Abstract
Interpolators are widely employed in the frequency estimation of sinusoidal signals. However, for a real-valued sinusoidal signal, the existing interpolators do not consider the negative frequency component, which leads to a frequency estimation error floor. To solve this problem and further improve the estimation accuracy, three new interpolators are proposed in this paper. These three new interpolators consist of two initial interpolators and one fine interpolator. In the proposed algorithm, the initial interpolators consider both the positive and negative frequency components and are utilized first to eliminate this error floor and obtain an initial frequency estimate. Then, the fine interpolator for the frequency estimation of a complex sinusoid is exploited to improve the accuracy of the initial frequency estimate. The theoretical analysis demonstrates that the frequency estimation mean square error of the proposed algorithm is almost equal to the Cramer-Rao lower bound. Compared with the existing time-domain analysis algorithms, the proposed algorithm has better estimation performance, especially in the case of a low signal-to-noise ratio. Compared with the existing frequency-domain analysis algorithms, the proposed algorithm has lower computational complexity and a wider valid estimation range.
Highlights
Frequency estimation for a real valued sinusoid in white noise is a classic problem in many fields, such as wireless communication [1], radar [2] and electric power grids [3]
The algorithm based on principal singular value decomposition (PSVD) in [7] can reach the Cramer-Rao lower bound (CRLB) with a lower signal-tonoise ratio (SNR) compared with weighted linear prediction (WLP)
Since the proposed initial interpolators are designed for a real sinusoid, they are not employed to obtain the initial frequency estimate fhere
Summary
Frequency estimation for a real valued sinusoid in white noise is a classic problem in many fields, such as wireless communication [1], radar [2] and electric power grids [3]. The algorithm based on principal singular value decomposition (PSVD) in [7] can reach the CRLB with a lower SNR compared with WLP As all these algorithms require matrix inversion, the computational complexity is O N 3 , which is very high. In [8], a four-point model-based unitnorm constrained least squares algorithm was proposed This algorithm has a low complexity, but its estimation performance is poor. Many interpolators have been proposed in [9]–[20] for the frequency estimation of a complex sinusoid. The interpolators in all these algorithms do not consider the negative frequency component, which leads to a frequency estimation error floor. A fine interpolator is proposed to further improve the accuracy of the frequency estimate
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