Edge computing (EC) is an essential component of large-scale intelligent manufacturing systems for Industry 4.0, which promises to provide a preprocessing platform for the massive data generated by the terminals and guarantee lower delay and more security compared to directly processing data in cloud computing. Nevertheless, access authentication is a crucial security issue of current EC systems, and, thus, this article presents a solution to enhance the access classification accuracy by exploiting the physical layer information. Our method employs a weighted voting scheme for channel state information based authentication using a single sample which includes sample segmentation, grouping, and weighted voting and finally achieves the fast and low complexity secure-access requirement of the EC system without increasing the individual devices' sample size and computational complexity. Experimental results utilizing public datasets and field-measured datasets demonstrate that the proposed weighted voting method has higher accuracy and robustness than existing methods.