Electromagnetic Degrees of Freedom for Continuous-Aperture Array (CAPA) Systems

The spatial degrees of freedom (DoFs) of a continuous-aperture array (CAPA)-based continuous electromagnetic (EM) channel are analyzed. To this end, a simplified spatial model is derived using the Fresnel approximation. Leveraging this model and Landau's theorem, a closed-form expression for the spatial DoFs is derived. It is demonstrated that the number of DoFs is proportional to the transmit and receive aperture sizes while being inversely proportional to the propagation distance. Numerical results are provided to validate the accuracy of the derived expressions.