Sum-rate Analysis of Slotted ALOHA with Buffered Inter- and Intra-Slot SIC under Mixture Gamma Fading

This paper presents an analytical framework for Buffered-SIC (successive interference cancellation) slotted ALOHA (BSIC-SA) systems with real-time feedback under composite fading channels. The BSIC-SA employs buffered inter-slot SIC to utilize the residual signals from previous slots and intra-slot SIC under random fading for enhanced packet recovery. The received signal-to-noise ratio (SNR) is modeled by a mixture gamma (MG) distribution, which generalizes the exponential SNR model of Rayleigh fading by incorporating both exponential and power terms in its probability density function (PDF). By exploiting the series representations of the lower and upper incomplete gamma functions, closed-form expressions for the state transition probabilities in the Markov process of a two-device system are derived. The transmission probability and coding rate are jointly optimized to maximize the achievable sum rate. Our proposed analysis accommodates various fading environments without requiring separate derivations for individual channel models. Numerical analyses and simulation results confirm the validity of the proposed framework and demonstrate the achievable maximum sum rate for multi-device BSIC-SA systems.