This paper addresses robust beamforming design for rate splitting multiple access (RSMA)-aided multiple-input single-output (MISO) visible light communication (VLC) networks. In particular, since the channel capacity of VLC is yet unknown, we derive the first theoretical bound of channel capacity of RSMA-aided VLC networks, i.e., achievable rates with closed-form expressions. For the perfect channel state information (CSI) scenario, we investigate the beamforming design to minimize the transmitted power of RSMA-aided VLC networks under the quality of service (QoS) constraint of each user and the optical power constraints, and propose a constrained-convex-concave programming (CCCP)-based beamforming design algorithm to obtain high-quality beamformers. Moreover, for the imperfect CSI scenario, we propose a robust CCCP-based beamforming design scheme for RSMA-aided VLC networks by exploiting semidefinite relaxation (SDR) technique and S-lemma. Numerical results show that the proposed RSMA schemes offer a significant spectral efficiency gain over the existing space-division multiple access (SDMA) scheme and non-orthogonal multiple access (NOMA) scheme.
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