  This paper models an active intelligent reflecting surface (IRS) -assisted
wireless communication network, which has the ability to adjust power between
BS and IRS. We aim to maximize the signal-to-noise ratio of user by jointly
designing power allocation (PA) factor, active IRS phase shift matrix, and
beamforming vector of BS, subject to a total power constraint. To tackle this
non-convex problem, we solve this problem by alternately optimizing these
variables. Firstly, the PA factor is designed via polynomial regression method.
Next, BS beamforming vector and IRS phase shift matrix are obtained by
Dinkelbach's transform and successive convex approximation methods. To reduce
the high computational complexity of the above proposed algorithm, we maximize
achievable rate (AR) and use closed-form fractional programming method to
transform the original problem into an equivalent form. Then, we address this
problem by iteratively optimizing auxiliary variables, BS and IRS beamformings.
Simulation results show that the proposed algorithms can effectively improve
the AR performance compared to fixed PA strategies, aided by passive IRS, and
without IRS.
