In this work we examine the performance of a Location Spoofing Detection System (LSDS) for vehicular networks in the realistic setting of Rician fading channels. In the LSDS, an authorized Base Station (BS) equipped with multiple antennas utilizes channel observations to identify a malicious vehicle, also equipped with multiple antennas, that is spoofing its location. After deriving the optimal transmit power and the optimal directional beamformer of a potentially malicious vehicle, robust theoretical analysis and detailed simulations are conducted in order to determine the impact of key system parameters on the LSDS performance. Our analysis shows how LSDS performance increases as the Rician K-factor of the channel between the BS and legitimate vehicles increases, or as the number of antennas at the BS or legitimate vehicle increases. We also obtain the counter-intuitive result that the malicious vehicle's optimal number of antennas conditioned on its optimal directional beamformer is equal to the legitimate vehicle's number of antennas. The results we provide here are important for the verification of location information reported in IEEE 1609.2 safety messages.