  Due to its intrinsic ability to combat the double fading effect, the active
intelligent reflective surface (IRS) becomes popular. The main feature of
active IRS must be supplied by power, and the problem of how to allocate the
total power between base station (BS) and IRS to fully explore the rate gain
achieved by power allocation (PA) to remove the rate gap between existing PA
strategies and optimal exhaustive search (ES) arises naturally. First, the
signal-to-noise ratio (SNR) expression is derived to be a function of PA factor
beta [0, 1]. Then, to improve the rate performance of the conventional gradient
ascent (GA), an equal-spacing-multiple-point-initialization GA (ESMPI-GA)
method is proposed. Due to its slow linear convergence from iterative GA, the
proposed ESMPI-GA is high-complexity. Eventually, to reduce this high
complexity, a low-complexity closed-form PA method with third-order Taylor
expansion (TTE) centered at point beta0 = 0.5 is proposed. Simulation results
show that the proposed ESMPI-GA and TTE obviously outperform existing methods
like equal PA.
