Incremental Grassmannian Feedback Schemes for Multi-User MIMO Systems

The communication of side information forms a key component of several effective strategies for transmitter adaptation to slowly fading channels. When the relevant side information is a subspace, the feedback scheme can be viewed as a lossy source compression scheme on the Grassmannian manifold. Memoryless vector quantization on each fading block is a viable compression scheme, but it neglects any temporal correlation between the blocks. In this paper, we propose an incremental approach to Grassmannian quantization that takes advantage of temporal correlation. The approach leverages existing codebooks for memoryless quantization schemes and employs a quantized form of geodesic interpolation. Two schemes that implement the principles of the proposed approach are presented. In the first scheme, the choice of the step size in the incremental update is adapted to a first-order GaussMarkov model for the channel, which enables the use of higher resolution codebooks. In the second scheme, a single bit is allocated to the step size, which enables adaptation of the step size to the channel realization rather than the channel statistics. This provides substantial robustness against mismatches in the model for the temporal correlation. A distinguishing feature of the proposed approach is that the direction of the geodesic interpolation is specified implicitly using a point in a conventional codebook. As a result, the approach has an inherent ability to recover autonomously from errors in the feedback path. Simulation results demonstrate that these features result in improved performance over some existing schemes in a variety of channel environments.