We study irregular repetition slotted ALOHA (IRSA) with multi-antenna reception over Rayleigh block fading channels. An exact closed-form expression for the average decoding error probability ¯ϵm,L is derived for collision sizes m = 1 and m = 2 by applying the inclusion–exclusion principle, which generalizes known single-antenna results and remains valid for any finite number of antennas. Using this result, we develop a density-evolution-based analysis of multi-antenna IR-SA systems and characterize belief-propagation (BP) thresholds. Numerical results for the corresponding maximum a posteriori (MAP) decoding thresholds and converse bounds are also presented, demonstrating threshold saturation with spatial coupling.

This paper explores the optimization of transmission probability and code rate in multi-device slotted ALOHA systems employing successive interference cancellation (SIC) and feedback over Nakagami- m fading channels. Although previous research has derived the optimal probability and the code rate to maximize the sum rate in a two-device scenario analytically using Markov process, its extension to configurations with more than two devices remains challenging. The complexity of Markov modeling arises from two main challenges: 1) an increase in the number of devices greatly expands the state space, precluding the analytical determination of system throughput; 2) deriving transition probabilities in the Nakagami- m channel model is difficult. In this study, we use computer simulations to evaluate the sum rate and to search for the optimal transmission probability and code rate to maximize the sum rate of the systems. Our simulation findings reveal that at an average SNR the optimal code rate is independent of the number of devices and transmission probability. In a 30-device slotted ALOHA system with an SNR of 15 dB, the maximum sum rate of 2.9235 is almost achieved at a transmission probability of 0.0665 and an optimal code rate of approximately 4.02, regardless of the number of devices.

Throughput analysis for successive interference cancellation-based two-device slotted ALOHA with feedback is studied over Nakagami-m fading channels. Explicit expressions for the state transition probabilities are derived for a Markov process, thus facilitating the computation of the throughput. Through optimization of the transmission probability, it is shown that the maximum throughput is achieved for a given code rate.