AN EFFICIENT SET OF FEATURES FOR PULSE REPETITION INTERVAL MODULATION RECOGNITION

Transcription

1 AN EFFICIENT SET OF FEATURES FOR PULSE REPETITION INTERVAL MODULATION RECOGNITION J-P. Kauppi, K.S. Martikainen Patria Aviation Oy, Naulakatu 3, Tampere, Finland, ax Keywords: PRI modulation, pulse train, eature extraction. Abstract Pulse repetition interval (PRI) modulation recognition is one o the essential processes in Electronic Support (ES) receivers. The recognized PRI modulation type and other measured pulse train parameters usually reveal the unctional purpose o the radar and are o good use in emitter identiication. In this paper, a novel eature set or PRI modulation recognition is proposed. The selected eatures exploit both the statistical and the sequential inormation o pulse intervals to describe speciic modulation types. Ater eature extraction, a relatively simple multi-layer neural network is employed or classiying dierent PRI modulation types. With simulations, the eature set is shown to be capable o identiying all well-known PRI types. 1 Introduction Due to evolving radar technology and dierent radar unctions, operative pulsed radars utilize various pulse repetition requencies and alter consecutive PRIs either intentionally or unintentionally. Measuring pulse train timing parameters can give important inormation on the type and unction o the transmitting radar. This inormation is urther used in radar emitter identiication process that is an essential part o most radar intercept receivers. [5, 6] Many characteristics can be revealed about the radar unction, i PRI modulation type is recognized. Besides, it is ar more easy to estimate the modulation parameters or urther emitter identiication. In this paper, we will ocus on automatic recognition o the PRI modulation type. However, it is worth noting that the presented methods can be applied to recognize also other kind o modulation, such as requency agility. There is a growing need or improved modulation recognition techniques in ES receivers because radar signal waveorms are becoming more complex. In addition to that, modern radars can employ secret operation modes during crisis, which means that radar threat level must be evaluated without any prior knowledge o the waveorm parameters. This increases the need or advanced modulation recognition, which can unveil characteristics o the radar in such an unknown environment. There are a ew PRI modulation types in which most radar pulse trains can be classiied as a whole or piece by piece. An extensive set o classes consists o six dierent PRI modulations named Constant, Stagger, Jittered, Sliding, Dwell and Switch, and Periodic PRI [6]. Jittered PRI is meant to describe intentional random PRI variation and that is to be distinguished rom usually much slighter unintentional jitter, which orms in receiver s interception process and in some radar transmitters. In general, each PRI modulation type can be deined by unction F( n) = tn + 1 tn = xn, n = 1,2, K, N 1 (1) where t n is the time o arrival (TOA) o the nth pulse in the received train o N pulses. Fig. 1 illustrates the shape o the unction or examples o the six PRI modulation types in ideal receiver conditions. Few unclassiied papers concerning PRI modulation recognition have been published. Traditionally, the pulse train analysis is based on histograms that describe statistical properties o pulse intervals [1 3]. a) n b) n c) n d) n e) n ) n Figure 1. Examples o dierent PRI types: a) Constant, b) Stagger, c) Jittered, d) Sliding, e) Dwell and Switch, and ) Periodic PRI.

2 These methods, however, suer rom losing the sequential inormation o pulse trains, and a vast number o pulses is usually required. In addition, it is diicult to automatically choose proper histogram bin widths and detection thresholds, because they depend strongly on the number o pulses, deinterleaving perormance and the accuracy o timing. It is typical or histogram based methods that they can only dierentiate Constant, Stagger and Jittered PRI sequences. There are also some methods based on the order o dierent PRIs in the sequence. For instance, a neural network based classiier [4] has been proposed. However, it is restricted to process only certain number o pulses, and it has no ability to generalize periodic sequences with variable phases and requencies. Our goal has been to ind an automatic method to recognize all the six modulation types with arbitrary modulation parameters. We propose a set o ive careully chosen eatures, which are presented in the next section. These eatures can be extracted rom almost any pulse train and employed to classiy the pulse trains to the six modulation types. Ater the eature extraction, we use a relatively simple MLP (multi-layer perceptron) network as a classiier. The only parameters we have to ix beorehand are related to the modulation types itsel, e.g. proportional amount o unintentional jitter that is tolerated in Constant PRI to still distinguish it rom Jittered PRI. We also assume that simultaneously arriving pulse trains have been deinterleaved in the receiver beore PRI modulation recognition. However, in the simulations we take the noisy signal environment and receiver imperections into account and test the recognition capability with a wide set o corrupted pulse train measurements. 2 Feature selection In the context o PRI modulation recognition, the purpose o eature selection is to ind a set o eatures which provides unambiguous representation or dierent PRI types. Finding such a eature set is challenging or many reasons. Firstly, eatures should provide as much separation capability between dierent categories as possible. Simultaneously, they should be invariant or modulation parameter variations within the same category. This is particularly important in an unknown recognition environment, where strict assumptions about modulation parameter variations cannot be made. Features must also be robust or pulse train imperections to a great extent, and, inally, they should be reasonably simple to calculate to meet the ES receiver real-time processing requirements. Keeping in mind the demands stated above, we introduce ive careully chosen eatures to describe each six PRI modulation types. We divide the eatures into two categories: ones that describe the statistical properties and ones that describe the sequential inormation o the pulse sequences. Each eature value is scaled between 0 and 1 to make the inal classiication task easier. 2.1 Features based on statistical properties Histograms can be useul when determining the overall statistics o the dierent PRI modulation types. However, automatic recognition o Periodic, Jittered and Sliding PRI using histogram techniques is very diicult because the shape o the histograms or these PRI types depends highly on the choice o bin widths and the number o pulses in a pulse sequence. Histograms are more useul or detecting individual PRI peaks o Constant, Stagger and Dwell and Switch PRI. One o the main drawbacks o the current peak detection techniques is that they are very sensitive to pulse train imperections. Unintentional jitter, or example, causes PRI peaks to leak to adjacent histogram bins. To prevent such problems, we propose a new histogram technique where the histogram bin widths are chosen in a way that the individual PRI peaks are strictly stabilized into single bins. We deine unintentional jitter tolerance or each pulse interval x n as ε = 2 p (2) n x n where value or p is set based on the maximum expected unintentional jitter o stable pulse intervals. For example p = 0.01 assumes at most 1 % variation o the mean PRI, which is a typical limit or a Constant PRI [6]. In the proposed technique, we irst sort pulse intervals into ascending order. Sorting allows us to ind the irst pulse interval in each stable pulse interval group and deine histogram bin edges according to them. The irst histogram bin is established based on the shortest pulse interval in a pulse train, and each subsequent pulse interval inside the unintentional jitter tolerance o the shortest pulse is one by one collected into the same histogram bin. The second bin is then set based on the irst pulse interval that does not it to the tolerance o the irst bin. The procedure is continued until all the ordered pulse intervals have been collected. Fig. 2 illustrates the main idea and the beneits o the new histogram technique compared to the traditional one. In Fig. 2a, there are some consecutive pulse intervals o Dwell and Switch PRI, which originally belong to two distinct groups. Unintentional jitter o a pulse train is clearly visible, as well as one exceptional pulse interval value caused by a missing pulse. Horizontal lines illustrate one possible histogram bin arrangement in a traditional histogram calculation. We can see that groups o stable pulse intervals are split between two histogram bins, thus degrading the peak detection perormance. In Fig. 2b, the pulse intervals are sorted into ascending order. The bin edges are deined according to the shortest pulse intervals in each pulse interval group. It can be seen that unwanted spreading o pulse intervals between adjacent bins is avoided. More detailed description o the method is beyond the scope o this article. Next, we present two eatures based on the presented histogram technique.

3 ε 7 ε 14 in Fig. 2b also in the calculation o SDIF-histograms to avoid unwanted spreading o peaks indicating stable sum. By comparing Figs. 1b and 1c, it can be seen that pulse intervals in Stagger PRI ollow periodic pattern whereas ordering is random or Jittered PRI. This indicates that the eature should provide good separation between Stagger and Jittered PRI, i k max is properly chosen. 2.2 Features based on sequential inormation Figure 2. Forming o the histogram using a) traditional, and b) proposed histogram technique. Feature 1: Single histogram peak The irst eature describes the amount o constant pulse intervals in a pulse train. We calculate the eature as the ratio o the two highest histogram peaks in the modiied histogram as 1 = n max 1 n max (3) where n max-1 is the second highest and n max is the highest peak in the histogram. Feature values are expected to be lower or Constant PRI than or other modulation types, because it is the only PRI type that typically constitutes only one strong PRI peak in the histogram. Feature 2: Stable sum The second eature is obtained rom the higher order histograms which emphasize pulse train periodicities. The use o sequential dierence (SDIF) histograms has been proposed in [3]. The number o pulse interval occurrences in a k th order SDIF-histogram is M k = N k 1 (4) where N is the number o pulses in a pulse train and k is the dierence level o the SDIF-histogram. To obtain the eature describing the periodicity o a certain PRI type, we calculate histograms with various dierence levels and speciy the highest peak or each histogram. I one o these peaks is remarkably high compared to the total number o occurrences in the histogram, a stable sum indicating periodic pulse train could be expected. Hence, or the inal eature, we calculate the maximum o the highest peaks relative to total number o occurrences or each histogram as k k ( nmax M ), k = 2,3 kmax 2 = max,..., (5) k where n max is the highest histogram peak in the k th dierence level, and k max is the highest dierence level that is calculated. We emphasize that we use the technique presented ε 1 Although extremely useul, the presented eatures based on histogram techniques do not guarantee unambiguous separation o all the six PRI categories. Thereore, we propose additional eatures that are based on sequential inormation o the pulse intervals. The second dierence o TOAs is deined by dierentiating (1) as [4] zn = xn+ 1 xn, n = 1, 2,..., N 2 (6) We are only interested in the ordering o the consecutive pulse intervals, so we process (6) by a signum unction as s = sgn( z ) (7) The signum unction or each pulse interval change can be deined as 1, when zn < ε n sgn( zn ) = 0, when zn ε n (8) + 1, when zn > ε n where ε n is given in (2). Next, we propose 3 eatures based on the presented notations. Feature 3: Pulse interval changes We deine the eature describing the amount o pulse interval changes relative to the number o pulses in a pulse train as N 2 3 = k = 1 sk N 2 (9) where s k is the k th element o the vector s. The eature is eective in separating stable pulse trains rom those that are characterized by continuous pulse interval changes. Feature 4: Directional pulse interval changes When comparing dierent PRI types, we can see that the Sliding PRI is the only one or which the changes in consecutive pulse intervals occur mainly in one direction. The eature presenting directional pulse interval changes can be obtained as N 2 4 = sk N 2 (10) k= 1

4 Presented eature is supposed to give large values or Sliding PRI because the absolute value o the sum will increase as more pulses are collected. Other PRI types tend to get smaller eature values because they are either more stable or they contain both positive and negative pulse interval changes. For example eature value or Periodic PRI approaches to zero as the number o periods in a pulse train increase. Feature 5: Local extrema o pulse intervals Great number o local extrema o the unction (1) are characteristic or Jittered and Stagger PRI. This can be visually veriied in Fig. 1b and 1c. We present these extrema by dierentiating the signum o second dierence o TOAs (7) as hk = sk+ 1 sk, k = 1, 2,..., N 3 (11) The inal eature indicating the amount o local extrema relative to the number o pulses in a pulse train is deined as N 3 5 = k = 1 sgn( hk ) N 3 (12) PRI 1 4,000 μs Sliding: minimum and maximum PRI Others: mean PRI PRI deviation Stagger, Dwell and Switch % Jittered, Sliding, Periodic 5 50 % Number o stages in a period Stagger, Dwell and Switch 2 8 Number o periods in a pulse train Stagger Periodic, Sliding 1 20 Number o stages in a pulse train Dwell and Switch 2 25 Unintentional jitter Constant % Others % Additional and missing pulses 0 15 % Table 1. The value ranges o the pulse train parameters used in classiication capability evaluation. It is clear that the eature value will be near zero i there are only a ew local extrema in a pulse train, and will be higher or pulse trains containing several extrema. 2.3 Classiication capability o the chosen eature set Monte Carlo method was employed to evaluate the classiication capability o the chosen set o eatures. We generated 30,000 pulse trains o pulses with randomly chosen PRI modulation parameter values. To emulate real world pulse detection, a number o additional and missing pulses were included into the pulse trains, and the initial phase o periodic modulations was randomly varied. The value ranges o the pulse train parameters in the evaluation set are speciied in Table 1. However, it must be pointed out that the ranges have been chosen to just represent a realistic pulse signal environment, and the perormance o the classiication is not limited to these ranges. An important issue to consider in PRI modulation recognition is ambiguities o the modulation types caused by limited number o pulses in pulse trains. In some real-world situations, registered pulse trains do not carry enough inormation to enable an unambiguous identiication o a speciic modulation type. E.g. Dwell and Switch PRIs cannot be distinguished rom Constant PRIs beore more than one dwell stage is registered. To evaluate the method against pulse trains which are theoretically separable, we have let out those Periodic PRIs that are shorter than one modulation period. In addition, at least two stages o stable pulse interval bursts are simulated or each pulse train o Dwell and Switch PRIs. The curves in Fig. 3 represent the probability distributions o the eature values or each modulation type. I the distributions or some PRI categories do not overlap, the eature can separate those categories with good probability a) Feature value b) Feature value c) Feature value d) Feature value Dw ell and Sw itch Sliding Jittered Stagger Constant Periodic e) Feature value Figure 3. Distributions o 30,000 eature values or the six PRI modulation types: a) Feature 1, b) Feature 2, c) Feature 3, d) Feature 4 and e) Feature 5. Vertical lines illustrate the separating capability o the eatures.

5 The separating perormance o each eature is summarized in Table 2. Columns indicate the separation capability o each eature. Separation can be visually conirmed by vertical lines in Fig. 3. I a eature symbol or a certain PRI type is denoted as 1, the eature provides good separation rom another PRI type denoted as 0. We emphasize that the symbols indicate only the separation capability o the eatures and do not essentially represent ideal eature value or a given PRI type. Symbol X means that the eature does not necessarily provide very good separation capability or a given PRI type. However, by inspecting the rows in table 2, it can be seen that an unambiguous solution or each PRI type should be provided with very good probability irrespective o the value o X. It is also noteworthy that every eature is required or an unambiguous solution. Feature Constant X Stagger X X Jittered Sliding Dwell and Switch 1 X 0 0 X Periodic Table 2. Separating capability o each eature. 1 s can be separated rom 0 s with good probability. X means the eature gives ambiguous values or the speciic modulation type. 3 PRI modulation recognition simulations and results A simple MLP network was employed to test the recognition capability o the eatures. The network consisted o one hidden layer with three units. We generated 3,000 pulse trains o each PRI category with randomly chosen parameters and imperections based on Table 1. Ater extracting the eatures, we divided them randomly in two equal sets. Another was used or training and the other or testing the classiier. We trained the MLP via backpropagation using stochastic training and varying learning constant. Less than 20 epochs was needed to ind the global minimum o the cost unction. Ater training, classiication perormance was evaluated using the test set. To validate classiication results, we trained and tested the classiier three times choosing training and test sets randomly or each trial. The inal classiication accuracy was determined as an average o these simulations. The trained MLP showed very good classiying perormance, as can be seen in Table 3. We also tested recognition perormance o a linear classiier or the given eature set. It showed over 98% average accuracy or Constant, Jittered, Sliding, Periodic and Stagger PRI. However, it was somewhat diicult or the linear classiier to distinguish Dwell and Switch rom Constant PRI (7 % misclassiication). This indicates that while most o the PRI categories are nearly linearly separable in the eature space, nonlinear decision boundaries ormed by MLP ensure separation perormance or all modulation types. Properly classiied (%) Constant 99.3 Stagger 99.3 Jittered 99.3 Sliding 99.7 Dwell and Switch 99.4 Periodic 99.0 Table 3. PRI modulation recognition perormance using MLP (9,000 pulse trains). 4 Conclusion The problem was to ind a robust method to automatically recognize PRI modulation type o a pulse TOA sequence. The suggested method should be applicable regardless o the number o pulses in the sequence. We proposed a set o ive eatures that can be used to classiy radar pulse trains into six PRI types. We applied a MLP network or classiication, and the recognition perormance was tested with simulations. Over 99 % o the test sequences or each modulation type were properly classiied. The method turned out to be very robust or noisy signal environment, imperect pulse deinterleaving, and modulation parameter variations. Reerences [1] B. A. Barritt, N. J. Rau, Enhancing electronic combat system digital signal processing using neural networks, Proceedings o the IEEE National Aerospace and Electronics Conerence (NAECON), volume 3, pp , (1992). [2] H. K. Mardia, New techniques or the deinterleaving o repetitive sequences, Radar and Signal Processing, IEE Proceedings F, volume 136, issue 4, pp , (1989). [3] D. J. Milojević, B. M. Popović, Improved algorithm or the deinterleaving o radar pulses, Radar and Signal Processing, IEE Proceedings F, volume 139, issue 1, pp , (1992). [4] G. P. Noone, A neural approach to automatic pulse repetition interval modulation recognition, Proceedings o the Inormation, Decision and Control Conerence (IDC 99), pp , (1999). [5] D. C. Schleher, Electronic Warare in the Inormation Age, Artech House, (1999). [6] R. G. Wiley, ELINT: the interception and analysis o radar signals, Artech House, (2006).