On the instability of slotted Aloha with capture

We analyze the stability properties of slotted Aloha with capture for random access over fading channels when the number of users is very large. We consider the most commonly used power capture model, namely the one based on signal-to-interference-plus-noise ratio (SINK). Existing works have shown that for this model the capture capability alone can stabilize the slotted Aloha when the distribution of the received user power satisfies certain conditions. However, our analysis shows that as long as the received powers of all the users are independent and identically distributed with finite mean, the system is unstable. We further establish that power or probability control based on decentralized channel state information (CSI) can not render an infinite-user system stable.