Due to the massive number of devices in the M2M communication era, newchallenges have been brought to the existing random-access (RA) mechanism, suchas severe preamble collisions and resource block (RB) wastes. To address theseproblems, a novel sparse message passing (SMP) algorithm is proposed, based ona factor graph on which Bernoulli messages are updated. The SMP enables anaccurate estimation on the activity of the devices and the identity of thepreamble chosen by each active device. Aided by the estimation, the RBefficiency for the uplink data transmission can be improved, especially amongthe collided devices. In addition, an analytical tool is derived to analyze theiterative evolution and convergence of the SMP algorithm. Finally, numericalsimulations are provided to verify the validity of our analytical results andthe significant improvement of the proposed SMP on estimation error rate evenwhen preamble collision occurs.
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