Non-Alternating Globally Optimal MMSE Precoding for Multiuser VLC Downlinks

We study the minimum mean-squared error (MMSE) precoding for multiuser visible light communication downlink systems. Different from radio frequency systems, this problem does not admit a closed-form solution due to the light-emitting diode optical power constraints. To handle the difficult non-convex problem, we transform it into an equivalent convex form via the Charnes-Cooper transformation. In this way, we are able to achieve the globally optimal MMSE precoder by solving only one convex problem, thus requiring much lower complexity than the existing alternating algorithm. The proposed non-alternating method is also extended to robust the MMSE precoder optimization in the presence of statistical channel-state information errors.