ML estimation of population size when observing multiple fill levels in slotted Aloha

An open problem in slotted Aloha protocols is to optimally estimate the number of participants as such knowledge is crucial to select the optimal frame length. First results are known in literature based on observing the slot fill levels in case of empty slots and single occupancies (singleton slots). Advances in signal processing allow now also to decode successfully slots with higher fill levels, for example, due to multiple antennas. In this paper we derive the maximum likelihood estimator when arbitrary occupancies up to a maximal fill level R have been observed. Due to our novel approach, the derivation is rather simple and its implementation is of low complexity.