Ray description of the scattering from polygonal non-specularly reflecting intelligent surfaces for smart radio environments

Mobile traffic is experiencing an exponential growth in the last years, accompanied by the demand for high data throughput, short time latency and low energy consumption. These challenging requirements are difficult to satisfy using current wireless communication techniques. In this framework, the futuristic concept of smart radio environment (SRE) has recently emerged as a new paradigm for future communication systems (M. Di Renzo, et al., “Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come,” J Wireless Com Network, vol. 2019, 129, 2019). The revolutionary idea at the basis of this concept is the use of software-controlled metasurfaces (MTSs) to engineer the radio environment. In particular, these MTSs can be used as reflective relay, able to re-route the impinging signal in a desired direction. In order to perform this amazing functionality, different statuses of the reconfigurable MTSs must be designed to reflect the impinging field in a pre-defined direction, different from the specular one (the so-called “anomalous reflection). This is done by introducing a proper periodic modulation in the boundary conditions offered by the metasurface, so as to excite higher order diffraction modes. While simplified models used for a preliminary analysis of SREs have assumed an ideal MTS behavior, it has been shown in the literature that it is not in general possible to obtain a perfect anomalous reflection (V. S. Asadchy et al, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94, 075142 2016), and therefore part of the imping power will be inevitably radiated in some undesired direction, which in generally leads to a reduction of the link efficiency and possibly to detrimental interferences. Furthermore, the finite size of the MTS has also an impact on its scattering behavior. This effect must be taken into account in order to assess the overall performances of the wireless communication system. For this reason, it is fundamental to develop a tool for an accurate estimate of the scattering from a finite MTS characterized by periodic boundary conditions of impedance type. For an effective analysis, such tool should be efficient and easy to use for system performance estimation and network planning. This contribution provides a rigorous approach to derive a ray-representation of the field scattered from a generical polygonal MTS with periodic impedance boundary conditions. The proposed approach consists of two steps: first, the corresponding infinite periodic problem is analyzed for finding the current distribution in terms of a Floquet Wave expansion, then, such current distribution is windowed over the polygonal surface for calculating the scattered field through an asymptotic evaluation of the radiation integral (F. Capolino, et al., “Frequency-domain Green's function for a planar periodic semi-infinite phased array .I. Truncated Floquet wave formulation,” in IEEE Transactions on Antennas and Propagation, vol. 48, no. 1, pp. 67-74, Jan. 2000.). In this step, Stokes theorem is applied to find a closed form representation of the scattered field in terms of rays. The possibility of describing the field scattered by a reflective intelligent surface in terms of rays in the Fresnel zone of the scatterer paves the way for an efficient deterministic analysis of SREs. Details of the formulation will be presented at the conference, along with numerical results