Multi-rate coprime sampling for frequency estimation with increased degrees of freedom

Abstract

For frequency estimation, the recently proposed coprime sampling scheme receives increasing interest as it reduces sampling rate and exhibits high degrees of freedom. However, the virtual coarray generated by coprime configuration is a linear virtual array structure with some missing elements. This leads to information loss if only the contiguous part of the virtual coarray is used. In this paper, we propose a new approach to fix this problem. A multi-rate coprime sampling mechanism is designed to fill all the holes in the classical coprime virtual coarray. This is achieved by constructing new virtual coarrays containing the hole elements which can be selected to fill all the holes in the original virtual coarray. Furthermore, by properly setting the multi-rate coefficients to positive integers, our approach allows to reuse some samples obtained with the classical coprime sampling configuration. The closed-form expression of the positions of the holes is also given, which can be used to choose the appropriate multi-rate coefficients. Simulation results show that the proposed approach can increase the degrees of freedom without requiring additional samples. The estimation accuracy is also improved because our proposed approach fully exploits the information from the available samples.