In this paper, we propose a relative channel estimation error (RCEE) metric,
and derive closed-form expressions for its expectation Exprcee and
the achievable uplink rate holding for any number of base station antennas M,
with the least squares (LS) and minimum mean squared error (MMSE) estimation
methods. It is found that RCEE and Exprcee converge to the same
constant value when M→∞, resulting in the pilot power
allocation (PPA) is substantially simplified and a PPA algorithm is proposed to
minimize the average Exprcee per user with a total pilot power
budget P in multi-cell massive multiple-input multiple-output systems.
Numerical results show that the PPA algorithm brings considerable gains for the
LS estimation compared with equal PPA (EPPA), while the gains are only
significant with large frequency reuse factor (FRF) for the MMSE estimation.
Moreover, for large FRF and large P, the performance of the LS approaches to
the performance of the MMSE, which means that simple LS estimation method is a
very viable when co-channel interference is small. For the achievable uplink
rate, the PPA scheme delivers almost the same average achievable uplink rate
and improves the minimum achievable uplink rate compared with the EPPA scheme.Comment: 30 pages, 5 figures, submitted to IEEE Transactions on Communication