On the rank reduction properties of frequency invariant antenna array beamformers

A Frequency Invariant Beamfomer (FIB) is an antenna array beamforming structure capable of synthesizing far-field array factor (AF) patterns that exhibit minimal variation over an arbitrary range of frequencies. In this paper, we quantify the frequency dispersion properties of two FIBs, the Time-Sampling (Ward) FIB and the Frequency-Sampling FIB, using closed form expressions for the eigenvalues resulting from a simple two-sinusoid approximation model for a single wideband source. The results confirm the excellent rank reduction property of the FIBs, as seen in the diminished magnitude of the second bandwidth-induced eigenvalue of the covariance matrix. The frequency dispersion is then related to the optimum output powers obtained for each FIB in minimum variance distortionless (MVDR) wideband beamforming. The results show that the novel TS-FIB exhibits greater frequency dispersion, which subsequently translates to undesirable partial cancellation of the look direction signal in optimum constrained beamforming.