Given the wide deployment of IPSec/VPN (Virtual Private Networks) technology, there might be a redundancy in security protection in some configurations. Various commercial companies have replaced 802.11 security with IPSec/VPN to protect the wireless LAN (Local Area Network). How to do it in an efficient and lightweight way is a challenging research problem. This paper introduces a new lightweight identity authentication protocol, SOLA (Statistical One-bit Lightweight Authentication), for access control well suited for IEEE 802.11 networks with IP connections. This protocol prevents unauthorized access on a per packet basis. Since SOLA only adds one identity bit to each packet it will have a low impact on the network bandwidth and power consumption. The performance and efficiency of the SOLA protocol together with IEEE 802.11 is analyzed and evaluated via simulation.