Large-scale MIMO systems with a massive number N of individually controlled antennas pose significant challenges for minimum mean square error (MMSE) channel estimation, based on uplink pilots. The major ones arise from the computational complexity, which scales with $N^3$, and from the need for accurate knowledge of the channel statistics. This paper aims to address both challenges by introducing reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated. This is achieved by exploiting the inherent structure of the spatial correlation matrix induced by the array geometry. Specifically, we use a Kronecker decomposition for uniform planar arrays and a well-suited circulant approximation for uniform linear arrays. By doing so, a significantly lower computational complexity is achieved, scaling as $N\sqrt{N}$ and $N\log N$ for squared planar arrays and linear arrays, respectively.

翻译：基于上行链路导频的大规模MIMO系统，其海量独立控制天线数N给最小均方误差信道估计带来了重大挑战。主要挑战源于计算复杂度随$N^3$增长，以及对信道统计特性精确先验知识的需求。本文旨在通过引入低复杂度信道估计方法同时应对这两项挑战：所提方法在估计精度和上行链路频谱效率方面达到MMSE性能，并在需估计信道统计特性的实际场景中展现出更强的鲁棒性。这是通过利用阵列几何结构诱导的空间相关矩阵固有特性实现的。具体而言，对均匀平面阵列采用克罗内克分解，对均匀线性阵列采用适配的循环近似。由此，计算复杂度得以显著降低——方形平面阵列与线性阵列的复杂度分别按$N\sqrt{N}$和$N\log N$增长。