In some embodiments, a user equipment device (UE) implements a method for discovering the presence of neighboring UEs using an on-demand discovery signal transmission technique. This discovery process may be performed to enable the UEs to perform peer-to-peer communications with each other, wherein peer-to-peer communications is defined as direct communication between the UEs without involving a base station. The UE may be configured to transmit a discovery request signal when it has moved greater than a threshold amount since transmission of a prior discovery request signal. The discovery request signal causes one or more neighboring UEs to each transmit a discovery signal in response, and also causes the UE which generated the discovery request signal to transmit its own discovery signal. The received discovery signal from each of the neighboring UEs is useable to discover, or detect the presence of, these neighboring UEs.