Nested Grassmannian Codebooks for Quantizing MIMO Precoders on the Flag Manifold

In MIMO systems, the channel can be decomposed using Singular Value Decomposition (SVD). The resulting unitary matrices, used as precoders, are fed back to the transmitter to enhance rates. Their non-uniqueness enables efficient quantization on Flag manifolds. While previous studies have investigated manifold-based precoder feedback approaches, an incremental subspace-based quantization approach remains unexplored. We propose a nested Grassmannian quantizer for Flag elements, which incrementally builds codebook dimensions. Simulations show the proposed method effectively captures Flag elements and outperforms existing approaches, with significant gains.