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Signal integration, as an effective method of detecting weak target, is widely used in areas of radar, sonar, etc. In previous studies of long-time coherent integration, researchers usually established a multi-pulse echo model with linear frequency modulation (LFM) signal due to its good compression performance and large Doppler tolerance. Then, perfect analytical formula can be deduced to compensate for range migration and Doppler spread, which is helpful in analyzing the mechanism of long-time coherent integration in depth. However, besides LFM, a wide variety of signal waveforms are also used in modern sonar and underwater guidance system to meet the requirements for diverse applications. For instance, continuous wave (CW) pulse is often used in signal detection, high resolution direction of arrival (DOA) estimation, and velocity estimation, while large time-bandwidth product waveforms such as modulated signal, coded signal, and pseudo-random signal are utilized for special tasks like anti-interference detection, channel matching, and active concealed detection. Therefore, the formulas and corresponding instructive conclusions deduced by LFM have no generality when other sonar waveforms are used in pulse integration. In this paper, we focus on long-time coherent integration for arbitrary signal reflected by underwater target moving with a uniform velocity and propose a motion-compensated coherent integration method for arbitrary complex envelop signal. A kind of general ambiguity function (GAF) for transmitted signal is defined to present a unified expression based on GAF for the output of the matched filter. The operation not only helps us to describe and calculate the pulse compression form of the arbitrary complex envelop by using a general mathematical model, but also provides information about the range migration and Doppler frequency shift of the multi-pulse echo, which is needed in pulse range alignment and FFT integration. For the matched filter output expressed by the GAF, Keystone transform is utilized to correct the complex envelop of the multi-pulse echo and eliminate the range walk. Then, Doppler frequency shift is compensated for by performing FFT transform, and the long-time coherent integration for arbitrary complex envelop is realized. To verify the correctness of the proposed method, we carry out the computer simulation on both signal integration and detection performance by using four sonar waveforms, i.e., CW signal, LFM signal, m-sequence phase-coded signal, and Costas frequency hop coded signal. The simulation results show that the proposed motion-compensated coherent integration method is applicable to arbitrary complex envelop signal. We also design an anechoic water tank experiment scheme which can successfully obtain the multi-pulse echoes of constant moving target. The motion-compensated coherent integration of the experimental data of the above-mentioned four waveforms further validates the effectiveness of the proposed method.
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Keywords:
- arbitrary complex envelop /
- coherent integration /
- motion compensation /
- generalized ambiguity function
[1] North D O 1963 Proc. IEEE 51 1016
[2] Liu Z L, Liao G S, Yang Z W 2012 Acta Electron. Sin. 40 799(in Chinese) [刘志凌, 廖桂生, 杨志伟 2012 电子学报 40 799]
[3] Zhang L, Sheng J L, Duan J, Xing M D, Qiao Z J, Bao Z 2013 EURASIP J. Adv. Signal Process. 2013 33
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[10] Yu J, Xu J, Peng Y N, Xia X G 2012 IEEE Trans. Aerosp. Electron. Syst. 48 991
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[14] Ruan H, Wu Y H, Jia X, Ye W 2013 IEEE Geo. Rem. Sens. Lett. 11 128
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[17] Feng X A, Zhang Y M, Su J J 2014 J. Northwest. Polytechnical Univ. 32 882(in Chinese) [冯西安, 张杨梅, 苏建军 2014 西北工业大学学报 32 882]
[18] He H, Li J, Petre S 2012 Waveform Design for Active Sensing Systems: A Computational Approach (Cambridge: Cambridge Univ. Press) pp18-25
[19] Zhang Y M 2017 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [张杨梅 2017 博士学位论文 (西安: 西北工业大学)]
[20] Guo H W, Liang D N, Wang Y, Huang X T, Dong Z 2003 Proceedings of the 2003 International Society for Optics and Photon. AeroSense Orlando, United States, April 21-25, 2003 p1
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[1] North D O 1963 Proc. IEEE 51 1016
[2] Liu Z L, Liao G S, Yang Z W 2012 Acta Electron. Sin. 40 799(in Chinese) [刘志凌, 廖桂生, 杨志伟 2012 电子学报 40 799]
[3] Zhang L, Sheng J L, Duan J, Xing M D, Qiao Z J, Bao Z 2013 EURASIP J. Adv. Signal Process. 2013 33
[4] Dong Q, Zhang L, Xu G, Xing M D 2014 J. Xian Jiaotong Univ. 48 107(in Chinese) [董祺, 张磊, 徐刚, 邢孟道 2014 西安交通大学学报 48 107]
[5] Carlson B D, Evans E D, Wilson S L 1994 IEEE Trans. Aerosp. Electron. Syst. 30 102
[6] Carlson B D, Evans E D, Wilson S L 1994 IEEE Trans. Aerosp. Electron. Syst. 30 109
[7] Pang C S, Hou H L, Han Y 2012 J. Electron. Infor. Technol. 34 754(in Chinese) [庞存锁, 侯慧玲, 韩焱 2012 电子与信息学报 34 754]
[8] Yu J, Xu J, Peng Y N, Xia X G 2012 IEEE Trans. Aerosp. Electron. Syst. 47 1186
[9] Yu J, Xu J, Peng Y N, Xia X G 2012 IEEE Trans. Aerosp. Electron. Syst. 47 2473
[10] Yu J, Xu J, Peng Y N, Xia X G 2012 IEEE Trans. Aerosp. Electron. Syst. 48 991
[11] Xu J, Xia X G, Peng S B, Yu J, Peng Y N, Qian L C 2012 IEEE Trans. Sig. Proc. 60 6190
[12] Perry R P, Dipietro R C, Kozma A, Vaccaro J J 1994 Algorithms for Synthetic Aperture Radar Imagery (Bellingham: SPIE) p160
[13] Perry R P, Dipietro R C, Fante R L 1999 IEEE Trans. Aerosp. Electron. Syst. 35 188
[14] Ruan H, Wu Y H, Jia X, Ye W 2013 IEEE Geo. Rem. Sens. Lett. 11 128
[15] Zhao Y B, Zhou X P, Wang J 2013 J. Xidian Univ. Nat. Sci. 40 98(in Chinese) [赵永波, 周晓佩, 王娟 2013 西安电子科技大学学报自然科学版 40 98]
[16] Guo B F, Shang C X, Wang J L, Gao M G, Fu X J 2014 Acta Phys. Sin. 63 238406(in Chinese) [郭宝锋, 尚朝轩, 王俊岭, 高梅国, 傅雄军 2014 63 238406]
[17] Feng X A, Zhang Y M, Su J J 2014 J. Northwest. Polytechnical Univ. 32 882(in Chinese) [冯西安, 张杨梅, 苏建军 2014 西北工业大学学报 32 882]
[18] He H, Li J, Petre S 2012 Waveform Design for Active Sensing Systems: A Computational Approach (Cambridge: Cambridge Univ. Press) pp18-25
[19] Zhang Y M 2017 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [张杨梅 2017 博士学位论文 (西安: 西北工业大学)]
[20] Guo H W, Liang D N, Wang Y, Huang X T, Dong Z 2003 Proceedings of the 2003 International Society for Optics and Photon. AeroSense Orlando, United States, April 21-25, 2003 p1
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