This book covers the characterization and design of small array antennas for ultra-wideband (UWB) industrial linear frequency-modulated continuouswave (FMCW) RADAR systems. Although the techniques developed in this work are not limited to a certain application scenario, in particular the design of a four-element uniform linear and four-element uniform circular array antenna is considered. The antenna arrays are used for implementing direction-of-arrival (DOA) estimation in a novel UWB secondary RADAR system for industrial local positioning applications. The system‘s frequency range is from 6 GHz to 9 GHz and hence possesses a relative bandwidth of 40 %. State of the art industrial FMCW RADAR systems in contrast traditionally operate in the narrowband regime with relative bandwidths much smaller than 10 %. In consequence methods traditionally used for characterizing the antennas, for modeling the influence of the antennas on the RADAR system performance, for implementing direction-of-arrival estimation in FMCW RADAR systems, and for designing antenna arrays are not sufficient. Their application to UWB FMCW RADAR systems is carefully reviewed, and where necessary extended to take into account effects emerging due to the large relative bandwidth.