Convex relaxation for illumination control of multi-color multiple-input-multiple-output visible light communications with linear minimum mean square error detection

Visible light communications (VLC) using multi-color light-emitting diodes (LEDs) can support simultaneous high-speed data rate and high-quality lighting. However, since the radiation spectrum of LEDs has a limited width, spectral overlapping will result in multi-color cross talk even when optical filters are applied at the receivers. Moreover, since LEDs are used for illumination and wireless data transmission in the meantime, both lighting quality and communication performance must be considered in VLC systems. In this paper, we consider a multiple-input-multiple-output with low-complexity linear minimum mean square error detection to collaboratively manage the cross talk by maximizing the minimum signal-to-interference-plus-noise ratio (SINR) subject to chromaticity constraint based on MacAdam ellipse, luminance constraint, and signal range constraint. A sub-optimal convex relaxation is proposed to attack the SINR maximization problem. Extensive simulations indicate that the proposed method provides very efficient solutions and outperforms the conventional wave-division multiplexing scheme under the illumination constraint.