Phased Array Calibration based on Rotating-Element Harmonic Electric-Field Vector with Time Modulation

2025-04-17

AI Summary

Conventional calibration methods for phased arrays suffer from amplitude-phase mismatch among antenna elements and are highly sensitive to intrinsic phase errors of high-precision phase shifters. Method: This paper proposes a time-sequential modulation calibration technique based on Rotating Harmonic Electric-field Vectors (RHEV), employing only two 1-bit phase shifters operating in periodic switching mode. By precisely controlling the temporal offset between their switching sequences, the method manipulates the phase of the +1st-order harmonic while inherently resolving amplitude ambiguity. Contribution/Results: It replaces physical phase tuning with temporal delay, eliminating phase shifter–induced errors; leverages the element-uniqueness of the +1st-order harmonic to achieve array-size-independent, stable calibration. Numerical simulations and over-the-air (OTA) measurements validate substantial improvements in amplitude-phase calibration accuracy, reduced hardware complexity, and lower system error. The method demonstrates excellent robustness and scalability across arrays of diverse sizes.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Calibration is crucial for ensuring the performance of phased array since amplitude-phase imbalance between elements results in significant performance degradation. While amplitude-only calibration methods offer advantages when phase measurements are impractical, conventional approaches face two key challenges: they typically require high-resolution phase shifters and remain susceptible to phase errors inherent in these components. To overcome these limitations, we propose a Rotating element Harmonic Electric-field Vector (RHEV) strategy, which enables precise calibration through time modulation principles. The proposed technique functions as follows. Two 1-bit phase shifters are periodically phase-switched at the same frequency, each generating corresponding harmonics. By adjusting the relative delay between their modulation timings, the phase difference between the $+1$st harmonics produced by the two elements can be precisely controlled, utilizing the time-shift property of the Fourier transform. Furthermore, the +1st harmonic generated by sequential modulation of individual elements exhibits a linear relationship with the amplitude of the modulated element, enabling amplitude ambiguity resolution. The proposed RHEV-based calibration method generates phase shifts through relative timing delays rather than physical phase shifter adjustments, rendering it less susceptible to phase shift errors. Additionally, since the calibration process exclusively utilizes the $+1$st harmonic, which is produced solely by the modulated unit, the method demonstrates consistent performance regardless of array size. Extensive numerical simulations, practical in-channel and over-the-air (OTA) calibration experiments demonstrate the effectiveness and distinct advantages of the proposed method.

Problem

• Calibrate phased arrays with amplitude-phase imbalance issues
• Overcome phase shifter limitations in calibration methods
• Enable precise calibration using time modulation principles

Innovation

• Uses time modulation for precise calibration
• Employs 1-bit phase shifters with harmonics
• Controls phase via relative timing delays