  Non-orthogonal multiple access (NOMA) serves multiple users by superposing
their distinct message signals. The desired message signal is decoded at the
receiver by applying successive interference cancellation (SIC). Using the
theory of Poisson cluster process (PCP), we provide a framework to analyze
multi-cell uplink NOMA systems. Specifically, we characterize the rate coverage
probability of a NOMA user who is at rank $m$ (in terms of the distance from
its serving BS) among all users in a cell and the mean rate coverage
probability of all users in a cell. Since the signal-to-interference-plus-noise
ratio (SINR) of $m$-th user relies on efficient SIC, we consider three
scenarios, i.e., perfect SIC (in which the signals of $m-1$ interferers who are
stronger than $m$-th user are decoded successfully), imperfect SIC (in which
the signals of of $m-1$ interferers who are stronger than $m$-th user may or
may not be decoded successfully), and imperfect worst case SIC (in which the
decoding of the signal of $m$-th user is always unsuccessful whenever the
decoding of its relative $m-1$ stronger users is unsuccessful). The derived
expressions are customized to capture the performance of a user at rank $m$ in
an equivalent orthogonal multiple access (OMA) system. Finally, numerical
results are presented to validate the derived expressions.
