In the context of designing a next-generation ultrasonic polar scan (UPS) measurement system for viscoelastic material characterization, a novel approach is proposed, which draws on a set of cylindrically focused emitters in conjunction with a circular phased array (C-PA) receiver in order to create a portable measurement system while improving the data quality and ease the data interpretation. To explore the potential of the new approach and determine its optimal design parameters, a 3-D analytical model is presented to numerically simulate UPS experiments with the proposed system. Furthermore, a postprocessing procedure is worked out to treat the acquired raw data with the aim to deal with the integrating effect of finite size transducers and directly reconstruct the angle-dependent plane wave reflection coefficients of the sample under study. As the accuracy of the reconstruction heavily depends on various design parameters, a parameter study focusing on the influence of three main experimental parameters is performed to guide the optimal design. For each of these parameter studies, the UPS simulation results have been inverted, and the errors on the estimated C-tensor parameters have been deduced. First, it is shown that, for a given frequency, the radius of the C-PA must be large enough to capture both the specular and nonspecular reflected field, which is crucial to assure a correct reconstruction of the plane wave characteristics and find proper estimates of the C-tensor parameters. Second, the impact of the emitter and receiver lengths on the quality of the reconstruction and the C-tensor parameters has been investigated, yielding superior results upon increasing either of them. Finally, a dedicated study of the pitch of the C-PA elements and the angular range of the cylindrically focused emitters shows that aliasing effects disturb the results if the pitch is too large. However, this effect can somewhat be mitigated by employing multiple emitters with a restricted angular range. Using the knowledge of the abovementioned parameter studies, a simulated UPS experiment using a proper set of design parameters is performed for a cross-ply carbon epoxy laminate. The postprocessed reconstruction based on these data shows an excellent agreement with the theoretical plane wave results.