Offered load estimation in random access multipacket perception systems using the expectation-maximization algorithm

Abstract

This paper considers offered load estimation in probabilistic dynamic frame slotted ALOHA systems where the receiver can perceive multiple concurrent packets in a slot. This type of random access protocol finds current application in the areas of machine-to-machine communications and tag processing in RFID communications. The perception of multiple concurrent packets happens when a receiver is able to detect the number of received packets or to decode them. In the first case, we talk about multiple packet detection (MPD) whereas in the second we refer to multiple packet reception (MPR). The finite detection capability of MPD or separation capacity of MPR implies that, ideally, whenever the number of simultaneously received packets exceeds a given value M, a collision results and no information about the packets or their number can be extracted. Hence, we are confronted with an incomplete data estimation problem. We reformulate the problem so as to apply the expectation-maximization (EM) algorithm and derive the required iterative equations to obtain a maximum likelihood estimator for the offered load. A numerical example of the algorithm's execution is included and application scenarios are indicated. Simulation studies are presented to show that the proposed estimation method compares favorably with alternative techniques.