Beamforming is a space–time operation in which a waveform originating from a given source but received at spatially separated sensors is coherently combined in a time-synchronous manner. If the propagation medium preserves sufficient coherency among the received waveforms, then the beam-formed waveform can provide an enhanced signal-to-noise ratio (SNR) compared with a single sensor system. Beamforming can be used to determine the direction-of-arrival(s) (DOAs) and the location(s) of the source(s), as well as perform spatial filtering of two (or more) closely spaced sources. Beamforming and localization are two interlinking problems, and many algorithms have been proposed to tackle each problem individually and jointly (i.e. localization is often needed to achieve beamforming and some localization algorithms take the form of a beamformer). The earliest development of space–time processing was for enhancing SNR in communicating between the United States and the United Kingdom dating back before the World War II . Phase-array antennas based upon beamforming for radar and astronomy were developed in the 1940s . Since then, phase-array antennas utilizing broad ranges of radio frequencies (RFs) have been used for diverse military and civilian ground, airborne, and satellite applications. Similarly, sonar beamforming arrays have been used for more than 50 years.