  We introduce a "one shot" random access procedure where users can send a
message without a priori synchronizing with the network. In this procedure a
common overloaded control channel is used to jointly detect sparse user
activity and sparse channel profiles. The detected information is subsequently
used to demodulate the data in dedicated frequency slots. We analyze the system
theoretically and provide a link between achievable rates and standard
compressing sensing estimates in terms of explicit expressions and scaling
laws. Finally, we support our findings with simulations in an LTE-A-like
setting allowing "one shot" sparse random access of 100 users in 1ms.
