  A key feature in the design of any MAC protocol is the throughput it can
provide. In wireless networks, the channel of a user is not fixed but varies
randomly. Thus, in order to maximize the throughput of the MAC protocol at any
given time, only users with large channel gains should be allowed to transmit.
In this paper, compressive sensing based opportunistic protocol for throughput
improvement in wireless networks is proposed. The protocol is based on the
traditional protocol of R-ALOHA which allows users to compete for channel
access before reserving the channel to the best user. We use compressive
sensing to find the best user, and show that the proposed protocol requires
less time for reservation and so it outperforms other schemes proposed in
literature. This makes the protocol particularly suitable for enhancing R-ALOHA
in fast fading environments. We consider both analog and digital versions of
the protocol where the channel gains sent by the user are analog and digital,
respectively.
