  The adoption of reconfigurable intelligent surface (RIS) in wireless networks
can enhance the spectrum- and energy-efficiency by controlling the propagation
environment. Although the RIS does not consume any transmit power, the circuit
power of the RIS cannot be ignored, especially when the number of reflecting
elements is large. In this paper, we propose the joint design of beamforming
vectors at the base station, active RIS set, and phase-shift matrices at the
active RISs to minimize the network power consumption, including the RIS
circuit power consumption, while taking into account each user's target data
rate requirement and each reflecting element's constant modulus constraint.
However, the formulated problem is a mixed-integer quadratic programming (MIQP)
problem, which is NP-hard. To this end, we present an alternating optimization
method, which alternately solves second order cone programming (SOCP) and MIQP
problems to update the optimization variables. Specifically, the MIQP problem
is further transformed into a semidefinite programming problem by applying
binary relaxation and semidefinite relaxation. Finally, an efficient algorithm
is developed to solve the problem. Simulation results show that the proposed
algorithm significantly reduces the network power consumption and reveal the
importance of taking into account the RIS circuit power consumption.
