Holographic MIMO (hMIMO) systems with a massive number of individually controlled antennas N make minimum mean square error (MMSE) channel estimation particularly challenging, due to its computational complexity that scales as $N^3$ . This paper investigates uniform linear arrays and proposes a low-complexity method based on the discrete Fourier transform (DFT) approximation, which follows from replacing the covariance matrix by a suitable circulant matrix. Numerical results show that, already for arrays with moderate size (in the order of tens of wavelengths), it achieves the same performance of the optimal MMSE, but with a significant lower computational load that scales as $N \log N$. Interestingly, the proposed method provides also increased robustness in case of imperfect knowledge of the covariance matrix.

翻译：全息MIMO（hMIMO）系统采用大量独立控制的天线N，其最小均方误差（MMSE）信道估计面临严峻挑战，因为计算复杂度与$N^3$成正比。本文研究均匀线性阵列，并提出一种基于离散傅里叶变换（DFT）近似的低复杂度方法，该方法通过将协方差矩阵替换为合适的循环矩阵来实现。数值结果表明，对于尺度适中（波长量级为数十倍）的阵列，该方法在实现与最优MMSE相同性能的同时，计算负载显著降低至$N \log N$量级。有趣的是，该方法在协方差矩阵非理想已知的情况下还提供了更强的鲁棒性。