A General DoF and Pattern Analyzing Scheme for Electromagnetic Information Theory

Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, one of the most important research directions is degree of freedom (DoF) analysis. Existing research works on DoF analysis for EIT focus on asymptotic conclusions of DoF, which do not well fit the practical wireless communication systems with finite spatial regions and finite frequency bandwidth. In this paper, we provide mathematical definitions of the DoF for continuous electromagnetic fields. Moreover, we theoretically prove that the channel DoF is upper-bounded by the proposed functional DoF of electromagnetic fields. Furthermore, we use the theoretical analyzing tools from the Slepian concentration problem and extend them to three-dimensional space domains and four-dimensional space-time domains under electromagnetic constraints. Then we provide asymptotic DoF conclusions and non-asymptotic DoF analyzing scheme, which suits practical scenarios better, under different scenarios like three-dimensional antenna array. Finally, we use numerical analysis to provide some insights about the optimal spatial sampling interval of the antenna array, the DoF of three-dimensional antenna array, the impact of unequal antenna spacing, the orthogonal space-time patterns, etc.