1. A device for receiving signals comprising: an array of N signal-receiving elements for receiving N signals, where N is a natural number greater than or equal to three; sampling circuitry for sampling the N signals and providing output samples for the N signals; a processor for receiving and processing signals derived from the output samples, the processing including using a non-diagonal N×M matrix to produce a set of M beams, where M is a natural number greater than N, each of the M beams corresponding to a particular direction of signal arrival relative to the signal-receiving elements, the N×M non-diagonal matrix being derived in advance to increase the signal for each one of the M beams and to reduce the signal each of the other M−1 beams, for each of the M beams the processor producing an output of M beam vectors.