Digital beamforming for ultra‐wideband signals utilizing an extrapolated array generated by Carathéodory representation combining fractional delay filters based on high‐order Hermite interpolation

Abstract

Digital beamforming (DBF) for ultra‐wideband (UWB) signals plays a key role in many applications, and high spatial resolution and accurate digital delay of UWB signals are the focus of UWB DBF research. In this paper, we propose a novel DBF method utilizing an extrapolated array generated by Carathéodory representation combining fractional delay filters (FDFs) based on high‐order Hermite interpolation. The Carathéodory representation could extrapolate the aperture of the original uniform linear array (ULA) significantly and provide a better real‐time performance than the existing extrapolation technique based on the two‐dimensional autoregressive (2‐D AR) model. The FDFs based on high‐order Hermite interpolation not only improve the DBF performance when the frequency of the signals is close to the Nyquist rate but also reduce the sampling rate to half the Nyquist rate. The UWB linear frequency‐modulated (LFM) signal is used for simulation analysis. In contrast with traditional DBF methods and FDFs based on Lagrange interpolation, the proposed method has a much higher spatial resolution, has no false peak, and requires fewer sensors, as demonstrated by simulation results. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.