of the users in slot $n$. We assume that every user $i$ would know its instantaneous channel gain $H_{n,i}$ at the beginning of every slot, but that information is not available with other users in the network, including the base station. The channel state information $H_{n,i}$ can be made available to the user $i$ by the transmission of a pilot signal by the base station at the beginning of the slot. The base station seeks to identify and schedule the user with the highest channel gain in every slot (opportunistic scheduling), i.e., the base station seeks to schedule $$\arg \max_{\{i=1,\cdots,N\}} \{H_{n,1}, H_{n,2}, \cdots, H_{n,N}\}$$ in slot $n$. Define $X_{n,i} := F(H_{n,i})$, the cumulative distribution value in the slot $n$. Then, the vector $(X_{n,1}, X_{n,2}, \cdots, X_{n,N})$ is i.i.d. Uniform in $[0,1]$ for any channel distribution $F(\cdot)$. Further, the contention resolution problem can equivalently be described as $$\arg \max_{\{ i=1,\cdots,N\}} \{X_{n,1}, X_{n,2}, \cdots, X_{n,N}\}$$ Hence, without loss of generality, we will assume that $F(\cdot)$ is Uniform in $[0,1]$ and consider $(X_{n,1}, X_{n,2}, \cdots, X_{n,N})$ as the channel gain variables.

The base station resolves the identity of the user with the highest channel gain by coordinating the contention resolution process and by 