Variational Bayesian Learning for Channel Estimation and Transceiver Determination

We consider the design of linear precoders for the MISO Interfering Broadcast Channel (IBC) with partial Channel State Information at the Transmitter (CSIT) in the form of both channel estimates and channel covariance information. Most of the results can also be transposed to the SIMO Interfering Multiple Access Channel with linear receivers. We first point out that in the case of reduced rank covariance matrices, there is significant gain in sum rate by using LMMSE as opposed to Least-Squares (LS) channel estimates. We also analyze various beamforming designs exploiting partial CSIT. Then we go beyond assuming the availability of covariance CSIT and propose variational Bayesian learning (VBL) techniques to acquire it assuming TDD channel reciprocity. In particular a Space Alternating version of Variational Estimation (SAVE) allows a well founded alternative to AMP based techniques while being of similar complexity. The SAVE techniques can also be applied to obtain reduced complexity iterative techniques for determining the transmit/receive signals or beamformers themselves.