Abstract
In order to estimate the original phase of a sinusoid corrupted by additive noise accurately, this paper proposes a novel phase estimator which based on restricted phase unwrapping and Tretter’s phase estimation algorithm. Using appropriate linear combinations for observed phase, restricted phase unwrapping is easily performed on the basis of the principle of minimum phase error. A formula for evaluating the error probability of restricted phase unwrapping is presented. Simulation results show that the SNR threshold of restricted phase unwrapping method is much lower than that of traditional unwrapping methods, and the estimator derived attains the Cramer–Rao lower bound (CRB) at high SNR, which has better performance than the segmented DFT estimator developed in [10, 13] and the all-phase FFT estimator in [14].
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References
Tretter SA (1985) Estimating the frequency of a noisy sinusoid by linear regression. IEEE Trans Inf Theory 31(6):832–835
Rife DC, Boorstyn RR (1974) Single-tone parameter estimation from discrete-time observations. IEEE Trans Inf Theory 20(5):591–598
Qi G (2004) A new frequency estimator of single sinusoid based on Fitz’s algorithm. In: 7th IEEE international conference on signal processing. IEEE Press, Beijing, pp 1790–1793
Huang X, Deng Z (2009) An improved phase unwrapping algorithm and its application to instantaneous frequency estimation. Acta Electronica Sinica 37(10):2266–2272 (in Chinese)
McKilliam RG, Quinn BG, Clarkson IL et al (2010) Frequency estimation by phase unwrapping. IEEE Trans Signal Process 58(6):2953–2963
Fu H, Kam PY (2012) Sample-autocorrelation-function-based frequency estimation of a single sinusoid in AWGN. In: 75th IEEE vehicular technology conference. IEEE Press, Yokohama, pp 1–5
Kay S (1989) A fast and accurate single frequency estimator. IEEE Trans Acoust Speech Signal Process 37(12):1987–1990
Mengali U, Morelli M (1997) Data-aided frequency estimation for burst digital transmission. IEEE Trans Commun 45(1):23–25
Li X, Xu L, Zhou X (2009) High accuracy complex sinusoid frequency estimator in low SNR environment. J Xidian Univ 36(6):1010–1014 (in Chinese)
Qi G, Jia X (2001) High-accuracy frequency and phase estimation of single-tone based on phase of DFT. Acta Electronica Sinica 29(9):1164–1167 (in Chinese)
Zhan Y, Zhang B, Pan X (2012) Simulation and modification of carrier estimation algorithm based on difference of FFT’s phase. J Syst Simul 24(11):2414–2417 (in Chinese)
Zhu L, Ding H, Ding K (2004) Phase regression approach for estimating the parameters of a noisy multifrequency signal. IEE Proc-Vis Image Signal Process 151(5):411–420
Li J, Wang Y (2009) DFT phase estimation algorithm and noise sensitive frequency region. J Electron Inf Technol 31(9):2099–2103 (in Chinese)
Huang X, Wang Z (2011) Anti-noise performance of all-phase FFT phase measuring method. J Data Acquisition Process 26(3):286–291 (in Chinese)
Zhang T, Ren Z, Chen G et al (2011) Improved spectrum analysis algorithm for all-phase time-shift phase difference. Syst Eng Electron 33(7):1468–1472 (in Chinese)
Dash PK, Hasan S (2011) A fast recursive algotithm for the estimation of frequency, amplitude, and phase of noisy sinusoid. IEEE Trans Industr Electron 58(10):4847–4856
Acknowledgements
This material is based upon project supported by the National Natural Science Foundation of China grant No. 11164008, and the Key Laboratory of Photoelectronics and Telecommunication of Jiangxi Province grant Nos. 2013001 and 2011013.
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Wang, F., Chen, Y., Ye, Z. (2014). A New Phase Estimator of Single Sinusoid by Restricted Phase Unwrapping. In: Wen, Z., Li, T. (eds) Practical Applications of Intelligent Systems. Advances in Intelligent Systems and Computing, vol 279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54927-4_7
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DOI: https://doi.org/10.1007/978-3-642-54927-4_7
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