A Measurement Method for the Phase Difference of Coherently Combined Distributed Apertures

Coherently Combined Distributed Apertures (CCDAs) offer a promising approach to achieve high-resolution sensing through coordinated small-aperture elements. Accurate phase difference measurement between distributed apertures remains a fundamental challenge—especially for practical scenarios of large-spacing CCDAs in compact measurement environments. This paper proposes a phase difference measurement methodology for CCDA systems, comprising a specialized multi-probe receiving system and a computational algorithm. The multi-probe receiving system employs three receiving antennas with optimized spatial spacing to capture coherently combined signals. Concurrently, the computational algorithm establishes a linear equation system that correlates the coherently combined signals’ powers with the phase difference between distributed apertures, enabling phase estimation via low-complexity computation. Notably, the measurement process operates without requiring any parameter adjustment to the distributed apertures, thereby preserving system operation. Theoretical accuracy of the proposed method is clarified through mathematical derivations while considering both thermal noise and circuit imperfections, and analyzed through Monte Carlo simulations. Measurement experiments of a CCDA prototype are conducted and the results indicate that the proposed method is feasible and accurate. The measured phase errors are constrained within ±7.2°, and 95% of cases are below ±5°. This advancement enhances the practicality of distributed aperture systems in real-time applications such as phased array radar and millimeter-wave communications.