  This paper considers pilot-based channel estimation in large-scale
multiple-input multiple-output (MIMO) communication systems, also known as
massive MIMO, where there are hundreds of antennas at one side of the link.
Motivated by the fact that computational complexity is one of the main
challenges in such systems, a set of low-complexity Bayesian channel
estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are
introduced for arbitrary channel and interference statistics. While the
conventional minimum mean square error (MMSE) estimator has cubic complexity in
the dimension of the covariance matrices, due to an inversion operation, our
proposed estimators significantly reduce this to square complexity by
approximating the inverse by a L-degree matrix polynomial. The coefficients of
the polynomial are optimized to minimize the mean square error (MSE) of the
estimate.
  We show numerically that near-optimal MSEs are achieved with low polynomial
degrees. We also derive the exact computational complexity of the proposed
estimators, in terms of the floating-point operations (FLOPs), by which we
prove that the proposed estimators outperform the conventional estimators in
large-scale MIMO systems of practical dimensions while providing a reasonable
MSEs. Moreover, we show that L needs not scale with the system dimensions to
maintain a certain normalized MSE. By analyzing different interference
scenarios, we observe that the relative MSE loss of using the low-complexity
PEACH estimators is smaller in realistic scenarios with pilot contamination. On
the other hand, PEACH estimators are not well suited for noise-limited
scenarios with high pilot power; therefore, we also introduce the
low-complexity diagonalized estimator that performs well in this regime.
Finally, we ...
