Ultra-Wideband Frequency-Invariant Beamforming Using a Generalized Nesting Array

This paper proposes an ultra-wideband frequency-invariant beamforming (FIB) using a generalized nesting array. To implement ultra-wideband (9:1 bandwidth ratio) FIB with a reduced number of array elements, the target frequency band is divided into subbands. The subarrays have integer multiples of inter-element spacing of half-wavelength at the maximum frequency according to the bandwidth ratio of subbands. Due to this integer multiple relationships, the array elements of the subarrays are superimposed so that the total number of array elements is reduced while maintaining FIB performance over the target frequency band. Then, the FIB weights are derived based on the desired beam pattern using the inverse Fourier transform. A Bartlett beamformer is used to generate FIB patterns of the proposed nesting array. In addition, we investigate the interrelationship between the minimum required number of array elements and design parameters (target bandwidth, beamwidth, and side lobe level). For validation, 21 printed log-periodic dipole array antennas are fabricated and measured. The direction finding performance is evaluated and compared to that of a 35-element uniform linear array. The direction of arrival (DoA) estimation results of the proposed array show a root-mean-square error of less than 2.02° for an incident angle within ±50° when a signal-to-noise ratio is 10 dB. It is demonstrated that the proposed array exhibits ultra-wideband FIB performance similar to a conventional uniform linear array but with much fewer elements.