Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation

Abstract

Both light emitting diode (LED) characteristics for illumination and communication simultaneously have made visible light communication-orthogonal frequency division multiplexing (VLC-OFDM) a strong competitive to radio frequency (RF). In this juncture, to improve signal to noise ratio (SNR) and coverage contour, the wavelet-OFDM is suggested for indoor VLC systems. In this paper, a wavelet VLC-OFDM is proposed for imaging multiple-input multiple-output (MIMO) systems. The proposed wavelet-OFDM is exploited for a hybrid space-frequency domain pre-equalization technique instead of the traditional fast Fourier transform (FFT)-OFDM technique. The Meyer filter is selected and employed in the proposed technique. A comparable achievement is elaborated for several numbers of channels to achieve the enhanced performance in terms of bit rate and coverage contour. In addition, a useful comparison is executed between our wavelet VLC-OFDM and the traditional FFT-OFDM for a hybrid space-frequency domain pre-equalization technique. The simulation results emphasize the superiority point of wavelet VLC-OFDM MIMO system by improving the coverage contour by ~20% over the traditional OFDM at a 10⁻³ bit error rate (BER) target. Hence, the proposed technique can be potentially executed in indoor VLC-MIMO systems.

1. Introduction

1.1. State of the Art Regarding FFT-OFDM and DWT-OFDM

White light-emitting diodes (LEDs) are considered a successful technology for the next decade. Due to low energy consumption, high performance, and high durability, white LEDs can be used in a large variety of communication systems to increase performance and minimize costs. Visible Light Communication (VLC) has the ability to carry data by modulating light. This limits the extra cost of VLC techniques which use LEDs. Additionally, these benefits enable people to access the Internet through the same visible light. Consequently, the demand for VLC has increased rapidly with the increase of LED power. Major research was undertaken to establish high data indoor VLC systems [1].

VLC has an uncontrolled spectrum, precisely from 400 to 700 μm, providing a huge bandwidth of communication that leads to high data rates. The VLC spectrum in adjacent communication cells can be reused. Intensity modulation/direct detection (IM/DD) is added to VLC systems, where the transmit messages can be modulated by light without taking phase information into account. Besides, it can be directly sensed by the detector. The essential properties of light made VLC more effective, more power-efficient because the LEDs are used in illumination and simultaneously are used in communication. Moreover, the VLC is more secure, does not need license and has the ability to deliver high data rates compared to RF communication. Hence, the proposed system has the above-mentioned properties and consequently has superiority over radio frequency systems.

Several VLC studies are involved in efficient modulation schemes like Orthogonal Frequency Division Multiplexing (OFDM) and Multiple Input Multiple Output (MIMO) to raise the data rate by maximizing the bandwidth. MIMO is used in many new technologies to increase data rate capacity and spectral efficiency [2,3,4]. MIMO systems contain multiple transmitter antennas and multiple receiver antennas. There are many types of MIMO techniques that are used for transmitting data over an indoor optical wireless channel to provide high link capacity and spectral efficiency, including spatial modulation (SM) and spatial multiplexing (SMP) [5].

The bandwidth limitation of LEDs is considered as one of the big challenges of achieving high efficiency in VLC systems [6]. Optical MIMO could be willing to offer a large data transmission rate by transferring data in the transponder and spatial spectrum [7].

Different pre-frequency domain equalization (Pre-FDE) mechanisms could be reported to improve LEDs bandwidth, such as analog Pre-FDE [6], digital Pre-FDE [8] in addition to the adaptive digital Pre-FDE [9].

VLC OFDM MIMO technique requires a detector for separating data from specific LEDs. Generally, there are two types of receivers with different concentrator designs that can be used in VLC-MIMO systems to increase VLC systems capacity [10]. These are categorized into two major optical categories; one of them is referred to imaging receiver (ImR) and the other is called a non-imaging receiver (NImR). The space division multiplexing VLC (SDM-VLC) technique is a promising technique for high speed indoor wireless communication. C. Chen et al. [11] suggested two protocols to boost an indoor SDM-VLC contour. There are two VLC link configurations: line-of-sight (LoS) which is mostly used in commercial systems and non-line-of-sight (Non-LoS) [12].

Thanks to OFDM for its high spectral efficiency, high capacity, and its ability to resolve multi-path channels. However, OFDM suffers from sensitivity to carrier frequency offset and synchronization errors. There is a lot of work that has been done to develop this, such as the short-time Fourier transform (STFT), the wavelet transform (WT), and wavelet packets (WP).

The traditional OFDM techniques utilize inverse fast Fourier transform/fast Fourier transform (IFFT/FFT) systems at the transceiver for data multiplexing to simultaneously relay them through subcarrier numbers. The cyclic prefix (CP) is added before data transmission to minimize the inter-symbol-interference/inter-channel-interference (ISI/ICI) and to increase the bandwidth efficiency. Furthermore, CP reduces the channels of spectral inclusion.

Wavelet (WT) fairly reflects a new term. It is used instead of FFT in OFDM. Wavelet-OFDM is named by orthogonal wavelet division multiplexing (OWDM), which is related to the inverse discrete wavelet transform (IDWT) rather than inverse discrete Fourier transform (IDFT) [13,14].

The great reason for utilizing DWT based on the OFDM system is the length of the basic functions which combat the narrowband interference better and inherently further resistant to ICI. R. Mishra et al. [15] studied the overview and performance estimation results of OFDM techniques including the traditional-OFDM and wavelet-OFDM. The authors in [16] proposed a new wavelet-OFDM analytical system which confirms Wi-Fi standard hiring the transmitter’s windowing function (rectangular waveform). Authors in [17] investigated a wavelet-OFDM for 4G of wireless communication. R. Asif et al. [18] elaborated the FFT-OFDM performance technique in opposite to WT based multicarrier system utilizing a simple zero-forcing (ZF) equalization in the time domain. Moreover, the wavelet has been applied in other different fields such as civil structures [19,20].

The Meyer WT is both orthogonal and symmetric [14]. This provides a numerical approach to the DWT/IDWT through the use of a low pass filter (LPF)/high pass filter (HPF). To implement a wavelet transformation, these filters must satisfy the orthonormal basis, which means that they must be normalized and orthogonal to each other. Wael. H et al. utilized (16-QAM, 32-QAM, 64-QAM, and 128-QAM) and different types of wavelet filters Daubechies (Db-3, Db-5, Db-8, Db-10) and Haar filter to compare the performance between the FFT-OFDM and WT-OFDM [21].

1.2. Frame Work

This section shows, in brief, the novelty of our work and difference between it and the related previous work. Furthermore, it explains clearly our framework. For once, an imaging VLC-MIMO technique based on traditional FFT-OFDM has been proposed by C. Chen et al. [22] with a raw 1.2 Gbps bit rate for various channels. The technique used the dual property of the space/frequency domain pre-equalization scheme. Towards the aim of Signal to Noise Ratio (SNR) and Bit Error Rate (BER) improvement, a pre-space domain equalization (Pre-SDE) is performed after the Pre-FDE at a target BER of 10⁻³. In comparison with the system which uses only Pre-FDE, a communication coverage improvement by 52.6% is achieved in our system.

In this paper, through VLC, we propose a wavelet-OFDM, instead of FFT-OFDM [22], for both the space and frequency domain pre-equalization technique for the first time. In the proposed system, due to the nature of WT overlapping symbols, the CP is eliminated. The removal of CP, which can be used to avoid multipath besides the Inter-Symbol Interference (ISI), enables the WT to make full use of its spectral efficiency. This leads to improving system performance in terms of the coverage contour and data rate. In this evaluation, we executed a Monte Carlo protocol to efficiently estimate an indoor VLC-MIMO performance characterized by N-channels. The obtained results reveal that the suggested system significantly enhances the SNR performance. Moreover, a performance comparison is performed between the suggested system based on the discrete Meyer (Dmey) wavelet (DWT-OFDM) and the FFT-OFDM for imaging VLC-MIMO systems for both the space and frequency domain pre-equalization technique. This comparison reflects the superiority of the DWT-OFDM proposed system over the FFT-OFDM one, in terms of the coverage contour for transmission and data rate. Thus, the suggested system can be a good applicant for light fidelity (Li-Fi) systems.

The remainder of this paper is organized as follows. Section 2 introduces the system model and numerical analysis of the proposed system involving all equations that are used to estimate technique performance. The simulation results are displayed and discussed in Section 3. Section 4 is devoted to the main conclusions.

2. System Model

The distribution of the wavelet-OFDM MIMO system is illustrated within this section. This depends on the transmitter, the channel, in addition to the receiver which is utilizing the multiplexed method. The number of transmitting and receiving antennas is N and M, respectively.

2.1. 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. Light Emitting Diode (LED) modules locations (m) [22].

N = 1	(2.5, 2.5, 3)
N = 2	(1.5, 2.5, 3) (3.5, 2.5, 3)
N = 3	(1.5, 1.5, 3) (3.5, 1.5, 3) (2.5, 3.5, 3)
N = 4	(1.5, 1.5, 3) (3.5, 1.5, 3) (1.5, 3.5, 3) (3.5, 3.5, 3)

. 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 ${\mathsf{{\rm X}}}_{\mathrm{N}}\left(\mathrm{i}\right)$ as N is the LED modules number and$0\le \mathrm{i}\le \mathrm{s}-1,$ 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 〖Χ〗_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.

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 $\mathsf{{\rm M}}$ waveforms $\mathsf{\varphi }\left(\mathsf{\kappa }\right),$ where $\mathsf{\varphi }\left(\mathsf{\kappa }\right)$ is the complex exponential basic functions and ${\mathsf{\Phi }}_{\mathrm{m}}$ 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]:

$$\mathrm{x}\left[\mathrm{k}\right]={{\displaystyle \sum }}_{\mathsf{\tau }}{{\displaystyle \sum }}_{\mathrm{m}=0}^{\mathrm{M}-1}{ \mathrm{a}}_{\mathrm{j}}{\mathsf{\Phi }}_{\mathrm{m}}\left[\mathrm{k}-\mathrm{sM}\right].$$

(1)

For performing the wavelet-OFDM technique mentioned in (1), we execute the Meyer wavelet. The Meyer wavelet is a limited frequency orthogonal wavelet. Meyer wavelet can be implemented in fast wavelet transform (FWT) and DWT because of its symmetry and orthogonality, in addition to its fast ability of localization and decaying from the central peak than any inverse polynomial [14].

OWDM is a program which is very flexible and simple. It has lower complexity with a low filter than FFT processors. Furthermore, the filter type selected must be dependent on the channel situation or the information source. A Dmey is a discrete form of the Meyer wavelet. The Meyer wavelet and scaling function is defined in the frequency domain [14].

• A parallel-to-serial (P/S) operation is performed to obtain the time domain signal.
• Pre-SDE is implemented by normalizing all data streams to ensure that the detected N-data have the same value of SNR. The Pre-SDE concept of an optical DCO-OFDM system is based on the VLC-MIMO N-channel imaging technique. The output optical power and the modulation index for every LED are P_opt and ξ, respectively. Pre-SDE is performed by using power allocation matrix A = diag (a₁; a₂; ⋯⋯; a_N) which adjusts all electrical powers modulating data.

Furthermore, the transmitted optical vector S could be calculated by Equation (2), where x is the modulated data vector [22]:

S = P_opt (1 + ξ A x).

(2)

The modulation index (ξ) is supposed to be the same for all LEDs. Because of A, the electrical powers of different modulating data may be diverse. To preserve a fixed average electrical power as soon as exciting Pre-SDE, power restrictions are required to the diagonal elements of matrix [22].

The signal is normalized and a digital-to-analog (D/A) conversion has been performed. At every stream, a DC bias is applied to get a unipolar signal. Hence, the complex-valued OFDM signal is given by:

x(t) = x_Re + j x_Im,

(3)

where x = (x₁ x₂, ⋯⋯ x_N)^T is a vector of modulating signals and x_i (i = 1, 2, ⋯⋯, N) is the normalized bipolar OFDM signal with variance σ²_xi = 1.

The electrical powers of different modulating signals may be different. To maintain a constant average electrical power when performing Pre-SDE, a power constraint is imposed on the diagonal elements of matrix A. These elements, a_i, satisfy the following equation [22]:

$$\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{a}}_{\mathrm{i}}^2=1.$$

(4)

2.2. Channel Estimation

2.2.1. White Gaussian Noise Estimation

The equalizer output includes a Gaussian noise with a total variance G_N, which is the sum of shot noise and thermal noise besides the ICI contributions using the optical path difference. We disregard the noise contributions from gate leakage current and 1/f noise:

$${\mathrm{G}}_{\mathrm{N}}={\mathsf{\sigma }}_{\mathrm{shot}}^2+{\mathsf{\sigma }}_{\mathrm{thermal}}^2+{\mathsf{\gamma }}^2{\mathsf{\sigma }}_{\mathrm{rISI}}^2.$$

(5)

The received power P_rISI by ICI is [26]:

$${\mathrm{P}}_{\mathrm{rISI}} ={{\displaystyle \int }}_{\mathrm{T}}^{\infty }\left({{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{LEDs}}{\mathrm{h}}_{\mathrm{i}}\left(\mathrm{t}\right)\otimes \mathrm{X}\left(\mathrm{t}\right)\right) \mathrm{dt}.$$

(6)

The shot noise variance is given by [26]:

$${\mathsf{\sigma }}_{\mathrm{shot}}^2=2\mathrm{q}\mathsf{\gamma }\left({\mathrm{P}}_{\mathrm{rSignal}}+{\mathrm{P}}_{\mathrm{rISI}}\right)\mathrm{B}+2{\mathrm{qI}}_{\mathrm{bg}}{\mathrm{I}}_2\mathrm{B},$$

(7)

where q is the electronic charge, B is the equivalent noise bandwidth, I_bg is background current. The noise bandwidth factors I₂ = 0.562.

The thermal noise variance is calculated by [27]:

$${\mathsf{\sigma }}_{\mathrm{thermal}}^2=\frac{8{\mathsf{\pi }\mathrm{kT}}_{\mathrm{k}}}{\mathrm{G}}{\mathsf{\eta }\mathrm{AI}}_2{\mathrm{B}}^2+\frac{16{\mathsf{\pi }}^2{\mathrm{kT}}_{\mathrm{k}}\mathsf{\Gamma }}{{\mathrm{g}}_{\mathrm{m}}}{\mathsf{\eta }}^2{\mathrm{A}}^2{\mathrm{I}}_3{\mathrm{B}}^3.$$

(8)

Furthermore, both sides clarified noise from feedback-resistor, and noise from FET channels, respectively. Similarly, k is Boltzmann constant, T_K is the absolute temperature, G is the open-loop voltage gain, η is the constant photodetector capacitance (PD) per unit area, Γ is the FET channel noise factor, ${\mathrm{g}}_{\mathrm{m}}$ is the FET trans-conductance, I₃ = 0.0868, ${\mathrm{T}}_{\mathrm{k}}$ = 295 K, Γ is the FET channel noise, G = 10 dB, g_m = 30 m_S, Ƞ = 1.5, Γ = 112 pF/cm², even B = 100 Mbps. In our work, the surrounding current comes from the direct sum light [27].

2.2.2. Non-Imaging LOS Channel Gain

A generalized Lambertian radiation pattern can model the LOS irradiance of LED as shown in Figure 3. The vector ${\mathsf{\upsilon }}_{\mathrm{RS}}$ can be written as ${\mathsf{\upsilon }}_{\mathrm{RS}}$ = [a, b, c] = [X_R, Y_R, Z_R]–[X_S, Y_S, Z_S], where [X_S, Y_S, Z_S] and [X_R, Y_R, Z_R] are the positions of transmitter and receiver, respectively [28]. The optical LOS channel gain between the tth LED lamp and the rth PD is proved by:

$${\mathrm{h}}_{\mathrm{rt}}\left(0\right)=\{\begin{array}{c}\frac{\left(\mathrm{m}+1\right){\mathrm{A}}_{\mathrm{PD}}}{2{\mathsf{\pi }\mathrm{d}}_{\mathrm{rt}}^2}{\mathsf{\mu }\mathsf{\eta } \cos }^{\mathrm{m}}\left(\varnothing \mathrm{rt}\right)\cos \left(\mathsf{\theta }\mathrm{rt}\right),0\le \theta \le \mathsf{\varphi }\\ 0,\mathsf{\theta }>\mathsf{\varphi }\end{array}.$$

(9)

To conclude, m = −ln2/ln (cos Ψ_1/2) is the emitted lighting order with Ψ_1/2 is the semi-angle of the transmitter at half power, A_PD is the PD active area, d_rt is the distance between the tth LED lamp and the rth PD, μ and η are the optical filter gain likewise the optical lens, respectively, ϕ_rt is the emission angle, and θ_rt is the incident angle. Moreover, if θ_rt is outside the Field of View (FOV) of the receiver, the optical gain h_rt is zero and when an imaging non-diversity receiver (ImADR) is used, θ_rt becomes zero.

2.2.3. Non-Imaging LOS Channel Matrix

The general 4 × 4 MIMO channel matrix H is driven by:

$$\mathrm{H} = \left[\begin{array}{ccc}{\mathrm{h}}_{11}& \cdots & {\mathrm{h}}_{14}\\ ⋮& \ddots & ⋮\\ {\mathrm{h}}_{41}& \cdots & {\mathrm{h}}_{44}\end{array}\right].$$

(10)

Furthermore, the channel gain ${\mathrm{h}}_{\mathrm{rt}}$ is progressed, where r and t refer to the numbers of transmitters and receivers, respectively.

Similarly, the ICI is deserted by ImR or ImADR use, the matrix of the channel H of N-channel imaging VLC-MIMO technique is evidenced in [26]:

$$\mathrm{H} = \mathrm{diag} ({\mathrm{h}}_{11},{\mathrm{h}}_{22},\dots \dots .,{\mathrm{h}}_{\mathrm{NN}}).$$

(11)

2.3. The Receiver

We consider a VLC-MIMO indoor imaging receiver system based on wavelet-OFDM using one receiver (M) of the hybrid space-frequency domain pre-equalization system. The receiver location (scenario-room corner) is given by (0, 0, 0.85 m). The system block diagram is shown in Figure 4.

• The produced N serials of unipolar data have been used to drive N LED modules, respectively, as shown in Figure 1. The LED radiation light is sensed by an ImR or an ImADR at the detector side. The recipient side of the wavelet-OFDM VLC-MIMO technique is illustrated in Figure 4.
• An A/D conversion is utilized to convert the analog signals to digital. The 3-dB modulation bandwidth of LED is adjusted as 50 MHz.

The specific processes to perform digital Pre-FDE were fully illustrated in [22]. In the OFDM transmitter (Tx), a Pre-FDE has performed adaptively according to the estimated SNR information.

2.3.1. Received Wavelet-OFDM Data

DWT receiver is the reverse operation of IDWT. It performs a DWT according to the MATLAB toolbox. The transmitted signal ${\displaystyle \cup }$ [k] is the front-end receiver successive digitally modulated symbols to be transformed, the data is decomposed across filters, LPF and HPF related to CA in addition to the CD. CA is the output signal of the approximation coefficients or LPF and CD are the output data of the detailed coefficients or HPF to execute that operation. The data is transposed before converting from S/P and the wavelet family used is Demy wavelet.

${\displaystyle \cup }\left[\mathrm{k}\right]$ contains some zeros elements which are decomposed from CD information produced in the transmitter comparing to CA data. So, the CD data will be considered as imaginary data and the CA will be considered as real data to avoid any loss of data. That is all go via the DWT-OFDM receiver which can be seen in Figure 5.

The forward DWT is used to reconstruct the data symbol. The DWT-OFDM now could be obtained by a weighted sum of wavelet similar to scale carriers, which can be expressed as:

$$\mathrm{W}\left(\mathrm{t}\right)={{\displaystyle \sum }}_{\mathrm{j}\le \mathrm{J}}{{\displaystyle \sum }}_{\mathrm{k}}{\mathrm{w}}_{\mathrm{j},\mathrm{k}}\left(\mathrm{t}\right).{\mathsf{\Psi }}_{\mathrm{j},\mathrm{k}}\left(\mathrm{t}\right)+{{\displaystyle \sum }}_{\mathrm{k}}{ \mathrm{a}}_{\mathrm{j},\mathrm{k}}{\mathsf{\Phi }}_{\mathrm{J},\mathrm{k}}\left(\mathrm{t}\right),$$

(12)

where ${\mathrm{w}}_{\mathrm{j},\mathrm{k}}\left(\mathrm{t}\right) \mathrm{is} \mathrm{the} \mathrm{wavelet} \mathrm{coefficients} \mathrm{existing} \mathrm{at} \mathrm{the} {\mathrm{k}}^{\mathrm{th}} \mathrm{position} \mathrm{from} \mathrm{the} \mathrm{scale} \mathrm{j},{ \mathsf{\Psi }}_{\mathrm{j},\mathrm{k}}\left(\mathrm{t}\right)$ is the IDWT modulator as a sequence of wavelet,${ \mathsf{\Phi }}_{\mathrm{J},\mathrm{k}}\left(\mathrm{t}\right)$is the scaling function, and ${ \mathrm{a}}_{\mathrm{j},\mathrm{k}}$ is the approximation coefficient. The output of DWT consists of two vectors: the approximation coefficients (AC) and the detail coefficients (DC).

The wavelet modulation (IDWT) in addition to the wavelet demodulation is obtained according to the Mallet algorithm [14]. The IDWT depends on up-sampling and DWT depends on down-sampling by a factor of two to each other, and filtering the approximated coefficients as shown in Equation (10), relative to LPF/HPF, respectively.

2.3.2. Pre-SDE Equations

After propagation, the LED light is detected by an ImR or an ImADR that is supposed to calculate the photodetector responsivity, R. Firstly, the DC components are separated from the detected signals. Likewise, the electrical received signal vector y is acquired as [28]:

$$\mathrm{y} = \mathrm{R} {\mathrm{P}}_{\mathrm{opt}} \mathsf{\xi } \mathrm{HA} \mathrm{x} + \mathrm{n},$$

(13)

where n acts as the noise with variance and zero mean mentioned in [26,29]. H is the matrix of the channel, as well as n, is the additive vector of the noise. The detector will provide both LOS [28,30] and diffuse components in exemplary indoor environments. Note, in the traditional indoor areas, the detector can obtain both LOS and diffuse components. Once the receiver is positioned at room corners, the diffuse components are highest, while it is still at least 7 dB lower than the weakest LOS components in electric power. This is the reason for considering LOS only as our concerning study.

2.3.3. SNR Estimation

The calculated electrical signals of four SNRs are mentioned in [11]:

$${\mathrm{SNR}}_{\mathrm{i}}^{\prime }=\frac{{\left({\mathrm{Rp}}_{\mathrm{opt}}{ \mathsf{\xi }\mathrm{a}}_{\mathrm{i}}{\mathrm{h}}_{\mathrm{ii}}\right)}^2}{{\mathsf{\sigma }}_{{\mathrm{n}}_{\mathrm{i}}}^2}={\mathrm{a}}_1^2{\mathrm{SNR}}_{\mathrm{i}}, \mathrm{i} = 1,2, \cdots , \mathrm{N},$$

(14)

where SNR_i = (R P_opt ξ h_ii)² σ²_xi /σ²_ni, i = 1, 2, ….., N. R is the photodiode responsivity, P_opt is the LED output power, ξ is the modulation index, and h_ii are the elements of the H matrix.

Therefore, Pre-SDE could be effectively employed [22]. To guarantee that the four received signals have the same SNR, as per Equation (4), the following requirement must be satisfied:

a²₁SNR₁ = a²₂ SNR₂ = ⋯⋯ = a²_NSNR_N.

(15)

By solving Equations (2) and (5), the N diagonal elements of matrix A can be obtained by [14,24]:

$${\mathrm{a}}_{\mathrm{i}}=\sqrt{\frac{\mathrm{N}}{{\mathrm{SNR}}_{\mathrm{i}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}\frac{1}{{\mathrm{SNR}}_{\mathrm{i}}}}}.$$

(16)

The diagonal elements of A have been provided based on the SNR value of every channel. So, the evaluated SNR values must be supposed to be transferred back to the ceiling via the uplink channels as feedback information. For the most part, the optical channel remains static, while users of VLC are usually in fixed positions or moving with a slightly slower speed. Hence, the uplink delay will provide a relative effect on Pre-SDE performance. However, it should be observed that the electrical power of every channel ought to be flexible to adapt to a confirmed extent to efficiently excite the Pre-SDE, in the pre-coded VLC-MIMO techniques [31]. Thus, for VLC-MIMO systems, the Pre-SDE can be supposed like a precoding system.

The SNR calculations are carried out in the wavelet-OFDM receiver (Rx), and the acquired SNR information is back to the wavelet-OFDM transmitter (Tx). By using the returns feedback of the SNR data, a sufficient modulation bandwidth could be offered to the OFDM data [22].

2.3.4. Received Data Estimation

In the VLC-MIMO techniques, the performance cannot be optimized as a stable modulation form. In addition, just LoS channel gains through the transmitter to the receiver are utilized as channel matrix coefficients. However, the non-LoS is proposed to show the difference between the BER performance of OFDM and wavelet-OFDM. The nonlinearity and limited bandwidth properties of LEDs have not been considered to achieve the significant enhancement of channel diversity. To decode and recover data from the obtained signals, a channel estimation matrix technique is used. MIMO de-multiplexing is performed because of its low complication, zero-forcing (ZF) is implemented using basic channel observation [10]. Therefore, in order to get the transferred data estimation X_est and decompose the detected streams of Y, a matrix inversion and multiplication should be required:

$${\mathrm{X}}_{\mathrm{est}}={\mathrm{H}}^{-1}\mathrm{Y}.$$

(17)

After ZF based MIMO de-multiplexing, we have [11]:

$$\tilde{\mathrm{x}}={\mathrm{H}}^{-1}\mathrm{y}= \mathrm{R} {\mathrm{P}}_{\mathrm{opt}} \mathsf{\xi } \mathrm{HA} \mathrm{x} +{\mathrm{H}}^{-1} \mathrm{n},$$

(18)

where H is the channel matrix for the 4 × 4 SDM-VLC system given by Equation (11) and n is the additive noise vector. Likewise, n_i (i = 1, 2, ⋯⋯, N) is represented as a zero-mean real-valued AWGN through variance σ² _ni. Both shot and thermal noises, given by Equations (7) and (8), respectively, are jointly added to total noise. The notation ${(.)}^{-1}$ indicates the inverse operator. diag(.) symbolized to the diagonal items, which are the results, are given within the rounded brackets. All blocks except the DWT-OFDM ones are explained in Ref. [22]. Here, we focus on DWT-OFDM blocks in detail.

3. Simulation Results and Discussion

3.1. Simulation Parameters

Here, we display the wavelet-OFDM geometric setup of the VLC-MIMO indoor system executed in a perfect 5 m × 5 m × 3 m room, clarified in Figure 6 [22]. The LED modules and the receiver are arranged and form a 4 × 4 VLC-MIMO technique [22]. Their locations in the ceiling are illustrated in Table 1. We suppose a receiver distribution scenario, with locations mentioned in Section 3.2. We consider various values for N = 1, 2, 3, and 4. The key parameter values in simulations are listed in

Table 2. Simulation parameters [22].

Room dimensions (width × length × height)	5 × 5 × 3 m3
Number of LED modules = N	4
Number of receivers = M	1
Receiving plane height	0.85 m
Half power semi angle (Ψ1/2)	60 deg
LED optical output power (Popt)	10 W
Modulation index (ξ)	0.3
Gain of optical filter (μ)	1
Lens gain (η)	1
Active area of PD (APD)	19.6 mm2
Photodiode responsivity (R)	0.53 A/W
Background current (Ibg)	190 μA
Bandwidth (B)	50 MHz
QAM	64
FOV of detector	150 deg
Number of carriers (QAM)	64
Number of frames = Number of symbols for each carrier (S)	1
Wavelet used (w)	‘Dmey’
Number of symbols	1000
Number of data	64

.

3.2. Simulation Results of Dmey Wavelet-OFDM and Discussion

Figure 7 displays the SNR performance of the N = 1, 2, 3, and 4, respectively, in a wavelet-OFDM channel imaging VLC-MIMO technique utilizing ImR and ImADR at (0, 0, 0.85) at the receiver side. For N = 1, with the increasing of the frequency, the SNR decreases whenever Pre-FDE is not employed for ImR as well as ImADR. The SNR is about 20 dB when Pre-FDE individually or with Pre-SDE is performed as shown in Figure 7a. For N = 2, as the chart illustrates in Figure 7b, the SNR is displayed for the two uneven channels with two different locations of the LED transmitters. When the Pre-FDE is not performed, the SNR is decreased with the increase in frequency. The SNR is higher in the case of ImADR than ImR. After performing the Pre-FDE and Pre-SDE, we found that the SNR of channel 1 is almost the same as channel 2. The Pre-SDE performance after Pre-FDE prevents the system from a large lack in the BER performances. The SNR decreases when a Pre-FDE is performed and Pre-SDE is not performed in two cases, ImR and ImADR, it is almost close to 20 dB of channel 1 and close to the 11 dB of channel 2. Both channels are different. This has a negative effect on the comprehensive BER performance of the system. While the SNR is about 18 dB whenever Pre-FDE is employed before Pre-SDE for the two channels. This near similarity drives the channel to BER improvement.

Accordingly, for N = 3 and N = 4, as displayed in Figure 7c,d, respectively, the SNR performance for different channels is very different when Pre-SDE is not performed. This difference negatively affects BER performances. The channels have almost the same SNR output when Pre-SDE is performed after Pre-FDE. In short, the SNR performance can be achieved when the Pre-FDE and Pre-SDE are employed.

For N = 1, SNR decreases whenever Pre-FDE is not employed for ImR as well as ImADR (pink and green marks). When Pre-FDE individually or with Pre-SDE is performed (red and blue marks), SNR is around 20 dB as shown in Figure 7a. The Pre-SDE flattened over 50 MHz bandwidth. For N = 2, SNR is displayed for the two uneven channels with two geometric setups of the LED transmitters. SNR decreases in channels 1 and 2 whenever Pre-FDE is not employed for ImR as well as ImADR (pink and green marks). When Pre-FDE individually is performed (blue marks), SNR of channel 1 is greater than that in channel 2. This is because channel 1 is closer to the detector which is located at the corner. When Pre-FDE is performed with Pre-SDE (red marks), SNR is around 17 dB as shown in Figure 7b. SNR is flattened over the 50 MHz bandwidth due to the Pre-SDE performing.

For N = 3, SNR is displayed for the three channels with three geometric setups of the LED transmitters. SNR decreases in channels 1, 2, and 3 whenever Pre-FDE is not employed for ImR as well as ImADR (pink and green marks). When Pre-FDE individually is performed (blue marks), SNR of channel 1 is greater than that in channel 2, and channel 2 is greater than channel 3. That is because channel 1 is the closest one to the detector. When Pre-FDE is performed with Pre-SDE (red marks), the SNR is ~19 dB as shown in Figure 7c. SNR is flattened over the 50 MHz bandwidth due to the Pre-SDE performing. For N = 4, SNR is displayed for the four channels with four geometric setups of the LED transmitters. SNR decreases in channels 1, 2, 3, and 4 whenever Pre-FDE is not employed for ImR as well as ImADR (pink and green marks). When Pre-FDE individually is performed (blue marks), SNR of channel 1 is greater than others. Again, this is because channel 1 is the closest one to the detector (at corner). SNR of channels 2 and 4 are almost the same, because both have the same distance from the detector (at corner). When Pre-FDE is performed with Pre-SDE (red marks), SNR is ~17 dB as shown in Figure 7d. SNR is flattened over the 50 MHz bandwidth.

Definitely, the SNR comparison should be carried out between the FFT-OFDM system and our suggested one. For the two systems, the SNR is improved when ImADR Pre-SDE is applied after Pre-FDE. For N = 1, the DWT-OFDM applying is almost the same as the FFT-OFDM. The SNR decreases with the increase of frequency when a Pre-FDE is not performed individually or with a Pre-SDE for two techniques. For DWT-OFDM, when N = 2, 3, and 4, the SNR is improved and more identical for all channels than FFT-OFDM. That occurs when both Pre-SDE and Pre-FDE ImADR are performed together. This near similarity can drive the overall channel to more BER improvement.

The BER performance of the N-channel imaging wavelet VLC-MIMO is investigated in Figure 8, which shows the BER performance along with the width-direction X and at length Y = 1.5 m for N = 1, 2, 3, and 4, respectively.

If the Pre-FDE is not performed, the BER remains above 10⁻³, and it is gradually reduced if Pre-FDE is used. The BER is substantially decreased when Pre-FDE and Pre-SDE are used in either ImR or ImADR. We notice that, in the ImADR case, the efficiency of BER is preferable to that of ImR. This is because of the ImADR’s high optical performance. For N = 1, with performing the Pre-SDE after Pre-FDE, the BER is decreased from 10⁻² to 10⁻⁴, which is when the ImADR is used instead of ImR. When N = 2, 3, and 4, as noticed in Figure 8a–c, the BER is improved for the overall channel according to SNR improvement.

The slight difference between the channels in SNR leads to large BER improvement. This improvement has occurred when the space-frequency pre-equalization domain is used. It is also noticed that the BER is reduced with the increasing numbers of LED modules. This is due to the increasing number of LED modules which leads to high capacity.

In the same way, the BER in the system proposed in [22] has been improved by performing the Pre-SDE with Pre-FDE. It remains above 10⁻³ when Pre-FDE is not used. In addition, when the Pre-FDE is utilized, the BER progressively starts to reduce. Similarly, by using the Pre-SDE after Pre-FDE for FFT-OFDM, BER has reached 2 × 10⁻² for N = 4 while it is reached 4 × 10⁻² for WT-OFDM. By using either ImR or ImADR, the system has to meet improvement. Though, the system is more improved by using ImADR than by using ImR. The BER is reduced to less than 10⁻⁵ for FFT-OFDM and is reduced to less than 5 × 10⁻⁶ for DWT-OFDM for ImADR along the X-direction. As noticed, the BER is improved by using DWT-OFDM than FFT-OFDM.

Figure 8 shows the BER performance with several numbers of LED modules individually (N = 1, 2, 3, 4). The BER is indicated along X-direction (from 0 to 5 m), with Y-direction = 1.5, and Z-axis is 0.85 m. From Figure 8a, at N = 1, when the pre-FDE and pre-SDE are not performed, (green marks), BER for ImADR is less than that for ImR. When the pre-FDE is performed, (blue marks), BER for ImADR is less than that for ImR. This is due to the high optical gain of ImADR. When the pre-SDE is performed after pre-FDE, (red marks), BER for ImADR is less than the BER for ImR, because of the high optical gain of ImADR. Similarly, for N = 2, 3, and 4, BER is decreased when Pre-SDE is performed after Pre-FDE for ImADR than for ImR. Since the spatial positions of the channels vary, they are uneven. This affects the channel overall behavior, and consequently the system BER.

Lastly, the DWT communication contour at 10⁻³ BER target for N = 1, 2, 3, and 4 is calculated, for the N- channel imaging VLC-MIMO technique. The coverage with Pre-FDE ImADR is larger than that of the Pre-FDE ImR as shown in Figure 9. For N = 1, as shown in Figure 9a, the coverage is almost identical for both Pre-FDE individually and for Pre-SDE after Pre-FDE ImR. In addition, for ImADR, it is identical for both Pre-FDE individually and for Pre-SDE after Pre-FDE. For N = 2 and 3, the contour coverage is increased, performing the Pre-FDE after Pre-SDE ImADR coverage is greater than that of the Pre-FDE after Pre-SDE ImR coverage. The ImADR coverage for N = 4 for Pre-FDE individually or before Pre-SDE is like a circle. We can calculate the coverage area by calculating the areas of the circles. The diameters for Pre-FDE individually or before Pre-SDE ImADR are 4 and 4.7 m, respectively, and for ImR are 2.3 and 3 m, respectively. The coverage along the direction of X is increased while it has no difference along the direction of Y. This is because the SNR of channel 1 is almost the same as channel 2. The SNR for all numbers of LED modules is the same whenever Pre-SDE is applied with Pre-FDE ImADR. Furthermore, X is the width, as well as, Y is the length of the room, respectively, as shown in Table 2. Coverage always increases and improvement achieved when Pre-SDE is applied with Pre-FDE in space-frequency domain pre-equalization technique as shown in Figure 9.

Either in our system proposed or the system which is proposed in Ref. [22], the coverage area increases when the Pre-FDE is proposed after Pre-SDE for ImR and ImADR. For FFT-OFDM, the coverage area has increased by 52.6% compared with the technique which utilizes the Pre-FDE only. On the other hand, the coverage area in our proposed DWT-OFDM is improved by an average of 72% as compared with the system which has used the Pre-FDE under FFT-OFDM conditions for all number of LED modules. For N = 4, the coverage contour is improved by 70% when replacing the FFT-OFDM by DWT-OFDM over the system which uses the Pre-FDE only. Following this, the coverage contour is improved by 17.4% when replacing the FFT-OFDM by DWT-OFDM at a target 10⁻³ BER over the system which uses Pre-SDE after Pre-FDE for N = 4, at which the improvement remains the same when N = 1. The improvement is changed with a different number of LED modules. This makes the average percentage of the improvement of the 4- LED modules equals 20% over the system which uses Pre-SDE after Pre-FDE.

According to the simulation that has been performed in Ref. [22] to the conventional OFDM,

Table 3. Simulation parameters comparison between FFT-OFDM [22] as well as DWT-OFDM, and their corresponding matrix values.

	Parameters	FFT-OFDM [22]	Present Work DWT-OFDM
Common requirements	Number of subcarriers	64	64
	Total number OFDM symbols	1000	1000
Transmitter	Input binary data	1 × 64,000	1 × 64,000
	QAM data	1 × 64,000	1 × 64,000
	Parallel data transmitted	1000 × 64	1000 × 64
	Parallel to serial data transmitted	1 × 64,000	1 × 64,000
	Normalized transmitted data	1 × 64,000	1 × 64,000
Receiver	Normalized received data	1 × 64,000	1 × 64,000	1 × 64,000
			1 × 128,000
	Serial data received	1 × 64,000	1 × 64,000
	Serial to parallel data received	64 × 1000	64 × 1000
	De-QAM data	1 × 64,000	1 × 64,000
	Output binary data recovery	1 × 64,000	1 × 64,000

shows the matrix-valued comparison between conventional-OFDM and our suggested wavelet-OFDM system whenever the hybrid space-frequency domain pre-equalization scheme is used. The results show that the received data of wavelet-OFDM is doubled. This is because of the use of two filters. For DWT-OFDM, it is required to double FFT-OFDM data. This is because the wavelet transmitter might have zero-padding components. The main disadvantage of FFT-OFDM is that the adding of CP by 6.25% of its data which does not contain any useful information and is just used to avoid the ISI and ICI [22]. The DWT inherently avoids the ISI and ICI. In the FFT-OFDM simulation, the IFFT/FFT size was 256 [22].

Table 3 indicates that the simulation parameters comparison between FFT-OFDM [22] and DWT-OFDM seem to be similar except in the parameter of the normalized received data of wavelet-OFDM which is doubled. The reason for this is the use of two filters in proposed system which is based on DWT-OFDM. For DWT-OFDM, it is required to double FFT-OFDM data, because the DWT-OFDM transmitter might have zero-padding components. Hence, this is the reason to duplicate the normalized received data parameter in the proposed system compared to other systems based on FFT-OFDM.

The system modulation bandwidth (BW) is 50 MHz. So, the AWG sampling rate for the system equals (1/BW) = 200 × 10⁶ samples/sec. The bit rate for the overall system is equal to (200 × 10⁶ samples/sec) × (log₂ 62) = 1.2 Gbps, where the QAM constellation order is 64. In the case where the number of channels equals 4, the data rate for all the systems is divided into 4 sections according to 4 LED modules. So, the data rate for every channel is equal to the data rate for the overall system divided by 4. For this reason, the expected data rate capacity is the capacity of all the system itself = 1.2 Gbps.

Similarly, in the practical FFT-OFDM system proposed in [22], the data rate for the overall system is equal to (4 × 300 × 10⁶ samples/sec) × (1-6.25/100) × (1-6/100) × (1-7/100) × log₂64 = 983.6 Mbps, where (6.25/100) is the CP percentage, (6/100) is the training sequence percentage (TS), and (7/100) is the forward error correction/channel coding (FEC) percentage as mentioned in [31], where all are added to data transmission.

According to our proposed practical DWT-OFDM system, the data rate capacity for all the system is equal to (4 × 300 × 10⁶ samples/sec) × (1-0) × (1-6/100) × (1-7/100) × log₂64 = 1049 Gbps, where 0 is related to no CP percentage added, (6/100) is the TS percentage, and (7/100) is the FEC percentage as mentioned in [31], where all are added to data transmission.

The data rate of the DWT-OFDM is higher than that of the traditional-OFDM. The favor of increment is back to removing the CP from our suggested system after transposing DWT-OFDM instead of FFT-OFDM.

Table 4. Comparison between traditional FFT-OFDM as well as present work (DWT-OFDM) for N = 4.

Comparison Parameters		FFT-OFDM (Ref. [22])	DWT-OFDM (Present Work)
Coverage contour	Diameter of the coverage contour employing only Pre-FDE ImADR (m)	3.4 (52.6%)	4 (70%)
	Diameter of the coverage contour employing Pre-SDE after Pre-FDE ImADR (m)	4.2	4.7
	Diameter of the coverage contour employing only Pre-FDE ImR (m)	2 (20%)	2.3 (25%)
Bit rate		983.6 Mbps	1.049 Gbps
BER (along X direction)		Less than 10−5	Less than 5 × 10−6

summarizes a comparison between the traditional FFT-OFDM as well as our suggested technique (DWT-OFDM) in terms of coverage contour, bit rate, and BER.

In a future work, the proposed system can be implemented in hardware with characteristics mentioned in Table 2, with room dimensions 5 × 5 × 3 m³. When the room dimensions are increased, only the numbers of transmitters and receivers will increase. For example, if we choose a standard room with dimensions 9 × 9 × 3 m³, the number of LED modules will be 6 modules. So, one needs 6 transmitters and 6 receivers, not 3 as in room dimensions with 5 × 5 × 3 m³. These numbers depend on the proper distribution for proper lighting distribution. Hence, the proposed system can also be applied to meeting rooms, hospitals, museums, hotels, police stations, and so on..., with different room dimensions and corresponding numbers of transmitters and receivers. The proposed system is considered environmentally friendly, cheaper, less power consumption, more secure, higher data rate compared to RF systems. Thus, the proposed system has advantage over the conventional systems [22]. Implementing a hardware simulation and producing patents for the proposed system are a very good attempt for more validation.

4. Conclusions

This paper suggests an indoor MIMO-VLC system based on the DWT-OFDM hybrid space-frequency domain pre-equalization technique instead of the traditional FFT-OFDM technique. Our proposed system contains Pre-FDE in addition to Pre-SDE in the transmitting corner and uses an imaging ImR and ImADR on the receiver side. The simulation results reveal that, the BER is improved by performing Pre-SDE in the space domain after Pre-FDE at a target BER equal to 10⁻³. The proposed system is evaluated and compared with the system based on the traditional-OFDM, in terms of the coverage contour and bit rate for various channels. The obtained results revealed that our proposed DWT-OFDM system is preferable over the FFT-OFDM, where the transmission distance and coverage contour are increased by an average of 20% over the FFT-OFDM technique, and the bit rate is increased to 1.049 Gbps. It is noted that, the suggested technique can be repeated for a large number of channels with different room dimensions. In addition, it is viable for the non-LOS channel. Furthermore, the pre-distortion can be used individually or with a pre-equalizer for more improvement. Moreover, the receiver locations can be changed to the center scenario. To conclude, the proposed system can be a good candidate for the indoor VLC applications. Implementing a hardware simulation and producing patents for the proposed system are a very good attempt for future work.