Simultaneous co-channel transmission and reception, denoted as in-band full-duplex (FD) communications, has been promoted as a solution to improve the spectral efficiency in wireless networks. For cellular networks, in addition to the existing aggregate interference in half-duplex transmission, the residual self-interference and cross-mode interference [i.e., between uplink (UL) and downlink (DL)] impose major obstacles for FD communications' deployment. Although the FD communication's promising impact on the overall network data rate has been established in the literature, the rate gains are achieved in the DL transmissions at the expense of marginal gain, or even degradation, for the UL transmissions. This paper, therefore, focuses on the analysis of UL ergodic rate in FD cellular networks where a minimum distance between BSs using the same time-frequency resource block is imposed. Hence, the mutually interfering BSs' locations are modeled by Matérn hard core point process. The distribution of the aggregate interference and the channel-to-interference-plus-noise ratio at the UL of a typical user are characterized using a stochastic geometry analysis. Several UL power control techniques are presented and their resulting ergodic rates are derived and compared. The simulation results suggest that the UL performance highly depends on the network parameters and the UL power control techniques.