Characterization of Radar Interference Sources in the Galileo E6 Band

Transcription

1 Aerotecnica Missili & Spazio, The Journal of Aerospace Science, Technology and Systems Characterization of Radar Interference Sources in the Galileo E6 Band B. Motella a, A. Tabatabaei Balaei b, L. Lo Presti c, M. Leonardi d, A. Dempster b a Istituto Superiore Mario Boella Torino, Italy b University of New South Wales Sydney, Australia c Politecnico di Torino Electronics Department, Torino, Italy d Tor Vergata University Roma, Italy Abstract In Global Navigation satellite System (GNSS) applications the signals at the user receiver antenna exhibit a very low power level (around -160 dbw), and can be impaired by interference sources. In the case the receiver operation is compromised by the presence of an interferer, an important issue is the identification of the undesired source. To achieve this goal, fixed and mobile monitoring stations can be deployed in critical areas to assist and alert users. Since the interference signals present characteristics very different from each others, specific monitoring techniques must be designed ad hoc for different classes of interferers. Moreover, in specific scenarios (e.g., airports), the type of the interference source might be known, and the issue is to recognize its presence in the received signal. The algorithm proposed in this paper is a technique to detect and characterize pulsed signals. Radar interferers that share portions of band with Galileo E6 are used as a case study. However the method can be also applied to other pulsed interfering signals. The technique is based on the analysis of the autocorrelation function of the received signal and it exploits the characteristics of both the noise and GNSS signals. Moreover the technique is adapted to two different types of Air Traffic Control Radar: the classical radar with unmodulated pulses (e.g. klystron radar), and the solid state radar, that use chirp signals. The simulation results show that the technique is able to recognize the interferer with a high level of accuracy. 1. Introduction A Global Navigation Satellite System (GNSS) receiver must solve different problems that can threaten the usefulness of the satellite signal, i.e. the ionosphere and troposphere delays, errors from ephemeris data or satellite clock, multipath effects, etc [1] [2]. Moreover, due to the fact that the useful signal reaches the receiver antenna at a very low power level (around 20 db below the noise floor), one of the main causes of degradation can be the presence of Radio Frequency Interference (RFI) signals. This problem is difficult both because the set of the possible interferers is extremely wide and because of the absence of knowledge about the undesired sources [3] [4]. Moreover it must be taken into account that a GNSS receiver can be c AIDAA, Associazione Italiana di Aeronautica e Astronautica damaged both by in-band signals or out-of-band ones that could fall in the GNSS band by means of secondary harmonics. In fact, because of the low received power level, interference monitoring is a particularly sensitive issue for GNSS systems. The monitoring algorithm we propose in this paper can be applied both at the user terminal level and at a monitoring station. In both cases the monitoring stations can be mobile, and monitor an unknown region. To discover the location of the RFI source, it is first important to characterize it. In facing this problem, some considerations must be made: The interference monitoring issue can be tackled both in the frequency or in the time domain. The spectrum monitoring is one of the 42

2 Characterization of Radar Interference Sources in the Galileo E6 Band 43 main and more direct mean to detect the presence of an undesired electromagnetic source. As we will see it is used in our case to estimate the interferer carrier frequency and activate the algorithm, but it can not be useful for individualizing all the interferer characteristics. On the other hand, in the time domain the interferer mixed with the useful signal could be discovered, but its parameters estimation will no be accurate enough. Alternatively to the frequency and the time domains, working in the autocorrelation function domain is also an option. If the scope is to identify which is the unknown signal, the method based on the ACF analysis could be more robust, even because the information related to the noise, GNSS, and interference are more separated between each others. The range of RFI signals can be of very different nature [5]. A macro-classification is narrowband and wide-band. A narrow-band RFI signal can be continuous wave (CW) modulated or pulsed. The presence of a narrowband signal is quite easily detected in the frequency domain if it is strong enough; in fact at the receiver the spectrum of a received GNSS signal is flat, because the GNSS signals in space are buried into in white noise. A peak emerging from the noise floor is a clear symptom of the presence of a narrowband RFI signal. In this paper we will show that a detected narrowband RFI signal can be recognized and characterized as a pulsed interference, if we work in the domain of the Auto- Correlation Function (ACF). For various reasons, such as application, computational power at one s disposal, receiver type, etc., the interference monitoring can have different objectives. Its aim can be the simply detection of the presence of an undesired source that could compromise the correct working of the receiver or the complete mitigation by deleting the effect of the interferer from the reception chain. Between these there are many different steps that eventually have to be solved (such as the characterization of the interference or its localization); The GNSS systems include several signals. The signals are different not only between the different system (GPS and Galileo), but also within the same system. In fact one system transmits different signals in different bands and also different signals in the same band w.r.t. the service they are dedicated to. For this reason the monitoring algorithm should be designed ad hoc both for the GNSS signal being considered and for the particular interference source one is trying to detect or mitigate [6]. This paper presents a method that can be considered a hybrid technique between detection and characterization. As we will see, the algorithm is able to detect the presence of an undesired source of interference and to estimate its power and time characteristics for a set of non-stationary signals. As we will see in detail, the algorithm can make the characterization of interference signals though they have a very low power level. In fact the main goal of the present work would be to propose a technique for early warning detection. In other words the idea is to use the algorithm to monitor a particular area and alert the users if these kinds of interferences are present. The fact that the algorithm works even when interferer power is very low is a key requirement for its application in a monitoring station. In fact the interferer reaching the monitoring station with a low power level will be stronger and more harmful for an user receiver closer to the interference source. The degradation due to interference depends not only on its carrier frequency but also on the satellite codes and on the relationship between its carrier and the satellites Doppler frequency. For this reason the characterization of the interferer at the monitoring station must be performed using a precorrelation technique, so as to isolate the RFI presence independently from the particular GNSS signals we have in view. The technique will be described for a class of radar signals that share a portion of the spectrum with the Galileo E6 band. The signals the technique is able to detect belong to two different classes: pulsed and chirp signals. These signals offer a realistic scenario. However the method is quite general, and can be applied to any kind of pulsed signals. The main purpose of the paper is to show how it is possible to separate noise, GNSS signals, and pulsed RFI signals in the ACF domain, where the isolated RFI contribution can be quite easily analysed and processed. Sections 2 and 3 describe the model of the received signal and the characteristics of the radar sources that share the band with the satellite navigation systems. The harmfulness of such interferers is described in section 4, where the degradation in terms of signal to noise ratio in shown. In section 3 two types of radar are described: primary and solid state. The algorithm has been adapted to both of them: section 6 is about the application of the algorithm to the primary radar, and section 7 to solid state. For these two cases, sections 6 and 7 describe the particular algorithm and summarize the simulation results. Section 8 concludes the paper.

3 44 B. Motella, A. Tabatabaei Balaei, L. Lo Presti, M. Leonardi, A. Dempster 2. Model of the received signal A GNSS interfered signal can be modeled as y(t) = y G (t) + y I (t) + N(t) (1) where y G (t) is the GNSS signal composed by the signals in space of all the satellites in view, y I (t) is the interference and N(t) is the Additive White Gaussian Noise (AWGN), due to the thermal noise introduced by the antenna and receiver front-end. In a GNSS digital receiver this signal is generally down-converted to an Intermediate Frequency (IF) f IF and transformed by the Analog to Digital Converter (ADC) to a sequence of samples y IF (nt s ), where T s = 1/f s, and f s is the ADC sampling frequency. A common situation is to have the IF signal in the frequency range (0, B IF ), and a sampling frequency f s = 2B IF. This implies B IF = 2f IF. In the following we assume to be in this situation. In fact an oversampling (f s > 2B IF ) would increase the complexity of the receiver operation, without adding any extra information on the signal filtered by the front-end filter. The GPS and Galileo satellites make use of the code division multiple access (CDMA) technique. Spread spectrum signals are transmitted including different ranging codes per signal, per frequency, and per satellite. The GPS code is a Gold code with a relatively short 1-ms period (i.e., the PRN sequence repeats every 1 ms). Therefore, the C/A code (neglecting the navigation data) has a line spectrum with lines 1 khz apart [1] [7]. The Galileo code is a short duration primary code modulated by a long duration secondary code. They use a tiered code construction; the code length varies with the frequency band and the modulation used [8]. To simplify the notation, from now on, we will consider a continuous-time signal y IF (t) rather than a discrete-time sequence y IF (nt s ). This signal can be modeled as a baseband signal y B (t) of the type y B (t) = y B,G (t) + y B,I (t) + N B (t) (2) up-converted to the IF frequency to generate y IF (t). The choice f s = 2B IF implies that the noise N B (t) can be considered white. A GNSS receiver extracts the position, velocity and timing (PVT) information from the baseband signal y B,G (t). Therefore the impact of the interference signal on the PVT heavily depends on the characteristics of the baseband signal y B,I (t). Therefore it is not possible to have a general approach for the detection and mitigation of any kind of signal y B,I (t). This paper is focused on the detection and characterization of pulsed signals. This is a case of real interest, as it will be shown in next section. 3. Pulsed Interference in the Galileo E6 band The algorithm we present is specifically designed for pulsed signals and in this case study it is applied to radar signals that transmit in the E6 Galileo band. However the algorithm can be adapted to other GNSS bands and to other types of pulsed interferers. The Galileo E6 band has the center frequency at f E6 = MHz with 40 MHz bandwidth ( MHz). Three different Galileo signals will be present: two of them will be accessible to some dedicated users through a Commercial Service (CS) provider, E6 B and E6 C. The third one will be used as the Public Regulated Service (PRS) for authorized users (E6 A ). The modulation is the BOC(10,5) for E6 A and BPSK(5) for E6 B and E6 C. BOC(f s, f c ), denotes a Binary Offset Carrier modulation with a subcarrier frequency f s and a code rate f c. BPSK(f c ) denotes Binary Phase Shift Keying with a code rate f c. All the frequencies are written as multiples of MHz. The received power level for the three signals will be -152 dbw [8]. The frequency band from MHz is used for long distance air surveillance (400 km) by primary radars. These systems emit pulsed signals characterized by a low duty cycle [9]. The transmitted pulses hit the target that back-scatter a portion of the incident energy, disclosing their position. In order to provide the aircraft route control, primary radar must have a range of 360 km, which is the maximum imposed by the curvature of the earth. It must be able to provide updated data every 8-12 s (Data Renewal Rate). Its angle discrimination must be less than 1.5 degrees, while its angle accuracy must be better than 0.2 degrees. The distance discrimination (resolution) has to be less than 600 m and the accuracy of the distance measurement less than 300 m. In order to satisfy all these requirements primary radar has a big antenna and transmits with a very high power level. In practice a surveillance radar works with peak power of 2MW and average power of 2 kw. Usually, for an L Band Radar transmitter without solid state technology transmitter, the Pulse Width, PW, (related to the discrimination ability) is 3 µs while the Pulse Repetition Time, PRT, is 3 ms [10]. In the case of solid state radar transmitter the peak power of the transmitter amplifier does not match these requirements (2 MW) and longer pulses must be used to maintain the average power needed to cover the radar maximum range requirement. In this case, instead of a simple pulse, a modulated signal, called a chirp signal, is transmitted to guarantee the range resolution of the radar (radar pulse compression). The chirp signal is typically a linearly frequency modulated signal ( between f c f 2, f c + f ) over the duration T of 2 the pulse. The chirp signal can be modeled with the

4 Characterization of Radar Interference Sources in the Galileo E6 Band 45 following expression: ( s(t) = cos 2πf 0 t + µ 2 t2) (3) where µ = 2π f T. It can be shown that, using this modulated signal, the range resolution of the radar does not depend on pulse width T but depends on the width of the chirp modulation; in particular, the range resolution of the radar becomes r = c 1 f instead of r = ct 2 2. Finally, in order to guarantee the performance of the L band-solid state ATC Radar, typically, two pulses are transmitted: a short pulse (typically about 30 µs long) and a long pulse (typically about 150 µs long) respectively for short and long coverage of the radar. Using the chirp techniques, to satisfy the range resolution requirement, the pulses are compressed (e.g. 3 µs compressed pulses are used). These kinds of radars can become an interference for GNSS signal even if the radar and the satellite navigation receiver are quite distant from each other. lines at 170 s and 470 s of the data collection time. This means that the satellite Doppler varies by 1 khz in the time interval ( s). In these two cases, (a) C/N 0 for T d = 16 ms 4. Analysis of the Signal to Noise Ratio degradation In this section we show how the pulsed signals described in section 3 impact on the GNSS signals. We consider a situation more general than the E6 Galileo bandwidth. We use the GPS signal, because we can acquire a real signal and perform some measurements by adding the interference we want to analyze. The situation for Galileo is similar. The impact of the interference will be analyzed by using an approach similar to the one presented by the authors in [13]. In particular we will look at the effect of the chirp signal on the carrier to noise density ratio (C/N 0 ) which is a good indication of the received GPS signal quality. In the receiver tracking system, which is a combination of a delay lock loop (DLL) and a phase lock loop (PLL), the carrier and code phase are tracked. The approach in [13] is to calculate the carrier to noise density ratio using the correlator output power resulting from each of the signals, interference and noise. For the special case when the interference is a continuous wave (CW) with fixed carrier frequency, it has been shown in [1] and [14], that its effect on C/N 0 depends on the Doppler frequency of the satellite signal and also on the duration of the integration and dump block used inside the loops. In Figure 1, using ther Kai Borre software receiver [15], C/N 0 is examined for PRN1 with Doppler change of 2.4 khz over 800 seconds. The dependence of this quantity on the loop updating rate (integrator) and the Doppler frequency is shown in these figures. The C/N 0 variation is shown versus the measurement time. It is evident that the interference carrier matches one of the code (b) C/N 0 for T d = 8 ms Figure 1. C/N 0 of PRN1 when interference is at 4.5 khz the level of noise has been intentionally kept low so that the effect of interference is more easily observed. So to investigate the effect of a specific type of interference on the received signal quality, tracking loop bandwidth, signal to noise ratio, and also the Doppler frequency of the received signal are the important parameters to be considered. The big troughs in the figures represent the time when the frequency of interference aligns with the frequency of one of the C/A code spectral lines. The ripples in the figures have to do with the tracking loop updating rate which is the same as the integration and dump period. In this case the interference is CW with fixed frequency and a GPS signal with changing Doppler frequency, similar

5 46 B. Motella, A. Tabatabaei Balaei, L. Lo Presti, M. Leonardi, A. Dempster to a real situation. In the case of pulsed CW as analyzed in [13], even though the duty cycle of the pulse and the pulse repetition time play important roles, the overall effect is similar to the CW RFI. In the case of swept CW, a chirp, the central frequency of the signal sweeps within a specific frequency bandwidth and with a specific rate. In the presence of this kind of interference, the GPS received signal quality depends on number of factors, such as the tracking loop dynamics, the sweeping rate of the carrier and the Doppler frequency of the C/A code. If the sweeping rate is much smaller than the loop dynamics, the effect is quite similar to a CW RFI with the difference that the Doppler frequency change is replaced with the sweeping carrier of the interferer. On the other hand the effect of fast sweeping signals (relative to the tracking loop dynamics), is similar to wide band noise. As discussed in section 3, a chirp signal is basically a swept pulsed CW signal. The effect that it has on the received signal quality is a combination of the effect of these interferences. In Figure 2 (a) the interference is a pulse with the pulse width of 3 µs and a duty cycle of 0.1% which means the Pulse Repetition Time (PRT) is 3 ms. The Doppler frequency of the signal is changing 2.4 khz over the period of 20 minutes in this figure. In Figure 2 (b), C/N 0 of the same signal in the presence of a chirp interference is analyzed. The characterization of this chirp signal will be explained in section 7. As for Figure 1, in this experiment the noise level is considered to be low to make the effect of interference more visible. It can be clearly seen that C/N 0 is seriously degraded because of the pulse and chirp interference. The specific pattern in the C/N 0 is the result of tracking loop dynamics and the RFI characteristics. (a) C/N 0 in presence of pulsed interference (b) C/N 0 in presence of chirp interference Figure 2. C/N 0 of PRN1 in the presence of pulse and chirp interference 5. Interference Characterization Based on the ACF The characterization algorithm proposed in this paper is especially tailored for pulsed signals and is based on the estimation and processing of the autocorrelation function (ACF) of the received signal. The algorithm works in the digital section of the receiver, and it is applied to the IF samples y IF (nt s ). The algorithm depends on the characteristics of the autocorrelation function of the baseband signal y B (t) introduced in (2). The autocorrelation function R B (τ) of y B (t) will contain three ACF terms due to the three signal components, namely R B,G (τ), R B,I (τ), and R B,N (τ), since the cross-correlation terms among the three components can be considered negligible, because the three signals are zero-mean independent processes. The variable τ is the classical delay lag introduced in correlation. Therefore R B (τ) can be approximated by the sum of the single ACFs of the noise, the useful signal and the interferer, that is R B (τ) = R B,G (τ) + R B,I (τ) + R B,N (τ) (4) The up-conversion to IF does not introduce additional terms in the autocorrelation R IF (τ), but only a modulation effect on of the individual ACFs. The characteristics of interest of R B (τ) are the following. R B (τ) is an even function composed mainly of three aligned symmetric ACFs: R B,G (τ), R B,I (τ), and R B,N (τ). Due to the orthogonality of the codes, the support of the ACF R B,G (τ) manly depends on the chip duration T c. Therefore the support is 2T c. The support of the fundamental period of R B,I (τ) is twice the duration T of the interfer-

6 Characterization of Radar Interference Sources in the Galileo E6 Band 47 ing pulse. In the case of interest the interfering pulse seriously impairs the sequence of chips, when the pulse covers several chips of the GNSS codes, that is T T c. In this case the support of R B,I (τ) is much bigger than the support of R B,G (τ). The support of R B,N (τ) is the smallest one. In the continuous-time domain the IF noise exhibits a constant spectral density in the IF bandwidth B IF, from which it eventuates that the ACF of N B (t) is a Sinc function with a main lobe in the range ±1/(2B IF ). After sampling, R B,N (τ) has the width of a single sample, in the same position of the main peaks of R B,G (τ) and R B,I (τ). We can say that the ACF of the interference component is not affected by R B,G (τ) and R B,N (τ) outside the support 2T c around the origin. This means that there is a region R I of R B (τ), τ > T c, where only the interference gives a contribution. The region R I is known a priori and can be used to estimate the characteristics of the interference. Figure 3 is a qualitative description of the three contributions to the autocorrelation of the received signal. Figure 3. Qualitative trend of the GNSS, noise, and interference autocorrelation functions If the interfering signal is a periodic sequence of pulses, R B,I (τ) is also periodic with the same period, say T r, of the signal. It is evident that in the actual measurements of the signal ACF this periodicity will emerge only if the set of measured data contains more than one period of y B,I (t). The noise ACF is not periodic either in the analog domain, and in the digital domain. The GNSS ACF loses its code periodicity, because of the data bits. As a consequence the presence of periodic peaks in the signal ACF is a clear symptom of the presence of a periodic pulse interference. The periodic peaks are not in theory corrupted by the AWGN ACF (which is a very narrow). The signal ACF contributes with some residual cross correlation terms, due to the fact that the GNSS PRN codes are not perfectly orthogonal, moreover they are very small because the signal is weak. In practice the measured ACF is affected by some estimation noise. It is interesting to observe that this estimation noise can be reduced by increasing the number of points used in the ACF measurement, at the expense of algorithm complexity. Moreover if the ACF peaks are so weak to be buried in the measurement noise, this means that the interfering signal is so weak that can be neglected. Of course this is not true for a monitoring station interested in detecting faraway RFI sources; the limit imposed by the estimation noise will determine the observability range of the monitoring station. This depends on the application. This aspect is beyond the scope of this paper, which is focused on the methods for pulse characterization. In the ACF domain, both the code and the noise are concentrated around the point τ = 0, while the interference spreads out in a reserved region, where it can be detected and estimated. The algorithm proposed in this paper exploits this ACF characteristic. The first operation of the algorithm is to estimate the ACF at IF. Then the ACF is in some sense down-converted to baseband to take advantage of the clean region R I where only the interference contribution is present. The goal of the whole algorithm is twofold: to detect the presence of the interferer and to estimate its time domain characteristics. The algorithm develops in two different steps (Figure 4): Detection. During the detection phase the algorithm establishes if there is an undesired signal present in the received signal. The detection phase is performed in the frequency domain by means of thresholds on the signal spectrum. Note that, because of the non-stationarity of the interference signal, the signal spectrum can provide information only about the spectral occupancy, but it cannot provide any information about its power level. As we will see later in the detection stage the carrier frequency of the interference can be estimated. This parameter is fundamental for the demodulation of the auto-

7 48 B. Motella, A. Tabatabaei Balaei, L. Lo Presti, M. Leonardi, A. Dempster 6. Characterization of interfering Pulsed Signals This section is devoted to the description of the characterization algorithm for pulsed interfering signals. The method is based on the estimation of the ACF of y IF (t), based on a segment of measured IF samples. The interfering pulsed signal at IF can be written as a periodic repetition of a single pulse of the type y IF,I (t) = A I p T (t) sin(2πf int t), where p T (t) = 1 for 0 < t < T, A I is the pulse amplitude, and f int is the interfering carrier in the IF range. The ACF component due to y IF,I (t) can be easily evaluated, for 0 < τ < T, as Figure 4. Interference Detection and Characterization Algorithm correlation function in the case of pulsed signals. The detection has the aim to activate/deactivate the characterization block. As shown in Figure 4, the decision is controlled by the output of the spectrum analysis. The detection can be considered a preliminary phase, in which the user can be alerted for the presence of an undesired electromagnetic source. Characterization. The characterization can be considered the core phase of the present algorithm. It provides the time domain characteristics of the interference and estimates its power level. Notice that it cannot be conceived as a single algorithm able to characterize any kind of interference signal. It is reasonable to imagine a situation where a fixed or mobile monitoring station is able to activate some specific characterization algorithms, once some anomalous spectral activity in the navigation bandwidth under examination has been detected. Each algorithm must be designed ad hoc for each specific type of possible interfering signals. We present an algorithm for the characterization of pulsed and chirp signals, which can be emitted by radars transmitting on the Galileo E6 band (see Section 3 for the details). The first parameter used to discriminate the type of signal is its Pulse Repetition Time. It is the easiest parameter to be estimated because it could be evaluated as the interval between two peaks of the autocorrelation function of the received signal. The value of the Pulse Repetition Time T r controls the type of algorithm to be applied, as shown in Figure 4. The complete operation of the algorithms for pulsed and chirp signals will be described respectively in Sections 6 and 7. Both the algorithms provide signal parameters estimation. R IF,I (τ) = = A 2 I = A2 I 2 A2 I 2 T τ 0 T τ 0 T τ 0 sin (2πf int t) sin (2πf int (t + τ)) dt = cos (2πf int τ) dt + cos (4πf int t + 2πf int τ) dt = = A2 I 2 cos (2πf intτ) [T τ] + A2 I [sin (2πf int (2T τ)) sin (2πf int τ)] = 8πf int = A2 I 2 cos (2πf intτ) [T τ] + A2 I cos (2πf int T ) sin (2πf int (T τ)) (5) 4πf int Remembering that f int is of the order of megahertz, we can write R IF,I (τ) = A2 I 2 cos (2πf 0τ) [T τ] (6) As the autocorrelation is always an even function, over the whole support τ < T, the ACF can be written as where R IF,I (τ) = cos (2πf 0 τ) R B,I (τ) (7) R B,I (τ) = A2 I 2 [T τ ] for τ < T (8) is the ACF of the interfering component at baseband. Therefore in the clean region R I it will be possible to extract, from an estimate ˆR IF (τ) of R IF (τ), an estimate of R B,I (τ), whose characteristics can allow the characterization of the interfering pulsed signal. Simulation results will prove the validity of the method.

8 Characterization of Radar Interference Sources in the Galileo E6 Band Algorithm Description The algorithm for the estimation of the interference parameters consists of different steps [16] [17]. A first rough estimation of the carrier frequency f int of the interference signal (Step 1) is provided by analyzing the IF signal in the frequency domain: the position of a peak in the IF spectrum is a simple and efficient way to give an estimate ˆf int of f int. By using ˆf int it is possible to wipe-off the carrier from the estimated ACF ˆR IF (τ) (Step 2), so providing in the clean region R I an estimate ˆR B,I (τ) of R B,I (τ) (see Figure 3). With post-processing techniques it is possible to extract from the baseband ACF the main characteristics of the signal (Step 3). In practice by minimizing the MSE (Minimum Squared Error) between the measured ACF and R B,I (τ) in the clean region R I, it is possible to estimate the pulse parameters (amplitude A I and pulse duration T ). Now by using the estimated parameters ÂI and ˆT it is possible to wipe-off the triangular shape from the measured ACF, so discovering if a residual frequency component f err = f int ˆf int is present into the signal; in this case an error was made during Step 1 and the algorithm can run again with the new frequency estimate (and iterate till satisfied). Because the interference spectrum is usually very concentrated around the central frequency, the frequency f err is generally very low and few samples of the residual carrier are present in the clean region R I. This means that FFT-based methods can not be used to estimate f err, and methods based on modal analysis [12] are preferred. In our experiment the basic Prony s algorithm [12] (Step 4) has proved able to give an adequate estimate ˆf err of f err. At this point we can repeat the ACF demodulation process using a new carrier ˆf int + ˆf err to demodulate the ACF. The new post-processing of the data (Step 5) allows us to obtain a better estimation of the time characteristic of the signal, from which a new estimate ˆf err can be provided. Then an iterative method can be implemented giving, at each iteration k, a sequence of values ˆf err [k], which will stop when ˆf err [k] ˆf err [k 1] is under a preassigned threshold. The final estimate provided by the iterative method will be denoted as ˆf err,p. In the case we analyzed the If at the first iteration ˆf err [1] is too high, then the first post-processing of the data is not able to estimate the pulse parameters within an acceptable error, while the introduction of Prony s method can allow better recognition of the undesired signal. In the cases have been analyzed, the algorithm stops at the second iteration ( ˆf err [2]), when a high level of accuracy has already been reached. The steps of the algorithm are shown by Figure Simulation Results The algorithm was tested varying the frequency error during the estimation of the interference carrier Figure 5. Estimation algorithm for pulsed signals and keeping constant the interference power: the simulation parameters are summarized in Table 1. Table 1 Simulation parameters Carrier to Noise Ratio GNSS Signal Power GNSS band Sampling frequency Intermediate frequency 45 dbwhz -160 dbw E MHz 2.56 MHz Table 2 shows the frequency error estimation provided by the application of Prony s method (that is the value ˆf err,p ) with respect to different values of the frequency error f err made during the rough frequency estimation. Table 2 Interference residual frequency estimation by means of Prony s method Frequency Prony Frequency Error f err (Hz) Estimation ˆf err,p (Hz) The accuracy of Prony s method varies from 2.3 Hz (for f err = 90 Hz) to 36 Hz (for f err = 150 Hz). In each case, as shown by the results summarized in Table 3, the introduction of Prony s method allows recovery of the frequency error and later estimation the signal characteristics within a certain level of accuracy. In fact the algorithm has been tested for different values of frequency errors (from 50 to 150 Hz by steps of 20 Hz). The parameters used to quantify the algorithm performance are the Pulse Width (PW), the Pulse Repetition Time (PRT) and the Power level (P).

9 50 B. Motella, A. Tabatabaei Balaei, L. Lo Presti, M. Leonardi, A. Dempster These parameters are estimated under three different conditions: - demodulating the ACF using the exact interference carrier frequency (ideal case); - demodulating the ACF using the spectrum estimation (the maximum error is bounded by the resolution frequency); - demodulating the ACF after recovering the frequency error by Prony s method. Table 3 Simulation results for pulsed signals estimation - Introduction of Prony s method during the ACF demodulation True No Without With f err Values Freq. Err. Prony Prony PW (µs) Hz PRT (ms) P (dbw) PW (µs) Hz PRT (ms) P (dbw) PW (µs) Hz PRT (ms) P (dbw) PW (µs) Hz PRT (ms) P (dbw) PW (µs) Hz PRT (ms) P (dbw) PW (µs) Hz PRT (ms) P (dbw) It is easy to observe (Table 3) that in many cases the estimation from the spectrum is not accurate enough to allow the algorithm to work properly. In fact, using the algorithm without Prony, it is able to estimate the PW with an acceptable level of accuracy, but it can not accurately estimate the PRT and the power of the interference. By introducing the second frequency estimation one can obtain similar performance that characterize the ideal case. 7. Characterization of interfering Chirp Signals We consider now the interference signal described in Section 3, which can be modeled at IF as x(t) = p 1 (t)c 1 (t) + p 2 (t)c 2 (t) (9) with p 1 (t) = P T1 ( t T 1 2 ) p 2 (t) = P T2 ( t T 2 2 ) P T (t) = { 1 if 0 t T 0 elsewhere ( c 1 (t) = cos 2πf 0 t + µ 1 2 t2) c 2 (t) = cos ( 2πf 0 t + µ2 2 t2) f 0 is the intermediate frequency T 1 = 32 µs T 2 = 150 µs B = 357 khz is the signal band µ 1 = 2πB T 1 µ 2 = 2πB T 2 Obviously the signal is sampled with a sampling frequency f s. The signal would be x [n] = x(nt s ) n = 0, 1, 2,... (10) Since the sampling does not affect the next treatment, for sake of simplicity hereafter the notation x(t) will be preserved Algorithm Description In section 6 we have seen how it is possible to demodulate the ACF of the pulsed signal and to use it to estimate the pulse parameters. On the contrary, since the carrier frequency of the chirp signals varies vs time, the ACF demodulation process must be modified in order to obtain the baseband ACF. The working of the algorithm proposed in this paper is described in Figure 6 and it foresees that the autocorrelation function is evaluated on the absolute value of the analytic signal of the interfering signal. Next section provides the mathematical proof for using the absolute value of the analytic signal for its demodulation.

10 Characterization of Radar Interference Sources in the Galileo E6 Band 51 c 2 (t) = e j[2πf0t+ µ 2 2 t 2 ] Figure 6. Characterization algorithm for chirp signals 7.2. Demodulation of Chirp Signals The first block of the scheme of Figure 6, through the evaluation of the Hilbert transform, generates the analytic signal of the input signal. We recall that the analytic signal of a generic signal y(t) can be easily expressed in the frequency domain as [11] Y (f) = 2u(f)Y (f) (11) where u(f) is the unit step function, and Y (f) is the Fourier transform of y(t). Evaluating the Fourier Transform of (9), one can write: with X(f) = = P 1 (f) [C 1+ (f) + C 1 (f)] + +P 2 (f) [C 2+ (f) + C 2 (f)] = = 1 2 [P 1+(f) + P 1 (f)+ P 1 (f) = F {p 1 (t)} P 2 (f) = F {p 2 (t)} +P 2+ (f) + P 2 (f)] (12) C 1 (f) = F {c 1 (t)} = C 2 (f) = F {c 2 (t)} = { C1+ (f) f 0 C 1 (f) f < 0 { C2+ (f) f 0 C 2 (f) f < 0 F {.} means the Fourier transform. By applying the transformation in (11) to (12), we obtain X (f) = 2u(f)X(f) = P 1+ (f) + P 2+ (f) (13) whose inverse Fourier transform is with x (t) = p 1 (t) c 1 (t) + p 2 (t) c 2 (t) (14) c 1 (t) = e j[2πf0t+ µ 1 2 t 2 ] Let us continue now the analysis of the scheme of figure 6, by considering the second block. The square of the absolute value is x (t) 2 = = p 1 (t) 2 + p 2 (t) 2 + 2p 1 (t)p 2 (t) ( cos 2πf 0 t + µ ( 1 2 t2) cos 2πf 0 t + µ 2 2 t2) (15) Because the supports of p 1 (t) and p 2 (t) are separated, the cross term in (15) is null, then x (t) 2 = p 1 (t) 2 + p 2 (t) 2 (16) For the same reason, the absolute value of the analytic signal can be written as x (t) = p 1 (t) + p 2 (t) (17) The received signal is composed of the sum of the interference x(t), the noise and the GNSS signal. Because the navigation signal is 20 db below the noise floor, it is possible to approximate the sum of the noise and the GNSS signal as an Additive White Gaussian Noise (AWGN) n(t) with mean m n and variance σ 2 n. The received signal becomes y(t) = x(t) + n(t) (18) Because of the linearity of the Hilbert transform, the analytic signal of the received signal becomes y (t) = x (t)+ n (t) (19) The square of its absolute value is y (t) 2 = x (t) 2 + n (t) 2 { x } + 2R (t) n (t) (20) This means that the square value of the analytic signal will be affected by a noise n a (t) equal to n a (t) = n (t) 2 { x } + 2R (t) n (t) (21) Its mean value can be easily evaluated as the variance of the analytic signal of the noise m na = σ 2 n (22) while its variance can be estimated by means of simulation. The capability to demodulate the received signal through the evaluation of the absolute value of its analytic signal is proved in Figure 7, where the two signals are compared within a time interval of 4 ms.

11 52 B. Motella, A. Tabatabaei Balaei, L. Lo Presti, M. Leonardi, A. Dempster - After calculating the number of periods N (dividing the signal length for its PRT, previously estimated), the amplitude of the signal is evaluated as E A = (23) NT 1 From the signal amplitude its power is immediately evaluated. Figure 7. Received signal and the absolute value of its analytic signal We have proved how it is possible to demodulate the chirp sequence by evaluating the absolute value of its analytic signal. This result has a fundamental role within the algorithm operation. The demodulation by means of the analytic signal avoids the issue of estimating the carrier frequency of the interference. In this case in fact we need neither the frequency estimation from the spectrum analysis nor its correction provided by means of Prony s method Simulation Results In order to test the algorithm designed for detecting and characterizing the Solid State Radars, it has been tested in a simulation environment (for the simulation parameters refer to Table 1). Table 7 summarizes the results obtained. The signal parameters to be evaluated are the width of two pulses of the fundamental period (T 1 and T 2 ), the width of the PRT and the signal power (see Table 4). Figure 8. Autocorrelation of the absolute value of the analytic signal of the received signal 7.3. Chirp signal autocorrelation After demodulating the signal, its autocorrelation function is calculated. Figure 8 shows the central peak of the ACF. From this function, it is easy to provide the estimation of the parameters, as shown in the figure. More specifically we need to evaluate the width of the two peaks of the fundamental chirp pulse (T 1 and T 2 ) and its power: After estimating the points H and J (Figure 8) and solving a system of two equations in two unknowns, it is easy to find the values of T 1 and T 2. The estimation of H and J is based on the study of the first derivative of the ACF, to find out when the gradient changes. Also the estimation of the signal power is based on the ACF shape analysis. Specifically: - The point E (Figure 8) is evaluated; Table 4 Simulation results for chirp signals estimation Power PRT T 1 T 2 P [dwb] [ms] [µs] [µs] [dwb] It is easy to observe how the time parameters are always estimated with a very high level of accuracy, while in the power estimation the error variance is bigger due to the noise present in the autocorrelation function of the absolute value of the analytic signal (see equation (22)). 8. Conclusions A technique able to detect and characterize the presence of pulsed interfering signal has been presented. The algorithm is designed to monitor the presence of radar signals that transmit within the E6 Galileo band.

12 Characterization of Radar Interference Sources in the Galileo E6 Band 53 The technique is based on the analysis of the autocorrelation function of the received signal and it exploits the characteristics of the ACFs of both the noise, the GNSS signal, and the interfering signals. The general algorithm has been adapted and applied to Air Traffic Control radars and solid state radar transmitters which are respectively modeled as pulsed and chirp signals. For both cases simulation results have proved the validity of the method. REFERENCES 1. E. Kaplan, Understanding GPS: principles and applications, Artech House, B. W. Parkinson, and J. J. Spilker, Global Positioning System: Theory and Applications, American Institute of Aeronautics and Astronautics, F. Butsch, A Concept for GNSS Interference Monitoring, ION GPS 99, Nashville TN, September F. Butsch, Radiofrequency Interference and GPS, GPS World, October R. J. Landry, A. Renard, Analysis of Potencial Interference Sources and Assessment of Present Solutions for GPS/GNSS Receivers, 4 th Saint Petersburgon on INS, May J. Grabowsky, C. Hegarty, Characterization of L5 Receiver Performance Using Digital Pulse Blanking, ION GPS 2002, Portland OR, September Interface Specification IS-GPS-200 Rev.D, IRN-200D-001, 7 th of March, Signal-In-Space Interface Control Document GAL OS SIS ICD/D.0, 23 th of May, D. K. Barton, Modern Radar System Analysis, Artech House, G. Galati, Radar e Navigazione, Texmat, L. Lo Presti, and F. Neri, L Analisi dei Segnali, CLUT, L. L. Sharf, Statistical Signal Processing. Detection, Estimation, and Time Series Analysis, Addison,Wesley, A. Tabatabaei Balaei, A. G. Dempster, and L. Lo Presti, Characterization of the effect of CW and pulse CW interference on the received satellite signal quality, to appear on IEEE Transaction on Aerospace and Electronic Systems. 14. A. Tabatabaei Balaei, B. Motella, and A. G. Dempster, A preventative approach to mitigating CW interference in GPS receivers, GPS Solutions, Volume 12, Number 3, July, K. Borre, D. M. Akos, and N. Bertelsen, A Software-Defined GPS and Galileo Receiver. A Single-Frequency Approach, Birkhauser, B. Motella, L. Lo Presti, Pulsed Signal Interference Monitoring in GNSS Applications, ENC GNSS 2006, Manchester, UK, May B. Motella, L. Lo Presti, M. Leonardi, A Technique of Interference Monitoring in GNSS Applications, Based on ACF and Prony Methods, ION GNSS 2007, Fort Worth, Texas, September 2006.