Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation

S S symmetry

Article Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation

Waleed K. Badawi , Marwa G. El-Hossary and Moustafa H. Aly *

Department of Electronics and Communication Engineering, Collage of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, Alexandria 1029, Egypt; [email protected] (W.K.B.); [email protected] (M.G.E.-H.) * Correspondence: [email protected]

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 −3 improving the coverage contour by ~20% over the traditional OFDM at a 10 bit error rate (BER) target. Hence, the proposed technique can be potentially executed in indoor VLC-MIMO systems.

Citation: Badawi, W.K.; El-Hossary, M.G.; Aly, M.H. Indoor Wavelet Keywords: visible light communication (VLC); wavelet-OFDM; orthogonal frequency division OFDM VLC-MIMO System: multiplexing (OFDM); imaging receiver (ImR); imaging angle diversity receiver (ImADR); pre- Performance Evaluation. Symmetry equalization; Meyer wavelet; Dmey wavelet 2021, 13, 270. https://doi.org/ 10.3390/sym13020270

Academic Editor: Palle E. 1. Introduction T. Jorgensen 1.1. State of the Art Regarding FFT-OFDM and DWT-OFDM Received: 17 January 2021 White light-emitting diodes (LEDs) are considered a successful technology for the next Accepted: 2 February 2021 Published: 5 February 2021 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

Publisher’s Note: MDPI stays neutral and minimize costs. Visible Light Communication (VLC) has the ability to carry data by with regard to jurisdictional claims in modulating light. This limits the extra cost of VLC techniques which use LEDs. Addi- published maps and institutional affil- tionally, these benefits enable people to access the Internet through the same visible light. iations. 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 Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. added to VLC systems, where the transmit messages can be modulated by light without This article is an open access article taking phase information into account. Besides, it can be directly sensed by the detector. distributed under the terms and The essential properties of light made VLC more effective, more power-efficient because the conditions of the Creative Commons LEDs are used in illumination and simultaneously are used in communication. Moreover, Attribution (CC BY) license (https:// the VLC is more secure, does not need license and has the ability to deliver high data rates creativecommons.org/licenses/by/ compared to RF communication. Hence, the proposed system has the above-mentioned 4.0/). properties and consequently has superiority over radio frequency systems.

Symmetry 2021, 13, 270. https://doi.org/10.3390/sym13020270 https://www.mdpi.com/journal/symmetry Symmetry 2021, 13, 270 2 of 19

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 [2–4]. 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 ap- proach 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]. Symmetry 2021, 13, 270 3 of 19

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 In- terference (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. Section2 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 Section3. Section4 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 Figure1. Symmetry 2021, 13, x FOR PEER REVIEW 4 of 19

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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.

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). FigureFigure 1. A wavelet-Orthogonal 1. A wavelet-Orthogonal Frequency FrequencyThe Division transmitter Division Multiplexing Multiplexing utilizes (OFD a 64 (OFDM)M) QAM indoor indoordigital imaging imagingmo Visibledulation Visible Light to Light Communication-map Communication- the serial bits Multiple into the Input Multiple Output (VLC-MIMO) transmitter utilizing the hybrid Pre Space Domain Equalization (Pre-SDE) system. Multiple Input Multiple Output (VLC-MIMO)OFDM symbols transmitter Χ(i) utilizing as N is the the LED hybrid modules Pre Space number Domain and Equalization 0≤i≤s−1, (Pre- while s is SDE) system. the number of the parallel data stream. 1. Firstly, the series input information is separated into N streams (according to N-trans- 3. Then, Hermitian symmetry (HS) is enforced to produce real values data. mitters), the positions of the LED modules are listed in Table 1. The data stream is 1. 4. Firstly,The Pre-FDE the series is inputperformed information by employing is separated the electrical-optical-electrical into N streams (according (EOE) to N- fre- converted from the data line to the data array, via a serial-to-parallel (S/P) converter. transmitters),quency response. the positions The LED of themodules LED moduleslocations are are listed listed in in Table Table1. 1 The [22] data and stream the meas- 2. The data is mapped to symbols by using quadrature amplitude modulation (QAM). is convertedured EOE fromfrequency the data response line to theof a data commercially array, via a available serial-to-parallel LED with (S/P) 50-MHz converter. modu- The transmitter utilizes a 64 QAM digital modulation to map the serial bits into the 2. Thelation data BW is mapped is illustrated to symbols in Ref. by [23]. using quadrature amplitude modulation (QAM). Χ (i) 0≤i≤s−1, OFDMThe transmitter symbols utilizes as aN 64 is QAM the LED digital modules modulation number to and map the serial bits while into thes is the number of the parallel data stream. TableOFDM 1. Light symbols EmittingX (Diodei) asN (LED) is the modules LED modules locations number (m) [22].and 0 ≤ i ≤ s − 1, while s is N 3. Then,the number Hermitian of the symmetry parallel data(HS) stream.is enforced to produce real values data. N = 1 (2.5, 2.5, 3) 3.4. TheThen, Pre-FDE Hermitian is performed symmetry by (HS) employing is enforced the to electrical-optical-electrical produce real values data. (EOE) fre- 4. NquencyThe = 2 Pre-FDE response. (1.5, is2.5, performed The 3) (3.5, LED 2.5, modules by 3) employing locations the are electrical-optical-electrical listed in Table 1 [22] and (EOE)the meas- fre- Nuredquency = 3 EOE response. (1.5,frequency 1.5, 3) The response(3.5, LED 1.5, 3) modulesof (2.5, a commercially 3.5, locations3) available are listed LED in Tablewith 150-MHz[ 22] and modu- the Nlationmeasured = 4 BW (1.5,is EOE illustrated 1.5, frequency 3) (3.5, in 1.5,Ref. response 3) [23]. (1.5, 3.5, of a 3) commercially (3.5, 3.5, 3) available LED with 50-MHz modulation BW is illustrated in Ref. [23]. 5.Table5. Wavelet 1.Wavelet Light Emitting transform transform Diode for for(LED) modulation modulation modules is locations performed.is perfor (m)med. [22] As. As shown shown in Figurein Figure1, the 1, blockthe block N = 1named named (2.5, IDWT IDWT 2.5, 3) is ais functiona function in thein the MATLAB MATLAB toolbox toolbox which which utilizes utilizes Low Low Pass Pass Filter Filter N = 2(LPF) (LPF) (1.5, and and High2.5, High 3) Pass(3.5, Pass Filter2.5, Filter 3) (HPF). (HPF). WT WT utilizes utilizes filters filters like like a vector a vector of approximation of approximation coefficientcoefficient (CA) (CA) and and a a vector vector of of detail detail coefficientscoefficients (CD). The signal signal is is divided divided into into sub- N = 3 (1.5, 1.5, 3) (3.5, 1.5, 3) (2.5, 3.5, 3) bands which are divided into low and high frequencies. OFDM symbol 〖Χ〗_N (i) N = 4sub-bands (1.5, 1.5, which 3) (3.5, are divided1.5, 3) (1.5, into 3.5, low 3) and(3.5, high 3.5, 3) frequencies. OFDM symbol _N (i)is is converted converted from from parallel parallel to to serial. serial. It It has has a a vector vector YY YY that that may may be be transposed transposed into into CA CAas as represented represented in in Figure Figure 22 which which is is called called approximated approximated coefficients. coefficients. 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 Table 1. Light Emitting Diode (LED) modules locations (m) [22]. (LPF) and High Pass Filter (HPF). WT utilizes filters like a vector of approximation N =coefficient 1 (CA) and a vector (2.5, of 2.5, detail 3) coefficients (CD). The signal is divided into sub- 〖〗 N =bands 2 which are divided (1.5,into 2.5, low 3) and (3.5, 2.5,high 3) frequencies. OFDM symbol Χ _N (i) is converted from parallel to serial. It has a vector YY that may be transposed into CA N = 3 (1.5, 1.5, 3) (3.5, 1.5, 3) (2.5, 3.5, 3) as represented in Figure 2 which is called approximated coefficients. N = 4 (1.5, 1.5, 3) (3.5, 1.5, 3) (1.5, 3.5, 3) (3.5, 3.5, 3)

SymmetrySymmetry2021 2021, 13, 13, 270, x FOR PEER REVIEW 55 of of 19 19

FigureFigure 2. 2.Proposed Proposed transmitter transmitter model model of of Discrete Discrete Wavelet Wavelet Transform Transform (DWT)-Orthogonal (DWT)-Orthogonal Frequency Fre- Divisionquency Division Multiplexing Multiplexing (OFDM). (OFDM).

TheThe signals signals are are up-sampled up-sampled by by LPF LPF coefficients coefficients while while the the HPF HPF filter filter can can be be performed performed byby the the convolution convolution with with Zero Zero Padding Padding (ZP) (ZP) data data Detail Detail Coefficient Coefficient (CD). (CD). This This is done is done to get to high-frequencyget high-frequency data. data. The LPFThe LPF filter filter contains contains approximation approximation coefficients. coefficients. Data Data is simulated is simu- bylated a MATLAB by a MATLAB toolbox. toolbox. The transmitted The transmitted signal si mustgnal be must in the be discretein the discrete domain domain x[k]. x[k]. VariousVarious wavelet wavelet families families have have several several filters filters containing containing different different values values of of CA CA as as well well asas CD.CD. AllAll ofof themthem seekseek toto satisfy satisfy the the WT WT bases. bases. TheThe CPCP isis notnot utilizedutilized forfor WT-OFDMWT-OFDM whichwhich isis due due to to the the wavelet wavelet orthogonality orthogonality overlapping overlapping attribute attribute and and its its better better stopband stopband attenuation.attenuation. UnlikeUnlike FFT-OFDM,FFT-OFDM, CP CP is is important important to to overcome overcome the the ISI. ISI. Each Each one one of of them them is is builtbuilt toto form form the the sum sum of Mof waveformsΜ waveformsφ(κ )ϕ,(whereκ), whereφ(κ )ϕis(κ the) is complex the complex exponential exponential basic functionsbasic functions and Φm andis the Φ scaling is the function. scaling function. The transmitted The tran signalsmitted may signal be shown may inbe ashown discrete in form.a discrete The transmittedform. The symboltransmitted is built symbol by performing is built by inverse performing DWT (IDWT)inverse [DWT14,24, 25(IDWT)]: [14,24,25]: [ ] = M−1 [ − ] x k ∑τ∑m=0 ajΦm k sM . (1) 𝑥[k] = ∑∑ a Φ[k − sM]. (1) ForFor performing performing the the wavelet-OFDM wavelet-OFDM technique technique mentioned mentioned in (1), in we (1), execute we execute the Meyer the wavelet.Meyer wavelet. The Meyer The wavelet Meyer is wavelet a limited is frequency a limited orthogonalfrequency wavelet.orthogonal Meyer wavelet. wavelet Meyer can bewavelet implemented can be implemented in fast wavelet in transform fast wavelet (FWT) transform and DWT (FWT) because and ofDWT its symmetry because of and its orthogonality, in addition to its fast ability of localization and decaying from the central symmetry and orthogonality, in addition to its fast ability of localization and decaying peak than any inverse polynomial [14]. from the central peak than any inverse polynomial [14]. OWDM is a program which is very flexible and simple. It has lower complexity with 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 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 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]. wavelet. The Meyer wavelet and scaling function is defined in the frequency domain [14]. 1.1. AA parallel-to-serialparallel-to-serial (P/S)(P/S) operation operation is performed to obtain the time domain signal. 2.2. Pre-SDEPre-SDE isis implementedimplemented byby normalizingnormalizing allall datadata streamsstreams totoensure ensure that that the the detected detected N-data have the same value of SNR. The Pre-SDE concept of an optical DCO-OFDM 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 system is based on the VLC-MIMO N-channel imaging technique. The output optical power and the modulation index for every LED are Popt and ξ, respectively. Pre-SDE power and the modulation index for every LED are Popt and ξ, respectively. Pre-SDE is performed by using power allocation matrix A = diag (a1; a2; ······ ; aN) which is performed by using power allocation matrix A = diag (a1; a2; · · ·; aN) which adjusts adjusts all electrical powers modulating data. all electrical powers modulating data.

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

S = Popt (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) = xRe + j xIm, (3) T where x = (x1 x2, ······ xN) is a vector of modulating signals and xi (i = 1, 2, ······ , N) is 2 the normalized bipolar OFDM signal with variance σ 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, ai, satisfy the following equation [22]: 1 N a2 = 1. (4) N ∑i=1 i

2.2. Channel Estimation 2.2.1. White Gaussian Noise Estimation

The equalizer output includes a Gaussian noise with a total variance GN, 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:

2 2 2 2 GN = σshot + σthermal + γ σrISI. (5)

The received power PrISI by ICI is [26]:

Z ∞ LEDs PrISI = ∑ = hi(t) ⊗ X(t) dt. (6) T i 1 The shot noise variance is given by [26]:

2 σshot = 2qγ PrSignal + PrISI B + 2qIbgI2B, (7)

where q is the electronic charge, B is the equivalent noise bandwidth, Ibg is background current. The noise bandwidth factors I2 = 0.562. The thermal noise variance is calculated by [27]:

2 2 8πkTk 2 16π kTkΓ 2 2 3 σthermal = ηAI2B + η A I3B . (8) G gm Furthermore, both sides clariﬁed noise from feedback-resistor, and noise from FET channels, respectively. Similarly, k is Boltzmann constant, TK 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, gm is the FET trans-conductance, I3 = 0.0868, 2 Tk = 295 K, Γ is the FET channel noise, G = 10 dB, gm = 30 mS, η = 1.5, Γ = 112 pF/cm , 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 Figure3. The vector υRS can be written as υRS = [a, b, c] = [XR,YR,ZR]–[XS, Symmetry 2021, 13, x FOR PEER REVIEW 7 of 19

ZS], where [XS, YS, ZS] and [XR, YR, ZR] are the positions of transmitter and receiver, respectively [28]. The optical LOS channel gain between the tth LED lamp and the rth PD is Symmetry 2021, 13, 270 7 of 19 proved by:

() μη cos(∅rt) cos(θrt) , 0 ≤ θ ≤ϕ h(0) = . (9) YS,ZS], where [XS,YS,ZS0,] and [X R ,Y R ,Z R ] are the positions of transmitter θ >ϕ and receiver, respectively [28]. The optical LOS channel gain between the tth LED lamp and the rth PD To conclude, m = −ln2/ln (cos Ψ1/2) is the emitted lighting order with Ψ1/2 is the semi- is proved by: angle of the transmitter at half power, APD is the PD active area, drt is the distance between

the tth LED lamp and( the(m +rth1)A PD,PD μ andm η are the optical filter gain likewise the optical 2 µη cos (∅rt) cos(θrt), 0 ≤ θ ≤ φ lens, respectively,hrt(0) =ϕrt is the2 πemissiondrt angle, and θrt is the incident angle. Moreover,. if θrt is (9) θ > φ outside the Field of View 0,(FOV) of the receiver, the optical gain hrt is zero and when an imaging non-diversity receiver (ImADR) is used, θrt becomes zero.

FigureFigure 3. 3.LineLine of ofSight Sight (LOS) (LOS) channel channel configuration conﬁguration [28] [28. ].

2.2.3. Non-ImagingTo conclude, LOS m = Channel−ln2/ln Matrix (cos Ψ 1/2) is the emitted lighting order with Ψ1/2 is the semi-angleThe general of the 4 × transmitter 4 MIMO channel at half matrix power, H A isPD drivenis the by: PD active area, drt is the distance between the tth LED lamp and the rth PD, µ and η are the optical ﬁlter gain likewise the h ⋯h optical lens, respectively, φrt is the emission angle, and θrt is the incident angle. Moreover, H = ⋮⋱⋮. (10) if θrt is outside the Field of View (FOV) of the receiver, the optical gain hrt is zero and when h ⋯h an imaging non-diversity receiver (ImADR) is used, θrt becomes zero. Furthermore, the channel gain h is progressed, where r and t refer to the numbers of2.2.3. transmitters Non-Imaging and receivers, LOS Channel respectively. Matrix Similarly,The general the 4ICI× is4 MIMOdeserted channel by ImR matrix or ImADR H is driven use, the by: matrix of the channel H of N-channel imaging VLC-MIMO technique is evidenced in [26]:   h11 ··· h14 = h ,h ,…….,h H diag ( . . . ). (11) H =  . .. . . (10) h41 ··· h44 2.3. The Receiver WeFurthermore, consider a VLC-MIMO the channel indoor gain hrt imagingis progressed, receiver where system r and based t refer on towavelet-OFDM the numbers of usingtransmitters one receiver and receivers,(M) of the respectively. hybrid space-frequency domain pre-equalization system. The receiverSimilarly, location the ICI (scenario-room is deserted by corner) ImR or is ImADR given by use, (0, the0, 0.85 matrix m). ofThe the system channel block H of diagramN-channel is shown imaging in Figure VLC-MIMO 4. technique is evidenced in [26]: • The produced N serials of unipolar data have been used to drive N LED modules, H = diag (h11, h22, ...... , hNN). (11) respectively, as shown in Figure 1. The LED radiation light is sensed by an ImR or an 2.3.ImADR The Receiver at the detector side. The recipient side of the wavelet-OFDM VLC-MIMO techniqueWe consider is illustrated a VLC-MIMO in Figure indoor 4. imaging receiver system based on wavelet-OFDM • usingAn oneA/D receiverconversion (M) is of utilized the hybrid to convert space-frequency the analog signals domain to pre-equalizationdigital. The 3-dB system.mod- Theulation receiver bandwidth location (scenario-roomof LED is adjusted corner) as 50 is MHz. given by (0, 0, 0.85 m). The system block diagram is shown in Figure4.

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Symmetry 2021, 13, 270 The specific processes to perform digital Pre-FDE were fully illustrated in [22]. In8 ofthe 19 OFDM transmitter (Tx), a Pre-FDE has performed adaptively according to the estimated SNR information.

FigureFigure 4. 4. AA Wavelet-OFDM Wavelet-OFDM indoor indoor imaging VLC-MIMO rece receiveriver by utilizing the hybrid Pre-SDE system.

2.3.1. Received Wavelet-OFDM Data • The produced N serials of unipolar data have been used to drive N LED modules, DWTrespectively, receiver as is shownthe reverse in Figure operation1. The of LED IDWT. radiation It performs light a is DWT sensed according by an ImR to the or MATLABan ImADR toolbox at. theThe detector transmitted side. signal The recipient ∪[k] is sidethe front-end of the wavelet-OFDM receiver successive VLC-MIMO digitally techniquemodulated is symbols illustrated to inbe Figure transformed,4. the data is decomposed across filters, LPF and• HPFAn A/Drelated conversion to CA in addition is utilized to the to CD. convert CA is the the analog output signals signal of to the digital. approximation The 3-dB coefficientsmodulation or LPF bandwidth and CD are of the LED output is adjusted data of as the 50 MHz.detailed coefficients or HPF to execute thatThe specificoperation. processes The data to performis transposed digital before Pre-FDE converting were fully from illustrated S/P and in the [22 wavelet]. In the familyOFDM used transmitter is Demy (Tx), wavelet. a Pre-FDE has performed adaptively according to the estimated [ ] SNR∪ information.k 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 imaginary2.3.1. Received data Wavelet-OFDMand the CA will Databe considered as real data to avoid any loss of data. That is all DWTgo viareceiver the DWT-OFDM is the reverse receiver operation which of can IDWT. be seen It performs in Figure a 5. DWT according to the MATLAB toolbox. The transmitted signal ∪ [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. ∪[k] 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 Figure5.

Figure 5. Proposed receiver model of DWT-OFDM.

Symmetry 2021, 13, x FOR PEER REVIEW 8 of 19

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.

Figure 4. A Wavelet-OFDM indoor imaging VLC-MIMO receiver by utilizing the hybrid Pre-SDE system.

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 ∪[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. ∪ [k] contains some zeros elements which are decomposed from CD information Symmetry 2021, 13, 270 produced in the transmitter comparing to CA data. So, the CD data will be considered9 of19 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.

FigureFigure 5. 5.Proposed Proposed receiver receiver model model of of DWT-OFDM. DWT-OFDM.

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: ( ) = ( ) ( ) + ( ) W t ∑j≤J∑kwj,k t .Ψj,k t ∑k aj,kΦJ,k t , (12) th where wj,k(t) is the wavelet coefficients existing at the k position from the scale j, Ψj,k(t) is the IDWT modulator as a sequence of wavelet, ΦJ,k(t) is the scaling function, and aj,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]: y = RPopt ξ HA x + 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]:

2 Rpopt ξaihii SNR0 = = a2SNR , i = 1, 2, ··· , N, (14) i σ2 1 i ni Symmetry 2021, 13, 270 10 of 19

2 2 2 where SNRi = (R Popt ξ hii) σ xi /σ ni, i = 1, 2, ... .., N. R is the photodiode responsivity, Popt is the LED output power, ξ is the modulation index, and hii 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: 2 2 2 a 1SNR1 = a 2 SNR2 = ······ = a NSNRN. (15) By solving Equations (2) and (5), the N diagonal elements of matrix A can be obtained by [14,24]: s N ai = . (16) SNR ∑N 1 i i=1 SNRi 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 Xest and decompose the detected streams of Y, a matrix inversion and multiplication should be required: −1 Xest = H Y. (17) After ZF based MIMO de-multiplexing, we have [11]:

−1 −1 ex = H y = RPopt ξ HA x + H 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, ni (i = 1, 2, ······ , N) is represented as a 2 zero-mean real-valued AWGN through variance σ 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. Symmetry 2021, 13, x FOR PEER REVIEW 10 of 19

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 sig- nificant 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 Xest and decompose the detected streams of Y, a matrix inversion and multiplication should be required:

X =H Y. (17) After ZF based MIMO de-multiplexing, we have [11]:

x =H y= R Popt ξ HA x +H 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, ni (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 (. ) indicates the inverse operator. diag(.) symbolized to the diagonal items, which are the re- Symmetry 2021, 13, 270 11 of 19 sults, 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 we display display the the wavelet-OFDM wavelet-OFDM geomet geometricric setup setup of the of theVLC-MIMO VLC-MIMO indoor indoor sys- systemtem executed executed in a inperfect a perfect 5 m × 5 5 m m× × 53 m room,× 3 m clarified room, clariﬁed in Figure in 6 Figure [22]. The6[ 22LED]. The modules LED modulesand the receiver and the are receiver arranged are arranged and form and a 4 form× 4 VLC-MIMO a 4 × 4 VLC-MIMO technique technique [22]. Their [22 locations]. Their locationsin the ceiling in the are ceiling illustrated are illustrated in Table in 1. Table We suppose1. We suppose a receiver a receiver distribution distribution scenario, scenario, with withlocations locations mentioned mentioned in Section in Section 3.2. We 3.2 .consider We consider various various values values for N for = 1, N 2, = 3, 1, and 2, 3, 4. and The 4. Thekey parameter key parameter values values in simulations in simulations are listed are listed in Table in Table 2. 2.

Figure 6. Three-dimensional conﬁguration of the imaging VLC-MIMO technique for N-channel [22].

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 2 Active area of PD (APD) 19.6 mm 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 Figure7 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, Symmetry 2021, 13, 270 12 of 19

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 Figure7a. For N = 2, as the chart illustrates in Figure7b, 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 Symmetry 2021, 13, x FOR PEER REVIEWis about 18 dB whenever Pre-FDE is employed before Pre-SDE for the two channels.12 This of 19

near similarity drives the channel to BER improvement.

(a) (b)

FigureFigure 7. 7.Signal Signal to to Noise Noise Ratio Ratio (SNR) (SNR) performance performance using using Imaging Imaging Receiver Receiver (ImR) (ImR) without without using using Pre- Pre- Frequency Frequency Domain Domain EqualizationEqualization (Pre-FDE) (Pre-FDE) and and without without using using Pre-Space Pre-Space Domain Domain Equalization Equalization (Pre-SDE), (Pre-SDE), Imaging Imaging Angle Angle Diversity Diversity Receiver Receiver (ImADR) without using Pre-FDE and without using Pre-SDE, ImADR with using only Pre-FDE and ImADR with using (ImADR) without using Pre-FDE and without using Pre-SDE, ImADR with using only Pre-FDE and ImADR with using Pre-FDE and Pre-SDE, at corner scenario (0, 0, 0.85) of the receiving plane for (a) N = 1, (b) N = 2, (c) N = 3, and (d) N = 4. Pre-FDE and Pre-SDE, at corner scenario (0, 0, 0.85) of the receiving plane for (a) N = 1, (b) N = 2, (c) N = 3, and (d) N = 4.

Accordingly,Accordingly, for for N N = = 3 3 and and N N = = 4, 4, as as displayed displayed in in Figure Figure7c,d, 7c,d, respectively, respectively, the the SNR SNR performanceperformance for for different different channels channels is is very very different different when when Pre-SDE Pre-SDE is is not not performed. performed. This This differencedifference negatively negatively affects affects BER BER performances. performances. The The channels channels have have almost almost the the same same SNR SNR outputoutput when when Pre-SDE Pre-SDE is is performed performed after after Pre-FDE. Pre-FDE. In In short, short, the the SNR SNR performance performance can can be be achievedachieved when when the the Pre-FDE Pre-FDE and and Pre-SDE Pre-SDE are are employed. 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

Symmetry 2021, 13, 270 13 of 19

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 Figure7a. 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 Figure7b. 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 Figure7c. 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 Figure7d. 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 Figure8, 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 Figure8a–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. Symmetry 2021, 13, x FOR PEER REVIEW 13 of 19

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 Symmetry 2021, 13, 270 14 of 19 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.

(a) (b)

Figure 8. Bit Error Rate (BER) performances along width-direction (X) and length Y = 1.5 m of (a) N = 1, (b) N = 2, (c) N = 3, and (d) N = 4.

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. Figure8 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 Figure8a, 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. Symmetry 2021, 13, 270 15 of 19

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 Figure9. For N = 1, as shown in Figure9a, 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 Symmetry 2021, 13, x FOR PEER REVIEWwidth, as well as, Y is the length of the room, respectively, as shown in Table2. Coverage15 of 19 always increases and improvement achieved when Pre-SDE is applied with Pre-FDE in space-frequency domain pre-equalization technique as shown in Figure9.

(a) (b)

−3 FigureFigure 9. 9.Communication Communication area area contour contour on on an an objective objective of of 10 10−3 BERBER ((aa)) NN == 1,1, ((b)) NN == 2, ( c) N = 3, 3, and and ( (d)) N N = = 4. 4.

Either in our our system system proposed proposed or or the the system system which which is proposed is proposed in Ref. inRef. [22], [ 22the], cov- the coverageerage area area increases increases when when the the Pre-FDE Pre-FDE is isproposed proposed after after Pre-SDE Pre-SDE for for ImR ImR and and ImADR. For FFT-OFDM,FFT-OFDM, thethe coveragecoverage areaarea hashas increasedincreased byby 52.6%52.6% comparedcompared withwith thethe techniquetechnique whichwhich utilizesutilizes thethe Pre-FDEPre-FDE only.only. OnOn thethe otherother hand,hand, thethe coveragecoverage areaarea inin ourour proposedproposed DWT-OFDM isis improvedimproved byby anan averageaverage ofof 72%72% asas comparedcompared withwith thethe systemsystem whichwhich hashas 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 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].

Symmetry 2021, 13, 270 16 of 19

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, Table3 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. Simulation parameters comparison between FFT-OFDM [22] as well as DWT-OFDM, and their corresponding matrix values.

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

Table3 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 Symmetry 2021, 13, 270 17 of 19

6 is equal to (200 × 10 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. Table4 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.

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

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

In a future work, the proposed system can be implemented in hardware with characteristics mentioned in Table2, 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 Symmetry 2021, 13, 270 18 of 19

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.

Author Contributions: Formal analysis, W.K.B. and M.G.E.-H.; Investigation, M.G.E.-H. and M.H.A.; Methodology, W.K.B.; Project administration, M.H.A.; Resources, W.K.B. and M.G.E.-H.; Software, M.G.E.-H.; Supervision, W.K.B. and M.H.A.; Writing—original draft, M.G.E.-H.; Writing—review & editing, M.H.A. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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