We first consider 2-user model. The baseband discrete-time model for the uplink AWGN channel with two users is $$y[m]=x_1 [m] + x_2 [m] + w[m]$$ where $w[m] \sim \mathcal{C N}\left(0,N_0\right)$ is i.i.d. complex Gaussian noise. User $k$ $\left(k=1,2\right)$ has an average power constraint of $P_k$.
In the multiuser case, the concept of Channel Capacity is extended to Capacity Region: this is the set of all pairs 􏷪$\left(R_1, R_2\right)$􏷫 such that simultaneously user 1 and 2 can reliably communicate at rate $R_1$ and $R_2$, respectively.