Designing a suitable measurement matrix for reconstruction of radar targets using compressive sensing

Document Type : Original Article

Authors

1 Master, Department of Telecommunication Electrical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran

2 Assistant Professor, Department of Telecommunications, Urmia University, Urmia, Iran

3 Associate Professor, Department of Telecommunications, Urmia University, Urmia, Iran

Abstract

Using of compressive sensing in radar systems caused to eliminate the matched filter from receiver, and to reduce the required receiver analog-to-digital conversion bandwidth in radar systems. One of compressive sensing parameters is measurement matrix. Measurement matrix for radar systems is usually random matrix. Although exact recovery of signal using random matrices is possible with high probability and this matrix is incoherent with every basis matrix but implementation of that is impossible in practice. So it is useful to use deterministic matrices as measurement matrix. One of these matrices is Alltop matrix that obtained from Alltop sequence. There are limitations in use of this matrix for compressive sensing. We not only will resolve These limitations in this article but also will present a suitable alternative for matched filter block based on compressive sensing that has better performance in comparison to matched filter and can reconstruct radar targets with lower error than matched filter.

Keywords

References

[1]     M. Rossi, A. M. Haimovich, and Y. C. Eldar, "Spatial compressive sensing for MIMO radar," IEEE Trans. Signal Process., vol. 62, no. 2, p. 419–430, Jan. 2014.##
[2]     M. F. Duarte and Y. C. Eldar, "Structured compressed sensing: From theory to applications," IEEE Trans. Signal Process., vol. 59, no. 9, p. 4053–4085, Sep. 2011.##
[3]     X. Tan, W. Roberts, J. Li, and P. Stoica, "Sparse learning via iterative minimization with application to MIMO radar imaging," IEEE Trans. Signal Process., vol. 59, no. 3, pp. 1088-1101, Mar. 2011.##
[4]     L. Anitori, A. Maleki, M. Otten, R. G. Baraniuk, and P. Hoogeboom, "Design and analysis of compressed sensing radar detectors," IEEE Trans. Signal Process., vol. 61, no. 4, pp. 813-827, 2013.##
[5]     R. Baraniuk and P. Steeghs, "Compressive radar imaging," in IEEE National Radar Conference - Proceedings, pp. 128-133, 2007.##
[6]     C. Knill, B. Schweizer, S. Sparrer, F. Roos, R. F. H. Fischer, and C. Waldschmidt, "High Range and Doppler Resolution by Application of Compressed Sensing Using Low Baseband Bandwidth OFDM Radar," IEEE Trans. Microw. Theory Tech., vol. 66, no. 7, pp. 3535-3546, Jun. 2018.##
[7]     D. Cohen, Y. C. Eldar, and A. M. Haimovich, "SUMMeR: Sub-Nyquist MIMO Radar," IEEE Trans. Signal Process., vol. 66, no. 16, p. 4315–4330, Aug 2018.##
[8]     Y. Yu, A. P. Petropulu, and H. V. Poor, "CSSF MIMO radar: Compressive-sensing and stepfrequency based MIMO radar," IEEE Trans. Aerosp. Electron. Syst., vol. 48, no. 2, p. 1490–1504, 2012.##
[9]     E. Giusti, D. Cataldo, A. Bacci, S. Tomei, and M. Martorella, "ISAR image resolution enhancement: Compressive sensing versus state-of-the-art super-resolution techniques," IEEE Trans. Aerosp. Electron. Syst., vol. 54, no. 4, p. 1983–1997, Aug 2018.##
[10]  M. H. Aghababaee, M. F. Sabahi, A. R. Forouzan, "Moving Target Detection in Stepped Frequency Radars using Compressive Sensing," Journal of Radar, vol. 4, no. 3, pp. 15-31, 2016 (In Pesian).##
[11]  E. J. Candès, J. Romberg, T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on information theory, vol. 52, no. 2, pp. 489-509, 2006.##
[12]  M. A Herman, T. Strohmer, "High-resolution radar via compressed sensing," IEEE transactions on signal processing, vol. 57, no. 6, pp. 2275-2284, 2009.##
[13]  W. Alltop, "Complex sequences with low periodic correlations (Corresp.)," IEEE Transactions on Information Theory, vol. 26, no. 3, pp. 350 - 354, May 1980.##
[14]  Y. Gu, N. A. Goodman and A. Ashok, "Radar Target Profiling and Recognition Based on TSI-Optimized Compressive Sensing Kernel," in IEEE Transactions on Signal Processing, vol. 62, no. 12, pp. 3194-3207, June 2014.##
[15]  L. C. Potter, E. Ertin, J. T. Parker, and M. Çetin, "Sparsity and compressed sensing in radar imaging," Proc. IEEE, vol. 97, no. 6, p. 1006–1020, 2010.##
[16]  S. Kingsley and Sh. Quegan, Understanding radar systems, SciTech Publishing, 1999.##
[17]  B. R. Mahafza, Radar signal analysis and processing using MATLAB, Chapman and Hall CRC, 2009.##
[18]  D. L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289 - 1306, April 2006.##
[19]  S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic Decomposition by Basis Pursuit," SIAM J. Sci Comp., vol. 20, no. 1, pp. 33-61, 1999.##
[20]  E. Candes and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n," Ann. Statist., vol. 35, no. 6, pp. 2313-2351, 2007.##
[21]  J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, p. 2231–2242, Oct. 2004.##
[22]  J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, "Beyond Nyquist: Efficient sampling of sparse bandlimited signals," IEEE Trans. Inf. Theory, vol. 56, no. 1, p. 520– 544, Jan. 2010.##
[23]  Y. Yu, A. P. Petropulu, and H. V. Poor, "MIMO radar using compressive sampling," IEEE J. Sel. Top. Signal Process., vol. 4, no. 1, p. 146–163, Feb. 2010.##
[24]  Y. Gu, N. A. Goodman, "Information-Theoretic Compressive Sensing Kernel Optimization and Bayesian Cramér–Rao Bound for Time Delay Estimation," IEEE Transactions on Signal Processing, vol. 65, no. 17, pp. 4525 - 4537, Sept. 2017.##
[25]  Y. Yu, A. P. Petropulu, and H. V. Poor, "Measurement matrix design for compressive sensing based MIMO radar," IEEE Trans. Signal Process., vol. 59, no. 11, p. 5338–5352, Nov 2011.##
[26]  E. Cand`es and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol. 23, no. 3, 2007.##
[27]  S. Foucart and H. Rauhut, A mathematical introduction to compressive sensing, Birkhäuser Basel, 2013.##
[28]  S. Khwaja and J. Ma, "Applications of compressed sensing for sar moving-target velocity estimation and image compression," in IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 8, p. 2848–2860, 2011.##
[29]  L. Zhao, L. Wang, G. Bi, and L. Yang, "An autofocus technique for high-resolution inverse synthetic aperture radar imagery," IEEE Trans. Geosci. Remote Sens., vol. 52, no. 10, p. 6392–6403, 2014.##
[30]  L. Zhang et al., "Resolution enhancement for inversed synthetic aperture radar imaging under low SNR via improved compressive sensing," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 10, p. 3824–3838, Oct. 2010.##
[31]  J. Yang, J. Thompson, X. Huang, T. Jin, and Z. Zhou, "Random-frequency SAR imaging based on compressed sensing," IEEE Trans. Geosci. Remote Sens., vol. 51, no. 2, p. 983–994, 2013.##
[32]  Q. Huang, L. Qu, B. Wu, and G. Fang, "UWB through-wall imaging based on compressive sensing," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 3 PART2, pp. 1408-1415, 2010.##
Radar
Volume 8, Issue 2 - Serial Number 24
February 2021
Pages 21-30

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History

  • Receive Date: 04 August 2020
  • Revise Date: 06 February 2021
  • Accept Date: 27 February 2021
  • Publish Date: 21 December 2020

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