Success Probability of Multiple-Preamble-Based Single-Attempt Random Access to Mobile Networks

We analyze the tradeoff between collision probability and code-ambiguity, when devices transmit a sequence of preambles as a codeword, instead of a single preamble, to reduce collision probability during random access to a mobile network. We point out that the network may not have sufficient resources to allocate to every possible codeword, and, if it does, this results in low utilization of allocated uplink resources. We derive the optimal preamble set size that maximizes the probability of success in a single attempt, for a given number of devices and uplink resources.