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Optical MIMO-OFDM with Generalized LED Index Modulation

Citation for published version:Yesilkaya, A, Basar, E, Miramirkhani, F, Panayirci, E, Uysal, M & Haas, H 2017, 'Optical MIMO-OFDM withGeneralized LED Index Modulation', IEEE Transactions on Communications, vol. 65, no. 8, pp. 3429 - 3441.https://doi.org/10.1109/TCOMM.2017.2699964

Digital Object Identifier (DOI):10.1109/TCOMM.2017.2699964

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Published In:IEEE Transactions on Communications

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https://doi.org/10.1109/TCOMM.2017.2699964

https://doi.org/10.1109/TCOMM.2017.2699964


IEEE TRANSACTIONS ON COMMUNICATIONS 1

Optical MIMO-OFDM with Generalized LED IndexModulation

Anil Yesilkaya, Student Member, IEEE, Ertugrul Basar, Senior Member, IEEE, Farshad Miramirkhani, StudentMember, IEEE, Erdal Panayirci, Life Fellow, IEEE, Murat Uysal, Senior Member, IEEE, and Harald Haas, Senior

Member, IEEE

Abstract—Visible light communications (VLC) is a promis-ing and uncharted new technology for the next generation ofwireless communication systems. This paper proposes a novelgeneralized light emitting diode (LED) index modulation methodfor multiple-input-multiple-output orthogonal frequency divisionmultiplexing (MIMO-OFDM) based VLC systems. The proposedscheme avoids the typical spectrum efficiency losses incurred bytime and frequency domain shaping in OFDM signals. This isachieved by exploiting spatial multiplexing along with LED indexmodulation. Accordingly, real and imaginary components of thecomplex time domain OFDM signals are separated first, thenresulting bipolar signals are transmitted over a VLC channel byencoding sign information in LED indexes. As a benchmark, wedemonstrate the performance analysis of our proposed systemfor both analytical and physical channel models. Furthermore,two novel receiver designs are proposed. Each one is suitable forfrequency-flat or selective channel scenarios. It has been shownvia extensive computer simulations that the proposed schemeachieves considerably better bit error ratio (BER) vs. signal-to-noise-ratio (SNR) performance than the existing VLC-MIMO-OFDM systems that use the same number of transmit and receiveunits (LEDs and photo diodes (PDs)). Compared with the single-input single-output (SISO) DC biased optical OFDM (DCO-OFDM) system, both spectral efficiency and DC bias can bedoubled and removed respectively simply by exploiting a MIMOconfiguration.

Index Terms—Visible light communications (VLC), multiple-input-multiple-output (MIMO) systems, orthogonal frequencydivision multiplexing (OFDM), optical-spatial modulation (OSM),LED index modulation, maximum-a-posteriori probability(MAP) estimator

A. Yesilkaya was and E. Panayirci is with the Department of Electricaland Electronics Engineering Kadir Has University, 34083, Istanbul, Turkey(E-mail: [email protected], [email protected])

E. Basar is with Istanbul Technical University, Faculty of Electricaland Electronics Engineering, 34469, Maslak, Istanbul, Turkey (E-mail:[email protected]).

F. Miramirkhani and M. Uysal is with the Department of Electrical andElectronics Engineering, Ozyegin University, 34794, Istanbul, Turkey (E-mail:[email protected], [email protected]).

A. Yesilkaya and H. Haas are with the LiFi R&D Centre, Institute forDigital Communications, The University of Edinburgh, Edinburgh, EH9 3JL,U.K. (E-mail: [email protected], [email protected]).

This paper was presented in part at the 2016 IEEE International Confer-ence on Communications (ICC 2016), Kuala Lumpur, Malaysia, which wasawarded as a best paper.

This work was supported by the European Cooperation in Science andTechnology (COST) - The Scientific and Technological Research Council ofTurkey (TUBITAK) Research Grant No. 113E307.

This work was partially supported by EPSRC under Established CareerFellowship Grant EP/K008757/1.

Manuscript received October 31, 2016; revised March 14, 2017; acceptedApril 19, 2017. Date of publication XXXXXX, 2017; date of current versionXXXXXX, 2017. The associate editor coordinating the review of this paperand approving it for publication was Guu-Chang Yang.

I. INTRODUCTION

OPTICAL wireless communications (OWC) are an at-tractive new technology which has a great potential for

the next generation wireless communications systems. Partic-ularly, visible light communications (VLC) systems operatingbetween the 400−800 nm range could be the optimal solutionfor indoor mobile communications scenarios. This is due tothe existing infrastructure, which can be reused and lightingand communication systems can be combined. Its distinctadvantages such as license-free application, low deploymentcost, wide bandwidth, energy efficiency and high securityhave made VLC one of the strongest candidates for beyond5G wireless communications standards. Orthogonal frequencydivision multiplexing (OFDM) and its modified versions forintensity modulation/direct detection (IM/DD) systems in VLChave attracted significant attention due to frequency-selectivebehavior of the VLC channels for moderate and high data ratesand the capability of easily achieving bit and power loading[1]. OFDM brings remarkable advantages in the presence ofintersymbol interference (ISI) caused by frequency selectivity.However, since the transmitted signals are bipolar, it is impos-sible to transmit them without any modifications. Therefore,direct current (DC) bias addition and associated power ineffi-ciency of optical OFDM constitute the main motivation behindthe new energy efficient optical OFDM systems.

Utilization of the IM/DD technique inherently requires lightintensity levels to be real and positive. These restrictions resultin challenging problems when the goal is to transmit IM/DDsignals and at the same time maintain the same spectral andpower efficiency that the coherent transmission systems have.To address those challenges, many different methods havebeen proposed in the literature. For instance, real time-domainsignals are directly obtained by using the conjugate symmetryproperty of the fast Fourier transformation (FFT), better knownas the Hermitian symmetry. However, the main novelties of theproposed systems stem from how they deal with the bipolarnature of the signals. One of the straightforward solutions toobtain positive signals is to add a DC bias after the inverse FFT(IFFT) operation. The resulting system is called DC biasedoptical OFDM (DCO-OFDM) [2]. An elegant solution to thebipolarity problem is to use the FFT antisymmetry propertythat have led to asymmetrically clipped optical OFDM (ACO-OFDM) given in [3]. In ACO-OFDM, the DC bias is signif-icantly reduced at the cost of sacrificing half of the spectralefficiency. In [4], a novel unipolar transmission system, called

2 IEEE TRANSACTIONS ON COMMUNICATIONS

U-OFDM, is proposed. The half-power (3 dB) penalty inACO-OFDM caused by the time domain clipping is solvedin U-OFDM by transmitting positive and negative framesseparately; however, both systems achieve only half of thespectrum efficiency compared to DCO-OFDM. A new methodproposed in [5] and [6], offers time domain superposition toachieve the same spectral efficiency as that of DCO-OFDMfor both U-OFDM and ACO-OFDM. Recently, MIMO andindex modulation transmission methods have started to attractsignificant attention in VLC literature to transmit additionalbits with reduced energy consumption. In [7], MIMO-VLCbased systems are investigated for multi-user case. Indexmodulation techniques, in which the indices of the buildingblocks of considered communications systems are used totransmit additional information bits, are particularly promisingfor energy and spectrum efficient IM/DD applications. Indexmodulation based transmission systems offer additional degreeof freedom to compensate for the lose of the phase dimension[8]. In [9], spatial modulation (SM), which is the most com-mon form of index modulation, is adopted for MIMO-VLCsystems. The performance of the SM and some of its variantsare investigated in [10] for VLC systems. Furthermore, a2 × 2 optical SM based structure is proposed in [11] to solvethe DC bias penalty issue by introducing two light emittingdiodes (LEDs) to send negative and positive signals. Usingthe advantage of different wavelengths in the visible band isanother promising solution to enhance the spectrum efficiencyby means of multi-channel communication [12–16].

In this work, we propose two novel 4 × 4 MIMO-basedoptical OFDM systems for operation in the presence offrequency-flat and frequency-selective channels. These twoschemes are called generalized LED index modulation op-tical OFDM (GLIM-OFDM) and extended GLIM-OFDM (e-GLIM-OFDM), respectively, where e-GLIM-OFDM is themodification of GLIM-OFDM to operate over frequency-selective VLC channels.

More specifically, the main contributions of the paper aresummarized as follows:• A novel 4×4 MIMO transmission-based technique, called

GLIM-OFDM, is proposed. This scheme requires no Her-mitian symmetry and DC bias to operate over frequency-flat VLC channels. In the proposed scheme, the real andimaginary parts of the complex time-domain OFDM sig-nals are separated into their real and imaginary parts, andthen these signals are transmitted over the MIMO-VLCchannel by using the index modulation based on activeLED indices. Higher spectral and power efficiencies areachieved by encoding the sign information of the complexsignals to the location of transmit LEDs. Furthermore,a novel conditional maximum a posteriori probability(MAP) estimator is employed to estimate those real andimaginary parts of the OFDM signals at the receiver.

• A novel 4 × 4 MIMO transmission-based technique,called e-GLIM-OFDM, is also proposed by modifying theGLIM-OFDM structure. Similarly, this scheme requiresno Hermitian symmetry and DC bias to operate overfrequency-selective VLC channels. Since it is not feasibleto estimate directly the real and imaginary parts of the

complex time-domain OFDM signals in this case, anefficient and feasible technique is proposed for the time-frequency domain transformations.

• Both analytical and computer software aided physicalVLC channel models are obtained for three differentscenarios: 1) Receivers located close to each other witha separation of 0.1 m, 2) Receivers are located apartwith a separation of 0.8 m, 3) Receivers are alignedto their corresponding luminaries while the separationbetween receivers is 0.1 m. Physical VLC channel modelsincluding realistic source, detector and reflection parame-ters are obtained by a ray-tracing approach. Furthermore,the proposed scheme is also adopted for the frequency-selective VLC channels.

• Finally, it is shown that the proposed GLIM-OFDM ande-GLIM-OFDM schemes have superior bit error ratio(BER) performances as compared with the referenceoptical MIMO transmission systems.

The rest of the paper is organized as follows. In SectionII, the system model for GLIM-OFDM is presented and thedesign of its receiver based on the conditional MAP estimatoris introduced. In Sections III and IV, the design of e-GLIM-OFDM is given and both analytical and physical VLC channelmodeling approaches are presented, respectively. Computersimulation results are provided in Section V and finally,conclusions are given in Section VI.

Notation: Throughout the paper, vectors are in bold low-ercase letters and matrices are in bold capital letters. Thetranspose of a matrix/vector is expressed by (.)T . Component-wise inequalities are given by and . Complex and realnormal distributions are given by CN (µ, σ2) and N (µ, σ2),respectively, where µ represents the mean and σ2 representsthe variance. R denotes the ring of real numbers. N × N FFTmatrix is denoted by F. Lastly, 0 and [A]m,n are N × N zeromatrix and (m, n)th element of a matrix A, respectively.

II. GLIM-OFDM IN THE PRESENCE OF FREQUENCY-FLATMIMO CHANNELS

The block diagram of the proposed GLIM-OFDMtransceiver for frequency-flat MIMO channels is given in Fig.1. N log2(M) information bits carrying vector u enters theGLIM-OFDM transmitter for transmission of each OFDMblock, where N is the number of OFDM subcarriers andM is the size of the considered signal constellation suchas M-ary quadrature amplitude modulation (M-QAM). TheDCO-OFDM, ACO-OFDM and non DC-biased OFDM (NDC-OFDM) schemes rely on Hermitian symmetry to produce realtime-domain signals after the IFFT operation. In the proposedscheme, the OFDM modulator directly processes the complexfrequency-domain OFDM frame xF without requiring Her-mitian symmetry. The resulting time-domain OFDM framexT =

[x1 · · · xN

]Tcannot be conveyed through a VLC

channel because of its complex-valued and bipolar (positiveand negative valued) elements. In order to solve this problem,a new LED index modulation based MIMO transmissiontechnique has been developed. After parallel-to-serial (P/S)conversion, using a similar technique as in [17] for each time-domain OFDM signal xk , where k = 0, 1, . . . , N − 1, first,

YESILKAYA et al.: GENERALIZED LED INDEX MODULATION OPTICAL OFDM FOR MIMO VISIBLE LIGHT COMMUNICATIONS SYSTEMS 3

M-QAM

Mod.N-IFFT P/S

MAPEst.S/PN-FFT

Τℜ ℑSeparator

𝑥𝑘,𝑅

𝑥𝑘,𝐼

𝑥𝑘,𝑅+

𝑥𝑘,𝑅−

𝑥𝑘,𝐼+

𝑥𝑘,𝐼−

Τℜ ℑCombiner

M-QAMDemod.

OpticalChannel

Τ+ −Separator

Τ+ −Separator

ො𝑥𝑘,𝑅MAP

ො𝑥𝑘,𝐼MAP

𝛩 ≥ 0ෝ𝑚, ො𝑛

ො𝑥𝑘ො𝐱𝑇ො𝐱𝐹ෝ𝐮

𝐮 𝐱𝐹 𝐱𝑇 𝑥𝑘

𝑦𝑘,1

𝑦𝑘,2

𝑦𝑘,3

𝑦𝑘,4

𝐇

Fig. 1. Block diagram of the GLIM-OFDM scheme for a 4 × 4 MIMO-VLC system.

the real and imaginary parts of the complex signal xk areseparated as xk = xk,R + j xk,I . Then, the resulting real, butbipolar signals xk,R and xk,I are processed by positive-negative(+/−) separators to obtain the following positive real-valuedsignals:

x+k,R =

xk,R if xk,R > 00 if xk,R < 0 x−k,R =

0 if xk,R > 0−xk,R if xk,R < 0

x+k,I =

xk,I if xk,I > 00 if xk,I < 0 x−k,I =

0 if xk,I > 0−xk,I if xk,I < 0.

(1)

These signals can be transmitted simultaneously from annR × nT MIMO VLC system, where nR and nT denote thenumber of receiver (Rx) and transmitter (Tx) units, respec-tively. It should be noted that, nT must be divisible by fourfor the proposed scheme where it is taken as nT = 4 in thiswork.

In the GLIM-OFDM scheme, LEDs transmit the absolutevalues of xk,R and xk,I signals and the index of the transmit-ting LED determines the sign of the corresponding signalssimilar to the NDC-OFDM scheme. However, unlike theNDC-OFDM, GLIM-OFDM completely avoids the Hermitiansymmetry at the input of IFFT as well as the accompanyingloss in spectral efficiency. Consequently, the spectral efficiencyof the proposed scheme becomes log2(M) [bits/s/Hz], which istwice that of NDC-OFDM and DCO-OFDM schemes, sinceHermitian symmetry is no longer required to produce real-valued OFDM symbols.

The positive and real-valued OFDM time samplesx+k,R, x−

k,R, x+

k,Iand x−

k,Iare transmitted over the nR ×4 optical

MIMO channel (represented by H) for k = 0, 1, . . . , N − 1 as

y = Hx + n (2)

where y =[yk,1 · · · yk,nR

]T∈ RnR×1 is the vector of

received signals that contains the electrical signals obtainedfrom PDs at the Rx units. In (2), n ∈ RnR×1 is the vector ofreal-valued additive white Gaussian noise (AWGN) samples,that models the shot noise and thermal noise. The elements ofn follows N

(0, σ2

w

)distribution, and are added to the received

signals in the electrical domain. The transmitted signal vector

x ∈ R4×1 is formed for GLIM-OFDM as

x =[x+k,R

x−k,R

x+k,I

x−k,I

]T(3)

where the signals emitted by the LEDs are indicated by theelements of x. According to (1), for a given OFDM signal,only two out of four elements of x are non-zero, i.e., twoLEDs are active (emitting light), while the other two LEDsremain inactive (turned off). As an example, for xk = −2.1 +j3.8, we have x =

[0 2.1 3.8 0

]T, i.e., the second LED

is active and it transmits the absolute value of the real partof xk and the third LED is also active for the transmission ofthe imaginary part of xk , which is positive. In this way, theproposed scheme utilizes the index modulation concept for theactive LED indices to transmit the complex OFDM signals.

In this study, we consider nR = 4 for ease of presentation,while a generalization is straightforward. We assume that theLEDs are operating within their dynamic range. Note that theoperation in (1) is not subject to non-linear distortions.

The 4 × 4 optical MIMO channel is represented by

H =

h1,1 h1,2 h1,3 h1,4h2,1 h2,2 h2,3 h2,4h3,1 h3,2 h3,3 h3,4h4,1 h4,2 h4,3 h4,4

(4)

where hr,t denotes the channel gain of the optical wirelesslink between the Tx unit (LED) t and the Rx unit (PD) r ,where (t, r) ∈ 1, 2, 3, 4. In this study, we consider the averageelectrical signal-to-noise ratio (SNRRx) at the receiver as givenin [18–20]:

SNRRx =Pelec

Rx

σ2n

=1σ2n

ζ(Popt

Rx

)2(5)

where ζ is the electrical-to-optical conversion factor that istaken as unity and Pelec

Rx is the average received electricalpower. The average received optical power can be expressedas,

PoptRx =

1nR

∑nR

r=1

∑nT

t=1hr,t I (6)

where I represents the mean optical intensity being emitted.Let us assume that E

xHF xF

= N , i.e., M-QAM constellation

is normalized to have unit-energy symbols. It can be shown


that if the inverse fast Fourier transform (IFFT) operation sat-isfies the normalization of E

xHT xT

= N , the elements of xT

follow CN (0, 1) distribution for large N values. Consideringthat xk,R and xk,I ∼ N (0, 1/2), due to the symmetry, all fourelements of x have the following clipped Gaussian probabilitydensity function (p.d.f.)

px±k,R (I )

(v) =1√π

e−v2u(v) +

12δ(v) (7)

where u(v) and δ(v) denote the unit step and Dirac delta func-tions, respectively. Then, the average electrical power emittedfrom the one LED of GLIM-OFDM scheme is obtained as,

I = Ex±k,R(I ) =

∫ ∞

0vpx±

k,R (I )(v)dv = 1/(2

√π). (8)

A. Conditional MAP Estimator of GLIM-OFDM

The transmission model given in (2) resembles that of theclassical single-carrier MIMO-SM systems; however, it differsfrom those models for two main reasons: Firstly, the receivedsignals are real in (2) and secondly, the transmitted data vectorx has a clipped Gaussian distribution. Furthermore, it is notpossible to forward the received signal vector y to the OFDMdemodulator directly, due to the fact that complex valuedsignals must be constructed first to obtain the estimate ofthe frequency domain OFDM block xF . A straightforwardsolution to the estimation problem formulated in (2) is the useof the zero-forcing (ZF) equalizer, which yields an estimateof x simply as

xZF = H−1y. (9)

After this operation, the receiver can determine the indicesof the active LEDs and corresponding signals by selecting thehigher magnitude signals from xZF [11]. Despite its simplicity,the ZF estimator can significantly enhance the noise powerthrough multiplication of n with H−1; furthermore, it doesnot consider the probability distribution of x as a a prioriinformation and consequently, it may produce negative-valuedestimates. To overcome the aforementioned drawbacks ofthe ZF estimator, in this section, we propose a novel MAPestimator for the GLIM-OFDM scheme by taking into accountthe prior information we have for the signal vector x.

The channel matrix H is defined in terms of its columnvectors as H =

[h1 h2 h3 h4

]and the observed signals

given in (2) can be rewritten as

y = hm xk,R + hn xk,I + n (10)

where xk,R = xk,R , xk,I = xk,I , m ∈ 1, 2 and n ∈ 3, 4. Itcan be easily shown that xk,R and xk,I have a folded Gaussian(half-normal) distribution having the following p.d.f

pxk,R (I ) (v) =2√π

e−v2u(v). (11)

Consequently, for a given pair (m, n), the conditional MAPestimates of xk,R and xk,I can be obtained as(

x (m,n)k,R

, x (m,n)k,I

)= arg max

xk,R, xk, Ip(xk,R, xk,I | y

)(12)

Algorithm 1 Conditional MAP Estimator

1: for m = 1 : 2 do2: for n = 3 : 4 do3: Estimate, x (m,n)

k,Rand x (m,n)

k,Ivalues from (17)

4: Estimate, (m, n) indices from (18)5: end for6: end for7: Combination of symbols: ±x (m,n)

k,R± j x (m,n)

k,Ivia (m, n).

where p(xk,R, xk,I | y

)is the p.d.f. of xk,R and xk,I, condi-

tioned on y. After simple manipulations, (12) could be writtenas (

x (m,n)k,R

, x (m,n)k,I

)=arg min

xk,R, xk, IMMAP (

m, n, xk,R, xk,I). (13)

where MMAP (m, n, xk,R, xk,I

)is the MAP estimation metric

defined as

MMAP (m, n, xk,R, xk,I

)= y − hm xk,R − hn xk,I 2

+ 2σ2w

(x2k,R + x2

k,I

). (14)

Using ‖a‖ = aTa and after some algebra, (14) can besimplified as

MMAP (m, n, xk,R, xk,I

)=

Ax2k,R + Bx2

k,I + Cxk,R + Dxk,I + Exk,R xk,I (15)

where

A = hTmhm + 2σ2

w B = hTnhn + 2σ2

w

C = −2yThm D = −2yThn

E = 2hTmhn. (16)

Taking the derivative of MMAP(m, n, xk,R, xk,I ) with respectto xk,R and xk,I and equating to zero yields the MAP estimatesfor xk,R and xk,I , conditioned on (m, n), as

x (m,n)k,R

=

[2BC − EDE2 − 4AB

]+, x (m,n)

k,I=

[2AD − ECE2 − 4AB

]+. (17)

where [x]+ := max([0, x]). Note that the optimal estimatesof q in (17) also guarantee that x (m,n)

k,R≥ 0 and x (m,n)

k,I≥ 0

for all Q and b, i.e. regardless of the SNR and the channelconditions.

In order to determine the indices of the active LEDs (i.e.,estimations of m and n) as well as the corresponding estimatesof xk,R and xk,I , the conditional MAP estimator determinesx (m,n)k,R

and x (m,n)k,I

for all possible (m, n) pairs, and thenobtains the unconditional (actual) estimates of xk,R and xk,Ias follows:

(m, n)=arg minm,n MMAP(m, n, x (m,n)

k,R, x (m,n)

k,I

),

where xMAPk,R= x (m,n)

k,R, xMAP

k,I= x (m,n)

k,I.

(18)

In other words, after the calculation of the MAP estimatesof xk,R and xk,I for all (m, n) ∈ (1, 3) , (1, 4) , (2, 3) , (2, 4)that considers all possible active LED scenarios, the condi-tional MAP estimator of the GLIM-OFDM scheme decideson the most likely active LED pair (m, n) and correspondingestimates of xk,R and xk,I ( xMAP

k,R, xMAP

k,I) by calculating the


MAP estimation metric given by (14) for all four scenarios.The</= combiner then calculates the estimate of the complexOFDM signal xk as

xk,R =

xMAPk,R

, if m = 1−xMAP

k,R, if m = 2 xk,I =

xMAPk,I

, if n = 3−xMAP

k,I, if n = 4

(19)In Algorithm 1, we summarize the steps of the proposed

MAP estimator. After this point, classical OFDM processingsteps such serial-to-parallel (S/P) conversion, FFT and M-ary demodulation are applied to obtain the estimate u of theinformation bit vector u.

B. Calculation of Mean Square Error

Given the estimates (m, n) of the indices of the active LEDsfor k = 0, 1, · · · , N − 1 and assuming that they are correct, wenow derive the mean-square error (MSE) for the estimates ofq = [xk,R xk,I ]T defined as

MSEy,q = EεTε

where ε represents the error vector, ε = q − q(m,n) and q ≡q(m,n) = [xk,R xk,I ]T . As can be seen from (10) and (17), qdepends linearly on y and the elements of the q are jointlyGaussian distributed. Consequently, ε is also Gaussian withzero mean and its covariance matrix is given as [21]:

C(m,n) = *,

1σ2q

I +1σ2n

HT H+-

−1

∈ R2×2 (20)

where H = [hm hn] ∈ RnR×2 and σ2q = σ

2xk,R (I )

is the varianceof the prior density of xk,R(I ) .

It can be easily shown from (11) that σ2q =

π−14π . Finally, for

k = 0, 1, · · · , N − 1, the MSE values of the estimates, x (m,n)k,R

and x (m,n)k,I

are equal to the diagonal elements of the errorcovariance matrix, namely,

MSE(x (m,n)k,R

)= [C(m,n)]1,1

MSE(x (m,n)k,I

)= [C(m,n)]2,2.

(21)

Finally the average MSE for xR(I ) =

[x0,R(I ), x1,R(I ), · · · , x0,R(I )]T can be obtained as follows,

MSE(xR(I )

)=

1N

N−1∑k=0

MSE(x (m,n)k,R(I )

). (22)

In Section V, using the calculated MSE values in (22),we present both analytical and computer simulation errorperformance of the MAP estimator for the GLIM-OFDMscheme.

III. GLIM-OFDM IN THE PRESENCE OFFREQUENCY-SELECTIVE MIMO CHANNELS

In this section, we propose a novel design for the GLIM-OFDM, which is called extended GLIM-OFDM (e-GLIM-OFDM) and suitable for the frequency-selective MIMO visiblelight channels. It is already known that frequency responsesof the front-end devices limits the data rates of the system.However, as data rate gets higher, multi-path characteristicsof the channel becomes more dominant, resulting in ISI. On

the other hand, OFDM is known to be an efficient techniqueto cope with the multi-path channel effects. However, MIMOfrequency selectivity for VLC channels is a quite new conceptand to the best of authors’ knowledge, e-GLIM-OFDM designand its performance in the presence of frequency-selectiveMIMO channel model are investigated for the first time inthe literature. Block diagram of the e-GLIM-OFDM schemeis given in Fig. 2. Unlike the GLIM-OFDM scheme for flatVLC channels, after performing LED index modulation, thetime-domain OFDM frame xT is extended into four vectorsand a cyclic prefix is appended to the beginning of eachtransmission vector. Accordingly, each luminary here transmitsits own data vector, which corresponds to a part of the overalltransmitted vector, λCP = [x+R x−R x+I x−I ]T ∈ R4(N+Lcp )×1

where x+R, x−R, x+I , x−I are the (N+Lcp)×1 real-valued vectorsafter the insertion of CP. For the sake of simplicity, a 4 × 4system is considered in this work. However, the extension tohigher MIMO systems can be easily performed. At the receiverside, (N + Lcp) × 1 real-valued received signal vectors areobtained from each of the PDs as, yi where i ∈ 1, 2, 3, 4. Theoverall received vector, ψCP = [y1 y2 y3 y4]T ∈ R4(N+Lcp )×1,can be expressed as

y1 = x+R ~ g1,1 + x−R ~ g1,2 + x+I ~ g1,3 + x−I ~ g1,4 + ρ1y2 = x+R ~ g2,1 + x−R ~ g2,2 + x+I ~ g2,3 + x−I ~ g2,4 + ρ2y3 = x+R ~ g3,1 + x−R ~ g3,2 + x+I ~ g3,3 + x−I ~ g3,4 + ρ3y4 = x+R ~ g4,1 + x−R ~ g4,2 + x+I ~ g4,3 + x−I ~ g4,4 + ρ4

(23)where ~ is the circular convolution operation, gr,t is the k ×1frequency-selective channel coefficients vector between tth

LED and r th PD and ρi’s are (N + Lcp) × 1 dimensionalreal-valued AWGN vectors. After computing FFT of the CPremoved received signal vector ψ, the circular convolutionoperation could be converted into matrix multiplication as,

Ωψ = G · Ωλ +Ωγ (24)

where Ω is the 4N × 4N diagonal FFT matrix, which couldbe given as,

Ω =

F 0 0 00 F 0 00 0 F 00 0 0 F

and G is a 4N × 4N sized complex matrix whose elementsare Gr,t = diag(Fgr,t ) and γCP = [ρ1 ρ2 ρ3 ρ4]T is the4(N + Lcp)×1 dimensional complex AWGN vector. Basic ZFequalization performed in the frequency-domain as,

ψZF = G−1 · Ωψ = Ωλ +G−1Ωγ. (25)

After performing IFFT for the each stream individually, wecan obtain the estimates of the transmission vectors and easilydetermine the indices of the active LEDs by comparing thecorresponding elements of (x+R, x

−R) and (x+I , x

−I ) vector pairs

for each subcarrier. Error performance of the proposed systemin the presence frequency-selective channels is investigated inSection V.


M-QAM

Mod.N-IFFT

NFFT

𝐱𝐑+

𝐱𝐑−

𝐱𝐈+

𝐱𝐈−

Τℜ ℑCombiner

MQAMDemod.

MIMOOpticalChannel

ෝ𝑚ො𝑛

ො𝐱𝑇ො𝐱𝐹ෝ𝐮

𝐮 𝐱𝐹 𝐱𝑇

𝐲𝟏

𝐲𝟐

𝐲𝟑

𝐲𝟒

𝐆

CP

CP

CP

CP

CP

CP

CP

CP

N-FFT

N-FFT

N-FFT

N-FFT

ZFDet.

𝐲F,1

𝐲F,2

𝐲F,3

𝐲F,4

N-IFFT

N-IFFT

N-IFFT

N-IFFT

Ind.Det.

𝐱𝐑+

𝐱𝐑−

𝐱𝐈+

𝐱𝐈−

Ƹ

Ƹ

Ƹ

Ƹ

LEDIndexMod.

Fig. 2. Block Diagram of the extended GLIM-OFDM Scheme for a 4 × 4 frequency-selective MIMO VLC channels

IV. PHYSICAL VLC CHANNEL MODELS

Determining the channel impulse response (CIR) in VLCsystems is a challenging task since the received power isclosely related to the channel link design. We want that theloss incurred in the optical channel is to be made as smallas possible as in an effort to reduce the transmission powerand to facilitate the use of simple and low-power receivers.To evaluate the received power, a commonly deployed VLCchannel model in earlier works [22–24] focuses on scenarioswhere channel gains are obtained with a limited number ofreflections (i.e., up to second order) specifically consideringzero order reflections (i.e., line-of-sight (LOS) response). Inthese studies, the analytical channel gains can be expressed as

hr,t =

(m+1)ArRp

2πd2r, t

cosm(φr,t

)cos

(ψr,t

), 0 ≤ ψr,t ≤ Ψ1/2

0, ψr,t > Ψ1/2(26)

where Ar denotes the photo-detector (PD) area, dr,t denotesthe distance between the corresponding LED and PD pair,Rp is the responsivity of the PD and assumed to be unity inthis study. Additionally, φr,t and ψr,t represent the angle ofirradiance and the angle of incidence, respectively, and m =− ln 2/ ln(cosΦ1/2) is the order of Lambertian emission, whereΦ1/2 denotes the semi-angle of the LED. Ψ1/2 is the field-of-view (FOV) semiangle of the PD. Since the effect of higherorder reflections is not taken into account in (26), the receivedpower is underestimated in this model.

The above channel model is limited to the assumption of aLambertian source and does not take into account the effectof reflections. Hence, a physical channel modeling approach isadopted in [1] that utilizes the ray-tracing based approaches.Ray-tracing takes the characteristics of propagation environ-ment (i.e., presence of human beings, objects, etc), lightsources (i.e., beamform) and detectors (i.e., rotation, field-of-view etc) into account precisely.

A. Frequency-Flat MIMO VLC Channels

In this study, we consider a 4 × 4 MIMO-VLC systemthat is operating in a 5 m × 5 m × 3 m typical room asillustrated in Fig. 3 with plaster ceiling/walls and a pinewood

floor. We model the table as a CAD object with coatingmaterial of pinewood. We assume four luminaries on theceiling with equidistant spacing of 2 m. In [25], the idealcase of 100 LED chips per each luminary is considered, whileby taking advantage of the simplification method [26], lessnumber of LED chips can be used to achieve the same channelparameters. Based on [26], we adopt the configuration inwhich a LED luminary array with the size of 0.6 m × 0.6m is employed consisting of 9 LED chips and each LED chipradiates 5 W with a view angle of 120°. This satisfies thetypical illumination levels for office environment [27]. Thefield-of-view (FOV) semi-angle and area of the PD are 85°and1 cm2, respectively. The PDs are located at a height of 0.8m, which is the standard height of a table. Coordinates ofthe luminaries and PDs are given in Table I for two differentconfigurations named as Config A (PDs are in the center of thetable with equidistant spacing of 0.1 m) and Config B (PDsare at the corners of the table with equidistant spacing of 0.8m). Luminaries and PDs are assumed to be facing verticallydownward to the floor and upward to the ceiling, respectively.

Based on the given scenarios and by taking advantage of theadvanced ray tracing features of the optical design software,we calculate the detected power and path lengths from sourceto detector for each ray. These parameters are used to obtainthe CIRs between each luminary and PD, and expressed as [1]

h(t) =Nr∑i=1

Piδ(t − τi) (27)

where Pi is the optical power of the ith ray, τi is thepropagation time of the ith ray and Nr is the number of raysreceived at the detector. Once we obtain CIRs, the fundamentalchannel parameters can be computed. Truncation time (Ttr ) isdefined as ∫ Ttr

0h(t)dt = 0.97

∫ ∞

0h(t)dt (28)

which denotes the region of CIR with the most energy con-centrated. While the above formula assumes 97 % of the totalenergy in the calculation, other percentages can be also chosenbased on the application. Channel DC gain (H0), root-mean-square (RMS) delay spread (τRMS) and mean delay spread


Fig. 3. Configuration A (Receivers in the center of the table) and B (Receivers at the corners of the table).

TABLE I. Physical parameters of the simulation environment

Parameters Values

Dimensions of the Room (W × L ×H) 5 m × 5 m × 3 m

Number of Luminaries 4

Number of LED Chips per Luminary 9

Model of LED Chips Cree Xlamp MC-E White

Power of LED Chips 5 W

Luminary (L) Positions (x, y, z) (m) L1: (-1.3, -0.7, 3) L2: (-1.3, 1.3, 3) L3: (0.7, 1.3, 3) L4: (0.7, -0.7, 3)

Photodetector (PD) Positions (x, y, z) (m)Conf A: PD1: (-0.05, -0.05, 0.8) PD2:(-0.05, 0.05, 0.8)

PD3: (0.05, 0.05, 0.8) PD4: (0.05, -0.05, 0.8)

Conf B: PD1: (-0.4, -0.4, 0.8) PD2: (-0.4, 0.4, 0.8)

PD3: (0.4, 0.4, 0.8) PD4: (0.4, -0.4, 0.8)

Viewing angle of Luminary 120

FOV semiangle of PD (degrees) 85

Area of PD 1 cm2

MaterialsWalls & Ceiling: Plaster

Floor & Desk: Pine Wood

(τ0) are also important parameters of a VLC channel, whichcan be defined as [28],

H0 =∫∞

0 h(t)dt,

τRMS =

√ ∫∞0 (t−τ0)2h(t)dt∫∞

0 h(t)dt,

τ0 =∫∞

0 t ·h(t)dt∫∞0 h(t)dt

.

(29)

The analytical channel gains for Configs A and B byconsidering the parameters given in the Table I are calculatedrespectively as follows:

HaA ≈ 10−5 ×

*....,

0.3489 0.3288 0.3104 0.32880.3288 0.3489 0.3288 0.31040.3104 0.3288 0.3489 0.32880.3288 0.3104 0.3288 0.3489

+////-

HaB ≈ 10−5 ×

*....,

0.4984 0.3005 0.2008 0.30050.3005 0.4984 0.3005 0.20080.2008 0.3005 0.4984 0.30050.3005 0.2008 0.3005 0.4984

+////-

.

Similarly, physical indoor VLC channel gains obtained forConfigs A and B by using our methodology and given pa-

rameters in Table I are as

HpA ≈ 10−5 ×

*....,

0.4866 0.4822 0.4533 0.48220.4822 0.4866 0.4822 0.45330.4533 0.4822 0.4866 0.48220.4822 0.4533 0.4822 0.4866

+////-

HpB ≈ 10−5 ×

*....,

0.6533 0.3955 0.3066 0.39550.3955 0.6533 0.3955 0.30660.3066 0.3955 0.6533 0.39550.3955 0.3066 0.3955 0.6533

+////-

.

The channel parameters for HpA and Hp

B are summarizedin Table II. It is observed that the channel gains obtainedwith the analytical method (i.e., LOS response) are smallerthan those ones obtained by the physical method. As a resultof this, we can take the effect of higher order reflectionsinto consideration in our methodology. Since the detectors areplaced at the corner sides of the table in Config B, they receivemore scattering from walls and therefore, the difference ofanalytical and physical channel gains increases with respectto that one in Config A.

TABLE II. Channel parameters for HpA and Hp

B

Configuration A(Receivers in Center, dRx = 0.1 m)

Configuration B(Receivers at the Corners, dRx = 0.8 m)

Channel Gain Ttr (ns) τ0 (ns) τRMS (ns) Ttr (ns) τ0 (ns) τRMS (ns)h1,1 40 14.22 10.18 37 12.40 8.98h1,2 40 14.44 9.79 40 15.22 10.40h1,3 40 14.52 9.84 42 17.28 11.23h1,4 40 14.44 9.79 40 15.22 10.40h2,1 40 14.44 9.79 40 15.22 10.40h2,2 40 14.22 10.18 37 12.40 8.98h1,3 40 14.44 9.79 40 15.22 10.40h2,4 40 14.52 9.84 42 17.28 11.23h3,1 40 14.52 9.84 42 17.28 11.23h3,2 40 14.44 9.79 40 15.22 10.40h3,3 40 14.22 10.18 37 12.40 8.98h3,4 40 14.44 9.79 40 15.22 10.40h4,1 40 14.44 9.79 40 15.22 10.40h4,2 40 14.52 9.84 42 17.28 11.23h4,3 40 14.44 9.79 40 15.22 10.40h4,4 40 14.22 10.18 37 12.40 8.98

B. Obtaining Frequency-Selective MIMO VLC Channels

In this subsection, we explain the methodology to obtainthe physical multi-path VLC channels. Environmental factors


such as humans inside the room, furniture structure includ-ing coating material types, location of the objects and thesources/detectors play a vital role on reflection and refractionpatterns. All of these material characteristics are taken intoaccount for higher order reflections and frequency-selectiveCIRs are acquired by employing the same methodology aspresented in the frequency-flat case.

For our investigations of the frequency-selective visiblelight channel models, we have used IEEE 802.15.7r1 refer-ence channel models obtained for manufacturing cells [29].In this configuration, six LEDs are located at the head ofthe robotic arm where they are located at the sides of acubical package. Each face of the cube is equipped withone transmitter ensuring 360 of coverage. The LEDs arecommercially available from Cree (MC-E) with non-idealLambertian pattern and a half viewing angle of 60. The FOVsemi-angle and the area of the detector are 35 and 1 cm2,respectively. Eight test points are also considered on the top ofthe cell boundaries. We select the CIRs between LED1, LED3,LED5 and LED6 as transmitters and D1, D3, D5 and D7 asreceivers (i.e., placed at the corners of cell boundaries). It isobserved that due to the delay difference in the VLC channelsunder consideration and the signaling rates higher than 100Mbits/sec, the multipath components are resolvable and can betreated as multi-tap channel leading to the frequency-selectivechannels. The resulting CIRs obtained for this configurationare given in the Appendix.

For the sake of reality, the sampling frequency fs for thechannel is taken as 100 MHz where the sampling period isTs = 10 ns. Since the maximum delay spread of the obtainedchannel is 60 ns, L = 6 taps frequency-selective VLC channelvectors are obtained by down-sampling. Length of the cyclicprefix in Section III is also chosen as Lcp = 6 in computersimulations to make sure that it equals to the maximum delayspread of the channel.

V. COMPLEXITY ANALYSIS AND COMPUTERSIMULATIONS

In this section, we present computational complexity anal-yses as well as the computer simulations to perform compar-isons with the reference schemes given in Table III.

A. Complexity Analysis

The details of the computational complexity of the proposedalgorithm is presented in Table III. For the GLIM-OFDMreceiver, to implement the conditional MAP algorithm forestimation of the real channel path gains in (16), it is necessaryto compute only C and D in (17). Since the channel isdeterministic and does not change with time, A, B and E canbe precomputed and stored in the receiver. Hence, it can beeasily checked that for all (m, n) pair where m = 1, 2 andn = 3, 4 for k = 1, 2, · · · , N values, 44N real multiplications(RM) and 16N real additions (RA)s are required. In addition,the computation of the MAP metric to determine the indices ofthe active LEDs requires 32N RM and 16N RA. On the otherhand, OFDM algorithm with an FFT size of N requires ap-proximately 4N log2(N ) real operations (multiplications plus

TABLE III. Comparison of MIMO systems

Modulation nR × nT Spectral Efficiency Optical Power, Ex ComplexityGLIM-OFDM 4x4 ∼ log2 M σ

2√π

∼ O(N log2 N

)e-GLIM-OFDM 4x4 ∼ log2 M σ

2√π

∼ O(N log2 N

)OSM-DCO-OFDM 4x4 ∼

log2(M ·nT )2

σ√2π

exp(−B2

2σ2 )+

B(1 −Q( Bσ ))

∼ O(N log2 N

)OSM-ACO-OFDM 4x4 ∼

log2(M ·nT )4

σ4√π

∼ O(N log2 N

)V-BLAST-ACO

OFDM4x4 ∼ log2 M σ

2√π

∼ O(N log2 N

)NDC-OFDM 4x4 ∼ log2(M · nT ) σ√

2π∼ O

(N log2 N

)

additions). Consequently, the overall complexity order in realoperations for GLIM-OFDM is 76N + 4N log2(N ) RM and32N + 4 log2(N ) RA, which makes ∼ O(N log2 N ).

To determine the computational complexity of e-GLIM-OFDM receiver, we refer to Fig. 2. Four N-FFT operations ofthe four received vectors (yF,k for k = 1, 2, 3, 4), require ap-proximately 16N log2(N ) real operations. The implementationof the following ZF detector in Fig. 2 requires approximately16N RM and 8N RA. The main reason is that the overallfrequency domain channel matrix G = [Gi, j] ∈ R4N×4N

is a 4 × 4 block matrix, in which each sub-block Gi, j ∈

G, for i, j = 1, 2, 3, 4 is a diagonal matrix. Since the channelsare deterministic and known to the receiver, G as well asG−1 can be pre-computed and stored at the receiver. Hence,the only computational complexity in implementing the ZFdetector comes from the multiplication of G−1 with the vectoryF = [yF,1, . . . , yF,4]T ∈ C4N . Moreover, from matrix algebra,it is known that the inverse of G is also a 4 × 4 blockdiagonal matrix. This property simplifies the computationalcomplexity substantially since the output of the ZF detec-tor can simply be determined by four separated reduced-dimensional matrix multiplications. Thus, the computationalcomplexity of the ZF detector is reduced from ∼ O(N2) to∼ O(N ). After ZF detector, four IFFT operations, to transformthe ZF detector output in the time-domain, requires again16N log2(N ) complex operations. After that, 32N RM and16N RA operations are required to determine the indicesof active LEDs and 4N log2(N ) operations required for theFFT procedure. Therefore, the overall complexity order in realoperations for e-GLIM-OFDM is 48N + 36 log2(N ) RM and24N + 36 log2(N ) RA, which makes ∼ O(N log2 N ).

Computational complexities of the GLIM-OFDM and e-GLIM-OFDM schemes are compared with the reference VLCsystems, such as parallel NDC-OFDM scheme, obtained bythe parallel concatenation of two 2× 2 NDC-OFDM schemes,[11], OSM-OFDM-ACO, OSM-OFDM-DCO schemes that arecombining optical spatial modulation (OSM) concept [30]with optical OFDM [31] methodology, and vertical Bell Labslayered space-time (V-BLAST) type OFDM-ACO scheme [32]in Table III. When a similar complexity analysis is carriedout for the above schemes, it is concluded that all the refer-ence systems have asymptotically same complexity, namely,∼ O(N log2 N ), as shown in Table III.

B. Performance of GLIM-OFDM

In this subsection, we provide BER performance compar-isons between the GLIM-OFDM scheme and the reference


35 40 45 50 55 60 65 70 75 80 85 90

SNR (dB)

10-4

10-3

10-2

10-1

100B

ER

OSM-DCO, M=4, B=7dBOSM-DCO, M=16, B=7dBOSM-DCO, M=64, B=13dBNDC-OFDM, M=4NDC-OFDM, M=8NDC-OFDM, M=16V-BLAST-ACO, M=4V-BLAST-ACO, M=8V-BLAST-ACO, M=16OSM-ACO, M=64GLIM-OFDM, M=4GLIM-OFDM, M=8GLIM-OFDM, M=16

Fig. 4. BER performance comparison of optical MIMO-OFDM schemes for2 (straight), 3 (dashed) and 4 (dotted) bits/s/Hz in analytic channel Ha

A.

15 20 25 30 35 40 45 50 55 60 65 70

SNR (dB)

10-4

10-3

10-2

10-1

100

BE

R


Fig. 5. BER performance comparison of optical MIMO-OFDM schemes for2 (straight), 3 (dashed) and 4 (dotted) bits/s/Hz in physical channel Hp

A.

TABLE IV. Pearson’s correlation coefficient values for channel configurations

Channel Configuration r

HaA 0.0236

HpA 0.0114

HaB 0.1982

HpB 0.1777

HpC 0.3878

systems with respect to average received electrical SNR. Spec-tral efficiencies and optical powers of the reference systemsare given in the Table III where B is the DC bias value forDCO-OFDM. In our comparisons, BER vs. SNR performancecurves are presented for the spectral efficiency values of 2,3 and 4 bit/sec/Hz in various VLC channel configurations,where the number of subcarriers is taken as N = 256.

In Figs. 4 and 5, the BER performance of the proposed

0 10 20 30 40 50 60

SNR (dB)

10-4

10-3

10-2

10-1

100

BE

R


Fig. 6. BER performance comparison of optical MIMO-OFDM schemes for2 (straight), 3 (dashed) and 4 (dotted) bits/s/Hz in analytic channel Ha

B.

0 10 20 30 40 50 60

SNR (dB)

10-4

10-3

10-2

10-1

100

BE

R



B.

system is compared with other reference MIMO systems forthe Config A (dTx = 0.1 m). It can be inferred from thesefigures that GLIM-OFDM outperforms the other referencesystems in Fig. 4, whereas this is not the case indicated by thecurves in Fig. 5. This can be explained as follows. The BERperformance of the GLIM-OFDM system is highly dependenton the correlation between diagonal (LOS/direct) and off-diagonal (NLOS/indirect) elements of the channel matrix. Ithas excellent BER performance when the channel matrix isclose to diagonal. Given the entries of the channel matrix,to determine how being "close" to the diagonal, a naturalapproach is to compute the correlation coefficient, r , betweenthe rows and columns of the channel matrix. Strong correlationmeans that r is close to one and the matrix entries tend to benear the diagonal. This is also robust, since the correlationcoefficient is unchanged if the channel matrix is scaled. Thecorrelation values in Table IV show that the channel matrices


Fig. 8. Configuration C (Receivers are aligned to their correspondent LEDsto have stronger LOS link with a less correlation).

of the different configurations considered in our computersimulations can be classified basically into three differentchannel structures. Such that, Ha

A and HpA have the weakest

correlation values and consequently, they are far from beingclose to a diagonal matrix structure. On the other hand, as Hp

Aand Hp

B can be considered having a modest diagonal structure,and the last channel matrix Hp

C in Table IV shows a strongdiagonal structure.

Based on this explanation, we can firmly state that thecurves presented in Fig. 4, obtained for Ha

A, indicate that muchbetter performance can be obtained for GLIM-OFDM thanthe other systems, while they yield similar performances forHp

A as shown in Fig. 5. According to Table IV, the channelcoefficients of Ha

A and HpA are very similar to each other

and far from having a diagonal structure. Consequently, theirBER performances are affected dominantly by the detectionerrors of the indices. On the other hand, the other referencesystems in the presence of these channels are also undersimilar effects depending on their system structures. As aresult, our extensive simulation studies have shown that suchperformance differences occur between GLIM-OFDM and theother schemes as indicated in Figs. 4 and 5. In Figs. 6 and 7,we compare the proposed system with other reference MIMOsystems in the presence of the analytical and physical channelconfigurations Ha

B and HpB, which have a modest diagonal

structure with dTx = 0.8 m (Config B). The results presentedin these figures show that the GLIM-OFDM scheme providesbetter BER performance than any other system with thesame spectral efficiency. Since the proposed MAP estimatorof GLIM-OFDM takes a-priori information into account, italways produces non-negative estimates based on the assump-tion that the signal has a unipolar p.d.f.

We now consider a modified implementation scenario forConfig A (dTx = 0.1 m) to make it more suitable for the MAPestimator by introducing a slight tilt on the PDs. In realisticVLC application scenarios, due to the random orientationsof mobile terminals, PD’s are considered to be located invarious positions and tilts (receivers around laptop screen or

0 5 10 15 20 25 30 35 40 45

SNR (dB)

10-4

10-3

10-2

10-1

100

BE

R



C.

on the aircraft seats etc.), resulting in the average channelmatrix close to diagonal. Hence, on average, the performanceof the proposed GLIM-OFDM is improved substantially whencompared to the other schemes.

In Fig. 8, a specially designed VLC structure is shown, toincrease the power of the LOS links. In this design, the PDs arerotated 45 in the xy-plane and tilted 60 in the yz-plane. As aresult, the Config C provides an increase in LOS link strengthand hence, an increase in the correlation coefficient r of thechannel matrix to make it more diagonal. The correspondingchannel matrix, which is obtained by the physical model, canbe given as

HpC ≈ 10−5 ×

*....,

0.5555 0.1866 0.1222 0.18660.1866 0.5555 0.1866 0.12220.1222 0.1866 0.5555 0.18660.1866 0.1222 0.1866 0.5555

+////-

.

In Fig. 9, GLIM-OFDM is compared with other MIMOreference systems for 2, 3 and 4 bits/sec/Hz spectral effi-ciencies for the physical channel model of Config C withdTx = 0.1 m. The simulation results presented in Fig. 9indicate that the proposed system uniformly outperforms of allother systems. Finally, in Fig. 10, the MSE vs. SNR curvesare shown for GLIM-OFDM by employing both analyticaland physical channel matrices. Moreover, theoretical MSEvalues are compared with the computer simulation results.We conclude from Fig. 10 that the theoretical and computersimulation curves match considerably well especially at highSNR values.

C. Performance of e-GLIM-OFDM

In this subsection, we present BER performance results ofthe e-GLIM-OFDM scheme. In Fig. 11, BER versus SNRcurves are given for the e-GLIM-OFDM system operatingat 2, 3 and 4 bits/sec/Hz spectral efficiency values in thepresence of frequency-selective MIMO channels with six taps,which was described in Section IV-B. As seen from Fig. 11,


0 10 20 30 40 50 60 70 80SNR (dB)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100M

SE GLIM-OFDM MSESimulation, M=4, N=256, Ha

A

GLIM-OFDM MSEAnalytical, HaA

GLIM-OFDM MSESimulation, M=4, N=256, HaB

GLIM-OFDM MSEAnalytical, HaB

GLIM-OFDM MSESimulation, M=4, N=256, HpA

GLIM-OFDM MSEAnalytical, HpA

GLIM-OFDM MSESimulation, M=4, N=256, HpB

GLIM-OFDM MSEAnalytical, HpB

GLIM-OFDM MSESimulation, M=4, N=256, HpC

GLIM-OFDM MSEAnalytical, HpC

HAa and HA

p

HBa and HB

p

HCp

Fig. 10. Analytical and simulated MSE comparison for analytic channels, HaA,

HaB and physical channels Hp

A, HpB, Hp

C.

10 15 20 25 30 35 40 45

SNR (dB)

10-4

10-3

10-2

10-1

100

BE

R

e-GLIM-OFDM, M=4e-GLIM-OFDM, M=8e-GLIM-OFDM, M=16

Fig. 11. BER performance of the enhanced-GLIM-OFDM (e-GLIM-OFDM)in frequency-selective MIMO VLC channels for 2 (straight), 3 (dashed) and4 (dotted) bits/s/Hz.

the enhanced scheme also achieves similar BER performancecompared to the first proposed scheme, which was operatingover flat VLC channels. Since the proposed method takesthe advantage of time and frequency domain transitions (byemploying FFT/IFFT pair twice) and ZF equalizations, it caneasily cope with both the inter-LED-interference (ILI) and ISI.

According to the computer simulation results, we canconclude that e-GLIM-OFDM is a feasible solution for themulti-path VLC channels. Since there do not exist any otherfrequency-selective MIMO-VLC based system in the litera-ture, comparison with a reference system is not possible forthe frequency-selective scenarios.

VI. CONCLUSIONS

VLC technologies, as well as the index modulation con-cept for MIMO systems, such as SM and subcarrier index

modulation for OFDM are gaining noticeable attention for thenext generation of wireless standards. In this paper, we haveproposed two novel and spectral efficient 4 × 4 LED indexmodulation based optical MIMO-OFDM systems with MAPestimation, where the first scheme is operating in frequency-flat channels and the second one in frequency-selective chan-nels. The proposed schemes offer twice the spectral efficiencyas that of DCO-OFDM by exploiting the advantage of LEDindex modulation to avoid Hermitian symmetry and DC bias.

For the error performance analysis, five different physicalchannel models have been obtained. It has been concluded thatthe first proposed system yields the best BER performancein the lowest correlated and almost diagonal case of thechannel matrix. In this particular model, the channel hasbeen diagonalized by directed LEDs to PDs to obtain themost powerful LOS links. Among the other two physical andanalytical models, the system has superior performance inthe presence of analytical channel gains (i.e., LOS channel).This is mainly due to the fact that highly correlated physicalchannel gains degrade the performance of the MAP estimatorto the level where it performs almost the same as the 4 × 4NDC-OFDM system. Finally, we conclude from the computersimulations that the BER performance of the second designedVLC system does not significantly affected by the degree offrequency selectivity of the channel, while retaining its spectralefficiency advantage over other MIMO-OFDM based VLCsystems.

APPENDIXFREQUENCY SELECTIVE CIRS

g1,1 ≈ 10−8 × [2.5107 1.3290 4.2021 5.2421 0.9347 0.4133]T ,g1,2 ≈ 10−8 × [13.869 4.3617 2.3950 0.4165 0.5569 0.2852]Tg1,3 ≈ 10−8 × [0.2502 2.5546 1.1561 1.0689 0.6099 0.5570]T ,g1,4 ≈ 10−8 × [16.220 4.4067 3.2170 1.6950 0.7968 0.2426]Tg2,1 ≈ 10−8 × [3.8362 1.2489 1.9733 2.8366 1.0588 0.7232]T ,g2,2 ≈ 10−8 × [257.69 9.0081 1.7300 2.9421 2.1824 0.2493]Tg2,3 ≈ 10−8 × [0.1758 3.5579 5.0503 1.2249 0.6706 0.2167]T ,g2,4 ≈ 10−8 × [127.47 10.155 0.1015 3.5622 2.7293 0.7926]Tg3,1 ≈ 10−8 × [130.23 8.0788 3.1797 1.7479 1.7082 0.3576]T ,g3,2 ≈ 10−8 × [0.1044 0.1007 0.6197 1.5607 0.5474 0.2261]Tg3,3 ≈ 10−8 × [0.4087 0.1467 3.0861 2.5029 0.3504 0.5618]T ,g3,4 ≈ 10−8 × [0.4368 2.9358 2.1694 2.1221 0.5044 0.4179]Tg4,1 ≈ 10−8 × [0.3185 6.2577 3.0124 0.9103 0.9437 0.4686]T ,g4,2 ≈ 10−8 × [5.1500 1.0373 1.9243 0.5546 0.1538 0.0613]Tg4,3 ≈ 10−8 × [0.4588 1.9667 3.4924 1.6399 0.6069 0.1007]T ,g4,4 ≈ 10−8 × [0.3313 13.331 2.8363 5.8317 1.4873 0.3917]T

ACKNOWLEDGMENT

We would like to thank the anonymous reviewers for theirconstructive and valuable comments, which improved thequality of paper substantially.

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Anil Yesilkaya (S’11) received the B.Sc. (first classhonors) and M.Sc. degrees in electronics engineeringfrom the Kadir Has University, Istanbul, Turkeyin 2014 and 2016, respectively. He is currentlypursuing the Ph.D. degree at the Institute for Dig-ital Communications (IDCOM), The University ofEdinburgh. His current research interests includemultiple-input multiple-output visible light commu-nications and LiFi-based networking for aeronauticalcabin applications.

Ertugrul Basar (S’09, M’13, SM’16) received theB.S. degree with high honors from Istanbul Uni-versity, Turkey, in 2007, and the M.S. and Ph.D.degrees from Istanbul Technical University in 2009and 2013, respectively. He spent the academic year2011-2012 at the Department of Electrical Engineer-ing, Princeton University, New Jersey. He was anassistant professor at Istanbul Technical Universitybetween 2014 and 2017. Currently, he is an associateprofessor of Electronics and Communication Engi-neering at the same university. He was the recipient

of Istanbul Technical University Best Ph.D. Thesis Award in 2014 and has wonthree Best Paper Awards including one from IEEE International Conferenceon Communications (ICC 2016). He currently serves as an Associate Editor forIEEE COMMUNICATIONS LETTERS and IEEE ACCESS. He is also a regularreviewer for various IEEE journals, and has served as a TPC member forseveral conferences. His primary research interests include MIMO systems,index modulation, cooperative communications, OFDM, and visible lightcommunications. He is a senior member of IEEE and an inventor of twopending patents on index modulation schemes.

Farshad Miramirkhani (M’13) received his B.Sc.and the M.Sc. degree with high honors in elec-tronics and communication engineering from Uni-versity of Isfahan, Isfahan, Iran, in 2011 and 2014,respectively. He joined Communication Theory andTechnologies (CT&T) Research Group as a researchassistant working toward his doctorate under super-vision of Prof. Murat Uysal at Ozyegin University,Istanbul, Turkey, in 2014. The LiFi channels devel-oped by Prof. Murat Uysal and Mr. Miramirkhaniwere selected as the "LiFi Reference Channel Mod-

els" by the IEEE 802.15.7r Task Group during the IEEE’s latest meetingheld in Bangkok, Thailand, in September 2015. His current research interestsinclude optical wireless communications, indoor visible light communications,underwater visible light communications and channel modeling. He has servedas a reviewer for several prestigious journals and conferences for IEEE andOSA societies.


Erdal Panayirci (M’80-SM’91-F’03-LF’06) re-ceived the Diploma Engineering degree in ElectricalEngineering from Istanbul Technical University, Is-tanbul, Turkey and the Ph.D. degree in ElectricalEngineering and System Science from MichiganState University, USA. Until 1998 he has been withthe Faculty of Electrical Engineering at IstanbulTechnical University, where he was a Professor andHead of the Telecommunications Chair. Currently,he is professor of electrical Engineering and head ofthe electrical and electronics engineering department

at Kadir Has University, Istanbul, Turkey. Dr. Panayirci’s recent researchinterests include communication theory, advanced signal processing tech-niques and their applications to wireless electrical, underwater and opticalcommunications. He has published extensively in leading scientific journalsand international conference and co-authored the book Principles of IntegratedMaritime Surveillance Systems (Boston, Kluwer Academic Publishers, 2000).He has been the principal coordinator of a 6th and 7th Frame European projectcalled NEWCOM (Network of Excellent on Wireless Communications) andWIMAGIC Strep project for two years, representing Kadir Has University.Prof. Panayirci was an Editor for IEEE Transactions on Communications inthe areas of Synchronizations and Equalizations in 1995-2000. He served asa Member of IEEE Fellow Committee in 2005-2008. He was the TechnicalProgram Co-Chair of the IEEE International Conference on Communications(ICC-2006) and the Technical Program Chair of the IEEE PIMRC held inIstanbul, Turkey both held in Istanbul in 2006 and 2010, respectively. He wasthe Executive Vice Chairman of the upcoming IEEE Wireless Communica-tions and Networking Conference (WCNC) held in Istanbul in April 2014.Currently he is a member of IEEE GLOBECOM/ICC Management & Strategy(GIMS) Standing Committee and Head of the Turkish Scientific Commissionon Signals and Systems of URSI (International Union of Radio Science).

Murat Uysal (M’98-SM’07) received the B.Sc. andthe M.Sc. degree in electronics and communica-tion engineering from Istanbul Technical University,Istanbul, Turkey, in 1995 and 1998, respectively,and the Ph.D. degree in electrical engineering fromTexas A&M University, College Station, Texas, in2001. He is currently a Full Professor and Chairof the Department of Electrical and ElectronicsEngineering at Ozyegin University, Istanbul, Turkey.He also serves as the Founding Director of Centerof Excellence in Optical Wireless Communicaion

Technologies (OKATEM). Prior to joining Ozyegin University, he was atenured Associate Professor at the University of Waterloo, Canada, wherehe still holds an adjunct faculty position. Dr. Uysal’s research interests arein the broad areas of communication theory and signal processing with aparticular emphasis on the physical layer aspects of wireless communicationsystems in radio and optical frequency bands. He has authored some 270journal and conference papers on these topics and received more than7000 citations. Prof. Uysal currently serves on the editorial board of IEEETransactions on Wireless Communications. In the past, he was an Editorfor IEEE Transactions on Communications, IEEE Transactions on VehicularTechnology, IEEE Communications Letters, Wiley Wireless Communicationsand Mobile Computing (WCMC) Journal, Wiley Transactions on EmergingTelecommunications Technologies (ETT), and Guest Editor of IEEE JSACSpecial Issues on Optical Wireless Communication (2009 and 2015). He wasinvolved in the organization of several IEEE conferences at various levels.He served as the Chair of the Communication Theory Symposium of IEEEICC 2007, Chair of the Communications and Networking Symposium ofIEEE CCECE 2008, Chair of the Communication and Information TheorySymposium of IWCMC 2011, TPC Co-Chair of IEEE WCNC 2014 andGeneral Chair of IEEE IWOW 2015. Over the years, he has served on thetechnical program committee of more than 100 international conferences andworkshops in the communications area. His distinctions include the MarslandFaculty Fellowship in 2004, NSERC Discovery Accelerator SupplementAward in 2008, University of Waterloo Engineering Research ExcellenceAward in 2010, Turkish Academy of Sciences Distinguished Young ScientistAward in 2011 and Ozyegin University Best Researcher Award in 2014 amongothers.

Harald Haas (S’98-AM’00-M’03-SM’17) receivedthe Ph.D. degree from the University of Edinburgh,Edinburgh, U.K., in 2001. He is currently the Chairof Mobile Communications at the University ofEdinburgh, and is the Founder and Chief ScientificOfficer of pureLiFi Ltd, Edinburgh, U.K., and theDirector of the LiFi Research and DevelopmentCenter, University of Edinburgh. His main researchinterests include optical wireless communications,hybrid optical wireless and RF communications,spatial modulation, and interference coordination in

wireless networks. He first introduced and coined spatial modulation and LiFi.LiFi was listed among the 50 best inventions in TIME Magazine 2011. Hewas an Invited Speaker at TED Global 2011, and his talk: Wireless Datafrom Every Light Bulb has been watched online more than 2.4 million times.He gave the second TED Global lecture in 2015 on the use of solar cells asLiFi data detectors and energy harvesters which was viewed online more than1.7 million times. He holds 43 patents and has more than 30 pending patentapplications. He has published 400 conference and journal papers includinga paper in Science. He coauthors a book entitled: Principles of LED LightCommunications Towards Networked Li-Fi (Cambridge Univ. Press, 2015).He was a co-recipient of recent Best Paper Awards at the IEEE VehicularTechnology Conference (VTC-Fall) in Las Vegas in 2013, and VTC-Springin Glasgow in 2015. He was a co-recipient of the EURASIP Best Paper Awardfor the Journal on Wireless Communications and Networking in 2015, anda co-recipient of the Jack Neubauer Memorial Award of the IEEE VehicularTechnology Society. In 2012, he received the prestigious Established CareerFellowship from the Engineering and Physical Sciences Research Councilwithin Information and Communications Technology in the U.K. He receivedthe Tam Dalyell Prize 2013 awarded by the University of Edinburgh forexcellence in engaging the public with science. In 2014, he was selectedby EPSRC as one of ten Recognizing Inspirational Scientists and EngineersLeaders in the U.K. In 2016 he was recipient of the Outstanding AchievementAward of the International Solid State Lighting Alliance (ISA), and 2017 hewas elected Fellow of the Royal Society of Edinburgh.

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