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.

翻译：本两部分论文研究了大规模多输入多输出正交频分复用（MIMO-OFDM）系统的信道估计问题。在第一部分中，我们重新审视了用于大规模MIMO-OFDM信道估计的信息几何方法（IGA）。通过利用大规模MIMO-OFDM信道估计中测量矩阵元素的恒定模量特性以及渐近分析，我们发现：在IGA每次迭代中，所有辅助流形上分布的二阶自然参数彼此等价；在IGA的不动点处，所有辅助流形上分布的一阶自然参数渐近等价。基于这些结论，我们简化了IGA的迭代过程，并提出了一种用于大规模MIMO-OFDM信道估计的简化IGA。理论证明，在不动点处，简化IGA获得的后验均值是渐近最优的。该简化IGA可通过快速傅里叶变换（FFT）高效实现。仿真结果表明，简化IGA在有限迭代次数下能以低复杂度逼近最优性能。