In this paper, physical layer authentication based on the estimated channel state information (CSI) over the subcarriers of wireless orthogonal frequency division multiplexing (OFDM) systems has been studied to provide reliable and augmented authentication solutions for wireless communication devices. The binary hypothesis test with channel-discriminative functions that are based on measuring the difference between channel features and CSI profile clustering is investigated. A comprehensive performance evaluation for the considered channel-discriminative functions in frequency-selective fading channels is presented. Simulation results demonstrated that the security performance depends on the channel frequency selectivity. The decision metrics that measure the difference between the channel features demonstrated improved performance with the increase of channel variation over the subcarriers. In contrast, the CSI profile clustering method exhibited significant degradation in the performance for moderate and severe frequency selectivity conditions. Therefore, for the clustering method the channel fingerprint should be extracted from the neighboring subcarriers, while in other methods the channel features should be extracted from disjoint pilots in order to optimize the security performance over frequency-selective channels.