  This paper considers the jointly optimal pilot and data power allocation in
single cell uplink massive MIMO systems. A closed form solution for the optimal
length of the training interval is derived. Using the spectral efficiency (SE)
as performance metric and setting a total energy budget per co- herence
interval the power control is formulated as optimization problems for two
different objective functions: the minimum SE among the users and the sum SE.
The optimal power control policy is found for the case of maximizing the
minimum SE by converting it to a geometric program (GP). Since maximizing the
sum SE is an NP-hard problem, an efficient algorithm is developed for finding
KKT (local maximum) points. Simulation results show the advantage of optimizing
the power control over both pilot and data power, as compared to heuristic
power control policies.
