Robust Beamforming Design for Aggregated Visible Light Communication and Radio Frequency Systems

The robust beamforming design for the aggregated Visible Light Communication (VLC) and Radio Frequency (RF) system are studied for the first time. Specifically, with imperfect Channel State Informations (CSIs) of both VLC and RF channels, robust beam formers design schemes are proposed to minimize the transmit power of the aggregated VLC-RF system, while satisfying both the minimum rate requirements and dimming control constraints. However, there are infinite constraints of the robust beamforming design problem, which is intractable in general. Through Semi-Definite Relaxation (SDR), the non-convex original problem is relaxed firstly, and then conservative reformulated it into a convex Semi-Definite Program (SDP) by exploiting S lemma, which can be efficiently solved by interior point methods. Finally, the robust and effectiveness of the proposed robust aggregated VLC-RF scheme are verified by numerical simulation results.