Due to the black-box characteristics of deep learning based semantic encoders and decoders, finding a tractable method for the performance analysis of semantic communications is a challenging problem. In this paper, we propose an Alpha-Beta-Gamma (ABG) formula to model the relationship between the end-to-end measurement and SNR, which can be applied for both image reconstruction tasks and inference tasks. Specifically, for image reconstruction tasks, the proposed ABG formula can well fit the commonly used DL networks, such as SCUNet, and Vision Transformer, for semantic encoding with the multi scale-structural similarity index measure (MS-SSIM) measurement. Furthermore, we find that the upper bound of the MS-SSIM depends on the number of quantized output bits of semantic encoders, and we also propose a closed-form expression to fit the relationship between the MS-SSIM and quantized output bits. To the best of our knowledge, this is the first theoretical expression between end-to-end performance metrics and SNR for semantic communications. Based on the proposed ABG formula, we investigate an adaptive power control scheme for semantic communications over random fading channels, which can effectively guarantee quality of service (QoS) for semantic communications, and then design the optimal power allocation scheme to maximize the energy efficiency of the semantic communication system. Furthermore, by exploiting the bisection algorithm, we develop the power allocation scheme to maximize the minimum QoS of multiple users for OFDMA downlink semantic communication Extensive simulations verify the effectiveness and superiority of the proposed ABG formula and power allocation schemes.

本文针对深度学习语义编码器和解码器的黑箱特性所带来的性能分析难题，提出了一种Alpha-Beta-Gamma (ABG)公式，用于建模端对端测量与信噪比(SNR)之间的关系。通过该公式，研究了自适应功率控制方案，有效保障语义通信的服务质量(QoS)，并优化了功率分配方案，从而提升语义通信系统的能源效率。

基于实证结果的语义通信建模与性能分析