In this paper, we propose a novel reception/transmission scheme for half-duplex base stations (BSs). In particular, we propose a half-duplex BS that employes in-band uplink-receptions from user 1 and downlink-transmissions to user 2, which occur in different time slots. Furthermore, we propose optimal adaptive scheduling of the in-band uplink-receptions and downlink-transmissions of the BS such that the uplink-downlink rate/throughput region is maximized and the outage probabilities of the uplink and downlink channels are minimized. Practically, this results in selecting whether in a given time slot the BS should receive from user 1 or transmit to user 2 based on the qualities of the in-band uplink-reception and downlink-transmission channels. Compared to the performance achieved with a conventional full-duplex division (FDD) base station, two main gains can be highlighted: 1) Increased uplink-downlink rate/throughput region; 2) Doubling of the diversity gain of both the uplink and downlink channels.