Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

doi:10.21629/JSEE.2018.01.06

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (1): 58-66.doi: 10.21629/JSEE.2018.01.06

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Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

Shengyao CHEN*(), Feng XI()

School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2017-01-20 Online:2018-02-26 Published:2018-02-23
Contact: Shengyao CHEN E-mail:chenshengyao@njust.edu.cn;xifeng@njust.edu.cn
About author:CHEN Shengyao was born in 1985. He received his B.S. degree in communication engineering and Ph.D. degree in information and communication engineering from Nanjing University of Science and Technology, Nanjing, China, in 2006 and 2013, respectively. He is currently an associate professor in School of Electronic and Optical Engineering, Nanjing University of Science and Technology. His research interests include compressive sensing, radar signal processing and chaotic dynamical systems. E-mail: chenshengyao@njust.edu.cn|XI Feng was born in 1980. He received his B.S. degree in electronic engineering and Ph.D. degree in information and communication engineering from Nanjing University of Science and Technology, Nanjing, China, in 2003 and 2010, respectively. Currently, he is an associate professor in School of Electronic and Optical Engineering, Nanjing University of Science and Technology. His research interests include compressive sensing, radar signal processing, and wireless sensor networks. E-mail: xifeng@njust.edu.cn
Supported by:
the National Natural Science Foundation of China(61401210);the National Natural Science Foundation of China(61571228);This work was supported by the National Natural Science Foundation of China (61401210; 61571228)

Abstract

Abstract:

Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling (CS) pulse-Doppler (CSPD) radar are developed with different analog-to-information conversion (AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound (CRB) for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio (SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.

Key words: compressive sampling (CS), delay-Doppler estimation, Cramer-Rao bound (CRB)

Shengyao CHEN, Feng XI. Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar[J]. Journal of Systems Engineering and Electronics, 2018, 29(1): 58-66.

Figures/Tables 5

References 21

1	DONOHO D L. Compressed sensing. IEEE Trans. on Information Theory, 2006, 52 (4): 1289- 1306. doi: 10.1109/TIT.2006.871582
2	Candès E, ROMBERG J, TAO T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. on Information Theory, 2006, 2006, 52 (2): 489- 509.
3	Candès E J, TAO T. Near-optimal signal recovery from random projections: universal encoding strategies?. IEEE Trans. on Information Theory, 2006, 52 (12): 5406- 5425. doi: 10.1109/TIT.2006.885507
4	HEALY D. Analog-to-information (A-to-I) receiver development program. [2016-12-20]. http://www.federalgrants.com/Analog-to-Information-Receiver-Development-Program-Ato-I-11274.html.
5	TROPP J A, WRIGHT S J. Computational methods for sparse solution of linear inverse problems. Proceedings of the IEEE, 2010, 98 (6): 948- 958. doi: 10.1109/JPROC.2010.2044010
6	BARANIUK R G, STEEGHS P. Compressive radar imaging. Proc. of IEEE Radar Conference, 2007: 128-133.
7	TROPP J A, LASKA J N, DUARTE M F, et al. Beyond Nyquist: efficient sampling of sparse bandlimited signals. IEEE Trans. on Information Theory, 2010, 56 (1): 520- 544. doi: 10.1109/TIT.2009.2034811
8	YOO J, TURNES C, NAKAMURA E B, et al. A compressed sensing parameter extraction platform for radar pulse signal acquisition. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2012, 2 (3): 626- 638. doi: 10.1109/JETCAS.2012.2214634
9	MISHALI M, ELDAR Y C, ELRON A J. Xampling: signal acquisition and processing in union of subspaces. IEEE Trans. on Signal Processing, 2009, 59 (10): 4719- 4734.
10	XI F, CHEN S, LIU Z. Quadrature compressive sampling for radar signals. IEEE Trans. on Signal Processing, 2014, 62 (11): 2787- 2802. doi: 10.1109/TSP.2014.2315168
11	CHEN S, XI F. Quadrature compressive sampling for multiband radar echo signals. IEEE Access, 2017, 5, 19742- 19760. doi: 10.1109/ACCESS.2017.2753826
12	HERMAN M A, STROHMER T. High-resolution radar via compressed sensing. IEEE Trans. on Signal Processing, 2009, 57 (6): 2275- 2284. doi: 10.1109/TSP.2009.2014277
13	TEKE O, GURBUZ A C, ARIKAN O. A robust compressive sensing based technique for reconstruction of sparse radar scenes. Digital Signal Processing, 2014, 27 (4): 23- 32.
14	LIU C, XI F, CHEN S, et al. Pulse-Doppler signal processing with quadrature compressive sampling. IEEE Trans. on Aerospace and Electronic Systems, 2015, 51 (2): 1216- 1230.
15	BAR-ILAN O, ELDAR Y C. Sub-Nyquist radar via Doppler focusing. IEEE Trans. on Signal Processing, 2014, 62 (7): 1795- 181.
16	CHEN S, XI F, LIU Z. A general sequential delay-Doppler estimation scheme for sub-Nyquist pulse-Doppler radar. Signal Processing, 2017, 135, 210- 217. doi: 10.1016/j.sigpro.2017.01.012
17	CHEN S, XI F, LIU Z. A general and yet efficient scheme for sub-Nyquist radar processing. Signal Processing, 2018, 142, 206- 211. doi: 10.1016/j.sigpro.2017.07.018
18	ELDAR Y C, KUTYNIOK G. Compressed sensing: theory and applications. Cambridge: Cambridge University Press, 2012.
19	RICHARDS M A. Fundamentals of radar signal processing. New York: McGraw-Hill, 2005.
20	XI F, CHEN S Y, LIU Z. Quardrature compressive sampling for radar signals: output noise and robust reconstruction. Proc. of IEEE China Summit and International Conference on Signal and Information Processing, 2014: 790-794.
21	STOICA P, MOSES R L. Spectral analysis of signals. Upper Saddle River. NJ: Prentice-Hall, 2005.

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Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

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