On the Design of Broadbeam of Reconfigurable Intelligent Surface

Reconfigurable intelligent surface (RIS) has been identified as a promising disruptive innovation to realize a faster, safer and more efficient communication system. In this paper, we study the broad beamwidth design of RIS. A problem is formulated to achieve broadbeam with maximum and equal power gain within a pre-defined angular region given constraints of the unit modulus weights of RIS. Since the formulated problem is non-convex, where the optimal solution cannot be analytically obtained, we propose the difference-of-convex-based semi-definite programming (DC-SDP) algorithm. In addition, as important guidance of signal coverage for arbitrary angular regions, we mathematically derive the relationship between the angular range of the spatial sector and the maximum average received power. The upper bounds of the average received power with different RIS configurations are also obtained, where uniform rectangular array (URA) and uniform linear array (ULA) are considered. Simulation results demonstrate the effectiveness of our derivations and verify that our proposed DC-SDP algorithm is applicable in practical applications and outperforms other baseline methods. Overall, this work can be viewed as a foundation for the practical implementation of RIS on coverage enhancement and can also be seen as an initial step towards achieving channel estimation.