Collision Resolution Protocol via Soft Decision Retransmission Criterion

In massive multiple-input multiple-output (MIMO) crowded networks, the random access (RA) performance of strongest-user collision resolution (SUCRe) protocol can be improved by replacing the hard decision retransmission rule by a soft decision one, so that each user equipment (UE) decides to retransmit or not its pilot sequence with a suitable probability. We obtain this probability for each UE according to the probability of this UE being the strongest contender, while also proposing an analytical approximated probability expression for this event. Hence, the $k$th UE is able to calculate the probability of itself being the strongest contender in a pilot collision, choosing to retransmit or not its RA pilot in the next step of the protocol according to this probability, without requiring any excessive complexity or additional overheads. Our numerical results demonstrate significant improvements in comparison to the original SUCRe protocol, while maintaining its favorable feature of being a decentralized and uncoordinated approach.