The challenge of achieving high-precision direction-of-arrival (DOA) estimation with enhanced degrees of freedom (DOFs) under a limited number of physical array elements remains a critical issue in array signal processing. To address this limitation, this paper makes the following three key contributions: (1) a novel moving sparse array synthesis model incorporating time-frequency-spatial joint processing for coprime frequencies signal sources; (2) an optimized coprime frequencies-based unmanned aerial vehicle array (CF-UAVA) configuration with derived closed-form expressions for the distribution of synthesized array; and (3) two DOA estimation methods: a group sparsity-based approach universally applicable to the proposed aperture synthesis model and a joint group sparsity and virtual array interpolation tailored for the proposed CF-UAVA configuration. Comprehensive simulation results demonstrate the superior DOA estimation accuracy and increased DOFs achieved by our proposed aperture synthesis model and DOA estimation algorithms compared to conventional approaches.

This paper presents an innovative aperture synthesis strategy for moving sparse arrays with coprime frequencies, effectively integrating array motion and frequency diversity to significantly enhance the virtual array aperture. The proposed synthesis method achieves a substantial increase in virtual array elements compared to existing sparse array aperture synthesis techniques. A closed-form expression for the distributions of the synthetic virtual array is derived to characterize its structural properties. Building on this foundation, a direction-of-arrival (DOA) estimation method is developed within a group sparse framework, effectively leveraging the phase differences induced by coprime frequencies. Simulation results demonstrate that the proposed method outperforms existing aperture synthesis techniques in both DOA estimation accuracy and achievable degrees of freedom (DOFs), highlighting its superiority for high-resolution array signal processing.