  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.
