# Linear Precoding Designs for MIMO VLC Using Multi-Color LEDs under Multiple Lighting Constraints
## 1 Introduction  
In recent years, visible light communications (VLCs) have become an extremely promising new wireless communication technology [1]. Due to the large bandwidth of the visible light spectrum, VLC can provide high-speed wireless information transmission in indoor and outdoor scenarios [2]. Lighting-emitting diodes (LEDs) are commonly used as the transmitters in VLC. Generally, there are two kinds of LEDs, one is the phosphor-converted LED (pc-LED) and the other one is the multi-chip LED. Although pc-LEDs are easily accessible, their intrinsic modulation bandwidth is limited to MHz. Compared with pc-LEDs, multi-chip LEDs own a several times larger bandwidth and higher color rendering index. To achieve abundant illumination, numerous lamps need to be placed at the same time in some scenarios. Meanwhile, these LEDs can be used as transmitters in VLC. Multi-input data streams make the high transmission rate increase significantly. Therefore, the techniques on multiple-input multiple-output (MIMO) is extensively researched in VLC. The multi-color LEDs used in these systems can improve the density of transmitters, which would undoubtedly boost transmission rate further. MIMO VLC systems with multi-color LEDs can be used in both indoor and outdoor scenarios. In an indoor scenario, multi-color LEDs can work as the intelligent lighting solution owing to their dynamic controllable chromaticity; meanwhile, the data rate up to gigabit per second canbe further improved [3; 4; 5]. In the outdoor scenarios, there are also various applications for high speed MIMO VLC including outdoor traffic lighting systems, signboard and display screen interaction, underwater communication, etc. [6]. For example, in the underwater network, as the turbulence severely affects the underwater VLC channels, the MIMO VLC with multi-color LEDs would be more effective to mitigate turbulence effects in the underwater environment due to its higher diversity property [7]. To make full use of MIMO VLC systems, some methods have been developed by researchers. In [8; 9], the authors investigated the indoor channel characteristics of MIMO VLC systems. Besides the traditional non-imaging receiver, the imaging receiver, which is an effective candidate to separate signals from different directions, has been widely used in MIMO VLC [10]. Then, in [11; 12; 13], some signal design methods that exploited the spatial-collaborative property of MIMO VLC were brought forward and analyzed. Some advanced modulation formats such as orthogonal frequency division multiplexing (OFDM) are also employed in MIMO VLC systems [14]. To further improve the system performance, many transmitter design methods were put forward [15; 16; 17; 18]. In [15], an optical power allocation method was proposed to improve the spectral efficiency with the requirements of amplitude and total optical power and bit error rate (BER). Moreover, the authors of [16] proposed a robust precoding method to solve the max-min signal-to-interference-plus-noise ratio (SINR) problem with the consideration of the inter-user interference and imperfect channel estimation. In [17], a singular value decomposition-based Chebyshev precoding was proposed to improve the performance of nonlinear MIMO VLC. Based on [17], an adaptive precoding design was further investigated for a massive MIMO VLC system in [18]. When multi-color LEDs are used in MIMO, the overlapping spectrum of multiple colors would cause inevitable crosstalk interference [19]. In [20], the authors applied an array of multi-color LEDs in MIMO VLC and proposed an optimal precoding design method to minimize total mean-squared-error (MSE) with the consideration of the color interference. However, in their works, the CCT values were fixed, and the clipping distortion of exceeding electric amplitude was neglected. In [21], an illumination-adapted transceiver was designed under chromaticity, luminance and signal range constraints with an iterative algorithm.