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• The jointly optimization can be significantly higher than the literature. • The proposed scheme's performance is better than only transmit power optimization. • The energy efficiency decreases with parameter a and b increasing. • The joint optimization can improve the overall system energy efficiency. • The proposed scheme can reduce the system BER effectively and significantly. For the ambient backscatter communication system, a joint optimization algorithm based on the energy efficiency maximization criterion was proposed in this paper by designing a two-hop wireless information and energy transmission scheme. The source side of this system was configured with multiple antennas and employed Max Ratio Transmission (MRT) precoding method. The relay node (hot spots or tag node) utilized the power split approach to transmit information and harvest energy. In allusion to the established transmission system with large scale nodes, a joint optimization algorithm was applied to the number of source antennas, the transmission power and power splitting factor to obtain the maximum energy efficiency of the system. Using the high SNR approximation method transformed the non-convex into convex to solve the non-convex problem in the optimization target. The optimal solution of joint optimization for transmit power, antennas' number and power splitting factor was derived by using Lambert function function. Finally, the simulation results show that the proposed joint design achieves significant energy efficiency gain as compared to other optimized schemes. [ABSTRACT FROM AUTHOR]