Mutual Information for Electromagnetic Information Theory Based on Random Fields

Traditional channel capacity based on the discrete spatial dimensions mismatches the continuous electromagnetic fields. For the wireless communication system in a limited region, the spatial discretization may results in information loss because the continuous field can not be perfectly recovered from the sampling points. Therefore, electromagnetic information theory based on spatially continuous electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of communication systems. In this paper, we first model the communication process between two continuous regions by random fields. Then, we analyze a special case with parallel linear finite-length source and destination to derive the mutual information and the capacity bound. Specifically, we use Mercer expansion to derive the mutual information between the source and the destination. We introduce Fredholm determinant to provide a closed-form solution of the mutual information and provide numerical calculation scheme under non-white noise model. Finally, we build an ideal model with infinite-length source and destination which shows a strong correpsondance with the model in classical information theory in the time domain. The mutual information and the capacity are derived through the spatial spectral density.