We present an analytical form of ground-truth k-space data for the 2-D Shepp-Logan brain phantom in the presence of multiple and non-homogeneous receiving coils. The analytical form allows us to conduct realistic simulations and validations of reconstruction algorithms for parallel MRI. The key contribution of our work is to use a polynomial representation of the coil's sensitivity. We show that this method is particularly accurate and fast with respect to the conventional methods. The implementation is made available to the community.