  The performance of cooperative ambient backscatter communications (CABC) can
be enhanced by employing reconfigurable intelligent surface (RIS) to assist
backscatter transmitters. Since the RIS power consumption is a non-negligible
issue, we consider a RIS assisted CABC system where the RIS with energy
harvesting circuit can not only reflect signal but also harvest wireless
energy. We study a transmission design problem to minimize the RIS power
consumption with the quality of service constraints for both active and
backscatter transmissions. The optimization problem is a mixed-integer
non-convex programming problem which is NP-hard. To tackle it, an algorithm is
proposed by employing the block coordinate descent, semidefinite relaxation and
alternating direction method of multipliers techniques. Simulation results
demonstrate the effectiveness of the proposed algorithm.
