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In this paper, a radar system for local positioning applications is presented. The system consists of frequency modulated continuous-wave (FMCW) stations operating in W-band that are loosely coupled using time-delayed ramp start signals. A centralized signal processing approach allows to relax the required synchronization accuracy between the stations and further leads to a cancellation of phase noise and phase distortions caused by imperfect FMCW ramps. All stations are equipped with an antenna array and multiple receivers. Thus, a signal processing approach is developed in this work that combines the positive effects from the centralized processing with the information from the antenna array in a digital-beamforming based approach to improve the multipath robustness of the overall system. The developed theory is confirmed in measurements carried out with a prototype system consisting of two stations. Various measurements in multipath environments confirm the improved robustness leading to a worst-case root-mean-square position error of 15 mm under strong multipath conditions which were simulated inside an anechoic chamber.