The deployment of small-cell base stations in 5G wireless networks is an emerging technology to meet an increasing demand for high data rates of a growing number of heterogeneous devices. The standard algorithms designed for the physical layer communications exhibit security and privacy vulnerabilities. As a 5G network consists of increasingly small cells to improve the throughput, the knowledge of which cell a mobile user communicates to can easily reveal valuable information about the user's location. This paper investigates the location privacy of the access point selection algorithms in 5G mobile networks, and we show that the stable matching of mobile users to access points at the physical layer reveals information related to users' location and their preferences. Traditional location privacy is mainly treated at the application or network layer but the investigation from the physical layer is missing. In this work, we first establish a matching game model to capture the preferences of mobile users and base stations using physical layer system parameters, and then investigate the location privacy of the associated Gale-Shapley algorithm. We develop a differential privacy framework for the physical layer location privacy issues, and design decentralized differential private algorithms to guarantee privacy to a large number of users in the heterogeneous 5G network. Numerical experiments and case studies will be used to corroborate the results.