CORRELATION BASED CLASSIFICATION OF COMPLEX PRI MODULATION TYPES

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1 CORRELATION BASED CLASSIFICATION OF COMPLEX PRI MODULATION TYPES Fotios Katsilieris, Sabine Apfeld, Alexander Charlish Sensor Data and Information Fusion Fraunhofer Institute for Communication, Information Processing and Ergonomics (FKIE) Wachtberg, Germany Since April 27 Fotios is with Airbus Defence and Space GmbH Fraunhofer

2 Agenda. Introduction 2. Problem description 3. Proposed solution 4. Simulated examples 5. Summary & conclusions Fraunhofer FKIE 2 / 9

3 Introduction /3 Choice of a radar s pulse repetition interval (PRI) has great influence on target detection and tracking performance Interval might be constant: Or with some modulation: (3-level stagger) Fraunhofer FKIE 3 / 9

4 Introduction /3 Choice of a radar s pulse repetition interval (PRI) has great influence on target detection and tracking performance Interval might be constant: Or with some modulation: (3-level stagger) Fraunhofer FKIE 3 / 9

5 Introduction 2/3 Classification of pulse repetition interval modulation important for electronic warfare systems: Significant knowledge about the observed emitter Improvement of own electronic warfare system functions Literature: Standard PRI modulation types only Dwell & switch, stagger, constant, jittered, complex Fraunhofer FKIE 4 / 9

6 Introduction 2/3 Classification of pulse repetition interval modulation important for electronic warfare systems: Significant knowledge about the observed emitter Improvement of own electronic warfare system functions Literature: Standard PRI modulation types only Dwell & switch, stagger, constant, jittered, complex PRI.5 Dwell & switch Stagger Constant Jittered Time step Fraunhofer FKIE 4 / 9

7 Introduction 3/3 Automatic classification of complex PRI modulation sub-types remains unaddressed Common: Triangle, sawtooth, sine, and saturated sine PRI 2 Triangle Sawtooth Sine Saturated sine Time step Fraunhofer FKIE 5 / 9

8 Problem description /2 Consider a scenario where: A receiver observes an area of interest and records pulses emitted from different radars The received pulses are deinterleaved, i.e sorted by emitter Deinterleaving is a complex topic itself - not in scope Effects accounted for by considering spurious and missing pulses Problem formulation: Does the received signal exhibit a complex PRI modulation? If yes, of which sub-type: sawtooth, triangle, sine, or saturated sine? Fraunhofer FKIE 6 / 9

9 Problem description /2 Consider a scenario where: A receiver observes an area of interest and records pulses emitted from different radars The received pulses are deinterleaved, i.e sorted by emitter Deinterleaving is a complex topic itself - not in scope Effects accounted for by considering spurious and missing pulses Problem formulation: Does the received signal exhibit a complex PRI modulation? If yes, of which sub-type: sawtooth, triangle, sine, or saturated sine? Fraunhofer FKIE 6 / 9

10 Problem description 2/2 This is essentially a multi-class classification or multiple hypotheses testing problem: Hypothesis H : class C, i.e. sawtooth modulation Hypothesis H 2 : class C 2, i.e. triangle modulation Hypothesis H 3 : class C 3, i.e. sine modulation Hypothesis H 4 : class C 4, i.e. saturated sine modulation Hypothesis H : class C, i.e. none of the above We desire high probability of correct classification: P j C = P(C = C j C true = C j ), j =,..., 4 and low probability of misclassification:. Modulation type j is classified as some other type P j M v = P(C C j C true = C j ), j =,..., 4 2. Some other modulation types are classified as type j P j M v2 = P(C = C j C true C j ), j =,..., 4 Fraunhofer FKIE 7 / 9

11 Problem description 2/2 This is essentially a multi-class classification or multiple hypotheses testing problem: Hypothesis H : class C, i.e. sawtooth modulation Hypothesis H 2 : class C 2, i.e. triangle modulation Hypothesis H 3 : class C 3, i.e. sine modulation Hypothesis H 4 : class C 4, i.e. saturated sine modulation Hypothesis H : class C, i.e. none of the above We desire high probability of correct classification: P j C = P(C = C j C true = C j ), j =,..., 4 and low probability of misclassification:. Modulation type j is classified as some other type P j M v = P(C C j C true = C j ), j =,..., 4 2. Some other modulation types are classified as type j P j M v2 = P(C = C j C true C j ), j =,..., 4 Fraunhofer FKIE 7 / 9

12 Problem description 2/2 This is essentially a multi-class classification or multiple hypotheses testing problem: Hypothesis H : class C, i.e. sawtooth modulation Hypothesis H 2 : class C 2, i.e. triangle modulation Hypothesis H 3 : class C 3, i.e. sine modulation Hypothesis H 4 : class C 4, i.e. saturated sine modulation Hypothesis H : class C, i.e. none of the above We desire high probability of correct classification: P j C = P(C = C j C true = C j ), j =,..., 4 and low probability of misclassification:. Modulation type j is classified as some other type P j M v = P(C C j C true = C j ), j =,..., 4 2. Some other modulation types are classified as type j P j M v2 = P(C = C j C true C j ), j =,..., 4 Fraunhofer FKIE 7 / 9

13 Proposed solution Input: TOA difference of pulses t, cross-correlation threshold c min Output: Complex modulation type hypothesis decision H j : C = C j, j {,, 2, 3, 4} : 2: 3: 4: 5: 6: 7: 8: if then 9: : else : 2: end if Fraunhofer FKIE 8 / 9

14 Proposed solution Input: TOA difference of pulses t, cross-correlation threshold c min Output: Complex modulation type hypothesis decision H j : C = C j, j {,, 2, 3, 4} : evaluate lower envelope of t 2: smooth the lower envelope of t and get t (red line in Fig.) 3: 4: 5: 6: Elimination of the effect of lost pulses 7 6 Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope 7: 8: if then 9: : else : 2: end if t Time step Fraunhofer FKIE 8 / 9

15 Proposed solution Input: TOA difference of pulses t, cross-correlation threshold c min Output: Complex modulation type hypothesis decision H j : C = C j, j {,, 2, 3, 4} : evaluate lower envelope of t 2: smooth the lower ) envelope of t and get t (red line in Fig.) 3: evaluate ( t t, i.e. its autocorrelation ) 4: find the period of t using the peaks of ( t t 5: 6: 7: 8: if then 9: : else : 2: end if Complex PRI modulation induces distinct peaks Fraunhofer FKIE 8 / 9

16 Proposed solution Input: TOA difference of pulses t, cross-correlation threshold c min Output: Complex modulation type hypothesis decision H j : C = C j, j {,, 2, 3, 4} : evaluate lower envelope of t 2: smooth the lower ) envelope of t and get t (red line in Fig.) 3: evaluate ( t t, i.e. its autocorrelation ) 4: find the period of t using the peaks of ( t t 5: extract a period from t 6: create ideal signals t j, j =,..., 4 7: 8: if then 9: : else : 2: end if t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

17 Proposed solution Input: TOA difference of pulses t, cross-correlation threshold c min Output: Complex modulation type hypothesis decision H j : C = C j, j {,, 2, 3, 4} : evaluate lower envelope of t 2: smooth the lower ) envelope of t and get t (red line in Fig.) 3: evaluate ( t t, i.e. its autocorrelation ) 4: find the period of t using the peaks of ( t t 5: extract a period from t 6: create ideal signals t j, j =,..., 4 7: find j = arg max j [( t t j )], j =,..., 4 ) 8: if ( t t j > c min then 9: choose hypothesis H j : C = C j : else : choose hypothesis H : C = C 2: end if t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

18 Simple example : Favourable case In this case we assume very reliable prior information: Normalized cross-correlation threshold c min =.8 Duration of the emitted signal D = 2 time units We sample.8 periods of the signal Drop-out ratio of %, i.e. % of the emitted pulses are lost Saturation of sat. sine is known to be.7 PRI mod. P C P M v P M v2 Sawtooth.96.. Triangle Sine Sat. sine PRI mod. P C P M v P M v2 Dwell & switch N/A. N/A Stagger N/A N/A Constant N/A N/A Jittered N/A.3 N/A Fraunhofer FKIE 9 / 9

19 Simple example 2: Unfavourable case In this case we assume reliable prior information but more pulses are lost: Normalized cross-correlation threshold c min =.8 Duration of the emitted signal D = 2 time units We sample.8 periods of the signal Drop-out ratio of 2%, i.e. 2% of the emitted pulses are lost Saturation of sat. sine is known to be.7 PRI mod. P C P M v P M v2 Sawtooth.9.5. Triangle Sine Sat. sine PRI mod. P C P M v P M v2 Dwell & switch N/A.7 N/A Stagger N/A.8 N/A Constant N/A N/A Jittered N/A.3 N/A Fraunhofer FKIE / 9

20 Simple example 3: Unfavourable case 2 In this case we assume unreliable prior information: Normalized cross-correlation threshold c min =.8 Duration of the emitted signal D = time units We sample.5 periods of the signal Drop-out ratio of 2%, i.e. 2% of the emitted pulses are lost Saturation of ideal sat. sine is.8 instead of the true value.7 PRI mod. P C P M v P M v2 Sawtooth Triangle Sine Sat. sine PRI mod. P C P M v P M v2 Dwell & switch N/A.2 N/A Stagger N/A.2 N/A Constant N/A N/A Jittered N/A.2 N/A Fraunhofer FKIE / 9

21 In depth look into the performance The following settings were used: Normalized cross-correlation threshold c min =.8 Duration of the emitted signal D = time units Mean pulse repetition interval PRI {.,.25,.5,..., 3, 3.5, 4} time units Higher value means less pulses emitted in the same time Number of observed signal periods D/T {,.,.2,..., 3} Ratio of emitted signal duration D and signal period T Higher value means less pulses per period in the same observation time Fraunhofer FKIE 2 / 9

22 In depth look into the performance The following settings were used: Drop-out ratio d {,.2,.2,...,.7} Monte Carlo runs Pulses randomly dropped at each run based on the drop-out ratio We examine the: Probability of correct classification Both definitions of the probability of misclassification Fraunhofer FKIE 3 / 9

23 Example: Sawtooth PRI modulation Very high probability of correct classification P C over a broad range of signal reception settings. Fraunhofer FKIE 4 / 9

24 Example: Sawtooth PRI modulation Very low probability that sawtooth is classified as another complex modulation type P M v over a broad range of signal reception settings. Fraunhofer FKIE 5 / 9

25 Example: Sawtooth PRI modulation Very low probability that other modulation types are classified as sawtooth P M v2 over a broad range of signal reception settings. Fraunhofer FKIE 6 / 9

26 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

27 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

28 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

29 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

30 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

31 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

32 .68 Sample period =..68 Sample period = Conclusions Sample period = Sample period = Sample period = Sample period = Sample period = Sample period = Sawtooth modulation correctly classified in almost all cases Non-complex PRI modulations practically never identified as complex Most false classifications of triangle and sine are due to confusion with saturated sine Crucial part: Reliable extraction of the lower envelope of the received signal Lower envelope should resemble one of the ideal complex modulation types At least.2 periods should be observed Best performance for: D/T {.2,..., 2}, meanpri {.,..., 2}, d {.2,...,.46} Prior information about the received signal crucial for its correct classification Knowledge about the signal period can be used for adapting the observation duration Significant pulse drop-out ratios can be tolerated Up to 5% under some favourable conditions Fraunhofer FKIE 7 / 9

33 Summary 7 6 First algorithm in the open literature that classifies complex PRI modulation types Classification of complex PRI modulation with good statistics under varying signal reception conditions Information from an emitter database plays a crucial role Almost complete rejection of signals having non-complex PRI modulation Low computational complexity algorithm Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope t Time step t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

34 Summary 7 6 First algorithm in the open literature that classifies complex PRI modulation types Classification of complex PRI modulation with good statistics under varying signal reception conditions Information from an emitter database plays a crucial role Almost complete rejection of signals having non-complex PRI modulation Low computational complexity algorithm Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope t Time step t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

35 Summary 7 6 First algorithm in the open literature that classifies complex PRI modulation types Classification of complex PRI modulation with good statistics under varying signal reception conditions Information from an emitter database plays a crucial role Almost complete rejection of signals having non-complex PRI modulation Low computational complexity algorithm Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope t Time step t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

36 Summary 7 6 First algorithm in the open literature that classifies complex PRI modulation types Classification of complex PRI modulation with good statistics under varying signal reception conditions Information from an emitter database plays a crucial role Almost complete rejection of signals having non-complex PRI modulation Low computational complexity algorithm Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope t Time step t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

37 Summary 7 6 First algorithm in the open literature that classifies complex PRI modulation types Classification of complex PRI modulation with good statistics under varying signal reception conditions Information from an emitter database plays a crucial role Almost complete rejection of signals having non-complex PRI modulation Low computational complexity algorithm Sawtooth after 2% pulse drop-off Smoothed sawtooth lower envelope t Time step t Ideal sawtooth Ideal triangle Ideal sine Ideal sat. sine Extracted period from received signal Time step Fraunhofer FKIE 8 / 9

Thank you for your attention! Fotios Katsilieris, Sabine Apfeld, Alexander Charlish e-mail: Fotios.

38 Thank you for your attention! Fotios Katsilieris, Sabine Apfeld, Alexander Charlish {Sabine.Apfeld, Fraunhofer FKIE 9 / 9

IT S A COMPLEX WORLD RADAR DEINTERLEAVING. Philip Wilson. Slipstream Engineering Design Ltd.

IT S A COMPLEX WORLD RADAR DEINTERLEAVING Philip Wilson pwilson@slipstream-design.co.uk Abstract In this paper, we will look at how digital radar streams of pulse descriptor words are sorted by deinterleaving