Cramér-Rao Bound of Joint DOA-Range Estimation for Coprime Frequency Diverse Arrays

Abstract

Frequency diverse array (FDA) produces a beampattern with controllable direction and range by slightly shifting the carrier frequencies across the elements, which is attractive in many applications. By further incorporating coprime array structure and coprime frequency offsets, improved degrees-of-freedom and spatial/range resolutions have been achieved. For such a relatively new array configuration, theoretical performance analyses are essential to explore the potentials and to facilitate practical implementation. In this work, we consider coprime-FDA-based joint/separate angle-range estimation of far-field targets that exhibit two different types of Swerling fluctuation behavior, which are respectively modelled as deterministic and stochastic sources. Analytical expressions of the Cramér–Rao bounds (CRB) and numerical simulations for both cases are provided. The results reveal that the relationship between CRB and coprime FDA parameters is not simply monotonic. As shown in the numerical simulations, the CRB of coprime FDA outperforms that of uniform FDA-MIMO for more than 60% under commonly-adopted coprime patterns. The presented results can be used as a guideline for optimal design of coprime FDA.

Keywords

• Cramér–Rao bound (CRB)
• direction of arrival (DOA)
• parameter estimation
• coprime array
• frequency diverse array (FDA)