Abstract
The frequency estimation of multiple complex sinusoids in the presence of noise is important for many signal processing applications. As already discussed in the literature, this problem can be reformulated as a sparse representation problem. In this letter, such a formulation is derived and an algorithm based on sparse cyclic coordinate descent (SCCD) for estimating the frequency parameters is proposed. The algorithm adaptively reduces the size of the used frequency grid, which eases the computational burden. Simulation results revealed that the proposed algorithm achieves similar performance to the original formulation and the Root-multiple signal classification (MUSIC) algorithm in terms of the mean square error (MSE), with significantly less complexity.
Highlights
Parametric frequency estimation has been an active research area for many years.As a consequence, several methods have been proposed in the literature for addressing this problem
two-step iterative shrinkage/thresholding (TwIST) is an interesting approach based on the iterative shrinkage/thresholding (IST) algorithm that was originally proposed for image restoration, but we can notice that its performance for the simulated scenario of frequency estimation was inferior to Root-multiple signal classification (MUSIC) and the proposed method
We proposed an adaptive algorithm based on sparse cyclic coordinate descent (SCCD) for the frequency estimation problem that requires significantly less computational effort than its basic version
Summary
Parametric frequency estimation has been an active research area for many years. As a consequence, several methods have been proposed in the literature for addressing this problem. The proposed method is an extension of the sparse cyclic coordinate descent (SCCD) algorithm that significantly reduces the complexity further, allowing for efficient hardware implementations even for a large number of measurements. Convex optimization methods have very good performance guarantees, which make them a reliable tool for sparse signal recovery but with the drawback that these methods typically have a higher computational cost for large-scale problems Iterative approaches such as sparse cyclic coordinate descent (SCCD) [21] were introduced for solving these problems. The main idea of the proposed method is to effectively reduce the size of the grid (i.e., to reduce the number of columns of the matrix A) for estimating the frequency parameters This will allow one to reduce the computational complexity, and subsequently the number of required mathematical operations in comparison to the original formulation. The proposed method achieves similar performance to the Root-MUSIC algorithm, but with significantly less computational complexity
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