Weighted Sum-Rate Maximization and Task Completion Time Minimization for Multi-Tag MIMO Symbiotic Radio Networks

Symbiotic radio (SR) has recently emerged as a promising paradigm for enabling spectrum- and energy-efficient massive connectivity in low-power Internet-of-Things (IoT) networks. By allowing passive backscatter devices (BDs) to coexist with active primary link transmissions, SR significantly improves spectrum utilization without requiring dedicated spectrum resources. However, most existing studies on multi-tag multiple-input multiple-output (MIMO) SR systems assume homogeneous traffic demands among BDs and primarily focus on rate-based performance metrics, while neglecting system-level task completion time (TCT) optimization under heterogeneous data requirements. In this paper, we investigate a joint performance optimization framework for a multi-tag MIMO symbiotic radio network. We first formulate a weighted sum-rate (WSR) maximization problem for the secondary backscatter links. The original non-convex WSR maximization problem is transformed into an equivalent weighted minimum mean square error (WMMSE) problem, and then solved by a block coordinate descent (BCD) approach, where the transmit precoding matrix, decoding filters, backscatter reflection coefficients are alternatively optimized. Second, to address the transmission delay imbalance caused by heterogeneous data sizes among BDs, we further propose a rate weight adaptive task TCT minimization scheme, which dynamically updates the rate weight of each BD to minimize the overall TCT. Simulation results demonstrate that the proposed framework significantly improves the WSR of the secondary system without degrading the primary link performance, and achieves substantial TCT reduction in multi-tag heterogeneous traffic scenarios, validating its effectiveness and robustness for MIMO symbiotic radio networks.