Generalized Coprime Sampling of Toeplitz Matrices for Spectrum Estimation

Increased demand on spectrum sensing over a broad frequency band requires a high sampling rate and thus leads to a prohibitive volume of data samples. In some applications, e.g., spectrum estimation, only the second-order statistics are required. In this case, we may use a reduced data-sampling rate by exploiting a low-dimensional representation of the original high-dimensional signals. In particular, the covariance matrix can be reconstructed from compressed data by utilizing its specific structure, e.g., the Toeplitz property. Among a number of techniques for compressive covariance sampler design, the coprime sampler is considered attractive because it enables a systematic design capability with a significantly reduced sampling rate. In this paper, we propose a general coprime sampling scheme that implements effective compression of Toeplitz covariance matrices. Given a fixed number of data samples, we examine different schemes on covariance matrix acquisition for performance evaluation, comparison, and optimal design, based on segmented data sequences.