LOW SNR TRESHOLD IN RAPID ESTIMATORS OF COMPLEX SINUSOIDALS

Igor Djurovic, Vladimir V. Lukin

Abstract


A task of estimation of complex sinusoid frequency is considered. A particular but practically important case of low signal-to-noise ratio (SNR) is studied. The low SNR threshold, commonly overlooked in development of the rapid estimator of complex sinusoidals, is addressed. Signals of different length are considered and SNR is varied in wide limits. It is demonstrated that a simple interpolation with factor 2 lowers the SNR threshold by 1.5dB for the most complicated practical situations. Further interpolation does not bring any improvement. This allows proposing a compromise practical algorithm that provides accuracy close to the limit and is still very simple and fast.

Keywords


DFT, frequency estimators, SNR threshold.

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References


Rife, D., Boorstyn, R. Single tone parameter estimation from discrete-time observations. IEEE Transactions on Information Theory, 1974, vol. 20, no. 5, pp. 591-598. doi: 10.1109/TIT.1974.1055282.

Quinn, B. G. Estimating frequency by interpolation using Fourier coefficients. IEEE Transactions on Signal Processing, 1994, vol. 42, no. 5, pp. 1264-1268. doi: 10.1109/78.295186.

Quinn, B. G., Hannan, E. J. The estimation and tracking of frequency. Cambridge University Press, 2001, pp. 180-185.

Quinn, B. G. Estimation of frequency, amplitude, and phase from the DFT of a time series. IEEE Transactions on Signal Processing, 1997, vol. 45, pp. 814-817. doi: 10.1109/78.558515.

Candan, C. A method for fine resolution frequency estimation from three DFT samples. IEEE Signal Processing Letters, 2011, vol. 18, pp. 351 -354. doi: 10.1016/j.sigpro.2014.01.012.

Candan, C. Fine resolution frequency estimation from three DFT samples: Case of windowed data. Signal Processing, 2015, vol. 114, pp. 245-250. doi: 10.1109/LSP.2016.2564102.

Yang, C., Wei, W. A noniterative frequency estimator with rational combination of three spectrum lines. IEEE Transactions on Signal Processing, 2011, vol. 59, no. 10, pp. 5065-5070. doi: 10.1109/TSP.2011.2160257.

Zakharov, Y. V., Baronkin, V. M., Tozer, T. C. DFT-based frequency estimators with narrow acquisition range. IEEE Proceedings Communications, 2001, vol. 148, no. 1, pp. 1-7. doi: 10.1049/ip-com:20010060.

Provencher, S. Esimation of complex singletone parameters in the DFT domain. IEEE Transactions on Signal Processing, 2010, vol. 58, pp. 3879-3883. doi: 10.1109/TSP.2010.2046693.

Aboutanios, E., Mulgrew, B. Iterative frequency estimation by interpolation on Fourier coefficients. IEEE Transactions on Signal Processing, 2005, vol. 53, no. 4, pp. 1237-1242. doi: 10.1109/TSP.2005.843719.

Aboutanios, E. Generalised DFT-based estimators of the frequency of a complex exponential in noise. Proc. of Image and Signal Processing (CISP), 2010, vol. 6, pp. 2998 -3002. doi: 10.1109/CISP.2010.5647526.

Aboutanios, E. Estimation of the frequency and decay factor of a decaying exponential in noise. IEEE Transactions on Signal Processing, 2010, vol. 58, no. 2, pp. 501-509. doi: 10.1109/TSP.2009.2031299.

Djurovi´c, I. Estimation of the sinusoidal signal frequency based on the marginal median DFT. IEEE Transactions on. Signal Processing, 2007, vol. 55, no. 5, pp. 2043-2051. doi: 10.1109/TSP.2007.893211.

Djurovi´c, I., Lukin, V. V. Estimation of singletone signal parameters by using the L-DFT. Signal Processing, 2007, vol. 87, no. 6, pp. 1537-1544. doi: 10.1016/j.sigpro.2006.12.017.

Djukanovi´c, S., Djurovi´c, I. Robust M-periodogram with dichotomous search. Signal Processing, 2011, vol. 91, no. 10, pp. 2410-2414. doi: 10.1016/j.sigpro.2011.04.011.

Djukanovi´c, S. An accurate method for frequency estimation of a real sinusoid. IEEE Signal Processing Letters, 2016, vol. 23, no. 7, pp. 915-918. doi: 10.1109/LSP.2016.2564102.

Djurovi´c, I. Rapid frequency estimators in wireless sensor networks. IEEE Sensors Journal, 2016, vol. 16, no. 13, pp. 5337 – 5343. doi: 10.1109/JSEN.2016.2561976.

Aboutanios, E. Estimating the parameters of sinusoids and decaying sinusoids in noise. IEEE Instrumentation & Measurement Magazine, 2011, vol. 14, no. 2, pp. 8-14. doi: 10.1109/MIM.2011.5735249.

Quinn, B. G. Recent advances in rapid frequency estimation. Digital Signal Processing, 2009, vol. 19, no. 6, pp. 942-948. doi: 10.1016/j.dsp.2008.04.004.

Koski, A. E. Rapid Frequency Estimation, PhD Thesis, Worcester Polytechnic Institute, 2006. 148 p.

Quinn, B. G., Kootsookos, P. J. Threshold behavior of the maximum likelihood estimator of frequency. IEEE Transactions on Signal Processing, 1994, vol. 42, no. 11, pp. 3291-3294. doi: 10.1109/78.330402.

Knockaert, L. The Barankin bound and threshold behavior in frequency estimation. IEEE Transactions on Signal Processing, 1997, vol. 45, no. 9, pp. 2398 - 2401. doi: 10.1109/78.622965.

Sekhar, S.-C., Sreenivas, T. V. Signal to noise ratio estimation using higher order moments. Signal Processing, 2006, vol. 86, pp. 716-732. doi: 10.1016/j.sigpro.2005.06.002.




DOI: https://doi.org/10.32620/reks.2016.2.03

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