Channel Estimation for Massive MIMO: An Information Geometry Approach

In this paper, we investigate the channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Using the sampled steering vectors in the space and frequency domain, we first establish a space-frequency (SF) beam based statistical channel model. The accuracy of the channel model can be guaranteed with sufficient sampling steering vectors. With the channel model, the channel estimation is formulated as obtaining the
$a \ posteriori$
information of the beam domain channel. We solve this problem by calculating an approximation of the
$a\ posteriori$
distribution's marginals within the information geometry framework. Specifically, by viewing the set of Gaussian distributions and the set of the marginals as a manifold and its
$e$
-flat submanifold, we turn the calculation of the marginals into an iterative projection process between submanifolds with different constraints. We derive the information geometry approach (IGA) for channel estimation by calculating the solutions of projections. We prove that the mean of the approximate marginals at the equilibrium of IGA is equal to that of the
$a \ posteriori$
distribution. Simulations demonstrate that the proposed IGA can accurately estimate the beam domain channel within limited iterations.