This paper characterizes the estimation performance of synthetic aperture (SA) techniques in the context of moving GNSS receivers. Under the assumption of a stationary channel, SA techniques transform a single antenna into a virtual array. We first introduce a model for the GNSS signal received by a single moving antenna. Leveraging this model, SA processing enables direction-of-arrival (DOA) and beamforming on a single antenna. The model does not make use of the narrowband assumption, which makes it suitable for relatively large trajectories. In addition, it includes the effects of the polarization mismatch between the received signal and the receiving antenna. Then, the proposed model is used to derive the Cram´er-Rao lower bound (CRB) for the joint estimation of the received signal amplitudes, synchronization and DOA parameters. We compute the CRB for two different antenna motions, with results depending on the antenna trajectory as well as on the scenario geometry. Results highlight how SA processing profits from spatial and polarization diversities, pointing out its potential for DOA estimation and beamforming applications in moving GNSS platforms, such as unmanned air vehicles or smartphones.