Fast and Accurate Spectrum Estimation via Virtual Coarray Interpolation Based on Truncated Nuclear Norm Regularization

Abstract

Compared with the Nyquist sampling scheme, the coprime sampling scheme reduces the requirement of sampling rate significantly and simultaneously shows high degrees of freedom. Actually, the information received by the sampler is not fully utilized due to the non-uniformity of derived second-order virtual coarray. In addition, the virtual signals corresponding to the non-uniform virtual coarray may be contaminated by noise, which could affect the accuracy of spectrum estimation. In this letter, we propose a novel virtual coarray interpolation method for the inexact Toeplitz covariance matrix based on truncated nuclear norm regularization. The missing elements and exact covariance matrix can be obtained simultaneously by solving the covariance matrix completion problem that contains the error term and non-Toeplitz errors propagation control term. Simulation results demonstrate the superiorities of the proposed spectrum estimation method in terms of accuracy and computational complexity.