Degrees of Freedom and Spatial Sampling in Electromagnetic Fields

Electromagnetic (EM) fields constitute the fundamental physical medium carrying information in wireless communications and sensing. It is therefore critically important to investigate the fundamental structure of wireless signals and information under the physical laws governing EM wave propagation. In this letter, we derive the spatial bandwidth of harmonic EM fields in a physically intuitive manner to assess the degrees of freedom (DoFs) of EM fields. Based on the resultant DoF analysis, spatial sampling algorithms are developed to determine antenna placement for EM field measurements, using both global and local spatial bandwidths, respectively. Numerical simulations are conducted to demonstrate the validity of the proposed sampling algorithms.