Bit Efficient Toeplitz Covariance Estimation

Hongwei Xu; Zai Yang

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arXiv · 2412.12678

Bit Efficient Toeplitz Covariance Estimation

Hongwei Xu·Zai Yang

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Abstract

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic error bounds and analyze the convergence rates of the proposed estimator. Our results show that the estimator is near-optimal and imply that reducing data resolution within a certain range has a limited impact on the estimation accuracy. Numerical experiments are provided that validate our theoretical findings and show effectiveness of the proposed estimator.

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BibTeX RIS

Hongwei Xu, Zai Yang. 2024-12-17. Bit Efficient Toeplitz Covariance Estimation. https://arxiv.org/abs/2412.12678

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