###### Abstract  
Visible Light Communication (VLC) is a promising field in optical wireless communications, which uses the illumination infrastructure for data transmission. The important features of VLC are electromagnetic interference-free, license-free, etc. Additionally, Multiple-Input-Multiple-Output (MIMO) techniques are enabled in the VLC for enhancing the limited modulation bandwidth by its spectral efficiency. The data transmission through the MIMO-VLC system is corrupted by different interferences, namely thermal noise, shot noise and phase noise, which are caused by the traditional fluorescent light. In this paper, an effective precoding technique, namely Block Bi-Diagonalization (BBD), is enabled to mitigate the interference occurring in the indoor MIMO-VLC communications. Besides, a Quadrature Amplitude Modulation (QAM) is used to modulate the signal before transmission. Here, the indoor MIMO-VLC system is developed to analyze the communication performance under noise constraints. The performance of the proposed system is analyzed in terms of Bit Error Rate (BER) and throughput. Furthermore, the performances are compared with three different existing methods such as OAP, FBM and NRZ-OOK-LOS. The BER value of the proposed system of scenario 1 is 0.0501 at 10 dB, which is less than that of the FBM technique. bit error rate; block bi-diagonalization-based precoding; multiple-input-multiple-output; shot noise; thermal noise; phase noise; visible light communication +
Footnote †: journal: Accepted: 30 June 2020;  
_Article_  
A Block Bi-Diagonalization-Based Pre-Coding for  
Indoor Multiple-Input-Multiple-Output-Visible Light Communication System  
[PERSON], [PERSON], [PERSON], [PERSON]  
spectrum, etc [5]. Moreover, the main feature of the VLC that is unique from remaining optical wireless communication systems, e.g., infrared communication is that it has the capacity to deliver the illumination and communication at the same time [6]. The VLC technology uses the Light Emitting Diodes (LEDs) in transmitters due to the characteristics of low cost, illumination and higher bandwidth as well as the photodetectors (PDs) used in receivers [7]. The additional characteristics of LEDs are higher lifetime, mercury-free, low power consumption and high brightness [8; 9]. However, the VLC system faces many challenges such as LED non-linearity, shadowing and blocking, limited mobility and Inter-Symbol Interference (ISI) due to multipath [10]. In order to overcome the aforementioned problems, the Multiple-Input-Multiple-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) are utilized for enhancing the ability of the VLC systems [11; 12]. The incorporation of MIMO improves the performances of VLC, especially in high range data transmission [13]. The problems faced by the MIMO VLC system are given as follows: Generally, the MIMO VLC channel exists in static Line Of Sight (LOS) conditions. The correlations due to the static LOS are associated to the LED array parameters and PDs array. The transmission performance is highly affected due to the strong correlation in the channel matrix [14]. An effective precoding technique is to be developed for avoiding the interference and achieve user fairness [15]. The major contributions of this research paper are stated as follows:  
* In this paper, a \(4\times 4\) indoor MIMO-VLC system is developed to improve the data rate and reliability in data transmission. Here, \(4\times 4\) is defined as the installation of 4 LEDs in the transmitter side and 4 PDs in the receiver side. * Block Bi-Diagonalization (BBD)-based precoding is presented in this communication system to remove the inferences caused due to the thermal noise, shot noise and phase noise. This is because these noise constraints affect the signal, which is transmitted through the MIMO-VLC system. Additionally, the BBD-based precoding used in this VLC system has less computation complexity. * Quadrature Amplitude Modulation (QAM)-based modulation also improves the transmission of the MIMO-VLC transmitter.