In-band full-duplex (FD) communication is considered a potential candidate to be adopted by the fifth generation (5G) cellular networks. FD communication renders the entire spectrum simultaneously accessible by uplink and downlink, and hence, is optimistically promoted to double the transmission rate. While this is true for a single communication link, cross-mode interference (i.e., interference between uplink and downlink) may diminish the full-duplexing gain. This paper studies FD operation in large-scale cellular networks with real base stations (BSs) locations and 3GPP propagation environment. The results show that the uplink is the bottleneck for FD operation due to the overwhelming cross-mode interference from BSs. Operating uplink and downlink on a common set of channels in an FD fashion improves the downlink rate but significantly degrades (over 1000-fold) the uplink rate. Therefore, we propose the $α$-duplex scheme to balance the tradeoff between the uplink and downlink rates via adjustable partial overlap between uplink and downlink channels. The $α$-duplex scheme can provide a simultaneous $30\%$ improvement in each of the uplink and downlink rates. To this end, we discuss the backward compatibility of the $α$-duplex scheme with half-duplex user-terminals. Finally, we point out future research directions for FD enabled cellular networks.