  Device-to-Device (D2D) discovery is a key enabler of D2D communications for
the direct exchange of local area traffic between proximity users (UEs) to
improve spectral efficiency. The direct D2D discovery relies on the
capabilities of the D2D UEs to autonomously indicate their presence to
proximity D2D UEs. {Despite} its potential of reducing energy and signalling
burden, the direct D2D discovery {has not drawn adequate attention}. In this
paper, we propose a direct D2D discovery scheme based on the random backoff
procedure, where D2D UEs randomly choose a backoff interval and retransmit a
beacon. Compared with existing schemes, the performance of the proposed scheme
can be significantly enhanced in terms of the discovery probability and the
discovery delay. Several useful guidelines for its design are proposed based on
our analysis. Finally, numerical results provide valuable insights on the
performance tradeoff inherent to the proposed D2D discovery scheme.
