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.

翻译：传统基于离散空间维度的信道容量与连续电磁场不匹配。对于有限区域内的无线通信系统，空间离散化可能导致信息损失，因为连续场无法从采样点完美恢复。因此，基于空间连续电磁场的电磁信息论对于揭示通信系统的基本理论容量界变得必要。本文提出了连续收发器之间性能极限的分析方法。具体而言，我们通过随机场对两个连续区域之间的通信过程进行建模。然后，针对白噪声模型，利用Mercer展开推导了源端与目的端之间的互信息。为了得到闭式表达式，引入了基于有理谱自相关函数的解析方法。此外，利用Fredholm行列式对一般自相关函数进行了数值计算方案的推导。进一步的工作将白噪声模型扩展到有色噪声，并讨论了该模型下的互信息。最后，我们构建了一个具有无限长源端和目的端的理想模型，该模型与经典信息论中的时域模型具有强对应关系，并通过空间谱密度推导了互信息与信道容量。