  In this paper, we demonstrate the optimal power allocation for QPSK, 16-QAM,
and 64-QAM modulation schedules and the role of channel quality indicator
(CQI). We used sigmoidal-like utility functions to represent the probability of
successful reception of packets at user equipment (UE). CQI as a feedback to
the base station (BS) indicates the data rate that a downlink channel can
support. With Levenberg-Marquardt (LM) Optimization method, we present utility
functions of different CQI values for standardized 15 Modulation order and
Coding Scheme (MCS) in $3^{rd}$ Generation Partnership Project (3GPP). Finally,
we simulate and show the results of the optimal power allocation algorithm.
