Design of a random access network for compressed sensing

For networks that are deployed for long-term monitoring of environmental phenomena, it is of crucial importance to design an efficient data gathering scheme that prolongs the lifetime of the network. To this end, we exploit the sparse nature of the monitored field and consider a Random Access Compressed Sensing (RACS) scheme in which the sensors transmit at random to a fusion center which reconstructs the field. We provide an analytical framework for system design that captures packet collisions due to random access as well as packet errors due to communication noise. Through analysis and examples, we demonstrate that recovery of the field can be attained using only a fraction of the resources used by a conventional TDMA network, while employing a scheme which is simple to implement and requires no synchronization.