A smart antenna for a base station comprises a plurality of antenna arrays each capable of forming a multiplicity of separate overlapping narrow beams in azimuth, the arrays being positioned such that the totality of beams formed by the arrays provides a substantially omni-directional coverage in azimuth A plurality of r.f. transceivers is provided each for transmitting and receiving r.f. signals for one or more calls, with switching matrix means for connecting each transceiver with one or other of the arrays via beamformers. Each transceiver is connected by a switch matrix to a particular array to exchange r.f. signals with a remote station located in the area covered by one of the narrow overlapping beams. Means are provided for selecting for a given call more than one of the best received signals from the multiplicity of narrow overlapping beams and the selected signals are combined to form a single receive signal input for the r.f. transceiver for the given call.