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.

翻译：本文研究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。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）。通过利用测量矩阵元素的恒定幅度特性，我们发现所有辅助流形上分布的二阶自然参数彼此等价，且一阶自然参数在不动点处渐近等价。基于这些结果，我们简化了IGA的处理流程，提出了一种用于大规模MIMO-OFDM信道估计的高效IGA（EIGA），该方法可通过快速傅里叶变换（FFT）实现高效计算。随后，我们建立了其收敛的充分条件，并据此确定了保证收敛的阻尼因子取值范围。利用测量矩阵的特定性质，我们证明该阻尼因子取值范围具有足够的宽度。进一步地，我们证明了在不动点处，EIGA得到的后验均值是渐近最优的。仿真实验表明，EIGA能够在有限迭代次数内以较低复杂度达到最优性能。