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 propose analyzing schemes for the performance limit between continuous transceivers. Specifically, we model the communication process between two continuous regions by random fields. Then, for the white noise model, we use Mercer expansion to derive the mutual information between the source and the destination. For the close-form expression, an analytic method is introduced based on autocorrelation functions with rational spectrum. Moreover, the Fredholm determinant is used for the general autocorrelation functions to provide the numerical calculation scheme. Further works extend the white noise model to colored noise and discuss the mutual information under it. Finally, we build an ideal model with infinite-length source and destination which shows a strong correpsondence with the time-domain model in classical information theory. The mutual information and the capacity are derived through the spatial spectral density.