DOA Estimation Using Compressive Sensing Based on DFT Measurement Matrix

Document Type : Original Article

Authors

1 Electrical Engineering Department, Shahed University

2 Electrical Engineering department, Shahed University

Abstract

In this paper, a new method is proposed to estimate the direction of arrival (DOA) using non-uniform linear array structure and modeling the measurement matrix as a DFT matrix. In order to estimate the DOA using compressive sensing (CS), continuous angle space should be divided into a discrete set using small steps. This division, leads to the increment of mutual coherence between columns of the measurement matrix and performance of the sparse recovery algorithms is degraded. To solve this problem, we propose a new method in which DFT matrix with mutual coherence of zero is used as the measurement matrix. In order to increase the accuracy of estimation, the size of DFT matrix or the number of antennas should be increased. Implementation of an array with large number of antennas is complex and expensive. A solution to decrease the number of antennas is using a non-uniform linear array and constructing a virtual uniform linear array. A virtual uniform linear array can be constructed by vectorizing the correlation matrix of the received signal of a non-uniform linear array. Increasing the number of antennas in the virtual array will increase the size of DFT matrix. Therefore, the accuracy of DOA estimation will be increased. Simulation results show that DOA estimation using compressive sensing, based on DFT measurement matrix, has a good performance in terms of mean square error of estimation.

Keywords

References

   [1]      H. Krim and M. Viberg, ‘‘Two Decades of Array Signal Processing Research: The Parametric Approach,’’ IEEE Signal Processing Magazine, vol. 13, no. 4, pp. 67–94, 1996.
   [2]      H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory. New York, NY, USA: Wiley, 2002.
   [3]      T. E. Tuncer and B. Friedlander, Classical and Modern Direction-of-Arrival Estimation. New York, NY, USA: Academic, 2009.
   [4]      J. Li, D. Li, D. Jiang and X. Zhang, “Extended-Aperture Unitary Root MUSIC-Based DOA Estimation for Coprime Array,” IEEE Communications Letters, vol. 22, no. 4, pp. 752-755, 2018.
   [5]      J. Kim and C. S. Sin, “Impact of Mutual Coupling on Performance of DoA Estimation using MUSIC,” 2018 International Conference on Information and Communication Technology Convergence (ICTC), 2018, pp. 460-462.
   [6]      R. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation,” IEEE Transactions Antennas and Propagation, vol. 34, no. 3, pp. 276–280, 1986.
   [7]      D. Zhang, Y. Zhang, G. Zheng, C. Feng and J. Tang, “Improved DoA Estimation Algorithm for Co-Prime Linear Arrays Using Root-MUSIC Algorithm,” Electronics Letters, vol. 53, no. 18, pp. 1277-1279, 2017.
   [8]      G. Liu, H. Chen, X. Sun and R. C. Qiu, “Modified MUSIC Algorithm for DoA Estimation with Nyström Approximation,” IEEE Sensors Journal, vol. 16, no. 12, pp. 4673-4674, 2016.
   [9]      J. Capon, “High-Resolution Frequency-Wavenumber Spectrum Analysis,” Proceedings of the IEEE, vol. 57, no. 8, pp. 1408-1418, 1969.
[10]      X. Zhang, Z. He, B. Liao, X. Zhang and W. Peng, “Robust Quasi-Adaptive Beamforming Against Direction-of-Arrival Mismatch,” IEEE Transactions on Aerospace and Electronic Systems, vol. 54, no. 3, pp. 1197-1207, June 2018.
[11]      X. Wang, and M. Amin, “Design of Optimum Sparse Array for Robust MVDR Beamforming Against DoA Mismatch,” 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 1-5, 2017.
[12]      L. Lu and H. C. Wu, “Novel Robust Direction-of-Arrival-Based Source Localization Algorithm for Wideband Signals,” IEEE Transactions on Wireless Communications, vol. 11, no. 11, pp. 3850-3859, 2012.
[13]      L. Lu and H. C. Wu, “Robust Expectation–Maximization Direction-of-Arrival Estimation Algorithm for Wideband Source Signals,” IEEE Transactions on Vehicular Technology, vol. 60, no. 5, pp. 2395-2400, 2011.
[14]      L. Lu, H. C. Wu and S. C. H. Huang, “Robust Novel EM-Based Direction-of-Arrival Estimation Technique for Wideband Source Signals,” International Conference on Communications and Mobile Computing, pp. 72-76, 2010.
[15]      I. Ziskind and M. Wax, “Maximum Likelihood Localization of Multiple Sources by Alternating Projection,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, no. 10, pp. 1553–1560, 1988.
[16]      Tie-Jun Shan, M. Wax and T. Kailath, “On Spatial Smoothing for Direction-of-Arrival Estimation of Coherent Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, no. 4, pp. 806-811, August 1985.
[17]      R. Muhamed and T.S. Rappaport, “Direction of Arrival Estimation Using Antenna Arrays,” Tech. Rep. MPRG-TR96-03, Virginia Tech, Blacksburg, VA, 1996.
[18]      D. Malioutov, M. Cetin and A. S. Willsky, “A Sparse Signal Reconstruction Perspective for Source Localization with Sensor Arrays,” IEEE Transactions on Signal Processing, vol. 53, no. 8, pp. 3010-3022, 2005.
[19]      C. Zhou, Y. Gu, Y. D. Zhang, Z. Shi, T. Jin and X. Wu, “Compressive Sensing-Based Coprime Array Direction-of-Arrival Estimation,” IET Communications, vol. 11, no. 11, pp. 1719-1724, 2017.
[20]      X. Yang, C. C. Ko and Z. Zheng, “Direction-of-Arrival Estimation of Incoherently Distributed Sources Using Bayesian Sompressive Sensing,” IET Radar, Sonar & Navigation, vol. 10, no. 6, pp. 1057-1064, 2016.
[21]      M. Hawes, L. Mihaylova, F. Septier and S. Godsill, “Bayesian Compressive Sensing Approaches for Direction of Arrival Estimation with Mutual Coupling Effects,” IEEE Transactions on Antennas and Propagation, vol. 65, no. 3, pp. 1357-1368, 2017.
[22]      Q. Shen, W. Liu, W. Cui and S. Wu, “Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review,” IEEE Access, vol. 4, pp. 8865-8878, 2016.
[23]      B. Lin, J. Liu, M. Xie and J. Zhu, “Direction-of-Arrival Tracking via Low-Rank Plus Sparse Matrix Decomposition,” IEEE Antennas and Wireless Propagation Letters, vol. 14, pp. 1302-1305, 2015.
[24]      Z. Yang, J. Li, P. Stoica, and L. Xie, “Sparse Methods for Direction-of-Arrival Estimation,” arXiv:1609.09596, 2016.
 [25]      M. Elad, Sparse and Redundant Representations, From Theory to Applications in Signal and Image Processing, Springer, 2010.
[26]      Z. Shi, C. Zhou, Y. Gu, N. A. Goodman and F. Qu, “Source Estimation Using Coprime Array: A Sparse Reconstruction Perspective,” IEEE Sensors Journal, vol. 17, no. 3, pp. 755-765, 2017.
[27]      D. L. Donoho, and M. Elad, “Optimally Sparse Representation in General (nonorthogonal) Dictionaries via ℓ1 Minimization,” Proceedings of the National Academy of Sciences, vol. 100, no. 5, pp. 2197-2202, 2003.
[28]      G. Xu and Z. Xu, “Compressed Sensing Matrices from Fourier Matrices,” IEEE Transactions on Information Theory, vol. 61, no. 1, pp. 469-478, 2015.
[29]      S. Qin, Y. D. Zhang and M. G. Amin, “Generalized Coprime Array Configurations for Direction-of-Arrival Estimation,” IEEE Transactions on Signal Processing, vol. 63, no. 6, pp. 1377-1390, 2015.
[30]      Z. He, Z. Shi, L. Huang and H. C. So, “Underdetermined DOA Estimation for Wideband Signals Using Robust Sparse Covariance Fitting,” IEEE Signal Processing Letters, vol. 22, no. 4, pp. 435-439, 2015.
[31]      M. Yangg, A. M. Haimovich, B. Chen and X. Yuan, “A New Array Geometry for DOA Estimation with Enhanced Degrees of Freedom,” IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, pp. 3041-3045, 2016.
[32]      P. Pal and P. P. Vaidyanathan, “Coprime Sampling and the MUSIC Algorithm,” Proc. IEEE Digit. Signal Process. Workshop and IEEE Signal Process. Educ. Workshop (DSP/SPE), pp. 289–294, 2011.

Files

History

  • Receive Date: 31 January 2019
  • Revise Date: 05 April 2019
  • Accept Date: 17 May 2019
  • Publish Date: 07 October 2019

Share

How to cite

Statistics