Estimating Collision Set Size in Framed Slotted Aloha Wireless Networks and RFID Systems

In wireless networks and RFID systems, a collision set is a group of nodes such that the simultaneous transmission of two or more nodes generates destructive interference at the receiver and, consequently, the loss of all transmitted packets. Knowing the number of nodes in the collision set, i.e., the collision set size, it is possible to design effective channel access strategies that minimize the time required to read all the tags or, more generally, collect the packets generated by each node in the set. However, the collision set size is often unknown and, then, needs to be estimated. In this paper we propose a novel estimation method for Framed Slotted Aloha systems that applies a maximum likelihood argument on a Poisson approximation of the packet arrivals process to the transmission channel, yielding an estimate with minimal mean error and mean square error, with respect to the best-performing estimate algorithms in the literature having similar complexity.