Fast and accurate cardinality estimation in cellular-based wireless communications

Cardinality estimation is of fundamental importance in various wireless communication applications. The performance of any adaptive medium access control in the uplink channel is in fact affected by its accuracy. This paper provides a fresh look at this fundamental problem, and proposes a novel scheme for fast and accurate cardinality estimation. This scheme utilizes the experienced outage probability in detecting IDs of the devices in the uplink. It is observed that for practically relevant values of Signal-to-Interference-plus-Noise Ratio (SINR) threshold, e.g., β ≤ 10 dB, and spreading sequence length, e.g., N_c ≥ 7, the base station is able to estimate the true cardinality with vanishing error in only one shot, even if the network is so populated, e.g., the number of active devices N ≥ 100. Otherwise, one may apply the proposed method in couple of consecutive shots such that in each of which portion of the cardinality is estimated.