Electromagnetic Property Sensing and Channel Reconstruction Based on Diffusion Schrödinger Bridge in ISAC

Integrated sensing and communications (ISAC) has emerged as a transformative paradigm for next-generation wireless systems. In this paper, we present a novel ISAC scheme that leverages the diffusion Schr¨odinger bridge (DSB) to realize the sensing of electromagnetic (EM) property of a target as well as the reconstruction of the wireless channel. The DSB framework connects EM property sensing and channel reconstruction by establishing a bidirectional process: the forward process transforms the distribution of EM property into the channel distribution, while the reverse process reconstructs the EM property from the channel. To handle the difference in dimensionality between the high-dimensional sensing channel and the lower-dimensional EM property, we generate latent representations using an autoencoder network. The autoencoder compresses the sensing channel into a latent space that retains essential features, which incorporates positional embeddings to process spatial context. The simulation results demonstrate the effectiveness of the proposed DSB framework, which achieves superior reconstruction of the targets shape, relative permittivity, and conductivity. Moreover, the proposed method can also realize accurate channel reconstruction given the EM property of the target. The dual capability of accurately sensing the EM property and reconstructing the channel across various positions within the sensing area underscores the versatility and potential of the proposed approach for broad application in future ISAC systems.