Performance analysis for frequency diverse coprime array and difference coarray: from Cramér-Rao bound viewpoint

By extending the coprime array structure and coprime frequency offsets to frequency diverse arrays (FDAs), the designed frequency diverse coprime array (FDCA) utilizes the concept of virtual difference coarray to improve the degrees of freedom (DoF) and spatial/distance resolution. Nevertheless, it is essential to investigate the theoretical performance bounds of this relatively new array configuration. In this work, we investigate the Cramér-Rao Bounds (CRBs) for joint Direction of Arrival (DoA) and range estimation in FDCA. By considering the Fisher information corresponding to the parameters to be estimated in both the physical array and virtual difference coarray signals, we derive closed-form solutions for the CRB in the physical domain and Slepian-Bangs form for the CRB in the virtual domain. Simulation results indicate that transforming the signal from physical to the virtual domain enhances DoF without sacrificing theoretical detection accuracy.