  We investigate the channel estimation for massive multiple-input
multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems.
We revisit the information geometry approach (IGA) for massive MIMO-OFDM
channel estimation. By using the constant magnitude property of the entries of
the measurement matrix, we find that the second-order natural parameters of the
distributions on all the auxiliary manifolds are equivalent to each other, and
the first-order natural parameters are asymptotically equivalent to each other
at the fixed point. Motivated by these results, we simplify the process of IGA
and propose an efficient IGA (EIGA) for massive MIMO-OFDM channel estimation,
which allows efficient implementation with fast Fourier transformation (FFT).
We then establish a sufficient condition of its convergence and accordingly
find a range of the damping factor for the convergence. We show that this range
of damping factor is sufficiently wide by using the specific properties of the
measurement matrices. Further, we prove that at the fixed point, the a
posteriori mean obtained by EIGA is asymptotically optimal. Simulations confirm
that EIGA can achieve the optimal performance with low complexity in a limited
number of iterations.
