We propose an irregular repetition slotted ALOHA (IRSA) based uncoordinated random access scheme for energy harvesting (EH) nodes. Specifically, we consider the case in which each user has a battery that is recharged with harvested energy from the environment in a probabilistic manner. We analyze this scheme starting with a unit-sized battery at the nodes and extend the analysis to the case of a finite-sized battery. For both scenarios, we derive the asymptotic throughput expressions and obtain the optimized probability distributions for the number of packet replicas of the users. We demonstrate that for the case of IRSA with EH nodes, these optimized distributions perform considerably better than the alternatives, including slotted ALOHA (SA), contention resolution diversity slotted ALOHA (CRDSA), and IRSA, which do not take into account the EH process for both asymptotic and finite frame length scenarios.
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