A broadcast approach to random access

This paper considers a communication system where m synchronized transmitters access a shared medium independently of each other with probability p, and upon access each user transmits a signal subject to an average power constraint P. A common receiver observes the sum of the signals transmitted by the active users corrupted by additive Gaussian noise. Let the throughput denote the sum of the achievable rates of the active users. Assuming that the set of active user is known to the receiver only, we find an approximate characterization of the maximum expected throughput as a function of m, p, and P. Our result is within one bit from a corresponding information theoretic upper bound, for any value of the underlying system parameters.