Modeling and Performance Analysis for Semantic Communications Based on Empirical Results

TL;DR

This work introduces an empirical Alpha-Beta-Gamma (ABG) model that links end-to-end semantic-communication performance metrics to SNR for both data reconstruction and inference tasks, addressing the lack of theoretical tools due to DL-based encoders/decoders. The ABG form φ(ρ, nb) = α(nb) − γ/(1 + (βρ)^τ) with an nb-dependent upper bound α(nb) = c1 − c3/(1 + (c2 nb)^{c4}) captures the nonlinearity and saturation observed in DL-based systems, and parameter fitting is demonstrated across CNN, SCUNet, ViT, and Swin Transformer architectures. Building on ABG, the paper develops adaptive single-user power control, a Dinkelbach-based energy efficiency optimization, and a multi-user LP-based allocation for OFDMA downlink to maximize QoS metrics like MS-SSIM under channel constraints. Extensive simulations on CIFAR-10 show ABG fits MS-SSIM, PSNR, SSIM, and even inference BLEU metrics, and multi-user results reveal substantial improvements over fixed power schemes, highlighting the practical viability of ABG-guided resource allocation in semantic communications.

Abstract

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.

Figures (15)

• Figure 1: Typical semantic communication system.
• Figure 2: MS-SSIM performance and the corresponding ABG formulas versus SNR $\rho$ in CIFAR-10 dataset under Rayleigh channels: (a) CNN based semantic communication systems; (b) SCUNet based semantic communication systems; (c) Vision Transformer based semantic communication systems; (d) Swin Transformer based semantic communication systems.
• Figure 3: MS-SSIM performance versus the number of quantized bits $n_{\mathrm{b}}$ in CIFAR-10 dataset under Rayleigh channels: (a) CNN based semantic communication systems; (b) SCUNet based semantic communication systems; (c) Vision Transformer based semantic communication systems; (d) Swin Transformer based semantic communication systems.
• Figure 4: PSNR performance and the corresponding ABG formulas versus SNR $\rho$ in CIFAR-10 dataset under Rayleigh channels: (a) CNN based semantic communication systems; (b) SCUNet based semantic communication systems; (c) Vision Transformer based semantic communication systems; (d) Swin Transformer based semantic communication systems.
• Figure 5: PSNR performance of semantic communication systems versus the number of quantized bits ${n_{\mathrm{b}}}$ in CIFAR-10 dataset under Rayleigh channels: (a) CNN based semantic communication systems; (b) SCUNet based semantic communication systems; (c) Vision Transformer based semantic communication systems; (d) Swin Transformer based semantic communication systems.