  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.
