In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.

In this two-part paper, we investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In Part I, 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 in the massive MIMO-OFDM channel estimation and the asymptotic analysis, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other at each iteration of IGA, and the first-order natural parameters of the distributions on all the auxiliary manifolds are asymptotically equivalent to each other at the fixed point of IGA. Motivated by these results, we simplify the iterative process of IGA and propose a simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at the fixed point, the a posteriori mean obtained by the simplified IGA is asymptotically optimal. The simplified IGA allows efficient implementation with fast Fourier transformation (FFT). Simulations confirm that the simplified IGA can achieve near the optimal performance with low complexity in a limited number of iterations.