Digital beamforming with reduced number of phase shifting and time delay elements

A bilinear representation of polynomials is shown to result in an efficient method for digital beamforming in phased arrays, with much reduced number of phase shifting elements. The proposed structure is also shown to extend to arrays with arbitrary complex weights. The number of phase shifting elements used is of the order of the square root of the number of phases used, with no limitations on the achievable patterns. Only phase shifters and combiners are used, with no splitters. The same concept applies to reduction of the number of delay elements in wideband beamforming, and also in reduction of the number of delay elements in continuous-time FIR filters.