This paper describes the utilization of antenna arrays at the base stations of wireless communication systems. Multiple antennas can provide a processing gain to increase the base station range and improve coverage. Also, by exploiting the angular selectivity of an antenna array at the base stations of a wireless system, users may be spatially multiplexed to increase system capacity. We address several aspects of the reception and transmission problems that arise when the spatial dimension is considered. Both the forward and reverse channels are discussed and an overview of related research conducted at the signal processing group, KTH is presented.