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The L-band digital aeronautical communications system (LDACS) is a key enabler of the new air traffic services and operational concepts necessary for the modernization of the air traffic management (ATM). After its initial design, compatibility tests with legacy L-band systems, and functional demonstrations in the laboratory, the system is currently undergoing the standardization process of the International Civil Aviation Organization (ICAO). However, LDACS has not been demonstrated in flight yet. In this article, we present the first in-flight demonstration of LDACS, which took place in March and April 2019 in southern Germany and included four LDACS ground stations and one LDACS airborne station. We detail the experimental setup of the implemented LDACS ground and airborne stations together with the flight routes, the conducted experiments, and the frequency planning to ensure compatibility with legacy systems. In addition, we describe the demonstrated ATM applications and the security measures used to protect them. Based on the obtained measurement results, we evaluate the LDACS in-flight communication performance for the first time, including the achieved communication range, the measured end-to-end message latency, and the LDACS capability to provide quality of service by effectively prioritizing safety-relevant data traffic. Furthermore, we use the in-flight received signal power to assess the applicability of a theoretical path loss model. These flight trials contribute to the final steps in the development of LDACS by providing its in-flight communication performance and by demonstrating: first, its correct functionality in a realistic environment; second, its capability of supporting ATM applications and the advanced security measures that can be used to protect them; and third, its spectrum compatibility with legacy systems. We conclude that LDACS is ready to support ATM operations and that LDACS frequency planning can safeguard legacy systems successfully. [ABSTRACT FROM AUTHOR]