This paper considers a cellular system with a full-duplex base station and half-duplex users. The base station can activate one user in uplink or downlink (half-duplex mode), or two different users one in each direction simultaneously (full-duplex mode). Simultaneous transmissions in uplink and downlink causes self-interference at the base station and uplink-to-downlink interference at the downlink user. Although uplink-to-downlink interference is typically treated as noise, it is shown that successive interference decoding and cancellation (SIC mode) can lead to significant improvement in network utility, especially when user distribution is concentrated around a few hotspots. The proposed temporal fair user scheduling algorithm and corresponding power optimization utilizes full-duplex and SIC modes as well as half-duplex transmissions based on their impact on network utility. Simulation results reveal that the proposed strategy can achieve up to 95% average cell throughput improvement in typical indoor scenarios with respect to a conventional network in which the base station is half-duplex.