## 1 Introduction  
As an emerging short-range wireless communication technology, visible light communication (VLC) can be regarded as a potential solution for providing data transmission and the inherent lighting simultaneously, which attracts tremendous attention worldwide [1; 2; 3]. Meanwhile, serving as the transmitter of the VLC system, light-emitting diode (LED) lighting is rapidly replacing the conventional incandescent and fluorescent lighting due to the notable advantages of fast switching capability, high energy efficiency and long lifetime [4; 5]. Generally, there are two kinds of LEDs, one is the phosphor-converted LED (pc-LED) and the other is the multi-color LED. The pc-LEDs are low cost and easily accessible, and they occupy a large part of the market. Unfortunately, their intrinsic modulation bandwidth is limited to MHz. As for the multi-color LEDs, the white light illumination can be achieved by mixing the multiple monochromatic lights together. Although they are more expensive and complex, their higher modulation bandwidth and natural multi-channel properties show quite large potential of high-rate data transmission. Via wavelength-division multiplexing (WDM) technique, the multi-color LED based VLC system naturally forms a color-domain multiple input and multiple output (CMIMO) channels for multiple parallel data transmission, which can provide potential high transmission rate and high-quality illumination [6; 7]. It should be noted that quadrichromatic LED (QLED) with red/amber/green/blue (RAGB) colors has been recommended as an alternative to the red/green/blue LED (RGB-LED) to improve the color quality where proper color temperature can be provided for indoor lighting [8]. In essence, both illumination and communication requirements should be satisfied when we design the multi-color LED based VLC system, and the corresponding research has stimulated substantial interest in recent work. To improve communication performance, the work in Ref. [9] demonstrated an aggregate data rate of 4.5 Gbps WDM-VLC system using RGB LED and the work in Ref. [10] updated the data rate to an off-line 8 Gbps via high-order carrierless amplitude phase (CAP) modulation and hybrid post equalizer. Moreover, Ref. [11] proposed an optimization problem to maximize the multi-user sum-rate for the RGB-LED based VLC system under chromaticity and bit error rate (BER) constraints. To maximize the minimum Euclidean distance (MED) for communication performance optimization, Ref. [12] investigated the constellation design of color shift keying (CSK) to obtain better BER performance. Considering the energy consumption problem, Ref. [13] proposed an energy-efficient optimization design for the multi-color based VLC system. However, the overlapping spectra of the multi-color LED may cause an inevitable channel crosstalk problem for the VLC system, and the practical illumination requirements should be satisfied under the specific circumstances. Moreover, to improve the adaptivity for the practical illumination scenarios, Commission Internationale de l'Eclairage (CIE) [14] proposed quadrangle chromaticity tolerance region for LED products to replace a fixed chromaticity point in CIE1931 chromaticity diagram, which is neglected in previous works. Accordingly, with the characteristic of adjustable chromaticity tolerance region, multi-color LEDs can provide the proper correlated color temperature (CCT) for high-quality illumination. Motivated by the above-mentioned analysis, we propose a power-efficient illumination control optimization design for the multi-color LED based VLC systems to reduce energy consumption. More specifically, an optimal power allocation strategy is demonstrated to maximize power efficiency for the QLED based VLC systems with the consideration of the multi-color crosstalk problem and actual communication and illumination requirements where signal to interference plus noise ratio (SINR) and quadrangle chromaticity tolerance region constraints should be satisfied.