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Quasi ML algorithm for 2-D PPS estimation

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Abstract

The 2-D quasi-maximum likelihood algorithm for estimation of 2-D polynomial phase signals (2-D PPSs) is proposed. Estimation of all phase parameters is performed in an efficient manner using search only over a set of the window widths in the 2-D short-time Fourier transform (STFT). The mean squared error is on the Cramer–Rao lower bound that is big advantage with respect to all existing phase differentiation techniques even for low SNR. The proposed technique consists of two basic stages: rough estimation that is performed using 2-D STFT and fine stage with dechirping, downsampling, filtering, and polynomial interpolation. Obtained results are excellent even for 2-D PPSs of high-order or in the case when modulation is nonpolynomial.

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References

  • Allen, J. B. (1977). Short time spectral analysis, synthesis, and modification by discrete Fourier transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, 25(3), 235–238.

    Article  MATH  Google Scholar 

  • Boashash, B. (Ed.). (2003). Time-frequency signal analysis and applications. Amsterdam: Elsevier.

    MATH  Google Scholar 

  • Barbarossa, S., Di Lorenzo, P., & Vecchiarelli, P. (2014). Parameter estimation of 2-D multi-component polynomial phase signals: An application to SAR imaging of moving targets. IEEE Transactions on Signal Processing, 62(17), 4375–4389.

    Article  MathSciNet  Google Scholar 

  • Barbarossa, S., Scaglione, A., & Giannakis, G. B. (1998). Product high-order ambiguity function for multicomponent polynomial-phase signal modeling. IEEE Transactions on Signal Processing, 46(3), 691–708.

    Article  Google Scholar 

  • Bioucas-Dias, J., Katkovnik, V., Astola, J., & Egiazarian, K. (2008). Absolute phase estimation: Adaptive local denoising and global unwrapping. Applied Optics, 47(29), 5358–5369.

    Article  Google Scholar 

  • Chen, C., & Zebker, H. A. (2000). Network approaches to two-dimensional phase unwrapping: Intractability and two new algorithms. Journal of the Optimal Society of America, 17(3), 401–414.

    Article  Google Scholar 

  • Djukanović, S., & Popović-Bugarin, V. (2012). A parametric method for multicomponent interference suppression in noise radars. IEEE Transactions on Aerospace and Electronic Systems, 48(3), 2730–2738.

    Article  Google Scholar 

  • Djurović, I., Djukanović, S., Amin, M., Zhang, Y., & Himed, B. (2012, April). High-resolution time-frequency representations based on the local polynomial Fourier transform for over-the-horizon radars. In SPIE radar sensor technology conference, Baltimore, MD.

  • Djurović, I., Thayaparan, T., & Stanković, L. J. (2006). Adaptive local polynomial Fourier transform in ISAR. EURASIP Journal on Applied Signal Processing, Article ID 36093.

  • Djurović, I. (2015). On parameters of the QML PPS estimator. Signal Processing, 116, 1–6.

    Article  Google Scholar 

  • Djurović, I., Simeunović, M., Djukanović, S., & Wang, P. (2012). A hybrid CPF-HAF estimation of polynomial-phase signals: Detailed statistical analysis. IEEE Transactions on Signal Processing, 60(10), 5010–5023.

    Article  MathSciNet  Google Scholar 

  • Djurović, I., & Stanković, L. J. (2012). STFT-based estimator of polynomial phase signals. Signal Processing, 92(11), 2769–2774.

    Article  Google Scholar 

  • Djurović, I., & Stanković, L. J. (2014). Quasi maximum likelihood estimator of polynomial phase signals. IET Signal Processing, 13(4), 347–359.

    Article  Google Scholar 

  • Djurović, I., Wang, P., & Ioana, C. (2010). Parameter estimation of 2-D polynomial cubic signals using cubic phase function with genetic algorithms. Signal Processing, 90(9), 2698–2707.

    Article  MATH  Google Scholar 

  • Farquharson, M., & O’Shea, P. (2007). Extending the performance of the cubic phase function algorithm. IEEE Transactions on Signal Processing, 55(10), 4767–4774.

    Article  MathSciNet  Google Scholar 

  • Farquharson, M., O’Shea, P., & Ledwich, G. (2005). A computationally efficient technique for estimating the parameters of polynomial phase signals from noisy observations. IEEE Transactions on Signal Processing, 53(8), 3337–3342.

    Article  MathSciNet  Google Scholar 

  • Francos, J. M., & Friedlander, B. (1998). Two-dimensional polynomial phase signals: Parameter estimation and bounds. Multidimensional Systems and Signal Processing, 9, 173–205.

    Article  MathSciNet  MATH  Google Scholar 

  • Francos, J. M., & Friedlander, B. (1999). Parameter estimation of 2-D random amplitude polynomial-phase signals. IEEE Transactions on Signal Processing, 47(7), 1795–1810.

    Article  MathSciNet  MATH  Google Scholar 

  • Francos, J. M., & Friedlander, B. (1999). Optimal parameter selection in the phase differencing algorithm for 2-D phase estimation. IEEE Transactions on Signal Processing, 47(1), 273–279.

    Article  MATH  Google Scholar 

  • Friedlander, B., & Francos, J. M. (1996). Model based phase unwrapping of 2-D signals. IEEE Transactions Signal Processing, 44(12), 2999–3007.

    Article  Google Scholar 

  • Friedlander, B., & Francos, J. M. (1996). An estimation for 2-D polynomial phase signals. IEEE Transactions Image Processing, 5(6), 1084–1087.

    Article  Google Scholar 

  • Katkovnik, V., Astola, J., & Egiazarian, K. (2008). Phase local approximation (PhaseLa) technique for phase unwrap from noisy data. IEEE Transactions on Image Processing, 17(6), 833–846.

    Article  MathSciNet  Google Scholar 

  • Katkovnik, V., & Stanković, L. J. (1998). Periodogram with varying and data-driven window length. Signal Processing, 67(3), 345–358.

    Article  MATH  Google Scholar 

  • O’Shea, P. (2002). A new technique for instantaneous frequency rate estimation. IEEE Signal Processing Letters, 9(8), 251–252.

    Article  Google Scholar 

  • O’Shea, P. (2004). A fast algorithm for estimating the parameters of a quadratic FM signal. IEEE Transactions on Signal Processing, 52(2), 385–393.

    Article  MathSciNet  Google Scholar 

  • O’Shea, P. (2010). On refining polynomial phase signal parameter estimates. IEEE Transactions on Aerospace and Electronic Systems, 46(3), 978–987.

    Article  Google Scholar 

  • Peleg, S., & Porat, B. (1991). Linear FM signal parameter estimation from discrete-time observations. IEEE Transactions on Aerospace and Electronics Systems, 27(4), 607–614.

    Article  Google Scholar 

  • Porat, B. (1994). Digital processing of random signals: Theory and methods. Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Porat, B., & Friedlander, B. (1996). Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals. IEEE Transactions on Information Theory, 42(3), 995–1001.

    Article  MATH  Google Scholar 

  • Servin, M., Marroquin, J., Malacara, D., & Cuevas, F. (1998). Phase unwrapping with a regularized phase-tracking system. Applied Optics, 37(10), 1917–1923.

    Article  Google Scholar 

  • Sharma, J. J., Gierull, C. H., & Collins, M. J. (2006). The influence of target acceleration on velocity estimation in dual-channel SAR-GMTI. IEEE Transactions on Geoscience and Remote Sensing, 44(1), 134–147.

    Article  Google Scholar 

  • Sharma, J. J., Gierull, C. H., & Collins, M. J. (2006). Compensating the effects of target acceleration in dual-channel SARCGMTI. IEE Proceedings on Radar Sonar Navigation, 153(1), 53–62.

    Article  Google Scholar 

  • Stanković, L. J., Djurović, I., Stanković, S., Simeunović, M., & Daković, M. (2014). Instantaneous frequency in time-frequency analysis: Enhanced concepts and performance of estimation algorithms. Digital Signal Processing, 35, 1–13.

    Article  Google Scholar 

  • Stanković, L. J., Stanković, S., & Djurović, I. (2000). Space/spatial-frequency analysis based filtering. IEEE Transactions on Signal Processing, 48(8), 2343–2352.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, P., Djurović, I., & Yang, J. (2008). Modifications of the cubic phase function. Chinese Journal of Electronics, 17(1), 189–194.

    Google Scholar 

  • Wang, P., Djurović, I., & Yang, J. (2008). Generalized high-order phase function for parameter estimation of polynomial phase signal. IEEE Transactions on Signal Processing, 56(7), 3023–3028.

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This research is supported in part by Ministry of science of Montenegro through National Project “Intelligent search techniques for parametric estimation in communication and power engineering” and EU FP7 Project Foremont.

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  1. Faculty of Electrical Engineering, University of Montenegro, Podgorica, 81000, Montenegro

    Igor Djurović

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  1. Igor Djurović
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Correspondence to Igor Djurović.

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Djurović, I. Quasi ML algorithm for 2-D PPS estimation. Multidim Syst Sign Process 28, 371–387 (2017). https://doi.org/10.1007/s11045-015-0344-5

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