Bayesian approaches for combining noisy mean and covariance channel information

In this paper techniques are proposed for combining information about the mean and the covariance of the channel for the purpose of two applications. One is channel estimation, possibly in a parametric or physical model form. The other concerns (partial) channel state information at the transmitter (CSIT), typically used in MIMO systems for the design of spatial prefiltering and water-filling. For the purpose of channel estimation, it has recently become customary to combine mean and covariance information in a Bayesian approach, leading to a MMSE or MAP improved channel estimate. For the purpose of generating CSIT, the cases of mean or covariance information are still being treated separately. A Bayesian approach is presented here incorporating both pieces of information. The approach yields the existing cases of mean or covariance information as special instances. We then take the unified approach one step further by allowing not only the mean information to be noisy but also the covariance information.