High spatio-angular resolution diffusion MRI has been shown to provide accurate identification of complex fiber configurations. However, its application in clinics remains limited due to the long required acquisition time. Recently, we have developed a method relying on an accelerated kq-space undersampling scheme to recover the intra-voxel fiber configurations. In the current work, we generalize our method to consider a more realistic setting. We include into the kq-space measurement model the phase contamination induced by magnetic field inhomogeneities and motion during the signal acquisition. Simulations are performed on realistic synthetic data, considering both the cases when the phase is perfectly known, and when it is pre-calibrated. Results show that, in both the cases, the phase contamination does not penalize the recovery of the fiber configuration.