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A study on off-grid issue in DOA and frequency estimations

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Abstract

This work addresses the off-grid issue for DOA and frequency estimations when the dictionary based sparse signal recovery concept is adopted. By off-grid, we mean that the true values of signal, angles or frequencies in this case, are not exactly on the sampling grid created by utilizing the discrete dictionary technique. To handle this problem, off-grid is remodelled such that it is represented by an offset matrix that is a sparse matrix. And then, a direct estimate of the offset matrix is developed to compensate the off-grid by utilizing the fact that the offset matrix is a sparse matrix. Finally, by exploring the sparse property of DOAs/frequencies and offset matrix, a joint estimation approach is devised under optimization framework. Numerical studies demonstrate the effectiveness of the proposed approach.

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References

  • Bhaskar, B. N., Tang, G., & Recht, B. (2013). Atomic norm denoising with applications to line spectral estimation. IEEE Transactions on Signal Processing, 61(23), 5987–5999.

    Article  MathSciNet  Google Scholar 

  • Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1), 1–122.

    Article  MATH  Google Scholar 

  • Candès, E. J., & Tao, T. (2007). The dantzig selector: Statistical estimation when \(p\) is much larger than \(n\). Annals of Statistics, 35(35), 2313–2351.

    Article  MathSciNet  MATH  Google Scholar 

  • Chi, Y., Scharf, L. L., Pezeshki, A., & Caderbank, A. R. (2011). Sensitivity to basis mismatch in compressed sensing. IEEE Transactions on Signal Processing, 59(5), 2182–2195.

    Article  MathSciNet  Google Scholar 

  • Ding, D., Liu, H. Q., Li, Y., & Zhou, Y. (2015). Frequency estimation with missing measurements. In International conference on estimation, detection and information fusion, Harbin, Heilongjiang, China.

  • Fitz, M. P. (1994). Further results in the fast estimation of a single frequency. IEEE Transactions on Communications, 42(234), 862–864.

    Article  Google Scholar 

  • Herman, M. A., & Strohmer, T. (2010). General deviants: An analysis of perturbations in compressed sensing. IEEE Journal of Selected Topics in Signal Processing, 4(2), 342–349.

    Article  Google Scholar 

  • Kay, S. M. (1998). Fundamentals of statistical signal processing: Estimation theory. Englewood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Kim, D., Narasimha, M., & Cox, D. (1996). An improved single frequency estimator. IEEE Signal Processing Letters, 3(7), 211–214.

    Google Scholar 

  • Krim, H., & Viberg, M. (1996). Two decades of array signal processing research. IEEE Signal Processing Magazine, 13, 67–94.

    Article  Google Scholar 

  • Lank, G. W., Reed, I. S., & Pollon, G. E. (1973). A semicoherent detection and Doppler estimation statistic. IEEE Transactions on Aerospace and Electronic Systems, 9(2), 151–165.

    Article  Google Scholar 

  • Liu, A., Liao, G., Zeng, C., Yang, Z., & Xu, Q. (2011). An eigenstructure method for estimating DOA and sensor gain-phase errors. IEEE Transactions on Signal Processing, 59(12), 5944–5956.

    Article  MathSciNet  Google Scholar 

  • Liu, H. Q., Li, Y., & Truong, T.-K. (2015). Robust sparse signal reconstructions against basis mismatch and their applications. Information Sciences, 316, 1–17.

    Article  MathSciNet  Google Scholar 

  • Lu, Z., Ying, R., Jiang, S., Liu, P., & Yu, W. (2015). Distributed compressed sensing off the grid. IEEE Signal Processing Letters, 22(1), 105–109.

    Article  Google Scholar 

  • Malioutov, D., Cetin, M., & Willsky, A. S. (2005). A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transactions on Signal Processing, 53(8), 3010–3022.

    Article  MathSciNet  Google Scholar 

  • Rife, D. C., & Boorstyn, R. R. (1974). Single tone parameter estimation from discrete-time observations. IEEE Transactions on Information Theory, 20(5), 591–598.

    Article  MATH  Google Scholar 

  • So, H. C., & Chan, F. K. W. (2006). Approximate maximum-likelihood algorithms for two-dimensional frequency estimation of a complex sinusoid. IEEE Transactions on Signal Processing, 54(8), 3231–3237.

    Article  Google Scholar 

  • So, H. C., & Chan, F. K. W. (2006). A generalized weighted linear predictor frequency estimation approach for a complex sinusoid. IEEE Transactions on Signal Processing, 54(4), 1304–1315.

    Article  Google Scholar 

  • So, H. C., Chan, K. W., Chan, Y. T., & Ho, K. C. (2005). Linear prediction approach for efficient frequency estimation of multiple real sinusoids: Algorithms and analyses. IEEE Transactions on Signal Processing, 53(7), 2290–2305.

    Article  MathSciNet  Google Scholar 

  • So, H. C., Chan, F. K. W., Lau, W. H., & Chan, C.-F. (2010). An efficient approach for two-dimensional parameter estimation of a single-tone. IEEE Transactions on Signal Processing, 58(4), 1999–2009.

    Article  MathSciNet  Google Scholar 

  • Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood, and Cramer-Rao bound. IEEE Transactions on Acoustics, Speech and Signal Processing, 37(5), 720–741.

    Article  MathSciNet  MATH  Google Scholar 

  • Tang, G., Bhaskar, B. N., Shah, P., & Recht, B. (2013). Compressed sensing off the grid. IEEE Transactions on Information Theory, 59(11), 7465–7490.

    Article  MathSciNet  Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society Series B, 58(1), 267–288.

    MathSciNet  MATH  Google Scholar 

  • Van Harry, L. (2002). Trees, detection, estimation, and modulation theory, optimum array processing (part IV). New York: Wiley.

    Google Scholar 

  • Zhang, Q. T. (1995). Probability of resolution of the MUSIC algorithm. IEEE Transactions on Signal Processing, 43(4), 978–987.

    Article  Google Scholar 

  • Zhu, W., & Chen, B.-X. (2015). Novel methods of DOA estimation based on compressed sensing. Multidimensional Systems and Signal Processing, 26(1), 113–123.

  • Zhu, H., Leus, G., & Giannakis, G. B. (2011). Sparsity-cognizant total least squares for perturbed compressive sampling. IEEE Transactions on Signal Processing, 59(5), 2002–2016.

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was jointly supported by Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT1299, by the special fund of Chongqing Key Laboratory, by Foundation and Advanced research projects of Chongqing Municipal Science and Technology Commission under Grants cstc2014jcyjA40017, cstc2014jcyjA40027 and cstc2015jcyjA40027, by Science and Technology project of Chongqing Municipal Education Commission under Grants KJ1400425 and KJ130504, by the National Natural Science Foundation of China under Grants 61401050 and 61501072, by the Ministry of Education Scientific Research Foundation for Returned Overseas Chinese F201405, and by National High-tech R&D Program (863 Program, SS2015AA011303).

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Authors and Affiliations

  1. Chongqing Key Lab of Mobile Communications Technology, Chongqing University of Posts and Telecommunications, Chongqing, China

    Hongqing Liu, Luming Zhao, Dongyan Ding & Yong Li

  2. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China

    Yi Zhou

Authors
  1. Hongqing Liu
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  2. Luming Zhao
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  3. Dongyan Ding
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  4. Yong Li
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Correspondence to Hongqing Liu.

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Conflict of interest

Author Hongqing Liu has received research grants from Foundation and Advanced research projects of Chongqing Municipal Science and Technology Commission and Ministry of Education Scientific Research Foundation for Returned Overseas Chinese and China NSF. Author Yong Li has received has received research grants from Foundation and Advanced research projects of Chongqing Municipal Science and Technology Commission and China NSF. Author Yi Zhou has received research grant from Science and Technology project of Chongqing Municipal Education Commission.

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Liu, H., Zhao, L., Ding, D. et al. A study on off-grid issue in DOA and frequency estimations. Multidim Syst Sign Process 28, 735–755 (2017). https://doi.org/10.1007/s11045-015-0372-1

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  • DOI: https://doi.org/10.1007/s11045-015-0372-1

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