Phase Synchronization Error Calibration in Focused Energy Delivery for Precision Electronic Warfare

Phase synchronization errors are unavoidable in focused energy delivery (FED) scenarios, significantly impacting signal coherence and diminishing the effectiveness of spatial power distribution. To address this issue, this paper first conducts a theoretical analysis to demonstrate how phase synchronization errors degrade performance in spatial power control. A beacon-aided calibration framework is then proposed, designed for real-time operation and focused on calibrating phase synchronization errors induced by time synchronization errors. First, a practical calibration model that incorporates multiple non-ideal factors, such as UAV vibrations and oscillator phase noise, is established. However, this model is difficult to solve. To overcome its intractability and improve the calibration accuracy, a multi-stage process is employed to transform the problem into a solvable Quadratically Constrained Quadratic Program (QCQP). An efficient algorithm based on the Majorization-Minimization (MM) method is then utilized to solve the QCQP. To provide a fundamental performance benchmark, the Cramér-Rao Lower Bound (CRLB) is derived. Numerical simulations demonstrate that the proposed framework effectively compensates for phase synchronization errors, yielding significant improvements in spatial power control for FED.