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.
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