Degrees of Freedom with Small and Large Linear Surfaces in the Near Field

This paper examines the number of the communication modes, i.e., the degrees of freedom (DoF), that are available in a wireless setup with a small linear intelligent surface in the near field of a large linear intelligent surface. The framework allows for any orientation between the surfaces and any position in a two dimensional space assuming that the transmitting one is placed at the origin. Therefore, apart from the length of the two surfaces, four more parameters are considered, the Cartesian coordinates of the center of the receiving surface and two angles that model each surface rotation around its center. The paper starts with the deterministic calculation of the DoF for a generic geometric setup, which extends beyond the widely studied paraxial setting. Subsequently, a stochastic geometry framework is proposed to study the statistical behaviour of the DoF under a typical geometric setup in a mmWave network. Numerical results revealed the extreme capabilities in the achievable DoF provided by near-field communications and allow the derivation of key system-level insights for mmWave 6G networks.