Near Successive Refinement of Gaussian Vectors in Grassmannian Space

In this paper we look at the problem of successively refining the description of a Gaussian i.i.d. source in a Grassmannian space. This problem is relevant, for example, in the encoding of channel state information for the limited feedback MIMO broadcast channel. We show how it is possible to achieve an isotropic distribution of the error vector by applying unitary transformations, which simplifies the problem of finding optimal codebooks for the error quantisation. Reconstruction error analysis and numerical tests show how the proposed technique can, in practice, perform very close to the distortion- rate bound and suggest that, in some cases, these successive error descriptions can be optimal refinements of one another.