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Distance measurements in overmoded waveguides are an important application for industrial radar systems. The accuracy of the measurements is deteriorated by the appearance of higher order modes in the metal tube, although the frequency-modulated continuous-wave method is used with a large bandwidth. This paper describes the problems caused by dispersion and multimode propagation and presents a solution in the form of mode-matched antennas for feeding the overmoded waveguide. It is shown that different modes, e.g., the H11 and H01 modes, are equally well suited for precision distance measurements, as is demonstrated both by simulations and measurements.