Optimal and Robust Beamforming Design for Multiuser Semantic Interference Networks

In this paper, we investigate optimal and robust beamforming design for multi-user semantic multiple-input-single-output (MISO) interference networks. To provide semantic information transmission quality of service (QoS) guarantees, we proposes an ABG formula to measure relationship between semantic information transmission quality and signal-to-interference-plus-noise ratios (SINRs). Based on this ABG formula, we propose an optimal beamforming design scheme that can provide real-time transmission quality assurance for multiple users with the minimum power consumption. Moreover, for the users fairness considerations, we investigate beamformer design that maximizes the worst semantic QoS under transmission power constraints, which is non-convex. To address this challenge, we transform it into a quasi-convex problem by introducing an auxiliary variable, and then further reformulate it to a series of convex feasibility subproblems. Furthermore, considering the practical channel estimation errors, we propose a relaxation and restriction approach for robust beamformers design with bounded channel state information (CSI) errors in multi-user MISO interference networks, which convert infinite non-convex semantic QoS constraints to a finite number of linear matrix inequalities (LMIs) based on semidefinite relaxation (SDR) and S-lemma, respectively. The experimental results show that the proposed robust beamforming method can guarantee the QoS of users with CSI error, which significantly outperforms existing methods.