MIMO transmission subspace tracking with low rate feedback

The paper describes a low rate feedback algorithm for conveying partial channel state information - specifically, the dominant row subspace of the channel matrix - from the receiver to the transmitter in a continuously time-varying multiple-antenna environment. Since subspaces are points on a complex Grassmann manifold, variations in subspaces are treated as a piecewise geodesic process on the manifold. The receiver feeds back one bit to indicate the preferred sign of a random velocity matrix of the geodesic. Numerical results show that the performance of the proposed algorithm is better than the Grassmannian subspace packing approach at low-to-medium Doppler frequency and always better than the previously proposed gradient sign feedback scheme.