On the Capacity of the Channel Aware Slotted Aloha over Rayleigh and Nakagami-m Channels

We consider the channel aware slotted ALOHA protocol that has been recently proposed to improve the capacity of the traditional slotted ALOHA by using multi-user diversity. This type of diversity is commonly used in scheduling policies that allow terminals to transmit when their channel conditions are good. Here, we focus on a decentralized random access protocol where users decide to transmit only when their signal-to-noise ratio (SNR) is above a predefined threshold. We derive the formulas of capacity of the channel aware slotted ALOHA protocol in case of optimal power and rate adaptation over Rayleigh fading channels with different diversity techniques and over Nakagami-m fading channels. We also propose a modelization of the optimal probability of transmission as a function of the mean SNR and of the number of users.