THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. 2014 Dec.; 25(12), 12751283. http://dx.doi.org/10.5515/kjkiees.2014.25.12.1275 ISSN 1226-3133 (Print)ISSN 2288-226X (Online) ML PCM Maximum Likelihood Based Doppler Estimation and Target Detection with Pulse Code Modulated Waveform 양은정 이희영 송준호 Eunjung YangHeeyoung LeeJunho Song 요약 PCM(Pulse Code Modulation) code., (MFR: Multi-Function Radar). PCM (ambiguity function), (Doppler filter bank)., ML(Maximum Likelihood). (closed form) suboptimal,. Abstract Characteristics of PCM(Pulse Code Modulation) waveform are suitable for target tracking. Especially in terms of dwell time, it is desirable to detect and track a moving target with the single PCM waveform for a MFR(Multi-Function Radar) which carries out multiple tasks. General PCM waveform processing includes Doppler filter bank caused by the characteristics of ambiguity function, to detect target and estimate Doppler frequency, which induces hardware burden and computational complexity. We propose a ML(Maximum Likelihood) based Doppler estimator for a PCM waveform, which is the closed form suboptimal solution and computationally efficient to estimate Doppler frequency and detect a moving target. Key words: Pulse Code Modulation Waveform, Doppler Frequency Estimation, Multi-Function Radar, Target Detection. 서론 (MFR: Multi-Function Radar),.,. (ambiguity function) LFM(Linear Frequency Modulated) (surveillance), PCM(Pulse Code Modulated).,. coherent PT(Pulse Train) (Agency for Defense Development) Manuscript received August 26, 2014 ; Revised October 15, 2014 ; Accepted November 4, 2014. (ID No. 20140826-063) Corresponding Author: Eunjung Yang (e-mail: ejyang@add.re.kr) c Copyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved. 1275
THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 12, Dec. 2014.,. PCM., PT, PT dwell time [1]., dwell time PCM. PCM dwell time, (Doppler filter bank). (matched filter).,.,,, [2]..,. [3], [4] MMSE(Minimum Mean Squared Error).., nuisance, [5].,. PCM, ML(maximum likelihood).,. Morelli Mengali [6]. optimal MLE(Maximum Likelihood Estimation) MLE closed form suboptimal.,.. 신호모델및 MLE 기법 baseband (1). (1) zero mean Gaussian random variable. RCS,. PCM, swerling model II IV.,,. zero mean gaussian. sampling snapshot sequence (2). (2) snapshot sequence PCM. PCM, transposition. (diagonal matrix), zero mean complex Gaussian. sampling, (identity matrix). 1276
ML PCM (SNR: Signal to Noise Ratio). (2), log likelihood (3). complex conjugated transposition. MLE nuisance, log likelihood., (3) (4)., (4) (5),, complex conjugate. MLE,, closed form solution, (numerically). FFT(Fast Fourier transform), (4) DFT(Discrete Fourier Transform). FFT. 0 (zero padding) FFT. (interpolation).. 제안한도플러추정기법 3-1 Closed Form 추정기 closed form,., 0. (6).., (5).. (7) (6), (8). cos (7) (8), cos cos, (8) (9). 1277
THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 12, Dec. 2014. cos (9) (6) (8), (9). (10) (exponential term), closed form. (11). 3-2 Acquisition Range Extension (4) likelihood., MLE (unambiguous). acquisition range, MLE. acquisition range (10). MLE, snapshot sequence., acquisition range,., MLE acquisition range. PT (range ambiguity resolving). acquisition range,. (12). Acquisition Range, snapshot sequence. snapshot sequence, (12) (13). (13) snapshot sequence,., snapshot sequence,. (14) (14).. (14), acquisition range MLE.,. (14). acquisition range. Acquisition range MLE closed 1278
ML PCM form, (snapshot sequence),,.,, dwell time..,., sample sample. (11) closed form 2,.. (11). 1, closed form 그림 1. acquisition range Fig. 1. Acquisition range of the proposed algorithm with. acquisition range acquisition range., acquisition range,, MLE acquisition range. 3-3 Target Detection using Doppler Frequency PCM.,..,.. 모의실험결과 III. (absolute value) 1( ). bi-phase code poly-phase code. poly-phase code Frank code [2]. GHz X-band, subpulse duration usec., ms khz, 0.02. 4-1 도플러주파수추정오차분석 (Normalized Doppler frequency) MSE(Mean Squared Error),. 1279
THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 12, Dec. 2014. MLE CRB(Cramer-Rao lower bound) ( ). (15), (16) 2. 16, SNR 25 db. 2 10,000 Monte Carlo., CRB. MLE. 0.02, MLE. 그림 2., 16 Frank code, SNR 25 db Fig. 2. MSE of the proposed algorithm corresponding to normalized Doppler frequency with a frank code when db. 그림 3. Frank, 0.02, SNR 20 db Fig. 3. MSE of the proposed algorithm corresponding to code length with a Frank code when and db. 0.06. 3 snapshot sequence. 0.02, SNR 20 db., snapshot sequence., CRB, (6) (10). 4 SNR. 36, 0.02 10,000. SNR MSE, MSE CRB. SNR 15 db SNR CRB, 1280
ML PCM 그림 4. SNR, 36 Frank code, 0.02 Fig. 4. MSE of the proposed algorithm corresponding to SNR with a Frank code when..,. 4-2 표적의탐지성능분석 5.,.,. 36, 15 dbw.., (absolute value),. Frank code (ambiguity function)., 그림 5., 36 Frank code SNR 15 db Fig. 5. The results of the matched filter corresponding to Normalized Doppler frequency with db received target signal from Frank code.., 36, SNR 15 db 10,000 Monte Carlo.,.,.. MLE.. 6 1281
THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 12, Dec. 2014. Matched filter output, db 24 23 22 21 20 19 output without Doppler compensation output with Doppler filter bank with f center = f 3dB output with Doppler filter bank with f center = f 3dB /2 output with Doppler compensation 18-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 Normalized frequency 그림 6., 36 Frank code SNR 15 db Fig. 6. The comparison with results of the matched filter corresponding to normalized Doppler frequency with db received target signal from Frank code.., ambiguity function 3 db width ( ),.,.. 결론 PCM,. MLE closed form suboptimal..,.,. 부록 CRB. (2), joint probability function. ln ln (17),. CRB Fisher information, ln (17). (18) (19) CRB. References (20) [1] M. Skolnik, Introduction to Radar Systems, 2nd Ed., New York: McGraw-Hill, pp. 127-129, 1981. [2] M. Skolnik, Radar Handbook, 2nd Ed., New York: Mc- Graw-Hill, 1991. [3] S. Blunt, K. Gerlach, "Adaptive pulse compression via MMSE estimation", IEEE Trans. Aero. and Electro. Syst., vol. 42, no. 2, pp. 572-584, Apr. 2006. [4] S. Blunt, A. Shackelford, K. Gerlach and K. Smith, "Doppler compensation & single pulse imaging using adap- 1282
ML 기법을 이용한 PCM 파형에서의 표적 탐지 및 도플러 추정 tive pulse compression", IEEE Trnas. Aero. and Electro. Syst., vol. 45, no. 2, pp. 647-659. Apr. 2009. [5] L. Lawrence, I. Reed, and W. Sollfrey, "A comparison of average likelihood and maximum likelihood ratio tests for detecting radar targets of unknown Doppler frequen- cy", IEEE Trans. Inform. Theory, vol. 14, no. 1, pp. 104110, Jan. 1968. [6] M. Morelli, U. Mengali, "Carrier-frequency estimation for transmissions over selective channels", IEEE Trans. Commun., vol. 48, no. 9, pp. 1580-1589, Sep. 2000. 양은 정 송준 호 년 2월: 한국과학기술원 전기 및 전자 공학과 (공학사) 2006년 8월: 한국과학기술원 전기 및 전자 공학과 (공학석사) 2011년 2월: 한국과학기술원 전기 및 전자 공학과 (공학박사) 2011년 1월 현재: 국방과학연구소 [주 관심분야] 레이다 신호처리 2004 이희 영 년 2월: 부산대학교 전자전기통신공 학과 (공학사) 2006년 2월: 한양대학교 전자컴퓨터공학 과 (공학석사) 2006년 1월 현재: 국방과학연구소 [주 관심분야] 레이다 신호처리 및 통제 기 2004 년 월 서강대학교 전자공학과 (공학 사 년 월 포항공과대학교 전기 및 전자 공학과 공학석사) 년 월 현재: 국방과학연구소 레이다 신호처리 2005 2 : ) 2007 2 : ( 2007 2 [주 관심분야] 1283