  This paper provides the signal-to-interference-plus-noise ratio (SINR)
complimentary cumulative distribution function (CCDF) and average data rate of
the normalized SNR-based scheduling in an uplink cellular network using
stochastic geometry. The uplink analysis is essentially different from the
downlink analysis in that the per-user transmit power control is performed and
that the interferers are composed of at most one transmitting user in each cell
other than the target cell. In addition, as the effect of multi-user diversity
varies from cell to cell depending on the number of users involved in the
scheduling, the distribution of the number of users is required to obtain the
averaged performance of the scheduling. This paper derives the SINR CCDF
relative to the typical scheduled user by focusing on two incompatible cases,
where the scheduler selects a user from all the users in the corresponding
Voronoi cell or does not select users near cell edges. In each case, the SINR
CCDF is marginalized over the distribution of the number of users involved in
the scheduling, which is asymptotically correct if the BS density is
sufficiently large or small. Through the simulations, the accuracies of the
analytical results are validated for both cases, and the scheduling gains are
evaluated to confirm the multi-user diversity gain.
