The commensal symbiotic radio (CSR) system is proposed as a novel solution for connecting systems through green communication networks. This system enables us to establish secure, ubiquitous, and unlimited connectivity, which is a goal of 6G. The base station uses MIMO antennas to transmit its signal. Passive IoT devices, called symbiotic backscatter devices (SBDs), receive the signal and use it to charge their power supply. When the SBDs have data to transmit, they modulate the information onto the received ambient RF signal and send it to the symbiotic user equipment, which is a typical active device. The main purpose is to enhance energy efficiency in this network by minimizing energy consumption (EC) while ensuring the minimum required throughput for SBDs. To achieve this, we propose a new scheduling scheme called Timing-SR that optimally allocates resources to SBDs. The main optimization problem involves non-convex objective functions and constraints. To solve this, we use mathematical techniques and introduce a new approach called sequential quadratic and conic quadratic representation to relax and discipline the problem, leading to reducing its complexity and convergence time. The simulation results demonstrate that the proposed approach outperforms other outlined schemes in reducing EC.