On the Feedback Channel for MIMO Beamforming

The question on how much feedback we need for MIMO beamforming is addressed in terms of the distortion and reliability of MIMO beamforming feedback in this paper. We model MIMO beamforming feedback with noisy Gaussian binary erasure feedback channel, in which the MIMO forward link is modelled as a Gaussian channel and the reverse link is simplified as a Gaussian binary erasure channel. For the forward link channel quantization, an information-theoretic lower bound and a heuristic sphere-packing upper bound for the achievable rate- distortion region are given. For the reverse link channel feedback, the rate-reliability region is analyzed with Shannon bounds. Though a large codebook design with high-rate feedback is generally desired for less distortion, it may be unnecessary due to the limitation of channel estimation and feedback channel. Tradeoffs between codebook design and channel state information feedback are therefore revealed.