Figure 16, where the trend of the acquisition metric 𝛼 is plot versus the number 𝑁 of decomposition stages. mean 3 Acquisition performance is achieved using 1 ms of coherent 2.5 integration time and 20 noncoherent accumulations. eTh three lines referred to three different interference scenar- ios characterized by the presence of Narrowband interfer- 1.5 ence with, respectively, 40, 80,and 120 kHz of bandwidth. Increasing the acquisition stage increases the wavelet scale resolution andthusits frequencyselectivity.Inall thethree 0.5 interference scenarios, for increasing values of 𝑁 ,the WPD based algorithm provides better performance in capturing 0 0 1 2 3 4 5 6 7 89 and isolating narrowband interference, thus leading to better Frequency (MHz) interference suppression with a limited removal of useful signal components, as demonstrated by the increasing trend Figure 18: Modified Gaussian wavelet filters transfer functions. of 𝛼 in Figure 16. However, a saturation effect can be mean observed for higher value of 𝑁 (greater than 7). In such a region, acquisition performance is not anymore improving the ADC output has been achieved through an iterative since wavelet scale resolution is already comparable or nar- filtering process exploiting filter response derived by the rower with respect to the interference bandwidth. Moreover, Meyer wavelet family. Several other wavelet functions exist, as expected, performance of such technique is limited by andmostofthemare discussedin[35]. Figure 17 shows interference bandwidth. At higher interference bandwidth, the acquisition metrics 𝛼 with respect to the frequency max lower acquisition metric values are achieved. offset between the signal carrier and the interference carrier. Removal of the interference has been achieved for each 6.2.2. Wavelet Families Comparison and Interference Carrier interfered scenario exploiting 7 WPD stages and interference Offset. So far, time-scale representation of the signal at suppression process has been repeated using different mother (dB) mean Power spectral density (dB/Hz) (dB) max 12 International Journal of Navigation and Observation Wavelet scale resolution (kHz) acquisition performance improves. This is due to the fact that 1023 511.5 255.7 127.9 63.9 32 16 8 by increasing the wavelet filter length, wavelet function side- 31.6 lobe is lowered resulting in a better orthogonality between the subbands. 29.6 6.2.4. Computational Complexity. Although Wavelet based 27.6 mitigation algorithm provides high capability in interfer- ence suppression, its implementation is characterized by a 25.6 non negligible complexity. Computational burden is mainly determined by the number of wavelet decomposition stages 23.6 𝑁 which determines the number of filtering operations according to the exponential law 2 .Furthermore,the 3 4 5 6 7 8 910 same number of filtering operations is employed for signal reconstruction purposes. All filtering operations are realized Number of wavelet decomposition stages (N) with FIR filters with length 𝐿 . Each output sample is obtained 30 70 with L products and 1 single sum; thus the total number of 40 90 performed operations for decomposition and reconstruction 50 102 of 𝑛 samples of incoming signal is (14) 𝑂 (𝑛, 𝑁, 𝐿 )= 2⋅2 × (𝑛𝐿 + 𝑛 ). Figure 19: Acquisition metric 𝛼 with respect to the number mean of WPD stages 𝑁 and for different filter lengths of the modified However, the filter bank implementation allows for the Gaussian wavelet. processing sample by sample of the incoming signal, without any signal buffering process, at the price of the delay of the wavelet from which the wavelet filters transfer functions decomposition stage and by the reconstruction filter bank characterizing the uniform filters bank are originated. operating on the thresholded samples. Furthermore, better It can be observed that, by increasing the carrier offset efficiency of the method might be achieved by the combina- between the interfering signal and the GNSS signal, the tion of the WPD with the introduction of a frequency domain acquisition metrics may not have an increasing trend. This based predetection especially in those cases where interfer- is due to the fact that, for determined values of Δ ,the ence components are not spread all over the GNSS received Narrowband interference may fall in two different subbands signal spectrum but in a determined frequency region. In and thus interference removal may be negatively aeff cted if such a case, a controlled dyadic scaling operation iterated the wavelet subbands are overlapped. For such a reason, it is on determined subbands could be implemented. It has to be importanttohavewavelet filterresponsewhich is selectivein remarked that wavelet decomposition is already implemented the frequency domain. This property is well accomplished by for multimedia images and audio data compression coding a wavelet function derived from an orthogonalization process scheme, and the availability of Field Programmable Gate of a Gaussian function: the so-called modiefi d Gaussian Array (FPGA) allows the WPD implementation for real- function, which is described in [35]. Figure 18 shows the time application. Furthermore, the wavelet based algorithm wavelet filters transfer functions obtained from the Gaussian can represent an efficient postprocessing technique for inter- wavelet function. It can be observed that such Gaussian ference detection and characterization which can be easily wavelet filters are characterized by a more selective frequency implemented in potential GNSS interference monitoring response with less overlap between the subbands. stations with the aim of investigating the harsh interference For such a reason, interference removal exploiting environment in sensitive areas. wavelet filters response derived from the modified wavelet Gaussian overperforms the interference process performed 7. Conclusions exploiting other wavelet function, as shown in Figure 17. In this paper, an innovative interference mitigation algorithm 6.2.3. Wavelet Filter Length. Final investigation has been exploiting the Wavelet Packet Decomposition has been pre- performed in order to analyse the impact of the filter length sented. Detection and interference suppression mechanism on the interference suppression. In fact, all the wavelet has been described. Simulation results showed its eeff ctive- impulse responses are characterized by a fast decreasing ness in different interference scenarios. In particular, the amplitude in the time domain, thus allowing a good approxi- method is demonstrated to be eeff ctive with respect to the mated implementation by means of Finite Impulse Response classical blanker in multiple pulse interference representing (FIR) filters. However, the truncation of the filter response the DME/TACAN interference scenario on the Galileo E5a causes a loss in the orthogonality of the subbands. eTh same and GPS L5 frequency bands. 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