Limited feedback design for the spatially correlated multi-antenna broadcast channel

The broadcast problem with multiple antennas at the transmitter end and a single antenna at each user is studied in this work. A low-complexity transmitter architecture where linear beamforming is used to convey information to the users, and multi-user interference is treated as noise at the receiver unit of each user is considered. The vector channels that connect the transmitter to the users are assumed to be spatially correlated. The goal of this work is the design of a low-rate limited feedback framework to improve the achievable sum-rate of the system relative to a baseline scenario where only correlation information is known at the transmitter. While prior work considers either a codebook structure that is designed for spatially uncorrelated channels or for spatially correlated point-to-point systems, it is argued here that a “good” codebook design should incorporate a statistical version of the interference structure that is seen at each user. Further, instead of feeding back the codeword index that is best aligned to the user's channel vector, the index that maximizes an estimate of the signal-to-interference-and-noise ratio as perceived by the user is fed back. It is shown via numerical results that the proposed framework results in a substantial performance improvement over existing schemes across a large family of spatial correlation and across a practically relevant operating regime.