Department of Electrical Engineering · 2019-05-13 · Ficha Catalogr a ca Mathias, Luis Carlos...

Department of Electrical Engineering

Luis Carlos Mathias

Localization, Pre-distortion and Pre-equalization in

OFDM VLC Systems

Final year project presented to the

Department of Electrical Engineering

at Universidade Estadual de Londrina

(UEL) as a requirement for the con-

clusion of the Bachelor of Electrical

Engineering (BE) honours degree.

Londrina, PR2018

Luis Carlos Mathias


OFDM VLC Systems

Final year project presented to the Department

of Electrical Engineering at Universidade Es-

tadual de Londrina (UEL) as a requirement

for the conclusion of the Bachelor of Electrical


Area: Telecommunication Systems

Supervisor:

Dr. Taufik Abrao

Londrina, PR2018

Ficha Catalografica

Mathias, Luis CarlosLocalization, Pre-distortion and Pre-equalization in

OFDM VLC Systems. Londrina, PR, 2018. 30 p.

Final year project – Universidade Estadual de Londrina, PR. De-partment of Electrical Engineering.

I. Visible Light Communication. II. HPLED non linearities. III.HPLED attenuation. IV. VLC pre-distortion. V. VLC pre-equalization. VI. VLC position estimation.Department of Electrical Engineering

Luis Carlos Mathias


OFDM VLC Systems

Final year project presented to the Department

of Electrical Engineering at Universidade Es-

tadual de Londrina (UEL) as a requirement

for the conclusion of the Bachelor of Electrical


Area: Telecommunication Systems

Examination Board

MsC. Jaime Laelson JacobDepartment of Electrical Engineering (UEL)

Research Professor

Dr. Jose Carlos Marinello FilhoDepartment of Electrical Engineering (UEL)

Research ProfessorCo-Supervisor

Dr. Taufik AbraoDepartment of Electrical Engineering (UEL)

Senior Research ProfessorSupervisor

Londrina, 21 de dezembro de 2018

Acknowledgments

I thank God first for providing material and non-material resources. By my

parents who made me become a large part of the man I am today and by the

patience and support of my wife and son. Also for the patience, great effort and

contributions to the work on the part of my adviser Dr. Taufik.

I thank the support of colleagues and professors of the Department of Elec-

trical Engineering of UEL, especially Dr. Leonimer Mello and technician Mr.

Luiz Schmidt. All those who could contribute to the work even in the face of

innumerable difficulties.

I also remember that part of this work was financed by the Coordination for

the Improvement of Higher Education Personnel (CAPES), by resources from the

Postgraduate Support Program (PROAP), by the National Council for Scientific

and Technological Development (Contracts 202340 / 2011-2 and 303426 / 2009-

8) and partly by resources of the State University of Londrina (FAEPE / UEL

02/2011), Government of the State of Parana.

Abstract

Faced with the growing demand for data transmission, the study of the useof visible light for communication systems has now gained prominence due to theavailability of an immense and still unexplored spectral band. This allows veryhigh transmission rates to be made available in a current scenario of increasingradio frequency spectrum scarcity. However, the study of VLC localization hasbecome promising due to the fact that the global positioning system (GPS) signaldoes not penetrate indoors. The replacement of conventional lamps by the LEDtype also opens the possibility of modulation of light signals. Thus, the first partof this work proposes an architecture that enables the VLC receiver to discrimi-nate the powers of the transmitter LEDs of the luminaires in an OFDM scheme.By using OFDM, the proposal also allows data communication and maintains thelighting functionality of the luminaire. For this, in this scenario, a hybrid estima-tor is presented and evaluated, which cascaded the estimation of the location bythe angle of arrival (AoA) and by the received signal strength (RSS). However,the design of the electronic circuit of the transmitter and receiver present severalchallenges. On the transmitter side, the attenuation of the emitted signal forhigher frequencies and the non-linearity of the optical power in relation to thecurrent supplied to the LEDs are listed. In the receiver, the intrinsic capacitanceof the photodiode junction that ends up making it difficult to implement a tran-simpedance amplifier for frequency bandwidth. Therefore, the work proposes thestudy and the implementation of a pre-distortion and pre-equalization schemeusing a light feedback scheme in order to mitigate these effects.

Keywords: VLC localization, LED non linearities, attenuation, pre-distortion,pre-equalization, OFDM.

List of Contents

Abbreviations List

Conventions and Notations

1 Introduction 1

2 Results 6

3 Conclusion 8

Bibliography 9

Appendix A -- 3-D Localization with Multiple LEDs Lamps in OFDM-

VLC System 10

Appendix B -- Pre-distortion and Pre-equalization for Mitigation of

LED non Linearities and Low-pass Attenuation in OFDM VLC

Systems 23

Abbreviations List

ACO-OFDM Asymmetrically Clipped Optical OFDM

ADC Analog to Digital Conversion

AFE Analog-Front-End

AoA Angle of arrival

AWGN Additive White Gaussian Noise

BER Bit Error Rate

CLT Central Limit Theorem

CP Cyclic Prefix

DAC Digital to Analog Conversion

DC Direct Current

DCO-OFDM DC-biased Optical OFDM

DFT Discrete Fourier Transform

DPD Digital Predistortion

FET Field Effect Transistor

FFT Fast Fourier Transform

FoV Field of View

FSO Free Space Optical

F-DPD Fixed DPD

GPS Global Positioning

HPLED High Power LED

IFFT Inverse FFT

IM/DD Intensity Modulation with Direct Detection

LCM Location and Communication Mode

LED Light Emitting Diode

LFB-DPD Luminous Feedback DPD

LLF Log-Likelihood Function

LOM Location Only Mode

ML Maximum-Likelihood

MVUE Minimum Variance Unbiased Estimator

M-QAM M-ary Quadrature Amplitude Modulation

NLS Nonlinear Least Squares

OFDM Ortogonal Frequency Division Multiplexing

OWC Optical Wireless Communication

PAPR Peakto-Average Power Ratio

PD Photodiode/Photodetector

PDF Probability Density Function

QPSK Quadrature Phase Shift Keying

RF Radio Frequency

RMSE Root-Mean-Square Error

RND Random

RPS Real Physical System

RSS Received Signal Strength

SNR Signal-to-Noise Ratio

SO-OFDM Spatial Optical OFDM

TIA Transimpedance Amplifier

VAP Visible Light Access Points

VLC Visible Light Communication

WAoA Weighted AoA

W-DPD Without DPD

Conventions and Notations

The following mathematical notations where adopted in this work:

a Boldface lower case letters represent vectors;

A Boldface upper case letters denote matrices;

(·)−1 Inversion operator;

(·)T Transposition operator;

(·)† Moore-Penrose pseudo-inverse;

‖·‖n Norm of order n;

diag(·) Diagonalization Operation;

ker(·) Matrix kernel;

IK Identity matrix of order K;

Nµ, σ2 Gaussian distribution with mean µ and variance σ2;

Nµ,C Gaussian distribution with mean µ and covariance matrix C;

Ua, b Uniform distribution with boundaries a and b;

O(·) Complexity order of an operation or algorithm;

E [·] Statistical Expectation;

R Real numbers set;

C Complex numbers set;

∈ Belongs to the set.

1

1 Introduction

In the literature, OWC (Optical Wireless Communication) systems are widely

referred to as FSO (Free Space Optical) and VLC (Visible Light Communication).

FSO systems are used for the transmission of high data rates between two fixed

points at distances up to several kilometers (KHALIGHI; UYSAL, 2014). VLC,

however, is limited to operating in the visible light spectrum range where an

example of application is LiFi (Light Fidelity). This system uses its own ambient

lighting by implementing a complete wireless network system (HAAS et al., 2016).

VLC allows for greater data security because the signal is confined to the

infrastructure, which is not the case with the radio frequency (RF) system. VLC

is also notable for its immunity to RF interference and vice versa. That is, it does

not interfere with mission-critical equipment such as surgical centers or in aircraft

landing and/or takeoff situations. Another advantage is the possibility that the

multi-path fading can be averaged since the area of the photodetectors is very

large compared to the wavelength of the visible light (PATHAK et al., 2015). All

this in a scenario of increasing frequency spectrum shortage in RF communication

systems.

Figure 1.1: The range of light visible in the spectrum of electromagnetic waves(PATHAK et al., 2015).

The VLC has gained even more interest in recent years due to the increasing

replacement of conventional lamps with those of LEDs that are more durable

and of better energy and luminous efficiency (KOMINE; NAKAGAWA, 2004). In

this context, the LED lamp in addition to illuminating, allows transmitting data

1 Introduction 2

compared to the incandescent or fluorescent lamps.

However, the design of the electronic circuit of the transmitter and receiver

present several challenges. On the transmitter side, the attenuation of the signal

emitted by the transmitter LEDs for larger frequencies and the non-linearity of

the optical power in relation to the current supplied to the LED. And on the

receiver side, another limitation is the intrinsic capacitance of the junction of

the photodiode that makes it difficult to implement a transimpedance amplifier

(TIA) for frequency bandwidth.

Therefore, the present work makes a study and proposes the implementation

of a pre-equalization scheme in order to mitigate these effects. That is, a light fe-

edback scheme is still suggested in the transmitter module so that the undesirable

effects of the transmitter LED and the receiver photodiode are minimized.

The VLC transmitter is usually a light emitting diode (LED) based luminaire.

The process of generating white light in these LEDs is basically in two ways

(PATHAK et al., 2015). In the first form, the white light is obtained from the

combination of the blue LED light when crossing a yellow layer of the chemical

element phosphorus. Thus, by varying the thickness of the layer it is possible to

generate different color temperatures. The second form uses the additive mixture

of lights generated by red, green and blue colored LEDs (RGB system).

Figure 1.2: In a) the PSD of the fluorescent tubes of 40W and LEDtube ofPhilips. In b) comparison between the PSD of a blue and red LED strip.

Courtesy: Department of Physics of UEL.

The first-mentioned LED lamp, although easier to deploy and less costly,

has a limited switching speed of up to a few MHz, due to the luminous per-

sistence of the phosphor layer. Fig. 1.3 evidence this attenuation by the result

of a measurement of the electric gain of an experimental arrangement of a more

receiver-transmitter in a direct-viewing channel. The RGB lamp, because it does

not have the phosphor layer, presents this limitation more smoothly and also al-

1 Introduction 3

lows to use a data modulation scheme using the three different colors also called

Color Shift Keying (CSK) (SINGH; O’FARRELL; DAVID, 2014).

Figure 1.3: Attenuation verified from the measurement of the electric gain ofthe transmitter set plus receiver in a direct view channel (MINH et al., 2009).

Another problem for modulation in LED type transmitters is the non-linearity

between the current applied to the LED and the respective optical power obtained

(LENK; LENK, 2016). Fig. 1.4 presents a typical curve of an Osram SFH 4545

infrared LED. The AC signal represented in the dotted line represents that for

small signals only current modulation can be considered linear with optical power

issued.

Figure 1.4: Non-linearity of the optical power emitted as a function of theelectric current of an LED (OSRAM, 2016).

There are basically two types of light receiving devices: the discrete photo-

receptor and the image sensor (camera sensor). The photoreceptor is a semicon-

ductor that allows easy conversion of the light signal to current up to tens of

MHz (PATHAK et al., 2015). The image sensor is composed of a large number of

photodetectors arranged in an integrated circuit (IC). The sampling of the signal

of each photosensor is not done in parallel but by sweeping. This implies a low

sampling rate of a complete image and consequently a low data transmission.

In the signal reception, photoreceptors based on PIN photodiodes are usually

employed. This is a semiconductor that allows easy conversion of the light signal

1 Introduction 4

to current up to tens of MHz. Fig. 1.5, presents the equivalent electrical circuit of

a PIN photodiode. The parameters denoted here are: I the photocurrent genera-

ted by the incident light, RJ the junction resistance, CJ the junction capacitance,

RS the series resistance, and ID is the current in the dark. Since RS RJ , often

RS is neglected.

Figure 1.5: Equivalent circuit of a PIN photodiode (ZHEN, 2013).

For photodetection, there are basically two modes of operation of the pho-

todiode (ZHEN, 2013). The first one, the photovoltaic, does not require a bias

voltage. This mode is best suited for situations where higher linearity, higher

sensitivity, and lower noise are required. In the second way, the photoconductive

mode, a reverse bias voltage VBIAS is applied between its terminals. This confi-

guration enables applications that require a higher detection speed but has the

disadvantage of the dark current. The Tab. 1.1 gives a brief comparison between

these two modes.

Table 1.1: Comparison between photodetection modes of a PIN photodiode.

Photovoltaic Photoconductivedark current yes no

linearity ↑ ↓sensibility ↑ ↓

noise ↓ ↑speed ↓ ↑

The differences in the characteristics presented in Tab. 1.1 are due to the fact

that the reverse bias imposed by VBIAS reduces the junction capacitance (BOY-

LESTAD; NASHELSKY, 1998). Fig. 1.6 shows the increase of the depletion region

when a reverse bias is applied at a PN junction. Because the depletion region is

a non-electrically conductive region, it functions as a dielectric. Increasing if the

distance between the conducting regions has the same effect when the plates of

a capacitor distance, that is, the capacitance of the junction decreases.

The transimpedance amplifier (TIA), for photodetection schemes, plays a very

important role. This sub-circuit converts the current generated by the photodiode

to a proportional voltage that can be sampled in an analog-to-digital (ADC)

converter. Fig. 1.7 shows the basic settings for the two modes of operation of

1 Introduction 5

(a) Depolarized (Photovoltaic). (b) Reverse polarized (photoconductive)

Figure 1.6: Effect of the depletion region by changing the polarization of a PNjunction (BOYLESTAD; NASHELSKY, 1998).

(a) Photovoltaic TIA, (b) Photocondutive TIA.

Figure 1.7: Transimpedance amplifier basic circuits for both photodetectionmodes (ZHEN, 2013).

the photodiode including its transfer equations. Thus, in both cases, the element

that defines the gain of the TIA is the feedback resistor RF by the equation:

VOUT = I.RF . (1.1)

In addition to the brief introduction of the physical layer of the VLC system

of this chapter, this work is divided into two more chapters and two appendices.

In Appendix A, the paper dealing with the problem of locating a receiver in

an OFDM system in VLC environment with multi-LED luminaries is presented.

Already, Appendix B presents the work of dealing with the mitigation of the

effects of LED non-linearity and attenuation at high frequency applying pre-

digital distortion and pre-equalization. Chapter 2 presents a summary of the

main objectives and results of the two papers while Chapter 3 closes with the

final conclusion.

6

2 Results

The results of the activities developed during the period were divided into

two papers. This was intended to generate the following articles for publication

in periodicals:

[A] 3-D Localization with Multiple LEDs Lamps in OFDM-VLC System;

Authors: Luis Carlos Mathias and Taufik Abrao;

Status: Paper submitted to IEEE Access journal.

[B] Pre-distortion and Pre-equalization for Mitigation of LED non Linearities

and Low-pass Attenuation in OFDM VLC Systems;

Authors: Luis Carlos Mathias, Leonimer Flavio de Melo and Taufik Abrao;

Status: Finishing for submission.

In these two works are presented the analytical results and numerical simula-

tions, as well as the analysis of these. In the sequence, they are briefly presented

highlighting their main results.

In [A] the hybrid process of estimation of the position of a VLC receiver in a

known infrastructure was presented. The hybrid estimator uses the result of the

arrival angle estimator (AoA) as the starting point of the recursive estimator by

virtue of the received signal (RSS). The RSS estimator has better accuracy but

has convergence problems depending on the starting point of the search. Thus,

the hybrid estimator has the advantage of using the result of the AoA estimator

by making the search point of the RSS estimator closer to the exact one. This

corroborates for the faster convergence. In both estimators, it is necessary to

discriminate the received power generated by the different LEDs of the luminaires.

However, few studies show ways of discriminating LED power. As a novelty of

the work, a system architecture that discriminates the different potencies of the

luminaire LEDs was proposed and extensively analyzed using the Spatial Optical

OFDM (SO-OFDM) scheme. In this case, the proposed system simultaneously

allows the control of the luminosity level, the location of the mobile receiver and

its communication with the LED luminaire.

2 Results 7

Work [A] has already been submitted in two journals, where the reviewers

suggest the actual implementation of the system. From the challenges of this task

originated the work [B]. This is because, in the numerical simulations of the work

[A], as well as the other works in the literature, the problems of attenuation in

high frequencies and non-linearity of the luminous intensity emitted as a function

of the LED current were not considered. Thus, work [B] first experimentally

confirms the variations of the nonlinearity curves of the LED as a function of

temperature and then proposes a real-time nonlinearity correction scheme by

digital processing of the luminous feedback signal. The luminous feedback signal

is captured by a fixed photodiode and coupled to the LED lamp transmitter. It is

proposed that the feedback signal also allows the pre-compensation of the higher

attenuation of the higher frequency OFDM subcarriers. This is because the LED

and the photodiode and TIA assembly behave as low pass. This is to keep the

SNRs in the reception of the OFDM more homogeneous or to use a water-filing

scheme for example.

8

3 Conclusion

In this paper, some basic principles of VLC based systems were discussed.

For this, it delimited as the theme the problem of power discrimination for the

estimation of the location of a receiver and the characterization of the problems

of nonlinearity and attenuation together of a proposal to mitigate these problems.

Specifically, the work [A] confirmed the proposal of discrimination of the

powers transmitted by each LED of each VAP corroborating the implementation

of the localization schemes based on the hybrid locator that combines the WAoA

estimators with RSS in OFDM environments. It was confirmed that the initial

search point obtained by the WAoA estimator provided better results in relation

to accuracy, time and convergence percentage. This compared with the results

obtained from starting points defined from the centroid of the room or randomly.

It was verified that the penalty of the increase of the complexity of the estimator

is admissible if considered the improvement of the accuracy and the percentage

of convergence. It was possible to demonstrate analytically the proposal’s ability

to locate the receiver, transmit data and maintain the lighting function of the

LED luminaire.

The work [B] initially confirmed the good correlation of the experimental

modeling of the non-linear behavior of the luminous intensity emitted by the LED

as a function of its current. By means of the developed experimental arrangement,

it also confirmed the variation of this nonlinearity at different temperatures of the

semiconductor junction. This, in order to confirm the need for the proposed real-

time pre-distortion scheme. At different junction temperatures, it was confirmed

from numerical simulations the performance improvement in BER, mainly for

higher-order M-QAM modulation schemes. Finally, taking advantage of the signal

of the luminous feedback, it proposes a scheme for the pre-equalization of the

OFDM subcarriers still in the transmitter.

As a continuity of this work, we can list the numerical and experimental

confirmation of the pre-equalizer using the luminous feedback signal.

9

Bibliography

BOYLESTAD, R. L.; NASHELSKY, L. Dispositivos eletronicos e teoria decircuitos. Rio de Janeiro: Prentice-Hall do Brasil, 1998.

HAAS, H.; YIN, L.; WANG, Y.; CHEN, C. What is lifi? Journal of LightwaveTechnology, v. 34, n. 6, p. 1533–1544, March 2016. ISSN 0733-8724.

KHALIGHI, M. A.; UYSAL, M. Survey on free space optical communication: Acommunication theory perspective. IEEE Communications Surveys Tutori-als, v. 16, n. 4, p. 2231–2258, Fourthquarter 2014. ISSN 1553-877X.

KOMINE, T.; NAKAGAWA, M. Fundamental analysis for visible-light commu-nication system using LED lights. IEEE Transactions on Consumer Elec-tronics, v. 50, n. 1, p. 100–107, Feb 2004. ISSN 0098-3063.

LENK, R.; LENK, C. Practical modeling of leds. In: .Practical Lighting Design with LEDs. Wiley-IEEEPress, 2016. p. 304–. ISBN 9781119165347. Disponıvel em:<http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7906211>.

MINH, H. L.; O’BRIEN, D.; FAULKNER, G.; ZENG, L.; LEE, K.; JUNG,D.; OH, Y.; WON, E. T. 100-Mb/s NRZ visible light communications using apostequalized white LED. IEEE Photonics Technology Letters, v. 21, n. 15,p. 1063–1065, Aug 2009. ISSN 1041-1135.

OSRAM. SFH4545. High Power Infrared Emitter (940 nm). Regensburg,1 2016. Rev. 1.1.

PATHAK, P. H.; FENG, X.; HU, P.; MOHAPATRA, P. Visible light commu-nication, networking, and sensing: A survey, potential and challenges. IEEECommunications Surveys Tutorials, v. 17, n. 4, p. 2047–2077, Fourthquar-ter 2015. ISSN 1553-877X.

SINGH, R.; O’FARRELL, T.; DAVID, J. P. R. An enhanced color shift keyingmodulation scheme for high-speed wireless visible light communications. Journalof Lightwave Technology, v. 32, n. 14, p. 2582–2592, July 2014. ISSN 0733-8724.

ZHEN, Y. AN1494: Using MCP6491 Op Amps for Photodetection Ap-plications. : Microchip Technology Inc., 2013.

10

Appendix A -- 3-D Localization with

Multiple LEDs Lamps in OFDM-VLC

System

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identifier 10.1109/ACCESS.2018.DOI

3-D Localization with Multiple LEDsLamps in OFDM-VLC systemLUIS C. MATHIAS1, LEONIMER F. DE MELO1, TAUFIK ABRÃO.1, (Senior Member, IEEE)1Department of Electrical Engineering, State University of Londrina, Rod. Celso Garcia, PR-445 Km 380, CEP 86051-990, Londrina-PR, Brazil (e-mail:[email protected]; [email protected] [email protected])

Corresponding author: Taufik Abrao (e-mail: [email protected]).

“This work was supported in part by the National Council for Scientific and Technological Development (CNPq) of Brazil under Grants304066/2015-0; by the Londrina State University (UEL) and the Paraná State Government”

ABSTRACT Visible light communication (VLC) based localization is a potential candidate for wide rangeindoor localization applications. In this paper, we propose a VLC architecture with orthogonal frequencydivision multiplexing (OFDM) integrating into the same system several functionalities, e.g., the 3-D locationof a receiver, the data transmission, and the illumination intensity control. Herein we propose an originalmethodology for LED power discrimination applying spatial optical OFDM (SO-OFDM) structure forposition estimation. The hybrid locator initially makes a first estimate using a weighted angle-of-arrival(WAoA)-based locator which is then used as the starting point of the recursive estimator based on thestrength of the received signal (RSS). Hence, the first stage is deployed to increase convergence probability,reducing the root-mean-square error (RMSE) and the number of iterations of the second stage. Also, aperformance vs computational complexity comparative analysis is carried out with parameter variations ofthese estimators. The numerical results indicate a decade improvement in the RMSE for each two decadesof decrement of power noise on the receiver photodiode. The best clipping factor is obtained through theanalysis of locator accuracy and transmission capacity for each simulated system. Finally, the numericalresults also demonstrate effectiveness, robustness, and efficiency of the proposed architecture.

INDEX TERMS 3-D Position estimation, AoA, OFDM, RSS, VLC.

I. INTRODUCTION

V ISIBLE Light Communication (VLC) concept has nowgained prominence due to the availability of a vast and

still unexplored spectral band in the frequency range of visi-ble light, aiming at facing with the growing demand for datatransmission. VLC provides exceptionally high transmissionrates to the end user in a scenario of increasing frequencyspectrum shortage in RF communication systems.

The research related to a 3-D location in VLC environmenthas been promising due to several factors. The first occurs inapplications where the Global Positioning System (GPS) sig-nal cannot penetrate the environment application. The secondis due to the increasing replacement of conventional lampswith those of light emitting diode (LED) that are more long-lasting and of better energetic and luminous efficiency. In thiscase, the LED lamp infrastructure in addition to illuminating,can transmit data and can also allow the localization of amobile receiver. Thus, for a practical VLC system, it isdesirable to use the same transmission technology for bothpositioning and high-speed data transmission.

Due to the low cost and low complexity, the IntensityModulation with Direct Detection (IM/DD) is the mostpractical method of implementing a VLC system. In thismodulation type, the electric current of the LED transmittersis modulated to vary the transmitted light intensity. At thereceiver side, the received light intensity is converted directlyinto electrical current utilizing photodetectors. Thus, in theIM/DD, it is necessary that the signal in time must be real andpositive so that the light intensities of the LED transmittersare modulated directly [1].

A baseband modulation technique that is extensively ex-ploited in IM/DD due to the efficient use of the availablebandwidth is the Orthogonal Frequency Division Multiplex-ing (OFDM) [2]. Since, usually, a time OFDM signal isbipolar, several modulation techniques are found in the lit-erature to make it unipolar [3]. In this way, a real OFDMtime-frame is achieved by imposing a Hermitian symme-try on the vector of symbols mapped previous the InverseFast Fourier Transform (IFFT) block. In DC-biased opticalOFDM (DCO-OFDM), a bias signal is added to make the

VOLUME 4, 2016 1

Luis C. Mathias et al.: 3-D Localization with Multiple LEDs Lamps in OFDM-VLC system

time-signal positive. On the other hand, in the asymmetricallyclipped optical OFDM (ACO-OFDM), the transmitted signalis produced positive by sending only the odd subcarriers.The Flip-OFDM divides the original OFDM frame into twoparts by transmitting them separately [4]. The first frameis reassembled with positive points in time, and anotherframe is formed by inverting the polarity of the points intime that were negative. The ACO-OFDM and Flip-OFDMare commensurate regarding spectral efficiency and errorperformance, but the Flip-OFDM save nearly half of receivercomplexity over ACO-OFDM. However, the two techniqueshave approximately half the spectral efficiency compared tothe DCO-OFDM.

Two techniques are usually used in estimating the locationof a VLC receiver. The first one, the angle of arrival (AoA),takes the direction of the LED transmitters into considerationat the receiver side. The second technique, based on thelocation by Received Signal Strength (RSS), considers thestrength of the signal captured by the receiver due to thetransmitter LEDs [5]. In [6] also is proposed an integratedAoA-RSS localization method that finds out the 2-D positionof a mobile robot using an array of photodiodes (PDs).Moreover, the work [7] deals with the 3-D localization prob-lem and uses these two localization techniques. Althoughthe location by RSS is more accurate than the AoA-basedmethod, in general, its recursive estimator presents a non-convex structure and can achieve different results than thoseexpected [7]. In this way, the position estimation obtained bythe AoA locator can be used as the initial search point forthe RSS locator. Such strategy has the purpose of starting thesearch at a closer location, reducing the possibilities of diver-gence. This hybrid estimator considers the RSS informationof each LED separately. It is worth to note that in the previousworks, such as [6] and [7], no scheme has proposed for thediscrimination of the light powers received from each LED.

The works on the OFDM transmission scheme for thelocalization estimation purpose present just only 2-D esti-mators. For instance, the work [8] employs training symbolsin OFDM and uses RSS information for estimates of thedistances between the receiver and the LED transmitter byapplying a lateration technique. Such technique handles thegeometric analysis of the problem through triangles andcircles. Moreover, the work [9] reports an experimentaldemonstration of an indoor 2-D VLC positioning systembased on the OFDM transmission scheme that proposes todiscriminate the signals transmitted by three different LEDsusing coding in three OFDM subcarriers. Thus, the receiverretrieves all signals transmitted using a Discrete FourierTransform (DFT) operation. A Spatial Optical-OFDM (SO-OFDM) scheme with multiple LEDs is proposed in [10]trying to mitigate the OFDM Peak-to-Average Power Ratio(PAPR) problem in VLC. In this design, filtered subsets ofOFDM subcarriers are emitted by each LED, allowing thereceiver to discriminate the power received from each LED.

The contribution of this work is threefold, as summarisedin the following. a) It is proposed a VLC structure with power

discrimination at the receiver side aiming at improving the3-D indoor localization feature; b) an innovative hybrid 3-D building localization scheme is proposed that distributesa training symbols for each LED among the subcarriersarranged into SO-OFDM groups; c) based on extensive nu-merical simulations results, our hybrid location estimatorcan be implemented allowing a more precise 3-D locationby considering more RSS information of each LED frommultiple LED lamps infrastructure.

The paper is divided into five sections. Besides this in-troductory section, the section II develops the VLC systemmodel deployed in the AoA and RSS estimators which aredescribed in subsections II-C and II-D respectively. In Sec-tion III, the 3-D hybrid estimator obtained is applied to theSO-OFDM multiplexing scheme with DCO-OFDM. In Sec-tion IV numerical simulation results are considered aiming atcorroborating the quality of the 3-D location estimations forthe proposed scheme. Finally, in Section V the conclusionsare offered.Notation: IK is the K × K identity matrix and the field ofreal numbers is denoted by R. The transpose operation andthe Moore-Penrose are denoted by (.)ᵀ and (.)† respectively.The matrix kernel is denoted by ker(.). N (0,C) means theGaussian distribution with zero mean and covariance matrixC. U(a, b) holds for a uniform distribution with boundariesa and b.

II. HYBRID LOCALIZATIONThis section describes the system and the noise models, aswell as the RSS and the AoA position estimators.

A. VLC SYSTEM MODELThe VLC system can be modeled considering K visiblelight access points (VAP) with some M elements LEDstransmitting each [7]. Fig. 1 presents a schematic diagramof the 3-D system model depicting the position of vectors,normal versors, and angles in a Cartesian plane.

FIGURE 1: Schematic diagram representation for the 3-Dlocalization problem in a VLC system [7].

The position vectors and the orientation versor of thereceiver is denoted by rR = [x, y, z]ᵀ and nR =

2 VOLUME 4, 2016


[n(x)R , n

(y)R , n

(z)R ]ᵀ. The position vectors and the orientation

versor of the m-th LED transmitter of the k-th VAP arermk = [xmk, ymk, zmk]ᵀ and nmk = [n

(x)mk, n

(y)mk, n

(z)mk]ᵀ.

Thus, the vector denoting the distance between the transmit-ting element and the receiver can be given by:

vmk = rR − rmk = [amk, bmk, cmk]ᵀ ∈ R3×1. (1)

Hence, the DC optical channel gain between the receiver andthe m-th LED of the k-th VAP can be given by [7]:

Ωmk = κ ·∏(

θmkθFoV

)·∏(

ϕmkπ/2

)· f(vmk), (2)

whereκ = − (nL + 1)Apd

2π(3)

and

f(vmk) =

(vᵀmknmk

)nL vᵀmknR

‖vmk‖nL+32

=(amkn

(x)mk + bmkn

(y)mk + cmkn

(z)mk

)nL

(amkn

(x)R

+bmkn(y)R

+cmkn(z)R

)

(a2mk

+b2mk

+c2mk)

nL+32

,

(4)where ϕmk is the angle between the orientation versor of theLED transmitter and the incidence vector, θmk is the anglebetween the receiver orientation versor and the incidencevector,Apd is the area of the photodetector (PD) inm2, θFoVis the field of view (FoV) of the PD, nL is the mode numberof the Lambertian distribution. The FoV of receiver effectand the field of emission effect of LED transmitter are alsoconsidered in (2) using the rectangular function defined by:

∏(·) ∆

=

1, |·| ≤ 10, |·| > 1.

(5)

Details of the transmission angle, incident angle, FoV, andexample of a VAP arrangement with 4 LEDs in pyramidalformat are presented in Fig. 2. A greater FoV is attractivebecause the location estimators can evaluate all the LEDtransmitting powers. In contrast, it exposes the receiver to ahigher incidence of noise and interference.

VLC Receiver

kth VAP

Field of

view

Lambertian

Distribution

w’’w w’

w’’ww’

FIGURE 2: Details of the angles involved in the model andexample of a VAP with 4 LEDs in pyramidal format.

Now, considering that the transmitted optical power ofeach LED is equal to PT , the optical power of the m-th LEDof the k-th VAP in the receiver can be given by:

Pmk = ΩmkPT . (6)

Therefore, the total power received by the photodetectorin the VLC receiver is the sum of the optical powers receivedfrom each transmitter LED, i.e. PR =

∑Mm=1

∑Kk=1 Pmk.

Thus, the current generated is proportional to the powerreceived with additive white Gaussian noise (AWGN) [10].In this context, the electric gain GE can be given by:

GE = SledΩmkRpd, (7)

where Sled is the LED conversion factor in [W/A] and Rpdis the photodetector responsivity in [A/W ]. Both parametersconsider radiometric light power.

The photodetector responsivity Rpd is generally presentedin the datasheet of the PIN junction photodiodes. The LEDconversion factor Sled is a parameter that varies due to thenon-linearity of the luminous flux φV in [lm] as a functionof the electrical current Iled in [A] [11]. This relation forthe Cree® XHP70.2 6V LED device can be modelled by apolynomial quadratic function as [12]:

φV (Iled) = −31.29I2led + 705.35Iled + 20.7. (8)

The conversion from luminous flux to the radiated opticpower PT can be realized by a factor of 2.1[mW/lm] forphosphor-coated blue LED [13]. Moreover, using predistor-tion with upper and lower current limits of modulation Iu andIl, respectively, the LED conversion factor can be determinedby [10]:

Sled = 0.0021(ϕV (Iu)− ϕV (Il))

Iu − Il. (9)

B. NOISE MODELThe noise directly affects the accuracy of the estimator. It isshaped by the transfer function of the preamplifier topology.In this work, it will be considered a receiver with photode-tector with PIN junction diode and field effect transistor(FET) transimpedance amplifier (TIA) [14], [15]. The noisein the receiver is mainly composed by the shot noise andthe thermal noise. Such noise sources can be modeled asGaussian processes with zero mean and variances [1], [5],[15]:

σ2n = σ2

shot+σ2thermal = σ2

bg+σ2rs+σ2

dc+σ2thermal. (10)

The photo-generated shot noise corresponds to the fluctu-ations in the count of the photons collected by the receiver[15], [16]. The variances of the shot noise due to the back-ground radiation (bg), the received signal (rs), and the darkcurrent (dc) can be determined respectively by:

σ2bg = 2qRpdApdpbs∆λB, (11)

σ2rs = 2qRpdPRB, (12)

σ2dc = 2qIdcB, (13)

where q is the elementary charge, pbs is the backgroundspectral irradiance, ∆λ is the bandwidth of the optical filter,B is the equivalent noise bandwidth and Idc is the darkcurrent.

VOLUME 4, 2016 3


The thermal noise is independent of the received opti-cal signal and can be determined in terms of noise in thefeedback resistor and noise in the FET channel. Each term,respectively, contributes to the following variance [14], [15]:

σ2thermal =

8πkBTK

GolCpdApdI2B

2+16π2kBTKΓ

gmC2

pdA2pdI3B

3,

(14)where kB is the Boltzmann’s constant, TK is the absolutetemperature,Gol is the open loop gain,Cpd is the capacitanceper unit area of the photodetector, Γ is the FET channel noisefactor, gm is the FET transconductance, I2 = 0.562 is theTIA bandwidth factor, and I3 = 0.0868 is the TIA noisefactor.

C. RSS LOCALIZATIONIf the lighting infrastructure and distribution of the luminousflux of the LED transmitter are known, the receiver can deter-mine its location by the luminous RSS information [7]. Thus,to obtain a minimum variance unbiased estimator (MVUE),the following observation vector can be considered:

s = p(θ) + n ∈ RMK×1, (15)

where θ ∈ R3×1 is the vector that corresponds to the exactlocation of the VLC receiver, i.e., rR, n ∈ RKM×1 ∼N (0, σ2

nIKM ) is the additive noise vector. The vector p(θ) ∈RMK×1 is the vectorization of the matrix P (θ). The matrixP (θ) ∈ RM×K contains the exact RSS information in them-th row referring to the m-th LED transmitter and the k-thcolumn referring to the k-th VAP.

Considering the noise as additive white Gaussian noise(AWGN), the log-likelihood function (LLF) for the locationof the VLC receiver can be expressed as:

L(θ) = log(pdf(s,θ)), (16)

where the joint probability density function (PDF) is givenby:

pdf(s,θ) =1

(2πσ2n)

MK2

exp

(− 1

2σ2n

(s− p(θ))ᵀ (s− p(θ))

).

(17)

The joint PDF can be obtained from the product betweenthe marginal PDFs due to the consideration they are indepen-dent and identically distributed. Applying the log(.) operator,the maximum-likelihood estimation (ML) of rR problem canbe formulated by considering only the matrix operation of theexponential argument as:

rR = arg maxθL(θ)≡ arg max

θ(− (s− p(θ))

ᵀ(s− p(θ))) .

(18)As a result, (18) can be expressed as a nonlinear least squares(NLLS) problem given by:

rR = arg minθ

(‖s− p(θ)‖22

). (19)

That way, this estimator minimizes the Euclidean distancesbetween the observation vector s and the exact value of re-ceived intensities p(θ). Thus, one method to solve the system

of nonlinear equations is that of Newton-Rapson Multivariate[7], [17]:

θi+1 = θi − ηJ†(s− p(θi)

), (20)

where η ∈ (0, 1] is the step size and J is the Jacobian matrixof p(θ) in relation to θ. Whereas θ1, θ2 and θ3 correspond tothe positions x, y and z of VLC receiver. J can be given by:

J =

∂P11

∂x∂P11

∂y∂P11

∂z∂P21

∂x∂P21

∂y∂P21

∂z...

......

∂PMK∂x

∂PMK∂y

∂PMK∂z

. (21)

In (21), each row of J indicates how the RSS of each LEDtransmitter changes when the receiver moves on one of theaxes, x, y and z. Considering the chain rule (∂P∂x = ∂P

∂a∂a∂x ),

the row associated with the m-th LED transmitter of the k-thVAP can be calculated as:

∂Pmk∂x

∂Pmk∂y

∂Pmk∂z

ᵀ

=

∂Pmk∂amk∂Pmk∂bmk∂Pmk∂cmk

ᵀ

∂amk∂x

∂amk∂y

∂amk∂z

∂bmk∂x

∂bmk∂y

∂bmk∂z

∂cmk∂x

∂cmk∂y

∂cmk∂z

.

(22)From (1), the matrix in (22), i.e., the Jacobian of vmk with

respect to θ, becomes an identity matrix. Therefore, (22) canbe directly obtained by evaluating the partial derivatives of(6) by keeping one of the elements of the incidence vectorvmk as variable and the other elements as constants. Thus,the partial derivative in relation to the first element of vmkcan be written as:

df(vmk)damk

=(vᵀmknmk)

nL

‖vmk‖nL+3

2

×(n

(x)R + n

(x)mk

nL (vᵀmknR)

(vᵀmknmk)

− amk(nL+3) (vᵀ

mknR)‖vmk‖22

),

(23)being analogous for df(vmk)

dbmkand df(vmk)

dcmkby changing the

element amk for bmk and cmk, respectively, and changingthe elements of nmk and nR in relation to y and z, alsorespectively. Finally, the row vector can be determined by:

∂Pmk∂x

∂Pmk∂y

∂Pmk∂z

ᵀ

= κ·PT ·∏(

θmk

θFoV

)∏(φmk

π/2

)

∂f(vmk)∂amk

∂f(vmk)∂bmk

∂f(vmk)∂cmk

ᵀ

.

(24)Although the Lambertian distribution model offers a con-

vex set, the NLLS solution of (19) is not convex in general[7]. This is due to the fact that the set of possible solutionsassociated with each LED transmitter can become closer toeach other at various locations in the 3-D geometry. Thisinconvenience can be minimized by determining a betterstart-point for the NLLS estimator of (20). Hence, it can beutilized as an AoA estimator to determine the initial point θ0.

D. AOA LOCALIZATIONIn AoA localization method, the receiver checks and selectsthe transmitter LED that has the highest RSS for each VAP.Then, the estimator searches for a point that minimizes thesum of the distances (or quadratic distances) between the

4 VOLUME 4, 2016


receiving point and between all other lines that extend in thedirection of the K LED transmitters selected by the receiver[7].

Fig. 3 depicts the geometry of the AoA location includingthe distances between the VLC receiver positioned in θ andthe direction defined by the line Lmk extended in the normaldirection of an LED transmitter positioned on the top of theroom. That is, Lmk is the line that intersects rmk, collinearwith nmk and perpendicular to the plane. The matrixAmk ∈R3×3 projects any vector in the null space of nmk, that is,kernmk, which can be calculated by:

Amk = I3 − nmknᵀmk. (25)

Consequently, the entire vector in the column space ofAmk is orthogonal to the direction of Lmk. The intersectionpoint bmk can be obtained by projection of rmk vector inplane kernmk, i.e.:

bmk = Amkrmk, (26)

and the vectorial distance between the point θ and the lineLmk can be given by:

dmk = bmk −Amkθ. (27)

Origin

LED transmitterin a VAP

VLC receiver

FIGURE 3: Geometry of AoA localization. Adapted from[7].

Stacking the set of equations related to the selected LEDtransmitters we have:

d = b−Aθ. (28)

As reported at the beginning of this section, the estimatorsearches for a point that minimizes the sum of the quadraticdistances. In this way, the objective function can be estab-lished as:

rR = arg minθ

K∑

k=1m=ξk

‖dmk‖22 = arg minθ

K∑

k=1m=ξk

‖Amkθ − bmk‖22,

(29)where ξk is the index of LED transmitter that allowed thereception of greater luminous power from k-th VAP. Indeed,the AoA information considered is given by the LED trans-mitter of each VAP which is more directed to the receiver.

Considering that the concatenated matrix A is invertible,an estimator can be obtained by:

rR = A†b. (30)

However, identically treating the AoA information of eachtransmitter may cause a greater error in position estimation.This is because the AoA information of a farther transmitterLED has a lower signal-to-noise ratio (SNR) if compared toa closer transmitter LED. In other words, less reliable AoAinformation of the most distant LED transmitters causes abias in location estimation and degrades location accuracy. Tomitigate this problem, it is possible to consider an objectivefunction that minimizes the weighted sum of the quadraticdistances:

rR = arg minθ

K∑

k=1m=ξ

βmk ‖Amkθ − bmk‖22, (31)

where βmk is the weighting factor for the distance between θand Lmk.

In [7], it is analyzed the AoA of LED transmitters basedon weighted RSS information directly, i.e., weighted by therespective Pmk. Thus, the problem given in (31) correspondsto an unconstrained quadratic optimization problem that canbe solved by the LS method as:

rR = AW†bW , (32)

whereAW =K∑k=1m=ξ

PmkAmk and bW =K∑k=1m=ξ

Pmkbmk,

This weighted AoA (WAoA) provides a lower RMSEof the position if compared to the unweighted version [7].Because this estimator considers more RSS information ob-tained from the stronger signals, i.e., with a higher signal tonoise ratio (SNR) than those obtained by the weaker signals.

III. SPATIAL OPTICAL OFDM FOR POWERDISCRIMINATION OF MULTIPLE LEDSThe localization estimators need to discriminate the powers.In this sense, the SO-OFDM [10] is deployed to divide theOFDM subcarriers emitted by each LED. Beyond reducingthe PAPR, this scheme allows transmitting different signalson each of the M transmitter LEDs in each VAP. Suchstrategy permits the signal discrimination in the receiverby applying the hybrid estimator discussed in the previoussections. Next subsections elaborate on the sub-blocks asso-ciated to the proposed VLC-OFDM transmitter architecture,Fig. 4. Such topology allows two operation modes, i.e., datacommunication and spatial signal localization at the receiverside.

A. SUBCARRIER ALLOCATION FOR HYBRID VLCLOCALIZATION AND DATA TRANSMISSIONIn the proposed scheme, the data bits are QPSK modulated,generating the symbol vector XD. The fixed power level ofthe location subcarriers is intended to simplify the operation

VOLUME 4, 2016 5


DPD

DPD

DPD

P/SIFFT

P/SIFFT

P/SIFFT

ElectricalCurrent

Amplifier

Hard-Clipping

Parallelto Serial

DigitalPredistortion

InverseFast FourierTransform

HermitianSymmetry

S/P

Bank ofFilters

QPSKModulation

TxData Bits

CP+

CP+

CP+

CyclicPrefix

Addition

Digital toAnalog

Converter

DAC

DAC

DAC

...

...

...

...

...

...

...

...

...

...

Serial toParallel

SymbolDistribution

k

...

FIGURE 4: VLC-OFDM transmitter architecture implemented in each VAP.

of the location estimators1. Thus, without loss of generality,the elements are admitted scaled such that:

E[|XD[i]|2

]= 1; i = 1, ..., ND. (33)

For localization purpose, the elements of vector XD firstare distributed in the vector 2:

XDD

[(m− 1)

N

2M+ k

]= XD[m− 1] ;m = 1, ...,M ;

(34)where m represents the LED transmitter index of the VAP,k is the index of the VAP, M is the total number of LEDstransmitters in each VAP, K the total number of VAPs andN is the size of IFFT. The value of k must be unique andmust be predefined on each VAP of the infrastructure. In thisway, each VAP will transmit M symbols (in M subcarriers)and will not transmit in (M −1)K, making them available toother VAPs. This allows the discrimination of the powers ofeach VAP to the location estimator in the VLC receiver.

The distribution described by (34) leaves a residue ofN/2−M(K + 1) subcarriers available. This work proposestwo operation modes for the system. The first one, termedlocation only mode (LOM); in this case, all the power of theavailable optical modulation signal is used to allow a betteraccuracy of the estimator. In the second operation mode,named location and communication mode (LCM), the poweris distributed between the location and data transmissionsubcarriers; in this case, the greater transmission of dataoccurs in detriment of the location accuracy.

In LCM mode, strategically, it is proposed that these data-transmission subcarriers be distributed among the transmit-ter LEDs which allowed higher SNR at the receiver side.Multiple access can be obtained by redistributing the datasubcarriers between the VAPs next to each VLC receiver.

1The proposed architecture also allows data-carrying subcarriers to usehigher-order modulation with different power levels. In such case, theclipping analysis should be updated.

2Due to the pre-allocated power, these symbols can be deployed forchannel estimation and receiver synchronization purpose.

Considering the case of a VAP with better signal to noiseratio (SNR) in the receiver. This VAP can distribute theresidual symbols ofXD by:

XDD

[(m− 1)

N

2M+K + 1, ...,m

N

2M− 1

]= XD[i],

(35)with m = 1, ...,M and i = m, ..., N2

3. Thus, the vector XD

has size ND = N2 −M(K + 1). The elements of the vector

XDD that were not assigned by the two previous rules areaccepted as nulls, maintaining the length NDD = N

2 .Thus, in this symbol distribution scheme, the elements

XDD[0] and XDD[N2 ] responsible for the DC level are null;so, not interfering with the bias added to the OFDM framein order to keep it positive. In this work, it is assumed thatthe control of this signal is performed externally to allow thecontrol of the intensity of the illumination. Fig. 5 sketchesthe proposed subcarriers distribution in a VAP with k = 1, aswell as in a VLC receiver.

B. DCO-OFDMIn this work, the hybrid estimator is applied using the DCO-OFDM, although its application in the ACO-OFDM and Flip-OFDM should be equivalent.

After the serial to parallel conversion of XDD, with thepurpose in obtaining purely real-time points at the out ofthe IFFT block, the vector X of size N is generated afterapplying the following Hermitian symmetry:

X[i] =

XDD[i] ; i = 0, . . . , N/2− 1X∗DD[N − i] ; i = N/2, . . . , N − 1.

(36)

C. SO-OFDMThe Hermitian vectorX is then applied to the input of a filterbank of sizeM , i.e., a filter for eachm LED of the VAP. Thus,

3Herein, it is consided that there is no concomitant transmission of datasubcarriers in the same indoor environment. This is to avoid co-channelinterference.

6 VOLUME 4, 2016


FIGURE 5: Proposed distribution of localization and datasubcarriers for a) VAP transmitter k = 1; b) received sub-carriers in VLC receiver.

the OFDM frames Xm are obtained by filtering the originalOFDM frameX by means of:

Xm = HmX. (37)

A contiguous mapping subcarrier with an equal number ofsubcarriers per LED is proposed by:

Hm[i] =

H, i = (m− 1) N

2M , ...,m N2M − 1

0, otherwise(38)

whereH is a real-valued constant and i = 0, 1, ..., N2 −1. Thesecond half of Hm is obtained by mirroring using Hm[i] =Hm[N − 1− i] for i = N

2 , ..., N − 1. In this way, the filtersHm masks the subcarriers that are not to be transmitted.

In each vector Xm is performed the IFFT. Using theinverse discrete Fourier transform definition [2] in the trans-mitter:

xm[i] =1√N

N−1∑

n=0

Xm[n]ej2πni/N ; for 0 ≤ i ≤ N − 1;

(39)corresponds to a forward transform on the FFT block in thereceiver by:

Y [i] =1√N

N−1∑

n=0

y[n]e−j2πni/N ; for 0 ≤ i ≤ N − 1;

(40)where y is the vector of the sample time domain signal andY is the discrete frequency domain vector at the FFT output.

The signal in time obtained by IFFT block is convertedfrom parallel to serial, obtaining the points in time xm foreach group. The signal is hard-clipped aiming at fit thedynamic range of the driver:

um[i] =

Iu ; xm[i] > Iuxm[i] ; Il ≤ xm[i] ≤ IuIl ; xm[i] < Il.

(41)

In the signal um, the Digital Predistortion (DPD) is ap-plied to correct the non-linearity associated with the directcurrent in the LED and the optical power obtained by itpresented in subsection II-A. Also, the LED current of po-larization of the LED must be considered in DPD step. Thenthe cyclic prefix (CP) is added, following digital to analogconversion (DAC), the current amplification, and finally theelectric coupling to each LED of the VAP.

D. SUBCARRIER POWER ESTIMATION IN THE VLCRECEIVERGiven that the vector xm is the sum of independent randomvariables with zero mean, using the central limit theorem(CLT) it is possible to approximate its Gaussian distributionof zero mean [18]. Considering also N large enough, thevariance of the m-th group of subcarriers can be given byσ2m = E

[|xm|2

]. Considering now (33) and (38) we obtain:

σ2m =

2

N

N/2−1∑

i=0

|Hm[i]|2 =2

N

ND/M∑

i=1

H2 =2

N

NDM

H2.

(42)The severity of clipping suffered by a signal is quantified

by the clipping factor that is defined as the number ofstandard deviations per half of the dynamic range [18]:

γm =Iu − Il2 · σm

. (43)

Considering the CLT approximation for xm, a symmetricclipping (Iu = −Il), and the same variance σ2

m in all groups,the scaling factor C can be determined as [18]:

C = 1− erfc(γm√

2

). (44)

Applying (43) in (44), setting Iu and Il and arbitrating thevalue of scaling factor C, the standard deviation σm can beready determined. In a same way, the constant valueH of thebanks of filtersHm can be established using Eq. (42).

Considering (33), the magnitude of the i-th symbol at thereceiver side can be expressed in the frequency domain by:

|Y [i]| = H · C ·GE , (45)

where the electric gain GE is computed by (7).After the separation of the magnitude of symbols destined

for the location in the receiver, according to Fig. 6, thefollowing normalization is performed in order to make theelements of the observed vector of RSS information in (15)more suitable for the efficiency of the recursive locationestimator:

smk =|Ymk|

HCRpdSled= Ωmk + n; (46)

where smk, Ymk and n are respectively the RSS information,the magnitude of i-th symbol and the noise sample in thereceiver corresponding to the m-th LED of the k-th VAP.

Comparing (46) with (6), the transmitted power becomesunitary. Finally, it can be admitted the concatenation of the

VOLUME 4, 2016 7


Equalization SymbolDistribution

QPSKDemodulation

RxData Bits Normalization

ADC

CyclicPrefix

Remover

CP-

Analog toDigital

Converter

Trans-impedanceAmplifier

TIA FFT

FastFourier

Transform

WA A PositionoEstimation

RSS PositionEstimation

FIGURE 6: Architecture of proposed VLC receiver withreceiver position estimation capability.

smk elements in the vector of the exact RSS information sand as same for p(θ) with the concatenation of MK DCoptic gain elements.

IV. NUMERICAL RESULTSIn this section, we have demonstrated the effectiveness andefficiency of the proposed method by numerical simulationanalysis. Similar to [7]4, the adopted infrastructure was anempty room with dimensions 5×4×3 m where all four VAPdevices are positioned in the four upper corners of the room(K = 4). The VAPs’ directions are θwall = 45o betweenthe walls and θceiling = 35o below the ceiling. Each VAPhas four Cree® XHP70.2 6V LED transmitters (M = 4) in apyramid shape with a square base as shown in Fig. 2a. Theangle between the LED and the normal vector of each VAPis α = 15o. The VLC receptor parameters are θFoV = 85o,Apd = 1 cm2 and nR = [0; 0; 1]ᵀ 5. The noise parametersvalues deployed in our analyses are the same as that used in[15]. In the RSS recursive estimator, the step value for thesearch algorithm was η = 0.3. Initially, the adopted stoppingcriterion for the recursive estimator was an error ε ≤ 10−4mor a maximum number of iterations of the imax = 200.

Such direct infrastructure parameter values, including pa-rameters for the LED, photodetector, noise, the OFDM andfor the recursive RSS estimator deployed in numerical analy-ses are summarized in the Table 1. The indirect infrastructureparameter values obtained are the LED conversion factorSled = 1.4812 W/A applying eq. (9) and the noises variancesσ2bg = 4.0144 × 10−15 A2, σ2

dc = 1.6022 × 10−23 A2 andσ2thermal = 6.5631 × 10−17 A2 by applying (11), (13) and

(14). The shot noise variance σ2rs was estimated for each

4Notice that this work also makes a numerical analysis about the bestchoices of the orientations and angles involved in the infrastructure compo-nents. Hence, the best values found for such parameters will be consideredin our work for comparison purpose.

5A priori knowledge of the receiver orientation is plausible since itcan be estimated by a system composed by a three-axis accelerometersarrangement, commonly used in smartphones, among other portable devices.

analyzed position of the VLC receiver since it depends onthe received light power from the transmitted signal.

Next, the analysis of the proposed architecture is dividedinto three parts. In these subsections, the performance, theclipping noise effect on the hybrid estimator performance, aswell as the computational complexity of the estimators areevaluated.

A. PERFORMANCE OF 3-D LOCALIZATIONESTIMATORSAs a way of comparison, it has included the RSS estimatorsimulations considering the centroid of the room (C+RSS)and also a point obtained at random (RND+RSS) as startingpoints. In the latter case, the coordinates of the initial point θ0

were obtained using a random variable with uniform distribu-tion along the dimensions of the room. In the case evaluatedx ∼ U(0, 5), y ∼ U(0, 4) and z ∼ U(0, 3). To compare theperformance of the five localization methods, namely AoA,WAoA, C+RSS, RND+RSS and WAoA+RSS, the Euclideanerror and number of iterations required for convergencewere evaluated for one realization considering three differentpositions of the VLC receiver , a) rR,1 = [1.25, 1, 1]ᵀ,b) rR,2 = [1.25, 2, 1]ᵀ, and c) rR,3 = [2.5, 1, 1]ᵀ . Thenumerical results of the system operating in LCM and alsoin LOM modes are shown in Table 2. All the estimatorsby RSS reached very close Euclidean errors, and these aremuch smaller than AoA and WAoA. As expected, in all RSSestimators, the LOM mode confirmed better results due to thegreater emitted power of the localization signals. The Fig. 7depicts the graphical convergence behavior considering thefive estimators final positions and the convergence of recur-sive estimators in LCM mode. The remarkable superiorityof the WAoA+RSS hybrid method occurred both because ofthe smaller Euclidean error compared to AoA and WAoA,and because of the smaller number of iterations for theconvergence of the result when compared to C+RSS andRND+RSS.

The Fig. 8 shows the percentage of convergence, theRMSE and the average number of iterations i of thethree analyzed RSS-based estimators for LCM and LOMoperation modes. This analysis considered one hundredthousand achievements while keeping ε < 1 × 10−5

m. The exact positions of the VLC receiver were con-sidered random with uniform distributions of probabili-ties of rR =

[U(0, 5) U(0, 4) U(0, 2)

]ᵀand rR =[

U(0, 5) U(0, 4) U(0, 3)]ᵀ

. Therefore, in all receiverlocations, the hybrid estimator confirmed its better perfor-mance by the higher percentage of convergence, smallerRMSE and smaller number of iterations if compared to thetwo others RSS-based estimators.

To gain insight on the proposed hybrid WAoA-RSS per-formance, Fig. 9 depicts the mean of 100 achievements of theRMSE of the proposed OFDM hybrid WAoA+RSS estimatorfor z = 0.1, z = 0.8 and z = 2m height planes in the room.The achieved average RMSE value, i.e. RMSE, is shownfor each graph. Also, such numerical results considered a

8 VOLUME 4, 2016


TABLE 1: Adopted parameters values.

Infrastructure LED Photodetector Noise Model OFDM Hybrid EstimatorRoom dim.: 5× 4× 3 m nL = 10 Apd = 1 cm2 TK = 300 K B = 10 MHz θ0 = rR or RNDK = 4 Ibias = 1.5 A θFoV = 85o Gol = 10 N = 1024 η = 0.3M = 4 Iu = 1 A nR = [0, 0, 1]ᵀ gm = 30 mS ND = 496 ε < 1× 10−5mα = 20o Il = −1 A Rpd = 0.54 A/W Γ = 1.5 imax = 200θceiling = 35o Cpd = 112 pF/cm2 ∆λ = (780-380)nm=400 nmθwall = 45o Idc = 5 pA pbs = 5.8µW/(cm2nm)

TABLE 2: Euclidean errors (a) and number of iterations(b) from the four localization estimators, considering threedifferent positions and one realization.

(a) ‖rR − rR‖2 in [mm]

mode LCM LOM

VLC position rR,1 rR,2 rR,3 rR,1 rR,2 rR,3

AoA 578.0 423.0 518.6 578.0 423.0 518.6WAoA 505.1 267.7 407.6 493.7 273.3 407.2

RND+RSS 17.8 17.7 48.8 0.621 0.352 0.642C+RSS 17.8 17.7 48.8 0.617 0.343 0.646

WAoA+RSS 17.8 17.7 48.8 0.621 0.337 0.649

(b) Number of Iterations, i

mode LCM LOM

VLC position rR,1 rR,2 rR,3 rR,1 rR,2 rR,3

RND+RSS 29 33 39 29 33 41C+RSS 32 32 30 32 33 33

WAoA+RSS 28 26 26 28 27 28

fixed quantity of i = 30 iterations with pitch distance ofanalysis of 10 cm. In general, the greater accuracy of thehybrid estimator is in the central region of the room where theluminous power is higher than in the corners. Indeed, for suchlocation application the estimation of the corners reached anRMSE less than 350 mm (LCM mode) and 8 mm (LOMmode), while in the central regions it reached RMSE of lessthan 50mm (LCM mode) and 2 mm (LOM mode). In thisway, the numerical results obtained under LOM mode haveresulted in better localization accuracy than those presentedin [19]. This result confirms the effectiveness and accuracyof the proposed method in a 3-D target object localization,representedd by the optical receiver.

The variable portion of the noise power σ2rs contributed

little to the total noise variance. In the simulated systemenvironment, σ2

rs noise was about one hundred times smallerthan σ2

bg . Therefore, the location accuracy as a function of thefixed σ2

n was analyzed. Hence, the RMSE over 100 realiza-tions was obtained considering the same planes analyzed inFig. 9 and varying the σ2

n between 10−20A2 and 10−8A2.According to Fig. 10, it is observed that the RMSE decays adecade for each two decades of decrement in σ2

n.

B. CLIPPING NOISE EFFECT

The clipping generates a noise power that is added to thenoise in the photodetector. The noise clipping variance can

0.5

1

2

z[m

]

1.5

1.5 2.5

y [m]

2

rR=[1.25,1,1]

=[1.238,0.9962,1.012]

x [m]

=[1.238,0.9962,1.012]=[1.238,0.9962,1.012]

1 1.50.5 1

2.50.52.04 2

1

z[m

]

rR=[1.575,2,0.7293]

x [m]

1.5

2.02

y [m]

rR=[1.25,2,1] =[1.267,1.996,1.001]

=[1.267,1.996,1.001]

=[1.267,1.996,1.001]

1.5

rR=[1.236,2,1.267]

211.98

1

1.5

2

z[m

]

2.5

2 4

y [m]

3.51.5

x [m]

rR=[2.5,1.344,1.388]

3

rR=[2.49,1.381,1.144]=[2.509,1.048,0.9987]

=[2.509,1.048,0.9987]

=[2.509,1.048,0.9987]

rR=[2.5,1,1]

2.51

Exact

AOA

WAOA

RND+RSS

C+RSS

WAoA+RSS

0=[2.066,1.224,0.712]

0

0=[3.010,2.129,0.673]

0=[2.5,2,1.5]

T

T

T

T

T

TT

T

T

T

0=[2.5,2,1.5]T

T

=[2.5,2,1.5]T

T

T

T

T

0=[4.682,2.394,2.664]T

T

T

TT

T

rR=[1.735,1.296,0.8953]T~

TrR=[1.4,1.374,0.6956]^

^

~

~

^

4

4

29

32

28

33

32

26

39

30

26

FIGURE 7: Localization convergence among the five 3-Dlocalization methods for three different receiver positionsgiven by the marker "+". The symbol× indicates the startingpoints θ0 of the recursive estimators.

be estimated by [20], [21]:

σ2clip = σ2

m

[C − C2 + (1−Q(λl))λ

2l +Q(λu)λ2

u

− (ϕ(λl)− ϕ(λu) + (1−Q(λl))λl +Q(λu)λu)2

+ϕ(λl)λl − ϕ(λu)λu] ,(47)

where λl = Il/σm, λu = Iu/σm, with σm = Iu/γm by(43), Q(v) is the Q-function, and the Gaussian function

ϕ(v) =1√2π

exp

(−v

2

2

). (48)

VOLUME 4, 2016 9


90.2

95.6

100

79.9

94.7 94.7

90

95

100

78

94.394.5

Pro

babili

ty o

f

80

90

100

Converg

ence [%

]

0.3

0.43

0.049

0.58 0.56

0.360.28

0.42

0.001

0.460.52

0.25

0

0.2

0.4

0.6

0.8

39.3 39.2

31.1

46.7

53.5

41.238.938.7

30.8

43.7

50.0

37.8

20

30

40

50

60

RND+RSS C+RSS WAoA+RSS

FIGURE 8: Statistics simulation of location estimators byRSS in the LCM and LOM modes of operation.

With a symmetrical clipping, i.e, Iu = −Il, we have λu =−λl. Considering that ϕ(v) is a even function and that theQ-function has the property Q(v) = 1−Q(−v), eq. (47) canbe simplified:

σ2clip =

I2uγ2m

[C − C2 + 2Q (Iu/γm)

I2uγ2m

− 2ϕ (Iu/γm)Iuγm

].

(49)

Thus, the channel capacity with a symmetrical clipping forthe m-th group of subcarriers can be determined by:

Cm =B

N

NDM

log2

1 +

Iu2/(2γm

2)CGE(σ2n + σ2

clip

)NDNM

. (50)

Fig. 11 portrays an evaluation of the RMSE of the lo-cator in LCM mode obtained as a function of the clippingfactor γ considering an exact location of the receiver asrR,1 = [1.25, 1, 1]ᵀ with 1000 realizations. Fig. 11 alsopresents the theoretical capacity limit of data transmissionfor the m-th LED of the VAP k = 1 with better SNR atthe receiver. It is observed that with a low clipping factoroccurs severe degradation both in the localization estimatesprovided by the hybrid WAoA+RSS estimator and in capac-ity of data transmission. All capacity curves presented theiroptimal point for γm ≈ 7.4. In this condition, the RMSEof the location estimation stabilized at the minimum level,confirming the best operating point of the system. Indeed, forγ > 7.4, the channel capacity decreases very slightly due tothe fact that a more significant γ implies in a smaller σm andconsequently a lower SNR. In this way, the optimal operationpoint for the location mode of the proposed architecture canbe determined. Thus, considering the dynamic range of theLED and assuming the optimal clipping factor, the variance

of the group of subcarriers σ2m can be estimated by (43) and

then the constant H of the filter banks by (42).

C. COMPLEXITY OF THE HYBRID LOCALIZATIONALGORITHMThe number of multiplications and divisions was estimatedfor the computational complexity analysis of the estima-tors6. Considering the pseudo-random generation using lin-ear congruent generators [23], it would take about a dozenmultiplications to obtain the initial search position in theRND+RSS estimator. In the AoA and WAoA estimators, themore computational resources-consuming matrix operationis the Moore-Penrose pseudo-inverse. For AoA and WAoAlocator methods, the matrices A and Aw having dimensions3K × 3 results in a pseudo-inverse complexity of 54K + 27.Considering the multiplication by vector b, the final com-plexity of AoA locator results in CAoA = 63K + 27. Whilefor the WAoA, it requires CWAoA = 75K + 27 due tothe weighting multiplications needed for the determinationof the vector bw and the matrix Aw. Moreover, for theRSS locator, each determination of the Jacobian matrix Jhas complexity MK(3nL + 48)/2 and each iteration ofthe estimator requires 24MK + 27. As a result, a total ofCRSS = MK(3nL + 99)/2 + 27 operation per iteration isneed.

Fig. 12 depicts the complexity of AoA and WAoA locatorsin relation to K. In the same figure, it is presented the com-plexity surface for one iteration of RSS estimator regardingthe productM ·K and Lambertian mode nL. The complexityof the RSS estimator grows linearly with both M , K andnL. Moreover, in all plots, the complexities for the analyzedsystem configuration with parameters of Table 1 are alsoidentified. Indeed, for this specific scenario, the complexityof one iteration of RSS estimator was roughly three timesgreater than the AoA, WAoA complexities.

Considering that for lighting purpose an LED with highdirectivity is not attractive, the Lambertian distribution modenumber nL should reach the value of a few tens [10]. Thus,an asymptotic complexity of O(MK) for RSS locator maybe allowed, being reasonable against the asymptotic com-plexities of O(K) for the AoA and WAoA locators. Hence,the complexity penalty of using the WAoA+RSS estimatorcan be accepted taking into account the reasonable accuracyachieved and a higher percentage of convergence.

V. CONCLUSIONSWith the proposed SO-OFDM architecture it was possible todiscriminate the transmitted power from each LED of eachVAP at the photodiode receiver. The subcarrier power estima-tion referring to each LED at the receiver enabled the opera-tion of the proposed hybrid estimator based on weighted AoAcombined with the RSS method. Hence, our numerical resultshave demonstrated that the RSS-based recursive estimator

6It was considered the Gauss-Jordan algorithm for matrix multiplicationand inversion of matrices [22].

10 VOLUME 4, 2016


0

4

0.2

42

0.4

2

0 0

0

4

0.2

42

0.4

2

0 0

0

4

0.05

0.1

42

0.15

2

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0

4

0.005

42

0.01

2

0 0

0

4

0.005

42

0.01

2

0 0

0

4

1

10-3

2

42

3

2

0 0

1

2

3

4

5

6

7

10-3

FIGURE 9: RMSE of the hybrid WAoA-RSS estimator over 100 realizations with the receiver located in the three height planes,z ∈ [0.1, 0.8, 2]ᵀ m. The first line of graphics refers to the LCM mode and the second to the LOM mode.

10-20

10-15

10-10

10-5

10-4

10-3

10-2

10-1

100

101

LOM

LCM

FIGURE 10: RMSE as function of fixed power of noise forthe three height planes analyzed in Fig. 9.

becomes much more accurate with a manageable complexityincreasing if the WAoA estimator provides the start pointsearch. The WAoA locator, although results in a limitedprecision, it is close enough to allow convergence to the exactposition within a few numbers of iterations.

The numerical results also demonstrated the RMSE de-cays a decade for every two decades of decrement of noisepower. The clipping noise analysis allowed to determine theoptimum point of the system in terms of data transmissioncapacity and lower RMSE of the WAoA+RSS estimator.Hence, this parameter serves as a guide for the clipping limitdetermination that minimizes PAPR, allowing an improve-ment in the performance of the data VLC-OFDM system.

0 1 2 3 4 5 6 7 8 9 10

0

5

10

15

20

25

30

35

40

RMSE

1

2

3

40.5

1

2

3

FIGURE 11: RMSE of locator and channel capacity of eachm LED in the k = 1 VAP.

ACKNOWLEDGMENTThis work has been partially supported by the National Coun-cil for Scientific and Technological Development (CNPq) ofBrazil under Grants 304066/2015-0; by the Londrina StateUniversity (UEL) and the Paraná State Government. All theagencies are gratefully acknowledged.

REFERENCES[1] Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless com-

munications: system and channel modelling with Matlab. Boca Raton:CRC Press, 2012.

[2] J. Armstrong, “OFDM for optical communications,” Journal of LightwaveTechnology, vol. 27, no. 3, pp. 189–204, Feb 2009.

[3] R. Hassan and F. T. Z. Tuli, “Analysis of ACO-OFDM, DCO-OFDM andFlip-OFDM for IM/DD optical-wireless and optical-fiber system,” in 2015IEEE International Conference on Telecommunications and Photonics(ICTP), Dec 2015, pp. 1–5.

VOLUME 4, 2016 11


2 3 4 5 6 7 8 9 10

0

0.5

110

3

AoA

WAoA

0

30

2

4

100

103

20

6

80

8

60

10

10 40

200 0

1

2

3

4

5

6

7

8

9

103

ccc

c

(a)

(b)

FIGURE 12: Complexity for the three locator methods: a)AoA, WAoA; and b) RSS. Markers "•" identify the complex-ities for the previously analyzed configuration with parame-ters in Table 1.

[4] N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar commu-nication systems,” IEEE Trans. on Communications, vol. 60, no. 12, pp.3726–3733, Dec 2012.

[5] S. S. Saab and K. K. Saab, “A positioning system for photodiode deviceusing collocated leds,” IEEE Photonics Journal, vol. 8, no. 5, pp. 1–14, Oct2016.

[6] N. T. Nguyen, N. H. Nguyen, V. H. Nguyen, K. Sripimanwat, and A. Sueb-somran, “Improvement of the VLC localization method using the extendedKalman filter,” in TENCON 2014 - 2014 IEEE Region 10 Conference, Oct2014, pp. 1–6.

[7] A. Sahin, Y. S. Eroglu, I. Güvenç, N. Pala, and M. Yüksel, “Hybrid3-D localization for visible light communication systems,” Journal ofLightwave Technology, vol. 33, no. 22, pp. 4589–4599, Nov 2015.

[8] M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning withOFDM visible light communications,” in 2016 13th IEEE Annual Con-sumer Communications Networking Conference (CCNC), Jan 2016, pp.505–510.

[9] B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimentaldemonstration of an indoor VLC positioning system based on OFDMA,”IEEE Photonics Journal, vol. 9, no. 2, pp. 1–9, Apr 2017.

[10] M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light commu-nications using OFDM and multiple LEDs,” IEEE Trans. on Communica-tions, vol. 63, no. 11, pp. 4304–4313, Nov 2015.

[11] R. Lenk and C. Lenk, Practical Modeling of LEDs. Wiley-IEEE Press,2016, pp. 245–266.

[12] Cree, Cree XLamp XHP70.2 LEDs, 2017. [Online]. Available: http://www.cree.com/led-components/media/documents/ds-XHP702.pdf

[13] J. Grubor, S. Randel, K. D. Langer, and J. W. Walewski, “Broadbandinformation broadcasting using LED-based interior lighting,” Journal ofLightwave Technology, vol. 26, no. 24, pp. 3883–3892, Dec 2008.

[14] S. D. Personick, “Receiver design for digital fiber optic communicationsystems, I and II,” The Bell System Technical Journal, vol. 52, no. 6, pp.875–886, Jul 1973.

[15] T. Komine and M. Nakagawa, “Fundamental analysis for visible-light

communication system using LED lights,” IEEE Trans. on ConsumerElectronics, vol. 50, no. 1, pp. 100–107, Feb 2004.

[16] X. Zhang, J. Duan, Y. Fu, and A. Shi, “Theoretical accuracy analysis ofindoor visible light communication positioning system based on receivedsignal strength indicator,” Journal of Lightwave Technology, vol. 32,no. 21, pp. 4180–4186, Nov 2014.

[17] S. Kay, Fundamentals of Statistical Processing, Volume I: EstimationTheory. Prentice Hall, 1993.

[18] S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-basedoptical wireless communication systems,” IEEE Trans. on Communica-tions, vol. 60, no. 4, pp. 1072–1081, Apr 2012.

[19] J. Chen, M. Jiang, and B. Chen, “Optical OFDM aided enhanced 3-Dvisible light communication systems,” in 2015 IEEE/CIC InternationalConference on Communications in China (ICCC), Nov 2015, pp. 1–6.

[20] S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-basedoptical wireless communication systems,” IEEE Trans. on Communica-tions, vol. 60, no. 4, pp. 1072–1081, Apr 2012.

[21] S. Dimitrov and H. Haas, Principles of LED Light Communications,ser. Principles of LED Light Communications: Towards NetworkedLi-Fi. Cambridge University Press, 2015. [Online]. Available: https://books.google.com.br/books?id=vqewBgAAQBAJ

[22] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd. JohnsHopkins Univ Press, 1996.

[23] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. NewYork, NY, USA: Cambridge University Press, 1992.

12 VOLUME 4, 2016

23

Appendix B -- Pre-distortion and

Pre-equalization for Mitigation of LED

non Linearities and Low-pass

Attenuation in OFDM VLC Systems

1

Pre-distortion and Pre-equalization for Mitigation ofLED non Linearities and Low-pass Attenuation in

OFDM VLC Systems.Luis Carlos Mathias and Taufik Abrão, Senior Member, IEEE .

Abstract—Applications of visible light communica-tion (VLC) have increasingly gained importance dueto its several advantages and with the growth of theuse of LED lighting. The OFDM scheme has shownpromise for these applications. However, the variationof the nonlinearity of the optical power emitted bythe LED as a function of current, temperature andaging implies in the performance degradation of theOFDM VLC systems. The higher attenuation at highfrequencies, which is inherent to the LED and which isaccentuated by the effect of the intrinsic capacitance ofthe photodiode, is another factor of degradation due tothe reduction of the signal-to-noise ratio (SNR) at thereceiver for the higher frequency OFDM subcarriers.For the mitigation of these effects, the present workproposes a pre-distortion and digital pre-equalizationscheme using a luminous feedback signal still in thetransmitter.

Index Terms—LED non linearities, attenuation, pre-distortion, pre-equalization, VLC, OFDM.

I. Introduction

THE increasing demand for data transmission, theuse of HPLED (High Power Light Emitting Diode)

lighting, the scarcity and high cost of the radio frequency(RF) spectrum have made studies for the application ofvisible light communication (VLC) prominent [1]. Theseand other advantages corroborate in placing VLC as oneof the key technologies for 5G wireless systems [2].

However, the design of the electronic circuit of thetransmitter and receiver present several challenges. Onthe transmitter side, the attenuation of the light signalemitted and the non-linearity of the optical power inrelation to the current supplied to the HPLED degradethe performance of the OFDM in VLC. On the receiverside, another limitation is the intrinsic capacitance ofthe junction of the photodiode that makes it difficultto implement a transimpedance amplifier (TIA) for largeband of frequency.

In [3] and [4], the non-linearity of the active componentsof the modulator was mitigated using A-class amplifiercircuit for analog-front-end (AFE) as current sink withfeedback loop. However, it does not combat the non-linearity of the luminous flux emitted by the LED. The

L. C. Mathias and T. Abrão are with the Department of Elec-trical Engineering, State University of Londrina, Rod. Celso Gar-cia, PR-445 Km 380, CEP 86051-990, Londrina-PR, Brazil (e-mail:[email protected]; [email protected]).

work of [5] minimizes the attenuation problem by applyingpost-equalization but also does not solve the non-linearityof the LED emission. The experimental DAC proposed by[6], composed of an array of LEDs, corrects the problem ofthe nonlinearity of the LED, however, it requires a largenumber of LEDs to obtain a reasonable resolution. Thisrequirement causes yet another problem of non-linearitydue to the different channel attenuations generated dueto the different positions and distances of the HPLEDs.In [7], is employed a drive circuit which employs on-chipoptical feedback technique to supress non-linearity of theHPLED. However, it does not evaluate the attenuationproblem for larger frequencies.Therefore, the present work makes a study and pro-

poses the implementation of a pre-distortion and pre-equalization scheme in order to mitigate these effects.That is, a light feedback scheme is still suggested inthe transmitter module so that the undesirable effects ofthe transmitter HPLED and the receiver photodiode areminimized. In the section II is presented the VLC Systemmodel. The section V present the numerical results andthose obtained by the experimental arrangement. Finally,the section VI presents the main conclusions.

II. VLC SystemA. VLC Channel ModelConsidering that the position and orientation of the

HPLED is within the field of view of the photodetector,the DC optical channel gain between the receiver and theHPLED can be simplified by [8]:

Ωmk = −(n+ 1)2π cosn(ϕ)cos(θ)Apd

R2 ; (1)

where ϕ is the angle between the orientation versor ofthe HPLED transmitter and the incidence vector, θ isthe angle between the receiver orientation versor and theincidence vector, Apd is the area of the photo-detector(PD) in m2, and n is the mode number of the Lambertiandistribution. The greater the value of n, the more directiveis the distribution of light.

B. HPLED transmitterThe process of generating white light in HPLEDs lamps

is basically in two ways [1]. In the first form, the whitelight is obtained from the combination of the blue HPLED

2

light when crossing a yellow layer of the chemical elementphosphorus. The second form uses the additive mixtureof the lights generated by red, green and blue coloredHPLEDs (RGB system). The first-mentioned HPLEDlamp, although easier to deploy and less costly, has alimited switching speed of up to a few MHz, due to theluminous persistence of the phosphor layer [5]. Due to thishigher attenuation characteristic, this work will use thistype of HPLED as a form of evaluation for worst case.

Another problem for modulation in HPLED type trans-mitters is the non-linearity between the current appliedto the HPLED and the respective optical power obtained[9] [10]. According to [11] and [9], this nonlinearity can bemodeled using a second order polynomial function.

However, for lighting purposes, several studies have veri-fied a strong variation of the optical efficiency of HPLEDswhen faced with factors such as temperature and aging[12]–[15].

C. Receiver PhotodiodeIn the signal reception, photo-receptors based on PIN

photodiodes are usually employed because allows easyconversion of the light signal to current up to tens ofMHz[1]. The current generated is proportional to the powerreceived with additive white Gaussian noise (AWGN) [16].In this context, the electric gain GE can be given by:

GE(f) = Rpd(f)ΩmkSled(f), (2)

where Sled is the HPLED conversion factor in [W/A]and Rpd is the photodetector responsivity in [A/W ]. Thisparameter is a generally presented in the datasheet of thePIN photodiodes.

D. Noise ModelThe two primary sources of noise in the VLC receiver

are the received photocurrent and the noise coming fromreceiver electronics [17]. The dominant types of noise areshot noise and thermal noise [18] and can be modeled asGaussian process with zero-mean and variance [19]:

σ2n = σ2

shot + σ2thermal. (3)

Both noises are shaped by the transfer function of thepreamplifier topology. In this work, it will be considereda receiver with photo-detector with PIN diode and fieldeffect transistor (FET) transimpedance amplifier (TIA)[20]. The major source of noise in the optical link isthe photo-generated shot noise which corresponds to thefluctuations in the count of the photons collected by thereceiver [19]. Its variance can be determined by:

σ2shot = 2qB (Rpd (PR +Apdpbs∆λ) + Idc) ; (4)

where q is the elementary charge, B is the TIA bandwidthin Hz, pbs is the background spectral irradiance, ∆λ isthe bandwidth of the optical filter, Ibg is the backgroundcurrent and Idc is the dark current.

Thermal noise is independent of the received opticalsignal and can be determined in terms of noise in the

feedback resistor and noise in the FET channel. Each term,respectively, contributes in the following variance:

σ2thermal = 8πkBTK

GolCpdApdI2B

2 + 16π2kBTKΓgm

C2pdA

2pdI3B

3;(5)

where kB is the Boltzmann’s constant, TK is the absolutetemperature, Gol is the open loop gain, Cpd is the capac-itance per unit area of the photo-detector, Γ is the FETchannel noise factor, gm is the FET transconductance andI3 is the TIA noise factor.

III. Development of an HPLED analyzerThe prototype of Fig. 1 was developed with the pur-

pose of capturing the behavior of the luminous flux asa function of the current and also of the temperatureof a HPLED. Fig. 2 shows the detail of the thermal

CurrentController

TIA

TemperatureSensor

Fan

μC

USB

A0

(PWM)

VirtualSerialPort

AplicationScript Package

SupportCμ

Firmware

Recorded

ThermoelectricPlate

H Bridge

Driver

FanDriver

Heat Sink

D11(PWM)

(PW

M)

D3

D6

A4/A5

(I2C)

D10

Signal Conditioning

Term

al C

ouplin

gh

HPLED

Photo ediod

V_TIA

LPF

LPF

PC MATLAB®

a)

Peltier effectplate

PC

Photodiode

H BridgeMicrocontrolller

TIA

b)Fig. 1: Block diagram in a) and photo in b) of the experi-mental arrangement to verify nonlinearity as a function ofcurrent and temperature of the HPLED.

3

Fig. 2: Detail of the thermal coupling plate betweenaluminum heatsink, Peltier effect plate, HPLED and tem-perature sensor.

coupling between aluminum heat sink with fan, Peltiereffect plate, HPLED and temperature sensor. The pro-cedure for extracting the experimental data consisted ofinitially keeping the HPLED off, controlling the analysistemperature of the HPLED, then triggering the analysiscurrent of the HPLED for a very short period of time. Theshort operating time is intended not to significantly changethe temperature of the HPLED junction. The luminousintensity of the emitted pulse is then captured by the ADconversion of the voltage signal generated by the TIA plusphotodiode arrangement.

Fig. 3 shows the TIA output as a function of the DCcurrent applied to the HPLED. The photodiode BPW34from the manufacturer Osram and the white HPLED 1Wfrom the manufacturer Multicomp, both aligned with eachother at a distance of 3.9 cm were used. The TIA gainwas adjusted by 32kΩ. In addition to confirming the non-linearity of the voltage generated by the TIA as a functionof the current in the HPLED, it is possible to verify thatthe luminous efficiency decreases with the increase of thetemperature in the HPLED.

0 50 100 150 200 250 300 350

ILED

[mA]

0

0.5

1

1.5

2

2.5

3

3.5

4

VT

IA[V

]

0o

C

20o

C

40o

C

60o

C

80o

C

100o

C

Fig. 3: Variation of nonlinearity of a Multicomp 1W whiteHPLED.

Whereas by the datasheet [21] that with ILED = 350mA and T = 30oC the HPLED provides 115 lumens, theluminous flux φv for any temperature can be determinedby:

φv = 115 · VTIA(0 ≤ ILED ≤ 350mA)/VTIA(ILED = 350mA;T = 30oC). (6)

Finally, the conversion from luminous flux to the radiatedoptic power PT can be realized by a factor of 2.1[mW/lm]for phosphor-coated blue LED [22]. According to Subsec-tion II-B, the optical power curve can be adjusted by apolynomial function:

PT = A · I2LED +B · ILED + C; (7)

Thus, for all temperatures analyzed, the parameters ofthe polynomial fit were recorded in Table I. In all theadjustments, we obtained excellent correlation coefficientsR.

TABLE I: Parameters of polynomial adjustmentsT Parameters

[oC] A B C R-10 -0,23735 0,764263 0,009285 0.999970 -0.24969 0.763086 0.008686 0.9999810 -0.22750 0.751208 0.008882 0.9999920 -0.24060 0.745831 0.008781 0.9999830 -0.22566 0.742316 0.008848 0.9999740 -0.25976 0.734123 0.008910 0.9999350 -0.26767 0.730652 0.008128 0.9999760 -0.26323 0.722152 0.008205 0.9999870 -0.27341 0.713003 0.007769 0.9999780 -0.27189 0.698047 0.007694 0.9999790 -0.26485 0.680774 0.007487 0.99997100 -0.25532 0.661240 0.007331 0.99997

Therefore, the variation of the nonlinearity as a functionof the temperature is confirmed and considering thatthere is also variation of luminosity due to the aging ofthe HPLED [12]–[15], it is justified the necessity of acompensation scheme to combat this effect that causesdegradation of the performance of the communicationsystem.

IV. OFDM Scheme for HPLED Linearizationand Attenuation compensation

The Fig. 4 shows the block diagram of the proposedarchitecture for the compensation of the variable nonlin-earity of the LED and also for the pre-equalization of thepowers of the subcarriers detected in the receiver. It isused an Intensity Modulation / Direct Detection (IM/DD)scheme with DC-biased optical OFDM (DCO-OFDM).In this scheme, the data bits are M-QAM modulatedgenerating the symbol vector XD. Considering a lengthN of the input vector X of the Inverse Fast FourierTransform (IFFT), the length of XD is N/2−1 because ofthe element X[0] responsible for the DC level is null; so,not interfering with the bias added to the OFDM framein order to keep it positive 1.

1In this work, it is assumed that the control of this signal isperformed externally to allow the control of the intensity of theillumination.

4

-

Flat topWindow

a)

-

b)Fig. 4: Proposed OFDM Scheme for HPLED Linearization and Attenuation compensation. Transmitter in a) andreceiver in b).

With the purpose in obtaining purely real-time pointsat the out of the IFFT block, the vector X of sizeN is generated after applying the following Hermitiansymmetry:

X[i] =

XD[i] ; i = 0, . . . , N/2− 1X∗D[N − i] ; i = N/2, . . . , N − 1. (8)

In the sequence, the powers of the OFDM subcarriers aremodified by:

XG = X · g′, (9)

where g is the gain vector obtained by the Gain Estimator(GE) block. In vector XG is performed the IFFT. Usingthe IFFT definition [23] to generate the signal in the timedomain:

x[i] = 1√N

N−1∑

k=0XG[n]ej2πki/N ; for 0 ≤ i ≤ N − 1; (10)

which is converted from parallel to serial (P/S) and addedthe cyclic prefix (CP), obtaining the OFDM frame. Then,the signal is hard-clipped aiming at fit the dynamic rangeof the driver:

v[i] =

Iu ; u[i] > Iuu[i] ; Il ≤ u[i] ≤ IuIl ; u[i] < Il;

(11)

where Iu and Il are the upper and the lower current limitsof modulation respectively.

The severity of clipping suffered by a signal is quantifiedby the clipping factor that is defined as the number ofstandard deviations per half of the dynamic range [24]:

γ = Iu − Il2 · σv

. (12)

In the Digital Predistortion (DPD) block, is appliedthe linearization transformation of the transmitted optical

power [16] considering now the current of polarization Ibiasby:

PT (v + Ibias) = S · (v + Ibias) + P0; (13)

where the HPLED gain S = (PT (Iu)− PT (Il)) /(Iu − Il)and P0 = PT (Iu) − S(Iu). The signal after DPD is con-verted from digital to analog (DAC), amplified in currentand finally coupled to the HPLED.

V. Numerical and Experimental ResultsIn this section, we have demonstrated the effectiveness

and efficiency of the proposed method by numerical sim-ulation analysis. The parameters that served as the basisare presented in Table II. The transmitter HPLED andthe photodetector were aligned having angles φ = θ = 0o.The feedback photodetector has been inclined to receivepart of the light emitted by the LED, i.e., φ = 80o andθ = 0o.

TABLE II: Adopted parameters values.HPLED Photodetector OFDM

n = 0.5 Apd = 1 cm2 B = 10 MHzIbias = 175 mA Rpd = 0.54 A/W N = 1024Iu = 150 mAIl = −150 mA

A. Simulation of the DPD in Flat ChannelBy arbitrating the clipping factor γ = 3, the variance

σv = 0.05 was determined by the Eq. (12). Consideringin this first moment the flat channel, and the expectationof the symbol M-QAM, the value of the elements of thevector g are constant and were determined by:

g =

√σ2v

E[XD] (14)

The Fig. 5 presents the bit error rate (BER) results forthe system with fixed pre-distortion (F-DPD) calibrated

5

0 5 10 15 20 25

SNR = Eb/N

0[dB]

10-4

10-3

10-2

10-1

100

BE

R

0 5 10 15 20 25 30 35

SNR = Eb/N

0[dB]

10-4

10-3

10-2

10-1

100

BE

R

0 10 20 30 40 50

SNR = Eb/N

0[dB]

10-4

10-3

10-2

10-1

100

BE

R

0 10 20 30 40 50

SNR = Eb/N

0[dB]

10-4

10-3

10-2

10-1

100

BE

R

F-DPD (0o

C)

F-DPD (20o

C)

F-DPD (40o

C)

F-DPD (60o

C)

F-DPD (80o

C)

F-DPD (100o

C)

LFB-DPD

without DPD

b) 64-QAMa) 16-QAM

c) 256-QAM d) 1024-QAM

Fig. 5: BER for fixed DPD (F-DPD) with different temperatures in the HPLED, for DPD by luminous feedback(LFB-DPD) and for without DPD. All for different modulation orders in flat channel.

for fixed temperature of 50oC and for different real tem-peratures in the HPLED of 0, 20, 40, 60, 80 and 100oC. Inthe same graphs the results of the system without DPD(W-DPD) and for the proposed digital pre-distortion byluminous feedback (LFB-DPD) are presented. In Fig. 5it is possible to verify that for the F-DPD and for thesystem without DPD, a greater effect in the degradationof the performance occurs for larger orders of modulation.This can be attributed to the fact that the Euclideandistance between the QAM symbols is much smaller, beingmore susceptible to the detection errors generated bythe HPLED nonlinearity problems. In some cases, theresult was so poor that several BER curves stagnatedasymptotically close to the range of 0.05 < BER < 0.15.Another aspect was that in some situations of F-DPD,the performance was worse than the system without pre-distortion, i.e., in these cases it is better not to have thepre-distortion. This corroborates for the proposal of thiswork, that it is advantageous to have the pre-distortionby the luminous feedback signal (FDB-DPD). So much sothat in all modulation orders analyzed, FDB-DPD was theone that presented the best performance.

B. Proposed Experimental Setup

In Fig. 6 is presented the experimental scheme forvalidation of the digital pre-distortion and pre-equalization(DPDPE) in the real physical system (SFR). The arrange-ment was implemented in order to verify the proposalusing a playback-type approach, i.e., the signals to begenerated by the arbitrary wave generator (AWG) andthe signals captured by the oscilloscope in the SFR areprocessed off-line in a personal computer (PC). Thus, forthe light interface, three circuits were constructed, onelight transmitter and two light receivers. Fig. 7a showsthe electronic schematic of the transmitter that has thefunction of modulating the current signal on the LEDand also keeping the Ibias current responsible for theDC level of the illumination. Fig. 7b shows the TIAcircuit of the receivers with a post-amplifier of the ACcomponent of the signal. A summary of the TIA project ispresented in Appendix -A. The reverse polarization of thephotodiode has the purpose of reducing the capacitance ofthe photodiode and consequently increasing its speed andoperating frequency band.As the first experimental verification, it was obtained

from the frequency response of the electric gain GE . Fig.8 shows the behavior for four different 1W LED colors from

6

Digital StorageOscilloscope

CH2-DSO

Arbitrary Waveform

USB

PC

MATLAB ScriptDriverVISA

®

CH1-DSO

CH2-AWG

CH1-AWG (Dimmer - DC level)

(BasebandSignal)

LUZ

(Rx)

(Feedback)

VLC Tx

VLC Rx

(DSO)

USB

(Trigge

r)

Generator (AWG)

Fig. 6: Experimental arrangement for the validation of theproposed architecture.

a)

b)Fig. 7: Proposed circuit for HPLED driver in (a) and TIAcircuit in (b).

the manufacturer Multicomp. As shown in SubsectionII-B, the white HPLED showed the highest attenuationat higher frequencies.

VI. ConclusionIn this work, by means of an experimental arrangement,

it was possible to characterize the nonlinear behavior ofthe optical power emitted by a HPLED as a function ofthe current at different temperatures at its semiconductorjunction. In the literature review is also presented stud-ies where they record variations of non-linearity due tothe aging of HPLED, differences between manufacturing

0 2 4 6 8 10 12 14 16 18 20

f [MHz]

-70

-60

-50

-40

-30

-20

-10

0

GE

norm

aliz

ed [d

B]

Red

Green

Blue

White

Fig. 8: Normalized Electric Gain.

batches, etc., which can further aggravate this scenario.The performance degradation of the OFDM communica-tion system was also evaluated and confirmed. Resultsshowed that pre-distortion with fixed parameters (F-DPD)presented performances even worse than the system with-out DPD. The DPD proposal for luminous feedback stillin the transmitter device, allowed a better performance ofthe system correcting in real time the variation of nonlinearity. This arrangement also allows pre-equalizationof subcarriers in the face of higher attenuation at highfrequencies. In this way, an experimental arrangementwas developed for the physical implementation of theproposed pre-distortion and pre-equalization architecture.The higher attenuation of the white HPLED compared tothose of the red, blue and green colors was confirmed bythis arrangement.

A. Transimpendance Amplifier DesignThe feedback resistor RF determines the TIA gain for

low frequencies [25], i.e., VO

ID= RF . However an analysis

for higher frequencies requires considering the reactivecomponents of TIA. That way, the input capacitanceCIN = CD +CCM +CDIFF , where CD is the photodiodecapacitance, CCM and CDIFF are the common modecapacitance and the differential mode capacitance of op-amp respectively. Thus, the impedance of input is:

ZIN = 1sCIN

. (15)

The optimum value of compensation capacitor CF canbe determined by:

CF =√

CIN2π(GBP )RF

; (16)

where GBP is the operational amplifier gain bandwidthproduct.

7

The impedance of feedback circuit is:

ZF = RF ||1

sCF=

1CF

s+ 1RFCF

. (17)

That way, the TIA transfer function can be determined:

GTIA = VOID

= −ZF1 + 1+ZF /ZIN

A(s)

; (18)

where A(s) is the single pole op-amp model:

A(s) = AOLωAs+ ωA

; (19)

where AOL is the open loop gain and ωA can be deter-mined by:

ωA = 2πGBPAOL

. (20)

AcknowledgmentsThis work has been partially supported by the Na-

tional Council for Scientific and Technological Develop-ment (CNPq) of Brazil under Grants 304066/2015-0; bythe Londrina State University (UEL) and the Paraná StateGovernment. All the agencies are gratefully acknowledged.

References[1] P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible

light communication, networking, and sensing: A survey, poten-tial and challenges,” IEEE Communications Surveys Tutorials,vol. 17, no. 4, pp. 2047–2077, Fourthquarter 2015.

[2] H. Haas and C. Chen, Visible Light Communication in 5G.Cambridge University Press, 2017, pp. 289–332.

[3] K. L. Sterckx, “Implementation of continuous vlc modulationschemes on commercial led spotlights,” in 2012 9th Interna-tional Conference on Electrical Engineering/Electronics, Com-puter, Telecommunications and Information Technology, May2012, pp. 1–4.

[4] S. Fuada, T. Adiono, A. P. Putra, and Y. Aska, “A low-costanalog front-end (AFE) transmitter designs for OFDM visiblelight communications,” in 2016 International Symposium onElectronics and Smart Devices (ISESD), Nov 2016, pp. 371–375.

[5] H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung,Y. Oh, and E. T. Won, “100-mb/s nrz visible light commu-nications using a postequalized white led,” IEEE PhotonicsTechnology Letters, vol. 21, no. 15, pp. 1063–1065, Aug 2009.

[6] J. Yew, S. D. Dissanayake, and J. Armstrong, “Performance ofan experimental optical dac used in a visible light communica-tion system,” in 2013 IEEE Globecom Workshops (GC Wkshps),Dec 2013, pp. 1110–1115.

[7] A. W. M. Zuhdi, J. J. D. McKendry, R. K. Henderson, E. Gu,M. D. Dawson, and I. Underwood, “Gan based µled drive circuitfor visible light communication (vlc) with improved linearityusing on-chip optical feedback,” in 2016 IEEE Region 10 Con-ference (TENCON), Nov 2016, pp. 3394–3397.

[8] J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G.Messerschmitt, “Simulation of multipath impulse response forindoor wireless optical channels,” IEEE Journal on SelectedAreas in Communications, vol. 11, no. 3, pp. 367–379, Apr 1993.

[9] R. Lenk and C. Lenk, Practical Modeling of LEDs. Wiley-IEEEPress, 2016, pp. 245–266.

[10] Philips Lumileds, Power light source Luxeon Rebel,July 2017. [Online]. Available: www.led-tech.de/produkt-pdf/luxeon/DS56_Rebel.pdf

[11] H. Elgala, R. Mesleh, and H. Haas, “An led model for intensity-modulated optical communication systems,” IEEE PhotonicsTechnology Letters, vol. 22, no. 11, pp. 835–837, June 2010.

[12] C. Yu, J. Fan, C. Qian, X. Fan, and G. Zhang, “Luminous fluxmodeling for high power led automotive headlamp module,” in2017 18th International Conference on Electronic PackagingTechnology (ICEPT), Aug 2017, pp. 1389–1395.

[13] F. Rao, Z. C. Ge, and J. L. Zhu, “Effect of temperature andcurrent on luminous efficiency of high power led,” in Renewableand Sustainable Energy, ser. Advanced Materials Research, vol.347. Trans Tech Publications, 1 2012, pp. 310–313.

[14] W. Chi, T. Chou, C. Han, S. Yang, and K. Chiang, “Analysisof thermal and luminous performance of mr-16 led lightingmodule,” IEEE Transactions on Components and PackagingTechnologies, vol. 33, no. 4, pp. 713–721, Dec 2010.

[15] A. Keppens, W. Ryckaert, G. Deconinck, and P. Hanselaer,“Evaluation of current and temperature effects on high powerlight-emitting diode efficiencies,” in CIE Conference BudapestJune 2009. CIE, 2009.

[16] M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visiblelight communications using OFDM and multiple LEDs,” IEEETrans. on Communications, vol. 63, no. 11, pp. 4304–4313, Nov2015.

[17] Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Opticalwireless communications: system and channel modelling withMatlab. Boca Raton: CRC Press, 2012.

[18] S. S. Saab and K. K. Saab, “A positioning system for photodiodedevice using collocated LEDs,” IEEE Photonics Journal, vol. 8,no. 5, pp. 1–14, Oct 2016.

[19] T. Komine and M. Nakagawa, “Fundamental analysis forvisible-light communication system using LED lights,” IEEETrans. on Consumer Electronics, vol. 50, no. 1, pp. 100–107,Feb 2004.

[20] S. D. Personick, “Receiver design for digital fiber optic commu-nication systems, I and II,” The Bell System Technical Journal,vol. 52, no. 6, pp. 875–886, July 1973.

[21] 1W High Power LED, Multicomp, 2012.[22] J. Grubor, S. Randel, K. D. Langer, and J. W. Walewski,

“Broadband information broadcasting using led-based interiorlighting,” Journal of Lightwave Technology, vol. 26, no. 24, pp.3883–3892, Dec 2008.

[23] J. Armstrong, “OFDM for optical communications,” Journal ofLightwave Technology, vol. 27, no. 3, pp. 189–204, Feb 2009.

[24] S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in ofdm-based optical wireless communication systems,” IEEE Trans. onCommunications, vol. 60, no. 4, pp. 1072–1081, April 2012.

[25] X. Ramus, “Transimpedance considerations for high-speed am-plifiers,” Application Report SBOA122. Texas Instruments,2009.

Date post:	03-Jul-2020
Category:	Documents
Upload:	others
View:	5 times
Download:	0 times

Department of Electrical Engineering · 2019-05-13 · Ficha Catalogr a ca Mathias, Luis Carlos...

Documents