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1 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE Oct.; 25(10), ISSN (Print)ISSN X (Online) MPRF / PRF Real-Time PRF Selection for Search/Track in MPRF Waveform Airborne Radar 김태형 김은희 이성원 Tae-Hyung KimEun-Hee Kim*Sung-Won Lee 요약 / MPRF. MPRF, / PRF. / PRF. Abstract Airborne radar usually use MPRF(medium PRF) waveforms to detect and track look-down or all-directions air-to-air targets. To use MPRF waveforms, airborne radar have to operate optimal PRF schedules and select optimal PRFs able to detect look-down air-to-air targets, overcoming look-down clutter and resolving range/velocity ambiguities. In this paper, we propose a real-time search method for the optimal(and sub-optimal) PRFs able to detect and track targets in real-time change of situation for MPRF pulsed-doppler airborne radars. Key words: MPRF Waveforms, Airborne Radar, Real-Time PRF Selection, Air-to-Air, PRF Schedule. 서론 Low PRF(Pulse Repetition Frequency) high PRF MPRF(Medium Pulse Repetition Frequency). MPRF (look-down). MPRF (ambiguity), M-of-N PRF [1],[2]. M-of-N PRF N PRF, M PRF, PRF LIG()(LIG Nex1 Co., Ltd.) * (Defense System Engineering, Sejong University) Manuscript received July 10, 2014 ; Revised August 18, 2014 ; Accepted September 11, (ID No ) Corresponding Author: Tae-Hyung Kim ( thkim07@gmail.com) 1050 c Copyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved.

2 MPRF / PRF PRF. PRF. M N, M N 3-of-8 [1],[2]. MPRF /. / PRF, PRF / /. (/ ) PRF. PRF, eclipse (blind region), (ghost) [2],[3]. (,,, / ), PRF. MPRF PRF [1].,, PRF PRF. PRF PRF PRF. PRF [2]. MPRF pulse-doppler 3-of-8 ( sub-optimal) PRF., (MLC: Mainlobe Clutter), (SLC: Sidelobe Clutter) ( ) MLC/SLC PRF. PRF PRF ( ), PRF. PRF, SLC SLC.. 실시간탐색 PRF 집합선택 PRF. 1. 표 1. Table 1. Parameters for radar and clutter model. Parameter Carrier frequency Transmitted pulsewidth FFT size Fill in pulse Range resolution Blind range due to eclipsing Value 10 GHz 8 μs 128 bins 16 pulses 30 m 1,230 m Maximum duty 20 % Antenna 3 db beamwidth 5 Antenna scan rate Maximum GMT velocity rejected Maximum target Doppler Maximum detection range 60 /s 28 m/s ±133 khz(2,000 m/s) km(100 NM) Target radar cross-section 1 m 2 Clutter backscatter coefficient Antenna sidelobe gain 20 db 39 db 1051

3 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct 비실시간제한조건및비실시간과정 1. 1 (off-line) (on-line). PRF ( ). PRF PRI(Pulse Repetition Interval), PRI duty, PRI 2 PRI (visibility) [4]. 2 Doppler visibility. range visibility 그림 1. PRF Fig. 1. Flow chart for selecting PRF set in target search mode. 그림 2. PRI Fig. 2. Determination of maximum and minimum PRIs. eclipse. 2 (Joint visibility) 0.4 PRI. 3,733 Hz m/s +28 m/s, 56 m/s. PRI eclipse. 1,230 m eclipse. PRI PRI random PRI, PRI ( ) L(=82). L PRF ( trade- off ). L, PRF PRF,, L. (decodability), (beam) (scan rate). (/ / ) PRF /. 3-of-8 3 PRI

4 MPRF / PRF 그림 3. Fig. 3. Decodability.., 3 PRI 3. (M DR = nr u1 mr u2, r 1 =RnR u1 (PRI1 ), r 2 =RmR u2 (PRI2 ), R=, R u1 =PRI1, R u2 =PRI2 ) [1] M DR ( 4). 3-of-8 PRF. eclipse loses (GMT rejection) ( ) 그림 4. PRI Fig. 4. Check of decodability of PRI sets. 그림 5. Fig. 5. Calculation of blindness margin for a cell in interest region. 10 %., 90 % PRI. PRI, eclipse GMT (blindness margin). PRF PRI. 5 (, cell1),,. GMT rejection, eclipse. PRF. PRF 6. GMT, PRF Doppler., 0., 1. 0 blind cell, 1 visible cell.., PRF GMT rejection. eclipse,. 6(a). PRF. PRF 6(b). 1053

5 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct (a) PRF (0:, 1:, x:, =: ) (a) Blind region for a PRF(0: blind, 1: visible, x: array multiply, =: result).,. random search (local) (global). random search. 2-2 실시간제한조건 (b) PRF PRF (= 30/100) (b) Blind region for each PRF and visibility map for a PRF set (visibility=30/100) 그림 6. PRF Fig. 6. Calculation of PRF visibility in interest region. 그림 7. PRF Fig. 7. Visibility and visibility map of a PRF set. PRF.. CPI(Coherent Processing Interval), 60 CPI. CPI 144 PRI, CPI. 60 /s PRF set. ( ) PRF. MLC, SLC. PRF PRF. PRF GMT rejection eclipse., PRF PRF MLC, GMT rejection, eclipse, SLC. MLC. 8, MLC ( ) cos [3] (, cos,, ). 9 MLC ( )., MLC ( ). 그림 8. Fig. 8. Mainbeam and MLC width of airborne radar. 1054

6 MPRF / PRF 그림 11. Folded unfolded Fig. 11. Linear approximation of error between powers of folded and unfolded sidelobe clutter. 그림 9. MLC () () Fig. 9. Maximum Doppler of MLC by squint angel() and mainbeam width(). 그림 12. PRI SLC Fig. 12. SLC width and blind region for a PRI. 그림 10. SLC Fig. 10. Power of sidelobe clutter and target according to target ranges. sin sin cos cos SLC SLC. SLC 10, PRF SLC. SLC PRI (1) PRI SLC, SLC. PRI SLC unfolded folded. 11 SLC unfolded. SLC 12 SLC. 2-3 실시간과정및실시간 PRF 집합선택 PRF 1. 1 EA(evolution algorithm), 1055

7 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct cost. PRF ( ) 4 PRF random. 4 visibility 1 visibility 2. 2 mutation PRF. 4 PRF PRF visibility PRF. EA, cost PRF. ( ). EA [x](x: 0 1 ), PRF decoding. (2) (PRI ), (PRI ) m PRF., (3) mutation. (3) G random (mean 0, variance 1), m(i) std 1/8 0.9 i (i i ).. 실시간추적 PRF 선택 PRF. 3-1 추적 PRF 선택개념 (prediction). MPRF, 13 RD(/) / eclipse RD 그림 13. PRF RD Fig. 13. In case selecting optimal PRF, target position in RD (range/doppler) map. PRF (CFAR ). SLC SLC SLC PRF. SLC, SLC PRF. SLC. 3-2 부엽클러터의형태추정 SLC, H a. x-z ( x-z [5] ). x-y-z ( ) y P. R AP P, P,, P. P, [5]. 1056

8 MPRF 그림 14. 파형을 사용하는 항공기 레이더에서 탐색/추적을 위한 실시간 PRF 선택 지상 클러터 표현하는 수식 유도를 위해 사용 한 좌표계 Fig. 14. Coordinate system used for formula induction representing ground clutter. 위치 곡선의 도플러 방향에서 폴딩 그림 16. SLC Fig. 16. Folding of SLC curve in Doppler axis. 와 식 를 이용한 부엽 클러터 위치 곡선 그림 15. (4) Fig. 15. Sidelobe clutter curve by the formula (4). cos (4) 다음 그림은 매개변수 를 0에서 2π까지 변화시키 면서 변수 와 에 대한 RD 맵(unfolded RD map)을 그려본 것이다. 그림에서 보듯이 SLC의 전력이 존재하는 영역의 내부 와 외부의 경계를 이루는 곡선은 의 값 0(or 2π)과 π 에 의하여 형성되는 곡선이다. 그리고 이 경계 곡선(포물 선 모양)의 꼭지점은 이고, 인 지 점이다. 이제 SLC가 PRF 주기로 폴딩(folding)되어진 RD 맵을 생각해 보자. 그림 16은 그림 15를 PRF=1.2 khz의 주기로 폴딩하였 을 때의 그림이다(거리 방향에서의 SLC는 다른 방법으로 고려할 수 있으므로, PRI 주기로 폴딩되었을 때의 효과는 생략하였다). 위의 그림들에서 보듯이 SLC 경계곡선( 의 값이 0과 π일 때 곡선)의 내부와 외부 영역을 고려할 경계 곡선의 일치성 예 그림 17. SLC SLC Fig. 17. Corresponding properties of SLC and SLC boundary curve. 때 내부에 존재하는 곡선들은 폴딩되어도 SLC 경계곡선 내부에 있음을 알 수 있다. 그러므로 SLC 경계곡선으로 폴딩된 RD 맵에서 SLC의 전력이 존재하는 영역(SLC 경 계곡선의 내부)과 존재하지 않는 영역(SLC 경계곡선의 외부)을 알 수 있다. 즉, 우리는 SLC에 대한 경계곡선 수 식을 이용하여 SLC 전력의 존재 위치 및 영역 모양을 추 정할 수 있다. 그림 17은 시뮬레이션을 통해 구한 클러터 맵과 SLC 경계곡선을 같이 표현한 것이다. 그림에서 일치 여부를 확인할 수 있다. 그림에서 보듯이 시뮬레이션을 통한 클 러터 맵의 SLC와 SLC 경계곡선을 통한 SLC의 위치와 모 양이 일치하는 것을 볼 수 있다. 식 (4)를 통하여, SLC의 포물선 모양은 항공기의 속도 벡터와 관련이 있으며, 포 물선의 꼭지점은 항공기 고도와 속도와 관련이 있음을 알 수 있다. 그리고 포물선의 꼭지점 위치는 어떤 지점이 포물선의 내부(SLC 전력의 존재 영역) 및 외부(SLC 전력 이 존재하는 않는 영역)에 있는 지를 판단하는 임계점이다. 이제 폴딩된 RD 맵의 한 지점이 SLC 영역 내부(포물 선 내부)에 있는지, 외부(포물선 외부)에 있는지 판단하여 1057

9 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct SLC (, ) (, i ) (, j ). (5) RD (r p, f p ) SLC (clear ). and for 그림 18. Unfolded folded / SLC Fig. 18. SLC boundary curve and target in unfolded and folded RD maps.. 18 SLC ( (4) 0, π, 2π ). 18 PRF SLC. PRF. PRF,. 18 PRF RD. 18 SLC ( ) SLC. 18 SLC, SLC., unfolded RD SLC folded RD SLC (unclear ). PRF SLC /. 18 / (r p, f p ) PRF cos, cos (5). (5). T SLC =r p H a, (5) T SLC >0. T SLC <0 (r p, f p ) SLC (clear ). (5) PRF SLC /, SLC PRF PRF. 3-3 실시간추적 PRF 선택과정 PRF RD PRF. eclipse, PRI. eclipse PRI. MLC. MLC ( ) 1058

10 MPRF / PRF 3-2 T SLC (0<T SLC <SD th, SD th PRI SLC ), (5) PRF SLC PRF. (0<T SLC <SD th ) (5) PRF, PRF PRF/2 PRF.. 시뮬레이션및결과 4-1 실시간탐색 PRF 집합선택 그림 19. PRF Fig. 19. Real-time tracking PRF selection algorithm. (10 ) MLC. 19 (10 ) 1 3 db., MLC 0 MLC, MLC 9 (1). MLC PRF, 8. SLC PRI, SLC (alititude line ). SLC 10 11, 12 PRI. PRI SLC, RCS SLC PRI SLC., PRF PRF PRF. 1 3,048 m, (300, 0, 10), (=16.7, =14.7 ) PRF. 82., PRF. sub-optimal PRF. matlab 0.83 (intel 2.8 GHz CPU). 1 ( 1) PRF. [1],[2] 1. 1/10., 80 ms PRF. (dwell) 80 ms PRF. PRF (visibility map) (blind zone) [2].., PRF km, 02,000 m/s 1059

11 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct 여준다. 그림 21의 상단의 두 개의 RD 맵은 대공 표적이 (0<T <SD )의 범위에 있지 않는 경우에 결과로서, RD 맵 결과들에서 보듯이 표적이 최적의 추적 PRF 선택에 의해 SLC와 MCL의 전력이 없는 깨끗한 영역의 중간에 표적이 위치하는 것을 볼 수 있다. 그림 21의 하단은 대공 표적이 (0<T <SD )의 범위에 있을 때이며, 하단의 왼쪽 RD 맵은 식 (5)의 조건을 사용하지 않고 표적 도플러가 PRF/2에 가장 가까운 PRF 선택이라는 조건을 사용한 경 우의 결과이다. 그리고 하단의 오른쪽 RD 맵은 식 (5)의 조건을 이용하여 SLC 영역 외부에 표적이 위치하도록 PRF를 선택한 결과이다. 그림 21의 하단 RD 맵에서 보듯 이 단순히 RD 맵의 중앙에 표적이 위치하도록 하기보다 는(왼쪽 RD 맵) SLC 전력이 적은 도플러 위치에 표적이 위치하도록 PRF를 선택하는 것(오른쪽 RD 맵)이 필요하 다. 제안한 실시간 추적 PRF 선택 알고리즘의 실행 시간 은 1 ms 이하로서 실시간성 구현을 위한 충분한 결과다. SLC 선택된 집합의 가시성 및 음영 영역 맵 그림 20. PRF Fig. 20. Visibility and blind zone maps of selected PRF set. 때 90 % 이상의 탐지 가능 영역을 확보하였고, 음영속도 및 음영거리 발생을 최소화하고 있다. 4-2 실시간 추적 PRF 선택 표 1과 다음의 시나리오 상황에서 추적 PRF 선택을 실 험하였다. 시나리오 상황은 항공기 고도 25 km, 항공기는 150 m/s의 속도로 수평 비행, 대공 표적의 비행 고도 24 km, 대공 표적은 150 m/s의 속도로 비행, 대공 표적은 항 공기의 진행 방향을 기준으로 방위각 30 방향에서 상대 거리 30 km부터 10 km까지 다가옴, 그리고 항공기는 대 공 표적을 30 km부터 10 km까지 계속 추적하고 있는 경 우이다. 그림 21은 대공 표적을 추적하는 각 순간 상황에서 추 적 PRF 선택과 시뮬레이션으로 획득한 RD 맵의 예를 보 선택된 추적 들에 의한 맵들 그림 21. PRF RD Fig. 21. RD maps by selected tracking PRFs th SLC th Ⅴ. 결 론 파형을 사용하는 항공기 레이더의 공간 탐색을 위한 실시간 PRF 집합 선택 방법과 추적을 위한 실시간 PRF 선택 방법을 제시하였다. 탐색 PRF 집합 선택을 위한 조건들과 실시간성을 위하 여 그 조건들의 구체적인 구현 방법을 제시하고, 제안 알 고리즘이 충분한 결과를 나타냄을 보였다. 제안한 실시간 탐색 PRF 집합 선택 방법은 비실시간과 실시간 과정으로 나뉘며, 실시간 과정의 실행시간이 실시간성에 영향을 미 친다. 실시간 과정의 실행 시간에 대한 실험 결과는 코드 최적화와 임베디드 코딩으로 실행시간을 현저히 줄일 수 있고, 빔 스캔 단위로 PRF 집합을 실시간으로 선택하는 데 충분하다. 비실시간 과정을 통해서 선택된 후보들 간의 유사성이 없을수록 좋다. 다만 random search를 통해 후보들 간의 유사성을 배제시키는 효과를 주려고 했지만, 유사성이 높 은 후보들이 선택될 가능성을 배제시키지는 못한다. PRF 집합 후보들 간의 유사성을 측정하는 방법 및 배제시키 는 방법에 대해 좀 더 연구가 필요하다. 추적 PRF 선택을 위한 조건들과 실시간 PRF 선택을 MPRF

12 MPRF 파형을 사용하는 항공기 레이더에서 탐색/추적을 위한 실시간 PRF 선택 위한 알고리즘을 제시하였다. 부엽 클러터가 존재하는 영 역을 나타낼 수 있는 부엽 클러터 경계곡선을 유도하였 고, 이를 MPRF 파형으로 표적을 추적할 때에 부엽 클러 터의 영향을 최소화(부엽 클러터의 모양 및 위치를 파악 하여 도플러 방향에서 부엽 클러터가 없는 영역에 표적 을 위치하도록)하는 PRF를 선정하는 데 이용하였다. 이 것은 특히 항공기의 고도와 표적 거리가 비슷해지는 영 역에서만 사용하였다. 시뮬레이션을 이용한 실험 결과는 제안한 알고리즘이 효과적으로 동작함을 보여주고 실시 간 구현성에도 충분함을 보여준다. References [1] A. M. Kinghorn, N. K. Williams, "The decodability of multiple-prf radar waveforms", Proc. IEE Radar 97, 김태 형 년 3월: 부산대학교 전자공학과 (공학 석사) 2007년 3월: 부산대학교 전자공학과 (공학 박사) 2010년 11월: 국방과학연구소 연구원 2010년 12월 현재: LIG넥스원(주) ISR 연 구센터 연구원 [주 관심분야] 레이더 신호처리, 패턴인식 Conf. Publ., no. 449, Edinburgh, Oct. 1997, pp [2] C. M. Alabaster, E. J. Hughes, and J. H. Matthew, "Medium PRF radar PRF selection using evolutionary algorithm", IEEE Trans. Aerospace and Electronic Systems, vol. 39, no. 3, p. 990, Jul [3] G. Morris, L. Harkness, Airborne Pulsed Doppler Radar, 2nd edition, Artech House, Inc., [4] M. I. Skolnik, Radar Handbook, 2nd Edition, McGrowHill, [5] 김태형, 김은희, 손성환, "항공기 레이더의 MPRF 모 드에서 지상클러터를 표현한 곡선과 거리/도플러 맵 형성", 한국군사과학기술학회 종합학술대회, pp , 2011년 6월. 이성 원 1999 김은 희 년 2월: 아주대학교 정보컴퓨터공학 공학석사) 년 2월: 아주대학교 컴퓨터공학과 (공 학박사) 2014년 1월 현재: LIG넥스원(주) ISR 연 구센터 연구원 [주 관심분야] 레이더 신호처리, 레이더 2009 ( 2014 시스템, 무선통신 년 8월: 한국과학기술원 기계공학과 공학박사) 년 12월: LIG넥스원(주) ISR 연구센 터 연구원 2013년 12월 현재: 세종대학교 국방시스 템공학과 교수 [주 관심분야] 레이더 신호처리, 레이더 2004 ( 2013 시스템 1061

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