volume | PIER Journals

Abstract

Space borne accurate emitter localization has become an important and indispensable part of electronic warfare (EW) systems. In this paper, a system-level approach to design space borne receiver for accurate localization of long range co-channel radars (e.g. a network of similar surveillance radars) is presented. Due to the wide frequency range of modern radar signals, the receiver should have wide instantaneous bandwidth and requires high sampling rate analog-to-digital converters (ADCs). To address this issue, we propose a receiver structure with an appropriate sub-Nyquist sampling scheme and fast sparse recovery algorithm. The proposed sub-Nyquist sampler employs a three dimensional uniform linear array (ULA), followed by a modulated wideband converter (MWC). To accurately estimate the location of the co-channel radars from sub-Nyquist samples, a novel quad-tree variational Bayesian expectation maximization (QVBEM) algorithm is proposed. The QVBEM algorithm minimizes the computational load and grid mismatch error by iteratively narrowing the search area. This is done by smart grid refinement around radars' locations. To evaluate the performance of the proposed receiver, location finding of pulsed radars is studied through numerical simulations in various scenarios. The results show that the proposed QVBEM method has a significantly lower estimation error than conventional deterministic and Bayesian approaches, with a reasonably computational complexity.

1. Bond, P. R., "Space defense," Jane’s Space Systems and Industry 2011-2012, 27th Edition, 97-109, MPG Books Group, Surrey, UK, 2011. Google Scholar

2. Handbook of Space Technology, 1st Ed., 236-268, John Wiley & Sons Ltd., West Susex, UK, 2009.

3. Curtis, H. D., "Satellite attitude dynamics," Orbital Mechanics for Engineering Students, 3rd Edition, 543-617, Butterworth-Heinemann, 2013. Google Scholar

4. Donoho, D., "Compressed sensing," IEEE Trans. Inform. Theory, Vol. 52, No. 4, 1289-1306, Apr. 2006.
doi:10.1109/TIT.2006.871582 Google Scholar

5. Zhang, Z., Y. Xu, J. Yang, X. Li, and D. Zhang, "A survey of sparse representation: Algorithms and applications," IEEE Access, Vol. 3, 490-530, May 2015.
doi:10.1109/ACCESS.2015.2430359 Google Scholar

6. Mishra, A. K. and R. S. Verster, "Compressive sensing: Acquisition and recovery," Compressive Sensing Based Algorithms for Electronic Defense, 1st Edition, 33-60, Springer, 2017. Google Scholar

7. Ciuonzo, D., G. Romano, and R. Solimene, "Performance analysis of time-reversal MUSIC," IEEE Trans. Signal Process., Vol. 63, No. 10, 2650-2662, 2015.
doi:10.1109/TSP.2015.2417507 Google Scholar

8. Devaney, A. J., "Time reversal imaging of obscured targets from multistatic data," IEEE. Trans. Antennas. Propag., Vol. 53, 1600-1610, May 2005.
doi:10.1109/TAP.2005.846723 Google Scholar

9. Ciuonzo, D. and P. Salvo Rossi, "Noncolocated time reversal MUSIC: High-SNR distribution of null spectrum," IEEE Signal Proc. Lett., Vol. 24, No. 4, 397-401, 2017.
doi:10.1109/LSP.2017.2661246 Google Scholar

10. Ciuonzo, D., "On time-reversal imaging by statistical testing," IEEE Signal Proc. Lett., Vol. 24, No. 7, 1024-1028, Jul. 2017.
doi:10.1109/LSP.2017.2704612 Google Scholar

11. Eldar, Y. C. and G. Kutyniok, "Xampling: Compressed sensing of analog signals," Compressed Sensing: Theory and Applications, 88-147, Cambridge University Press, UK, 2012. Google Scholar

12. Sharma, S. K., E. Lagunas, S. Chatzinotas, and B. Ottersten, "Application of compressive sensing in cognitive radio communications: A survey," IEEE Commun. Survey & Tutorials, Vol. 18, No. 3, 1838-1860, Feb. 2016.
doi:10.1109/COMST.2016.2524443 Google Scholar

13. Salari, S., I. M. Kim, F. Chan, and S. Rajan, "Blind compressive-sensing-based electronic warfare receiver," IEEE Trans. Aerospace and Electronic Systems, Vol. 53, No. 4, 2014-2030, Aug. 2017.
doi:10.1109/TAES.2017.2680686 Google Scholar

14. Ramezani, E., M. F. Sabahi, and S. M. Saberali, "Joint frequency and two-dimensional direction of arrival estimation for electronic support systems based on sub-Nyquist sampling," IET Radar, Sonar & Navigation, Vol. 12, No. 8, 889-899, Apr. 2018.
doi:10.1049/iet-rsn.2017.0477 Google Scholar

15. Yaghobi, M., M. Lexa, F. Millioz, and E. Davies, "A low complexity sub-Nyquist sampling system for wideband radar ESM receivers," Proc. IEEE Int. Conf. Acoust., Speech, Sig. Proc. (ICASSP), Florence, Italy, 2014. Google Scholar

16. Rajan, S. and C. Wu, "An overview of compressive sensing-based receivers,", Technical Report, TR2013-149, Defense Research and Development Canada, Ottawa, Canada, Nov. 2013. Google Scholar

17. Lin, E., "Compressed sensing for electronic radio frequency receiver: Detection, sensitivity, and implementation,", Ph.D. Dissertation, Dep. Elect. Eng., Wright State Univ., Dayton, OH, USA, 2016. Google Scholar

18. Streetly, M., Jane’s Radar and Electronic Warfare Systems 2011-2012, 23rd Ed., lhs Jane’s, Coulsdon, UK, 2011.

19. Sabahi, M. F., M. Masoumzadeh, and A. R. Forouzan, "Frequency-domain wideband compressive spectrum sensing," IET Communications, Vol. 10, No. 13, 1655-1664, 2016.
doi:10.1049/iet-com.2015.0718 Google Scholar

20. Mishali, M. and Y. C. Eldar, "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE J. Sel. Top. Signal Process., Vol. 4, No. 2, 375-391, 2010.
doi:10.1109/JSTSP.2010.2042414 Google Scholar

21. Yang, E., X. Yan, and K. Qin, "Modulated wideband converter with run length limited sequences," IEICE Electron. Exp., Vol. 13, No. 17, 20160670, Sep. 2016.
doi:10.1587/elex.13.20160670 Google Scholar

22. Stein, S., O. Yair, D. Cohen, and Y. C. Eldar, "CaSCADE: Compressed carrier and DOA estimation," IEEE Trans. Process., Vol. 65, No. 10, 2645-2658, 2017.
doi:10.1109/TSP.2017.2664054 Google Scholar

23. Liu, L. and P. Wei, "A simplified sub-Nyquist receiver architecture for joint DOA and frequency estimation,", arXiv preprint arXiv:1604.05037v2, Feb. 2017. Google Scholar

24. Kumar, A. A., S. G. Razul, and C. M. S. See, "Carrier frequency and direction of arrival estimation with nested sub-Nyquist sensor array receiver," Proc. 23rd Eur. Signal Process. Conf. (EUSIPCO), 1167-1171, Aug. 2015.
doi:10.1109/EUSIPCO.2015.7362567 Google Scholar

25. Anal Kumar, A., S. G. Razul, and C. M. S. See, "Spectrum blind reconstruction and direction of arrival estimation of multi-band signals at sub-Nyquist sampling rates," Multidim. Syst. Sig. Proc., Vol. 29, No. 2, 643-669, Apr. 2018.
doi:10.1007/s11045-016-0455-7 Google Scholar

26. Chen, T., L. Liu, and D. Pan, "A ULA-based MWC discrete compressed sampling structure for carrier frequency and AOA Estimation," IEEE Access, Vol. 5, 14154-14164, 2017.
doi:10.1109/ACCESS.2017.2730223 Google Scholar

27. Liu, L. and P. Wei, "Joint DOA and frequency estimation with sub-Nyquist sampling for more sources than sensors," IET Radar Sonar Navig., Vol. 11, No. 12, 1798-1801, 2017.
doi:10.1049/iet-rsn.2017.0086 Google Scholar

28. Foucart, F. and H. Rauhut, "Sparse solutions of underdetermined systems," A Mathematical Introduction to Compressive Sensing, 1st Edition, 41-59, Springer, 2013. Google Scholar

29. Muthukrishnan, S., "Data streams: Algorithms and applications, foundations and trends," Theoretical Computer Science, Now Publishers, Boston, MA, 2005. Google Scholar

30. Ji, S., Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., Vol. 56, No. 6, 2346-2356, Jun. 2008.
doi:10.1109/TSP.2007.914345 Google Scholar

31. Tipping, M. E., "Sparse Bayesian learning and relevance vector machine," J. Mach. Learn. Res., Vol. 1, 211-244, 2001. Google Scholar

32. Tzikas, D. G., A. C. Likas, and N. P. Galatsanos, "The variational approximation for Bayesian inference," IEEE Signal Process. Mag., Vol. 25, No. 6, 131-146, Nov. 2008.
doi:10.1109/MSP.2008.929620 Google Scholar

33. Lundgren, M., L. Svensson, and L. Hammarstrand, "Variational Bayesian expectation maximization for radar map estimation," IEEE Trans. Signal Process., Vol. 64, No. 6, 1391-1404, Mar. 2016.
doi:10.1109/TSP.2015.2496287 Google Scholar

34. Byeon, M., M. Lee, K. Kim, and J. Y. Choi, "Variational inference for 3-D localization and tracking of multiple cameras," IEEE Trans. Neural Netw. and Learn. Syst., Vol. 99, 1-15, Jan. 2019. Google Scholar

35. Arjoune, Y., N. Kaabouch, H. El Ghazi, and A. Tamtaoui, "Compressive sensing: Performance comparison of sparse recovery algorithms," 2017 IEEE 7th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, Jan. 2017. Google Scholar

36. Chi, Y., A. Pezeshki, L. Scharf, and R. Caderbank, "Sensitivity to basis mismatch in compressed sensing," IEEE Trans. Signal Process., Vol. 59, No. 5, 2182-2195, May 2011.
doi:10.1109/TSP.2011.2112650 Google Scholar

37. Tang, G., B. N. Bhaskar, P. Shah, and B. Recht, "Compressed sensing off the grid," IEEE Trans. Inform. Theory, Vol. 59, No. 11, 7465-7490, Nov. 2013.
doi:10.1109/TIT.2013.2277451 Google Scholar

38. Lu, Z., R. Ying, S. Jiang, P. Liu, and W. Yu, "Distributed compressed sensing off the grid," IEEE Signal Proc. Lett., Vol. 22, No. 1, 105-109, Jan. 2015.
doi:10.1109/LSP.2014.2349904 Google Scholar

39. Yang, Z., L. Xie, and C. Zhang, "Off-grid direction of arrival estimation using sparse Bayesian inference," IEEE Trans. Signal Process., Vol. 61, 38-43, 2013.
doi:10.1109/TSP.2012.2222378 Google Scholar

40. Das, A. and T. J. Sejnowski, "Narrowband and wideband off-grid direction-of-arrival estimation via sparse Bayesian learning," IEEE J. Ocean. Eng., Vol. 3, No. 1, 108-118, Jan. 2018.
doi:10.1109/JOE.2017.2660278 Google Scholar

41. Samet, H. and R. A. Earnshaw, "An overview of quadtrees octrees and related hierarchical data structures," Theoretical Foundations of Computer Graphics and CAD, Vol. 40, Springer, Berlin, Germany, 1988. Google Scholar

42. Donoho, D. L., Y. Tsaig, I. Drori, and J. L. Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Trans. Inform. Theory, Vol. 58, No. 2, 1094-1121, 2012.
doi:10.1109/TIT.2011.2173241 Google Scholar

Dr. Esmaeil Ramezani

Dr. Mohammad Farzan Sabahi

Dr. Seyyed Mohammad Saberali