Bit-Efficient Toeplitz Covariance Estimation

This paper addresses the problem of estimating Toeplitz covariance matrices from partial entries of randomly quantized samples. To balance the trade-offs among the number of samples, the number of observed entries per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic upper and lower bounds for the proposed estimator, and analyze the corresponding convergence rates. Our results characterize how sparse observation and coarse quantization affect the performance of the proposed estimator and suggest that reducing data resolution within a certain range has limited impact on estimation accuracy. Numerical experiments are provided to validate the theoretical findings.