Improved algorithm of frequency estimation based on the iterative calculation of the autocorrelation sequence

V. G. Volkov¹ , U. N. Krivov ¹, I. V. Lukyanov ²

¹ OOO "NPP "LAMA", Rybinsk

²Federal State-Financed Educational Institution of High Professional Education "P.A.Solovyov Rybinsk State Aviation Technical University"

The paper is received on October 3, 2016

Abstract. One of the important problems in radio signals processing is the carrier frequency estimation. A review of known statistically efficient methods of frequency estimation is presented. These methods are not computationally efficient for critical to real-time tasks. For this reason, in practice, different methods of complexing are used. This provides acceptable results in practical applications. One of such methods is combining of the iterative procedure of autocorrelation sequence calculation (which provides an increase in the signal to noise ratio) and AR-frequency estimation.

This article presents an improved frequency estimation algorithm based on the iterative calculation of the autocorrelation sequence. The proposed algorithm requires nearly half operations of addition and multiplication. This is achieved by eliminating the inverse fast Fourier transform and the solution of the Yule-Walker equation. First term of autocorrelation sequence is used for frequency estimation. Goertzel algorithm is used for term calculation. A correct length selection rule for zero blocks which fill original signal, has been formulated.

The results of the simulation algorithm are provided. A comparison of the  mean square error with the Cramer-Rao bounds is provided. It is shown that analyzed algorithm provides a statistically efficient frequency estimation for a signal/noise ratio from –3 to 50 dB. This result is achieved by using three iterations and 64 samples number. Obtained empirical curves can be used for optimal selection of  parameters of discussed method for practical applications.

Keywords: frequency estimation, efficient estimator, autocorrelation sequence.

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