  Due to its ability of overcoming the impact of double-fading effect, active
intelligent reflecting surface (IRS) has attracted a lot of attention. Unlike
passive IRS, active IRS should be supplied by power, thus adjusting power
between base station (BS) and IRS having a direct impact on the system rate
performance. In this paper, the active IRS-aided network under a total power
constraint is modeled with an ability of adjusting power between BS and IRS.
Given the transmit beamforming at BS and reflecting beamforming at IRS, the SNR
expression is derived to be a function of power allocation (PA) factor, and the
optimization of maximizing the SNR is given. Subsequently, two high-performance
PA strategies, enhanced multiple random initialization Newton's (EMRIN) and
Taylor polynomial approximation (TPA), are proposed. The former is to improve
the rate performance of classic Netwon's method to avoid involving a local
optimal point by using multiple random initializations. To reduce its high
computational complexity, the latter provides a closed-form solution by making
use of the first-order Taylor polynomial approximation to the original SNR
function. Actually, using TPA, the original optimization problem is transformed
into a problem of finding a root for a third-order polynomial.Simulation
results are as follows: the first-order TPA of SNR fit its exact expression
well, the proposed two PA methods performs much better than fixed PA in
accordance with rate, and appoaches exhaustive search as the number of IRS
reflecting elements goes to large-scale.
