Beamforming for PIN Diode-Based IRS-Assisted Systems Under a Phase Shift-Dependent Power Consumption Model

Intelligent reflecting surfaces (IRSs) have been regarded as a promising enabler for future wireless communication systems due to their capability of customizing favorable propagation environments. 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, which implies that the beamforming quality of the IRS depends on the available power. Therefore, this phase shift-dependent power consumption (PS-DPC) introduces a challenging power allocation problem between the base station (BS) and the IRS, requiring to balance the BS transmit power and the IRS beamforming quality during system design. 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, we extend the beamforming design to the multi-user case, where 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. Specifically, when the available 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, which consequently reduces the beamforming quality at the IRS due to the limited PS-DPC budget.