  Intelligent reflecting surfaces (IRSs) have been regarded as a promising
enabler for future wireless communication systems. In the literature, IRSs have
been considered power-free or assumed to have constant power consumption.
However, recent experimental results have shown that for
positive-intrinsic-negative (PIN) diode-based IRSs, the power consumption
dynamically changes with the phase shift configuration. This phase
shift-dependent power consumption (PS-DPC) introduces a challenging power
allocation problem between base station (BS) and IRS. To tackle this issue, in
this paper, we investigate a rate maximization problem for IRS-assisted systems
under a practical PS-DPC model. For the single-user case, we propose a
generalized Benders decomposition-based beamforming method to maximize the
achievable rate while satisfying a total system power consumption constraint.
Moreover, we propose a low-complexity beamforming design, where the powers
allocated to BS and IRS are optimized offline based on statistical channel
state information. Furthermore, for the multi-user case, we solve an equivalent
weighted mean square error minimization problem with two different joint power
allocation and phase shift optimization methods. Simulation results indicate
that compared to baseline schemes, our proposed methods can flexibly optimize
the power allocation between BS and IRS, thus achieving better performance. The
optimized power allocation strategy strongly depends on the system power
budget. When the system power budget is high, the PS-DPC is not the dominant
factor in the system power consumption, allowing the IRS to turn on as many PIN
diodes as needed to achieve high beamforming quality. When the system power
budget is limited, however, more power tends to be allocated to the BS to
enhance the transmit power, resulting in a lower beamforming quality at the IRS
due to the reduced PS-DPC budget.
