This work contributes to the virtualization of the physical layer of wireless communication protocols, with focus on LTE. It describes the implementation of the uplink receiver side symbol processing functions of LTE at the base station physical layer, using a general-purpose computer equipped with a GPU. We describe the system components and the functions parallelization needed to make the virtualization process compatible with real-time operation, showing the bottlenecks of a software solution to make the LTE physical layer run on general purpose computers. Our validation experiments with a worst-case LTE frame scenario show the feasibility of the CPU/GPU approach. Moreover, since LTE uses common techniques with other wireless protocols, the presented results can also guide other virtualization efforts.