Decentralized Power Control for SIC-Based κ-Max Decoding Slotted ALOHA over Nakagami-m Fading Channels

This paper studies decentralized power control for successive interference cancellation (SIC)–based slotted ALOHA random access systems, extending the framework of Xu et al (DOI: 10.1109/JSAC.2013.131113). In this scheme, each active device independently selects its transmit power according to a probability distribution conditioned on its instantaneous channel gain. We introduce a generalized κ-max decoding scheme, where up to κ packets with sufficiently separated received power levels are decodable via SIC, extending the conventional two-packet (κ = 2) case. We further design channel-adaptive power profiles and derive analytical expressions for the achievable throughput. In particular, for κ = 3, a closed-form throughput expression is obtained. The analysis is conducted over Nakagamim fading channels, which provides a flexible model for a wide range of fading conditions. Numerical results demonstrate the throughput gain from κ = 2 to κ = 3 and validate the analysis. The optimal conditional transmission probabilities under fading reveal the power control mechanism that suppresses transmission under poor channel conditions while exploiting favorable channel realizations to improve throughput.