Stability analysis of random multiple access with SIC

Medium access control is witnessing renewed attention over the last decades, due to the Internet of Things and to the extensive development of advanced signal processing techniques, able to significantly expand the capacity of shared channel systems. This paper addresses a multiple access model encompassing Successive Interference Cancellation (SIC) at the receiver, aiming at establishing the stable achievable spectral efficiency. Both the transmission probability p and the target Signal-to-Interference-plus-Noise Ratio γ are adjusted dynamically by nodes, according to the overall number of backlogged nodes. Leveraging a Foster–Lyapunov approach and bounds on the number of decodable packets under a general SIC model, it is proved that the achievable stable spectral efficiency vanishes for fixed p and γ[jls-end-space/]. It vanishes as well if p and γ scale with the number of backlogged nodes in the wrong way. It is proved that only the product (Formula presented) matters and that a non-vanishing stable spectral efficiency is achieved, in case it scales inversely proportional to the number of backlogged nodes. Numerical evaluation demonstrates the trade-offs between stability, convergence to the asymptotic regime and mean access delay.