# Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation
## 2 System Model
### The Transmitter  
We consider a wavelet-OFDM indoor imaging VLC-MIMO transmitter technique which utilizes a hybrid space-frequency domain pre-equalization system with a 4-LED modules transmitter (1,..., N). Using LED is not sufficient to illuminate a room with these dimensions. However, in the proposed system, LED modules are used, and each module could consist of at least 60 distributed LEDs. The block diagram for the transmitter is illustrated in Figure 1.  
1. Firstly, the series input information is separated into N streams (according to N-transmitters), the positions of the LED modules are listed in Table 1. The data stream is converted from the data line to the data array, via a serial-to-parallel (S/P) converter. 2. The data is mapped to symbols by using quadrature amplitude modulation (QAM). The transmitter utilizes a 64 QAM digital modulation to map the serial bits into the OFDM symbols \(\mathrm{X_{N}(i)}\) as N is the LED modules number and \(0\leq\mathrm{i}\leq\mathrm{s}-1\), while s is the number of the parallel data stream. 3. Then, Hermitian symmetry (HS) is enforced to produce real values data. 4. The Pre-FDE is performed by employing the electrical-optical-electrical (EOE) frequency response. The LED modules locations are listed in Table 1[22] and the measured EOE frequency response of a commercially available LED with 50-MHz modulation BW is illustrated in Ref. [23]. 5. Wavelet transform for modulation is performed. As shown in Figure 1, the block named IDWT is a function in the MATLAB toolbox which utilizes Low Pass Filter (LPF) and High Pass Filter (HPF). WT utilizes filters like a vector of approximation coefficient (CA) and a vector of detail coefficients (CD). The signal is divided into sub-bands which are divided into low and high frequencies. OFDM symbol \(\mathbb{[X]}\)_N_ (i) is converted from parallel to serial. It has a vector YY that may be transposed into CA as represented in Figure 2 which is called approximated coefficients. \begin{table}
\begin{tabular}{l c} \hline N = 1 & (2.5, 2.5, 3) \\ \hline N = 2 & (1.5, 2.5, 3) (3.5, 2.5, 3) \\ \hline N = 3 & (1.5, 1.5, 3) (3.5, 1.5, 3) (2.5, 3.5, 3) \\ \hline N = 4 & (1.5, 1.5, 3) (3.5, 1.5, 3) (1.5, 3.5, 3) (3.5, 3.5, 3) \\ \hline \end{tabular}
\end{table} 
Table 1: Light Emitting Diode (LED) modules locations (m) [22]. Figure 1: A wavelet-Orthogonal Frequency Division Multiplexing (OFDM) indoor imaging Visible Light Communication-Multiple Input Multiple Output (VLC-MIMO) transmitter utilizing the hybrid Pre Space Domain Equalization (Pre-SDE) system. The signals are up-sampled by LPF coefficients while the HPF filter can be performed by the convolution with Zero Padding (ZP) data Detail Coefficient (CD). This is done to get high-frequency data. The LPF filter contains approximation coefficients. Data is simulated by a MATLAB toolbox. The transmitted signal must be in the discrete domain x[k]. Various wavelet families have several filters containing different values of CA as well as CD. All of them seek to satisfy the WT bases. The CP is not utilized for WT-OFDM which is due to the wavelet orthogonality overlapping attribute and its better stopband attenuation. Unlike FFT-OFDM, CP is important to overcome the ISI. Each one of them is built to form the sum of M waveforms \(\phi(\kappa)\), where \(\phi(\kappa)\) is the complex exponential basic functions and \(\Phi_{\text{m}}\) is the scaling function. The transmitted signal may be shown in a discrete form. The transmitted symbol is built by performing inverse DWT (IDWT) [14; 24; 25]:  
\[\text{x}[\text{k}]=\sum\
olimits_{\tau}\sum\
olimits_{\text{m}=0}^{\text{M}- 1}\text{a}_{\text{j}}\Phi_{\text{m}}[\text{k}-\text{sM}]. \tag{1}\]  
For performing the wavelet-OFDM technique mentioned in (1), we execute the Meyer wavelet. The Meyer wavelet is a limited frequency orthogonal wavelet.