This work tests the ability of a frequency-modulated continuous wave (FMCW) radar to measure the respiratory rate and the heartbeat of a subject in challenging indoor scenarios. To simulate a realistic configuration for ambient assisted living (AAL) applications, in which the thorax orientation towards the antenna is typically unknown, four different scenarios were considered. Measurements were performed on five volunteers positioned with the chest, left, back, and right side facing the antenna, respectively. The 5.8 GHz radar and the antennas used for the measurements were suitably designed for the considered application. To obtain a low cost and compact system, series-fed arrays were preferred over other antenna topologies. The geometry of the patches was opportunely shaped to reduce the side lobe level (SLL) and increase the bandwidth, thus ensuring good system performances. In all scenarios, the vital signs extracted from the radar signal were compared with the ones collected by a photoplethysmograph and a respiratory belt, used as references. A statistical analysis of the measured data on the different subjects and orientations was performed, showing that the radar was able to measure with high accuracy both the respiratory rate and the heartbeat in all considered configurations.