A Denoising Diffusion Probabilistic Model-Based Digital Twinning of ISAC MIMO Channel

Deep learning (DL) techniques have been extensively utilized to tackle challenges in the field of wireless communication, overcoming the limitations of traditional methods. However, training DL algorithms often requires large amounts of data, which is difficult to obtain in increasingly complex communication environments. Reducing the amount of data required for DL training is therefore an urgent problem to be solved. In this work, we develop a denoising diffusion probabilistic model (DDPM)-based digital twin (DT) framework of integrated sensing and communication (ISAC) multiple-input-multiple-output (MIMO) channel to address the data scarcity issue commonly found in DL-based scenarios. By sampling a small amount of data, our framework captures and simulates the data distribution, building a virtual data repository that can continuously provide samples to assist in executing control instructions to physical entities, even as the user equipment (UE) and target positions change. Specifically, we formulate the data generation problem as a distribution approximation task guided by the Kullback-Leibler (KL) divergence criterion and optimize it by meticulously designing a DDPM network composed of U-Net structure, time-embedding modules, and attention mechanisms. Moreover, we enhance the framework by formulating a task-driven objective function for two applications: 1) sensing channel estimation and 2) target detection. Numerical results demonstrate the superiority of our proposed DDPM-based DT framework compared with other data augmentation techniques in improving the performance of data-driven DL-based tasks, showcasing its robustness across diverse scenarios.