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In order to improve the secure access ability of LoRa terminals, this paper presents a physical layer-based authentication system for security enhancement. Different from the security access technology of cryptography, a lightweight gateway architecture called LW-LoRaWAN is proposed to realize a data frame-based authentication with radio frequency fingerprint (RFF). A novel RFF feature of Cross Power Spectral Density (CPSD) is used to achieve a fast authentication with one single frame. Theoretical analysis and experimental results show that the proposed system not only reinforces the authentication security of LoRa network but also protects the LoRa terminals against the Sybil attacks. 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