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Atomic Norm-Based DOA Estimation with Sum and Difference Co-arrays in Coexistence of Circular and Non-circular Signals

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Abstract

Sparse arrays can increase the array aperture and degrees of freedom through the construction of either sum or difference co-arrays or both. In order to exploit the advantages of sparse arrays while estimating directions of arrival (DOAs) of a mixture of circular and non-circular signals, in this paper, a gridless DOA estimation method is proposed by employing a recently introduced enhanced nested array, whose virtual arrays have no holes. The virtual signals derived from both sum and difference co-arrays are constructed based on atomic norm minimization. It is shown that the proposed method also works when the circular and non-circular signals come from the same set of directions. Simulation results are provided to demonstrate the performance of the proposed method.

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Data Availability Statement

The data included in this study may be available upon reasonable request by contacting with the corresponding author.

References

  1. B.N. Bhaskar, G. Tang, B. Recht, Atomic norm denoising with applications to line spectral estimation. IEEE Trans. Signal Process. 61(23), 5987–5999 (2013). https://doi.org/10.1109/TSP.2013.2273443

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Cai, W. Liu, R. Zong, B. Wu, Sparse array extension for non-circular signals with subspace and compressive sensing based doa estimation methods. Signal Process. 145, 59–67 (2018). https://doi.org/10.1016/j.sigpro.2017.11.012

    Article  Google Scholar 

  3. H. Chen, C. Hou, W. Liu, W.P. Zhu, M.N.S. Swamy, Efficient two-dimensional direction-of-arrival estimation for a mixture of circular and noncircular sources. IEEE Sens. J. 16(8), 2527–2536 (2016). https://doi.org/10.1109/JSEN.2016.2517128

    Article  Google Scholar 

  4. H. Chen, C. Hou, W.P. Zhu, W. Liu, Y. Dong, Q. Wang, Joint diagonalization based 2d doa estimation for mixed circular and strictly noncircular sources. in 2017 IEEE Radar Conference (RadarConf), pp. 0001–0005 (2017). https://doi.org/10.1109/RADAR.2017.7944160

  5. H. Chen, C. Hou, W.P. Zhu, W. Liu, Y.Y. Dong, Z. Peng, Q. Wang, Esprit-like two-dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization. Signal Process. 141, 48–56 (2017). https://doi.org/10.1016/j.sigpro.2017.05.024

    Article  Google Scholar 

  6. H. Chen, W. Wang, W. Liu, Joint doa, range, and polarization estimation for rectilinear sources with a cold array. IEEE Wirel. Commun. Lett. 8(5), 1398–1401 (2019). https://doi.org/10.1109/LWC.2019.2919542

    Article  Google Scholar 

  7. X. Chen, X. Zhang, J. Yang, M. Sun, How to overcome basis mismatch: From atomic norm to gridless compressive sensing. Acta Autom. Sin. 42(3), 335–346 (2016). https://doi.org/10.16383/j.aas.2016.c150539

    Article  Google Scholar 

  8. P. Chevalier, A. Blin, Widely linear mvdr beamformers for the reception of an unknown signal corrupted by noncircular interferences. IEEE Trans. Signal Process. 55(11), 5323–5336 (2007)

    Article  MathSciNet  Google Scholar 

  9. R. Cohen, Y.C. Eldar, Sparse convolutional beamforming for ultrasound imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65(12), 2390–2406 (2018). https://doi.org/10.1109/TUFFC.2018.2874256

    Article  Google Scholar 

  10. F. Gao, A. Nallanathan, Y. Wang, Improved music under the coexistence of both circular and noncircular sources. IEEE Trans. Signal Process. 56(7), 3033–3038 (2008). https://doi.org/10.1109/TSP.2007.916123

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Guo, Y.D. Zhang, T. Chen, Doa estimation using compressed sparse array. IEEE Trans. Signal Process. 66(15), 4133–4146 (2018). https://doi.org/10.1109/TSP.2018.2847645

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Liu, G Liao, Q. Xu, C. Zeng, A circularity-based doa estimation method under coexistence of noncircular and circular signals, in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2561–2564 (2012). https://doi.org/10.1109/ICASSP.2012.6288439

  13. C. Liu, P. Vaidyanathan, Super nested arrays: lnear sparse arrays with reduced mutual coupling-part ii: High-order extensions. IEEE Trans. Signal Process. 64(16), 4203–4217 (2016). https://doi.org/10.1109/TSP.2016.2558167

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling-part i: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016). https://doi.org/10.1109/TSP.2016.2558159

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Liu, P.P. Vaidyanathan, P. Pal, Coprime coarray interpolation for doa estimation via nuclear norm minimization. in 2016 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2639–2642 (2016). https://doi.org/10.1109/ISCAS.2016.7539135

  16. C.L. Liu, P. Vaidyanathan, Cramér-rao bounds for coprime and other sparse arrays, which find more sources than sensors. Digital Signal Process. 61, 43–61 (2017). https://doi.org/10.1016/j.dsp.2016.04.011. Special Issue on Coprime Sampling and Arrays

  17. Z. Liu, Z. Huang, Y. Zhou, J. Liu, Direction-of-arrival estimation of noncircular signals via sparse representation. IEEE Trans. Aerosp. Electron. Syst. 48(3), 2690–2698 (2012). https://doi.org/10.1109/TAES.2012.6237619

    Article  Google Scholar 

  18. M. Lustig, D.L. Donoho, J.M. Santos, J.M. Pauly, Compressed sensing mri. IEEE Signal Process. Mag. 25(2), 72–82 (2008). https://doi.org/10.1109/MSP.2007.914728

    Article  Google Scholar 

  19. P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010). https://doi.org/10.1109/TSP.2010.2049264

    Article  MathSciNet  MATH  Google Scholar 

  20. B. Picinbono, P. Chevalier, Widely linear estimation with complex data. IEEE Trans. Signal Process. 43(8), 2030–2033 (1995)

    Article  Google Scholar 

  21. G. Qin, M.G. Amin, Y.D. Zhang, Doa estimation exploiting sparse array motions. IEEE Trans. Signal Process. 67(11), 3013–3027 (2019)

    Article  MathSciNet  Google Scholar 

  22. S. Qin, Y.D. Zhang, M.G. Amin, Generalized coprime array configurations for direction-of-arrival estimation. IEEE Trans. Signal Process. 63(6), 1377–1390 (2015). https://doi.org/10.1109/TSP.2015.2393838

    Article  MathSciNet  MATH  Google Scholar 

  23. A. Raza, W. Liu, Q. Shen, Thinned coprime array for second-order difference co-array generation with reduced mutual coupling. IEEE Trans. Signal Process. 67(8), 2052–2065 (2019). https://doi.org/10.1109/TSP.2019.2901380

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Roy, T. Kailath, Esprit-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989). https://doi.org/10.1109/29.32276

    Article  MATH  Google Scholar 

  25. R. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986). https://doi.org/10.1109/TAP.1986.1143830

    Article  Google Scholar 

  26. Q. Shen, W. Liu, W. Cui, S. Wu, Y.D. Zhang, M.G. Amin, Low-complexity direction-of-arrival estimation based on wideband co-prime arrays. IEEE ACM Trans. Audio Speech Lang. Process. 23(9), 1445–1456 (2015). https://doi.org/10.1109/TASLP.2015.2436214

    Article  Google Scholar 

  27. J. Steinwandt, F. Roemer, M. Haardt, G. Del Galdo, Deterministic cramér-rao bound for strictly non-circular sources and analytical analysis of the achievable gains. IEEE Trans. Signal Process. 64(17), 4417–4431 (2016). https://doi.org/10.1109/TSP.2016.2566603

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Steinwandt, F. Roemer, M. Haardt, G.D. Galdo, R-dimensional esprit-type algorithms for strictly second-order non-circular sources and their performance analysis. IEEE Trans. Signal Process. 62(18), 4824–4838 (2014). https://doi.org/10.1109/TSP.2014.2342673

    Article  MathSciNet  MATH  Google Scholar 

  29. P. Stoica, E.G. Larsson, A.B. Gershman, The stochastic crb for array processing: a textbook derivation. IEEE Signal Process. Lett. 8(5), 148–150 (2001). https://doi.org/10.1109/97.917699

    Article  Google Scholar 

  30. G. Tang, B.N. Bhaskar, P. Shah, B. Recht, Compressed sensing off the grid. IEEE Trans. Inf. Theory 59(11), 7465–7490 (2013). https://doi.org/10.1109/TIT.2013.2277451

    Article  MathSciNet  MATH  Google Scholar 

  31. L. Teng, Q. Wang, H. Chen, W. Zhu, W. Liu, J. Cai, Doa estimation for coexistence of circular and non-circular signals based on atomic norm minimization, in 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 1–5 (2020). https://doi.org/10.1109/SAM48682.2020.9104368

  32. P.P. Vaidyanathan, P. Pal, Sparse sensing with co-prime samplers and arrays. IEEE Trans. Signal Process. 59(2), 573–586 (2011). https://doi.org/10.1109/TSP.2010.2089682

    Article  MathSciNet  MATH  Google Scholar 

  33. Q. Wang, X. Wang, H. Chen, X. Zhu, W. Liu, W. Yan, L. Wang, An effective localization method for mixed far-field and near-field strictly non-circular sources. Digital Signal Process. 94, 125–136 (2019). https://doi.org/10.1016/j.dsp.2019.06.003. Special Issue on Source Localization in Massive MIMO

  34. X. Wang, Z. Chen, S. Ren, S. Cao, Doa estimation based on the difference and sum coarray for coprime arrays. Digital Signal Process. 69, 22–31 (2017). https://doi.org/10.1016/j.dsp.2017.06.013. http://www.sciencedirect.com/science/article/pii/S1051200417301276

  35. X. Wang, L. Wan, M. Huang, C. Shen, K. Zhang, Polarization channel estimation for circular and non-circular signals in massive mimo systems. IEEE J. Select. Top. Signal Process. 13(5), 1001–1016 (2019). https://doi.org/10.1109/JSTSP.2019.2925786

    Article  Google Scholar 

  36. X. Wu, W.P. Zhu, J. Yan, A toeplitz covariance matrix reconstruction approach for direction-of-arrival estimation. IEEE Trans. Veh. Technol. 66(9), 8223–8237 (2017). https://doi.org/10.1109/TVT.2017.2695226

    Article  Google Scholar 

  37. X. Wu, W.P. Zhu, J. Yan, A high-resolution doa estimation method with a family of nonconvex penalties. IEEE Trans. Veh. Technol. 67(6), 4925–4938 (2018). https://doi.org/10.1109/TVT.2018.2817638

    Article  Google Scholar 

  38. X. Wu, W.P. Zhu, J. Yan, Gridless two-dimensional doa estimation with l-shaped array based on the cross-covariance matrix, in 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3256–3260 (2018). https://doi.org/10.1109/ICASSP.2018.8461481

  39. Z. Zheng, Y. Huang, W.Q. Wang, H.C. So, Direction-of-arrival estimation of coherent signals via coprime array interpolation. IEEE Signal Process. Lett. 27, 585–589 (2020). https://doi.org/10.1109/LSP.2020.2982769

    Article  Google Scholar 

  40. Z. Zheng, S. Mu, Two-dimensional doa estimation using two parallel nested arrays. IEEE Commun. Lett. 24(3), 568–571 (2020). https://doi.org/10.1109/LCOMM.2019.2958903

    Article  Google Scholar 

  41. Z. Zheng, W. Wang, Y. Kong, Y.D. Zhang, Misc array: a new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect. IEEE Trans. Signal Process. 67(7), 1728–1741 (2019). https://doi.org/10.1109/TSP.2019.2897954

    Article  MathSciNet  MATH  Google Scholar 

  42. C. Zhou, Y. Gu, X. Fan, Z. Shi, G. Mao, Y.D. Zhang, Direction-of-arrival estimation for coprime array via virtual array interpolation. IEEE Trans. Signal Process. 66(22), 5956–5971 (2018). https://doi.org/10.1109/TSP.2018.2872012

    Article  MathSciNet  MATH  Google Scholar 

  43. C. Zhou, Y. Gu, S. He, Z. Shi, A robust and efficient algorithm for coprime array adaptive beamforming. IEEE Trans. Veh. Technol. 67(2), 1099–1112 (2018). https://doi.org/10.1109/TVT.2017.2704610

    Article  Google Scholar 

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Acknowledgements

This work is sponsored by the National Natural Science Foundation of China under Grant Nos. 61871282 and 62001256, the Key Laboratory of Intelligent Perception and Advanced Control of State Ethnic Affairs Commission under Grant MDIPAC-2019102, and by Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ19F010002.

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Authors and Affiliations

  1. Schcol of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China

    Liping Teng & Qing Wang

  2. Faculty of Information Science and Engineering, Ningbo University, Ningbo, 315211, China

    Hua Chen

  3. Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK

    Wei Liu

  4. Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, H3G 1M8, Canada

    Wei-Ping Zhu

  5. Department of Electronic Engineering, Xidian University, Xi’an, 710071, China

    Jingjing Cai

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  1. Liping Teng
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  3. Hua Chen
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  4. Wei Liu
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Correspondence to Hua Chen.

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Part of the work in this paper has been published by 11th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2020) conference [31]

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Teng, L., Wang, Q., Chen, H. et al. Atomic Norm-Based DOA Estimation with Sum and Difference Co-arrays in Coexistence of Circular and Non-circular Signals. Circuits Syst Signal Process 40, 5033–5053 (2021). https://doi.org/10.1007/s00034-021-01708-7

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