The technology in this application multiplexes transmission associated with multiple users onto the same unsolicited grant service (UGS) radio resource(s) in a packet-based, radio communications system. Normally, the radio resources in a packet-based communications system are dynamically scheduled in response to radio resource requests associated with specific user devices, and the scheduled communications are designed not to use the same radio resource at the same time. However, an unsolicited grant of radio resources for communication between multiple user devices and the packet-based communications system is also established. The communications between those multiple user devices and the packet-based communications system use at least some of the same radio resources associated with the unsolicited grant at the same time. Because of this at least partial radio resource overlap/collision, each of the multiple user's data to be transmitted via the UGS is associated with a user-specific radio resource pattern. A user's radio resource pattern permits a radio receiver to extract that user's data from the received UGS signal that include multiple user transmissions.