a kernel-based subspace estimator for frequency super-resolution at quasi-linear time complexity

We introduce two FFT-based ESPRIT algorithms for line spectral estimation which have lower time complexities than the original ESPRIT algorithm’s O(N^3). The preferred method, named FFT-ESPRIT, can be characterized as being a kernel-based subspace estimator that achieves super-resolution at O(N log N) for frequency estimates. First, we demonstrate two estimations of the signal subspace via an integral transformation on the row space of the data matrix and the data matrix itself. The subspace-based methods are approximate in nature, and yet perturbation bounds reveal a noise regime in which FFT-ESPRIT exceeds ESPRIT’s performance. We demonstrate the behavior of the algorithm across different SNR regimes and show that the estimated signal subspace is statistically efficient. Numerical simulations show that FFT-ESPRIT is more robust than the ESPRIT algorithm at the very low SNRs, and has a nearly identical performance as ESPRIT at higher SNRs.

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