Interference Alignment With Quantized Grassmannian Feedback in the K-User Constant MIMO Interference Channel

A simple channel state information (CSI) feedback scheme is proposed for interference alignment (IA) over the
$K$
-user constant multiple-input–multiple-output interference channel (MIMO IC). The proposed technique relies on the identification of invariants in the IA equations, which enables the reformulation of the CSI quantization problem as a single quantization on the Grassmann manifold at each receiver. The scaling of the number of feedback bits with the transmit power sufficient to preserve the multiplexing gain that can be achieved under perfect CSI is established. We show that the CSI feedback requirements of the proposed technique are better (lower) than what is required when using previously published methods (including state-of-the-art codebook-based as well as analog feedback techniques), for system dimensions (number of users and antennas) of practical interest. Furthermore, we show through simulations that this advantage persists at low SNR, in the sense that the proposed technique yields a higher sum-rate performance for a given number of feedback bits. Finally, to complement our analysis, we introduce a statistical model that faithfully captures the properties of the quantization error obtained for random vector quantization (RVQ) on the Grassmann manifold for large codebooks; this enables the numerical (Monte Carlo) analysis of general Grassmannian RVQ schemes for codebook sizes that would be impractically large to simulate.