Multiple simultaneous beams exist when an array of N elements is connected to a beamformer with 1M beam ports, where N and 1M may be different. Multiplebeam systems have many uses: in electronic countermeasures, in satellite communications, in multiple-target radars, and in adaptive nulling, for example. The last application uses adaption in beam space as it avoids several serious difficulties that arise with adaption in array space. (Mayhan, 1972). Not included in this chapter are array feeds f