Improved User-Specific Channel Estimation Using Geodesical Interpolation at the Transmitter

In this letter we study a precoding matrix (PM) interpolation in the context of user-specific channel estimation. We interpolate the fed-back PMs at the transmitter by the means of geodesic to enable continuous channel estimation across continuously scheduled frequency clusters in the receiver. The proposed scheme is compared to the case where a single PM is used for all sub-carriers within a frequency cluster and channel estimation can be performed only within that cluster. We compare the performance of geodesical interpolation on Grassmann, Stiefel, and Flag manifolds. For this purpose, we provide an iterative framework to obtain geodesics on Stiefel and Flag manifolds based on boundary conditions. We show by monte-carlo simulations that the interpolation of fed-back PMs at the transmitter improves significantly the quality of channel estimation.