Design Guidelines for Limited Feedback in the Spatially Correlated Broadcast Channel

A linear beamformer design for the broadcast channel where the base station is equipped with N_t antennas and signals to M = 2 users (each with a single antenna) and where the vector channels are spatially correlated is considered. This problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled (instead of the theoretically feasible N_t user scheduling) to minimize signaling overhead. The users are assumed to have perfect channel state information (CSI), whereas the base station has statistical information of the channels. In the first part of this work, the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum-rate between the perfect CSI and statistics-only extremes. In this direction, the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established. In the second part of this work, in scenarios with a large gap, limited feedback beamforming codebooks and a codeword selection metric are designed for the low-rate feedback setting. The main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal-to-interference-and-noise ratio (SINR) of each user. Extensions of this scheme are also proposed for the general N_t antenna case with M users, where M ≤ N_t. It is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as Grassmannian/Random Vector Quantization/single-user codebooks with the channel projection metric for codeword selection.