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Due to the broadcast nature of the wireless medium, wireless networks are especially vulnerable to Sybil attacks, where a malicious node illegitimately claims a large number of identities and thus depletes system resources. We propose an enhanced physical-layer authentication scheme to detect Sybil attacks, exploiting the spatial variability of radio channels in environments with rich scattering, as is typical in indoor and urban environments. We build a hypothesis test to detect Sybil clients for both wideband and narrowband wireless systems, such as WiFi and WiMax systems. Based on the existing channel estimation mechanisms, our method can be easily implemented with low overhead, either independently or combined with other physical-layer security methods, e.g., spoofing attack detection. The performance of our Sybil detector is verified, via both a propagation modeling software and field measurements using a vector network analyzer, for typical indoor environments. Our evaluation examines numerous combinations of system parameters, including bandwidth, signal power, number of channel estimates, number of total clients, number of Sybil clients, and number of access points. For instance, both the false alarm rate and the miss rate of Sybil attacks are usually below 0.01, with three tones, pilot power of 10 mW, and a system bandwidth of 20 MHz.