An incremental Grassmannian feedback scheme for linearly precoded spatial multiplexing MIMO systems

An effective strategy for transmitter adaptation on slow block-fading multiple-input multiple-output (MIMO) links is for the receiver to inform the transmitter of the subspace over which transmission should take place, and for the transmitter to allocate power uniformly over that subspace. The design of a feedback scheme to implement this strategy can be viewed as a (lossy) source compression problem on a Grassmannian manifold. Memoryless vector quantization on each fading block is one approach to that problem, but it neglects any correlation between blocks. In some recent work, several approaches have been proposed to take advantage of this correlation. In this paper we propose an alternative technique that leverages existing Grassmannian codebooks from memoryless schemes and employs a quantized form of geodesic interpolation. Distinguishing features of the proposed technique include the fact that it only requires a single codebook, and the fact that it enables the step length of the geodesic interpolation to be adapted to the channel realization, rather than the channel statistics. In some straightforward simulation experiments, the proposed approach provides better performance than an existing scheme.