  Millimeter-wave (mmWave) communications is considered as a key enabler
towards the realization of next-generation wireless networks, due to the
abundance of available spectrum at mmWave frequencies. However, mmWave suffers
from high free-space path-loss and poor scattering resulting in mostly
line-of-sight (LoS) channels which result in a lack of coverage. Reconfigurable
intelligent surfaces (RIS), as a new paradigm, have the potential to fill the
coverage holes by shaping the wireless channel. In this paper, we propose a
novel approach for designing RIS with elements arranged in a uniform planar
array (UPA) structure. In what we refer to as multi-beamforming, We propose and
design RIS such that the reflected beam comprises multiple disjoint lobes.
Moreover, the beams have optimized gain within the desired angular coverage
with fairly sharp edges avoiding power leakage to other regions. We provide a
closed-form low-complexity solution for the multi-beamforming design. We
confirm our theoretical results by numerical analysis.
