Codebooks in Flag Manifolds for Limited Feedback MIMO Precoding

Abstract:
We consider unitary codebook design problems for various precoded MIMO scenarios, and interprete them as generalized discretization problems of flag manifolds. As a concrete example, we consider codebooks for MIMO transmission with linear receivers. In this case, the problem reduces to discretizing permutation-invariant flag manifolds. A corresponding Lloyd algorithm is given, providing low-distortion codebooks. The achievable rate of the system applying the generated codebooks is compared by simulations. We find that for a N-by-N full-rank MIMO system with N > 2 and a linear receiver, the gain of precoding with a small number of feedback bits is small. This differs from the behavior of low-rank transmissions, where it is known that a small number of feedback bits allows near-optimal channel adaptation.