1

A Multiuser MIMO Indoor Visible LightCommunication System Using Spatial Multiplexing

Jie Lian, Student Member, IEEE, and Maıte Brandt-Pearce, Senior Member, IEEE

Abstract—Visible light communications is an energy efficientand cost effective solution for indoor wireless access. In thispaper, we propose a multiple input multiple output systemusing a centralized or decentralized transmitted power allocationalgorithm for supporting multiple users with multiple LEDs andphotodetectors. In the centralized power allocation algorithm, allthe LED lamps in the room are coordinated and controlled by acentral controller; each LED lamp supports all the users withinthe indoor area. The decentralized power allocation algorithmswe propose have similar bit error rate performance and lesscomputational burden compared to the centralized algorithm.In our decentralized algorithms, users are supported by asubset of the LEDs, and so the optimization problem size ofthe decentralized algorithms can be reduced, by as much as93%. For each receiver, multiple photodetectors with differentorientations are employed to improve the signal to interferenceplus noise ratio. In addition, some practical considerations suchas shadowing effects, illumination requirements, dimming controland transmitted power quantization are taken into account. Fromthe numerical results, the proposed adaptive power allocationalgorithms can adjust the transmitted power to reduce shadowingeffects. Furthermore, the transmitted power can be dimmed tosatisfy the illumination requirements within a range of tolerance.In this paper, the system uses an optical code division multipleaccess technique to support multiple users. Minimum meansquared error filters at the receivers are designed to diminish theeffect of multiple-access interference in the indoor VLC system.

Index Terms—Visible light communications, optical wirelesscommunications, MIMO, CDMA, power allocation, shadowingeffects, dimming control, computational burden, multiple accessinterference

I. INTRODUCTION

W ITH the rapid development of hand-held technology,high data rate wireless transmission has played a more

significant role in our daily lives. Since the radio frequency(RF) spectrum is so congested, and the data transmission rateof RF communications cannot satisfy the huge demand forlarge data transmission, visible light communication (VLC)has emerged as a possible new technology for next generationcommunications. VLC can easily be employed in indoor envi-ronments such as offices, homes, hospitals, airplanes and con-ference rooms [1]. VLC systems in which white light emittingdiodes (LEDs) are used as transmitters for communicationscan become the dominant indoor communication method due

This work was funded in part by the National Science Foundation (NSF)through the STTR program, under award number 1521387.

The authours are with Charles L. Brown Department of Electrical andComputer Engineering, University of Virginia Charlottesville, VA 22904.(Email:jl5qn@virginia.edu;mb-p@virginia.edu)

to their many advantages over RF communications [1], [2].VLC systems are built as dual use systems (illumination anddata transmission), and have a higher degree of security thanRF communication systems. In addition, LEDs are energyefficient light sources and have a long life expectancy [3].

In indoor VLC systems, one significant research challengethat has received some attention in recent years is how tosupport multiple users with high data rates while limitingthe multiple access interference (MAI). So far, three popularresearch trends have emerged. Multiple input and multipleoutput (MIMO) with precoding techniques were proposed tolimit the MAI and improve the signal to interference pulsenoise ratio (SINR) in [4], [5] and [6]. The second trendis to use color-shift-keying modulation over red-green-blue(RGB) LEDs and code division multiplexing access (CDMA)to support multiple users [7]. The third direction is to useresource allocation schemes to minimize the MAI. In thethird trend, orthogonal frequency division multiple access(OFDMA) and discrete multi-tone (DMT) modulation withtransmitted power allocation algorithms to limit the MAI wereproposed in [8] and [9], respectively.

Due to the nature of white LEDs (their nonlinearity andthe incoherent light they transmit), it is not easy to imple-ment a modulation requiring frequency-domain processing. Toavoid this problem, intensity modulation and direct detection(IM/DD) with on-off keying (OOK) modulation is applied.Then, direct-sequence optical code division multiple access(OCDMA) and minimum mean squared error (MMSE) filterare used to support multiple users in indoor VLC systems,since it can be applied by simply turning the LEDs on andoff [10]–[12]. OCDMA has considerable advantages comparedwith the recently popular orthogonal frequency-division mul-tiplexing (OFDM) technique. Since OFDM has a high peak toaverage power ratio (PAPR), some signals with high intensitywould be distorted from the nonlinearity of the LEDs. OFDMis sensitive to the phase offset between transmitted signals; wecan easily coordinate transmitters from different lamps whenusing OCDMA. Furthermore, the structure for the receivers issimple for OCDMA systems in comparison with OFDM.

We recently proposed centralized and decentralized powerallocation schemes for a single photodetector (PD) receiverVLC systems in [13] and [14], respectively. A centralizedpower allocation scheme for a multi-detectors receiver systemis proposed in [15]. In this paper, we extend the multi-detectorapproach to four decentralized power allocation schemes. Inaddition, we take some practical designing requirements intoaccount, including shadowing effects, different illuminationrequirements, transmitted power quantization, and the trans-mitters beamwidth selection. Computational burden for the

2

Fig. 1. The structure of the multiple LED-array lamp, (a) side view, (b)bottom view.

centralized and decentralized schemes are compared.The algorithms we propose in this paper have the following

advantages compared with other approaches• All the transmitted power is used for both data trans-

mission and illumination (no extra light needed just forillumination).

• Compared with the OFDM technique, our algorithms donot need to address the high PAPR.

• No DC bias is needed for the transmitted signals.• The structures of transmitters and receivers are simple.

In addition, we propose to model the shadowing effects as pathlosses in this paper. Our adaptive algorithms can reallocate thetransmit power and recompute the MMSE filters coefficientsto reduce the shadowing effects with the help of MIMOprocessing.

The rest of the paper is organized as follows. The systemmodel is described in Section II. The centralized and decen-tralized power allocation algorithms are derived in Section III.Some practical considerations for the system are discussed inSection IV. Finally, the paper is concluded in Section V.

II. SYSTEM DESCRIPTION

In a typical VLC system, the white LED lamps work aslight sources for illumination purposes as well as transmittersfor wireless communications. Since the light from the LEDsis incoherent, IM/DD is applied in a typical VLC system. Inthis paper, OCDMA over an OOK modulation is employed tosupport multiple users.

A. Transmitter and Receiver model

In this paper, we use a multiple LED lamp model for ourMIMO VLC system, as shown in Fig. 1 [13]. In each lamp,there are multiple LEDs with different inclination angles foreach lamp, and each LED can be controlled separately. Weassume there are N lamps with Q LEDs each.

The receiver model we use is proposed in [15, Fig. 1]. Eachreceiver contains V PDs with different inclination angles.

B. VLC MIMO Channel Description

An indoor optical channel can be divided into line ofsight (LOS) and diffuse components [16]. In this paper, forthe room size and symbol rate we consider, the intersymbolinterference (ISI) is negligible [13]. Since the intensity ofthe light diminishes through absorption and diffusion, onlya single reflection is considered for the diffuse component.

Transmitter

LED

,qk qr l

1,qk kr z2,sk kr z

ds

difS

,qs qr l

,qs sr z

2,qk kr z

,sk sr z

Receiver

Fig. 2. Angles between the radiation direction and the paths to user

Using the multiple LEDs and multi-detector models, the LOSpart of the channel gain between the qth LED and vth detectorof the kth user can be written as [13]

h(0)qkv =

ReAr (m+ 1) cosm〈−→rqk,−→lq 〉 cos〈−→rqk,−→zkv〉

2πd2qk

. (1)

The once-reflected part can be described as

h(1)qkv =

‹Sref

ReAr (m+ 1) cosm〈−→rqs,−→lq 〉 cos〈−→rqs,−→zs〉

2πd2qs

cosm〈−→rsk,−→zs〉 cos〈−→rsk,−→zhv〉πd2

sk

ρds,

(2)

where Ar is the area of each PD, Sref is the area of thereflection surface in the indoor environment, ds is a differentialarea of the reflection surface, ρ represents the reflectioncoefficient. dqk is the distance between LED q and user k. −→rqsis the unit vector pointing from LED q towards the differentialarea of the reflection plane. Similarly, −→rqk and −→rsk are unitvectors pointing from LED q towards the kth user and from ds

to user k, respectively. In addition,−→lq represents the radiation

unit direction vector for the center of the beam from the qthLED. −→zs is the normal unit vector of ds. −→zkv represents thenormal unit vector for the vth detector of the kth user. In(1) and (2), the notation 〈x, y〉 represents the angle betweenvectors x and y. Fig. 2 illustrates this notation. In addition, Reis the responsivity of the detector, and m is the Lambertianmode of the light source, which is related to the LED’s halfpower semiangle Φ1/2 by m = − ln 2/ ln(Φ1/2).

The channel gain between the qth LED and vth detector ofuser k is given by

hqkv = h(0)qkv + h

(1)qkv. (3)

C. Transmitted and Received Signals

We assume that the indoor VLC network has N ×Q = NQLEDs with K users, and each user has V PDs with differentorientations. Let ik(t) be the signal that is intended for userk, which is represented as ik(t) = dk · ck(t), where dk isthe 0, 1 data for user k, and ck(t) is the OCDMA codewaveform for user k. The qth LED sends a linear combinationof the users’ data as

xq(t) =

K∑k=1

pqkik(t), (4)

3

where pqk ∈ [0, pmax] is the transmitted power of the qth LEDallocated to transmitting the data of user k. Assuming a peakradiation power limit of pmax, which is the maximum opticalpower radiated from each LED, the constraint

∑Kk=1 pqk ≤

pmax needs to be applied on the allocated powers. These powerlevels are organized in a NQ ×K matrix denoted as P. Eachelement in matrix P represents the power allocation from eachLED to a user.

After the indoor MIMO channel, the signal received by thevth detector of user k can be written as [13], [15]

r(v)k (t) =

NQ∑q=1

hqkvxq(t) + n(v)k (t),

k = 1, . . . ,K

v = 1, . . . , V(5)

where n(v)k (t) is the noise added to the vth detector of user

k. In this paper, shot noise from ambient light and thermalnoise are considered. The signal received by user k is a linearcombination of the signal from each detector, which can berepresented as

rk(t) =

V∑v=1

µkvr(v)k (t), (6)

where µkv is the weight assigned to the vth detector by thereceiver algorithm of user k.

After the MMSE filter for user k, wk, is applied, thereceived signal for user k can be represented in matrix formas [14]

yk = dTBkCwk + nTkwk, (7)

where d =(d(1), d(1), . . . d(K)

)is the data vector, and C

represents the OCDMA code matrix [15]. In this paper, weuse optical orthogonal code (OOC) as the OCDMA code. Tofacilitate the formulation, we define Bk = diag

((Hkuk)TP

),

where uk = (µk1, µk2, · · · , µkV )T and

Hk =

h1k1 h1k2 · · · h1kV

h2k1 h2k2 · · · h2kV

......

. . ....

hNQk1 hNQk2 · · · hNQkV

. (8)

III. CENTRALIZED AND DECENTRALIZED POWERALLOCATION SCHEMES

In this section, we describe a centralized power allocationalgorithm and several decentralized algorithms, all using themulti-detector model.

A. Centralized Multiple Detector Power Allocation Joint Op-timization (CM-PAJO)

For CM-PAJO, we modify the power allocation joint opti-mization (PAJO) algorithm in [13] to account for the multi-detector model. Each LED serves all the users in this indoorenvironment. In order to eliminate the MAI, each lamp needsto exchange information (channel information sent back fromusers) with other lamps and allocates power to the users jointly.

Following the derivation in [13], the SINR for user k canbe written as

SINRk =wTk CTBkEkΣdEkB

TkCwk

wTk CTBkAkΣdAkBT

kCwk + σ2wTk wk

, (9)

where Ek is defined as a matrix with a 1 in its (k, k)th elementand zeros in all other places, and Ak = I−Ek. Σd = EdTdis the correlation matrix for the data, and I is the identitymatrix. σ2 represents the noise variance. The bit error rate foruser k can be approximated by BERk ≈ Q

(√SINRk

).

To optimize the transmitted power allocation, we considertwo optimization criteria: to minimize the maximum BERamong all the users or to minimize the average of BERfor all the users. Through optimization, we obtain the powerallocation and received signal weights as

Fairness : [P∗,U∗] = arg minP,U

maxk

BERk (10)

orMin-BER : [P∗,U∗] = arg min

P,U

∑k

BERk, (11)

where U = (u1,u2, · · · ,uK). P∗ is the optimal powerallocation, and U∗ is the optimal receiver weight matrix. Inthe Appendix, we prove that every element µkv in U∗ satisfiesthe following property: ∃ x, s.t. µkx = 1 and µkv = 0 for allv 6= x.

The MMSE receiver in (7) and (9) can be derived as follows.The mean-squared error Jk for user k is defined as

Jk = Ed,n(dTBkCwk + nTkwk − dk)2, (12)

where Ed,n represents expectation with respect to the datavector d and the noise nk. Solving for ∂Jk

∂wk= 0, the MMSE

linear receiver wk can be obtained as

wk =(CTBkΣdBkC + σ2I

)−1CTBkqk, (13)

where qk = Ed · dk.

B. Decentralized Multiple Detector Power Allocation Algo-rithms

In a large room with many LED lamps, the centralizedalgorithm presented above becomes prohibitively complex. Inthis section, we describe four decentralized power allocationalgorithms better suited to such environments. For the de-centralized algorithms, we define a circular access area foreach lamp. This artificially defined access area is less than theactual illumination area of the lamps such that only the userswho are in the access area can be served by the lamp. Tocover the entire indoor area, there may be some overlap of theaccess areas from different lamps. Each user must be servedby at least one lamp, and each lamp can serve more than oneuser. For all the decentralized power allocation algorithms, themulti-detector receiver model is used to improve the SINR.

Unlike the centralized algorithm, the decentralized VLCoptimization can be divided into parallel optimization threads.For each optimization thread, the transmit power allocationand filter design work independently from other threads. Thereis no channel information exchange between the differentoptimization threads. In this section, without loss of generality,the ”Fairness” optimization criterion of (10) is used in eachthread; the ”Min-BER” criterion is easily derived using (11).For all techniques, the lamps must know the data and channelstate information for the users in its access area.

4

1) Decentralized Equal Power Allocation (DEPA): ForDEPA, each lamp works independently and allocates thetransmitted power equally to the users in its access area. Ifthere are no users in an access area, the transmitted power isused for lighting only. All the lamps must remain synchronizedsince a user may receive its signal from more than one lamp.

2) Power Allocation Disjoint Optimization (PADJO): Allthe lamps work independently in PADJO, and each lampoptimizes the power allocated to the users in its own accessarea. Since we assume there are N lamps in the indoorenvironment, there are N optimization threads, and all threadscan work in parallel. Similar to DEPA, there is no channel in-formation exchange between lamps. The optimization processcan be solved following (10). Note that all lamps must remainsynchronized.

3) Weighted Decentralized Multi-detector Power AllocationJoint Optimization (WDM-PAJO): For WDM-PAJO, all thelamps work independently. They need to know how manyaccess points serve each users, yet there is still no channelinformation exchange between lamps. Thus, there are Nthreads for WDM-PAJO. The SINR for each user can beweighted by λk to normalize for the extra power receivedby users that are served by multiple lamps. The algorithmcalculates

[P∗Ωi, U∗] = arg min

P,Umaxk∈Ωi

Q(√

λk · SINRk

), (14)

which is similar to the PADJO, except it accounts for thenumber of lamps that serve user k, denoted λk. Ωi representsthe ith WDM-PAJO optimization thread. P∗

Ωiand U∗ are the

optimal power allocation matrices for the lamps and receiverweights vectors for each user in the ith thread using WDM-PAJO, respectively.

4) Partial Decentralized Multi-detector Power AllocationJoint Optimization (PDM-PAJO): In PDM-PAJO, the lampsand users are divided into different optimization threads de-pending on users’ locations. Different from PADJO, the lampsthat serve the same users can exchange channel informationin PDM-PAJO. Therefore, the lamps that work together forman optimization thread.

Since the threads can be operated in parallel and inde-pendently, the computational burden of PDM-PAJO is muchlower than CM-PAJO. For a thread, the optimization processis similar to the CM-PAJO case, which can be described as

[P∗Ωi, U∗] = arg min

P,Umaxk∈Ωi

Q(√

SINRk

), (15)

where Ωi represents the ith PDM-PAJO optimization threadwhich contains some lamps and users, P∗

Ωiand U∗ are the

optimal power allocation matrices for the lamps and receiverweights vectors for each user, respectively, in the ith threadusing PDM-PAJO.

C. Performance Comparison

In this section, numerical results on the performance of theproposed system are shown. To test the applicability of thesystem in different environments, we show results for bothsmall and large rooms. The parameters used to obtain the

TABLE IPARAMETERS USED FOR INDOOR ENVIRONMENT

Number of lamps for small room 4Number of lamps for large room 25Number of LEDs in each lamp 25PD number per user 1, 4, 7Dimming parameters for all LEDs γ = 1Responsivity 0.5A/WArea of the PD 0.01 cm2

Wall reflection coefficient 0.8Radiation optical power of each lamp 300 mWLED semiangle 30o

Cyclic 7-length OOC code index [17] 1, 2, 4Cyclic 25-length OOC code index [17] 1, 2, 7 1, 3, 10

1, 4, 12 1, 5, 14Minimum access area am = 9.8 m2

Data rate 70 Mb/s

5 m

5 m

2.5 m

2.5

m

1.77 m

5 m

5 m

2.5 m

2.5

m

1.77 m

Case 1 Case 2

Fig. 3. Top-down view of the two typical user position cases for the smallroom. The small circles represent the lamps and the squares represent theusers.

numerical results are shown in Table I. This is a baseline forall the numerical results in this paper.

For a small indoor environment, we consider two typicallamp and user positions, which are shown in Fig. 3. In Case1, all the users are located in a corner near one of the lamps.In Case 2, all the users are distributed in the room. Thenumerical results for the BER using ”Fairness” and ”Min-BER” optimization criteria from (10) and (11) for Cases 1 and2 are shown in Fig. 4. The BER curves can be represented asa function of the peak radiation power to noise ratio (PPNR),

40 45 50 55 60 65

10−3

10−2

10−1

100

Peak radiation power to noise ratio (dB)

BE

R

Best BER user Min−BERWorst BER user Min−BERBest BER user FairnessWorst BER user Fairness

Case 1

Case 2

Fig. 4. BER performance using ”Fairness” and ”Min-BER” for Case 1 and2 for CM-PAJO with a single detector and 7-length OOC codes, in the smallroom.

5

12.5 m

12

.5 m

1.77 m

2.5

m

2.5 m

Fig. 5. Top-down view of the positions of lamps and users in a large indoorenvironment. The small circles represent the lamps and the squares representthe users.

0 10 20 30 40 5045

50

55

60

65

Number of users

Req

uire

d pe

ak ra

diat

ion

pow

er to

noi

se ra

tio (d

B)

CM−PAJO, 1−detectorPDM−PAJO, 1−detectorWDM−PAJO, 1−detectorCM−PAJO, 7−detectorPDM−PAJO, 7−detectorWDM−PAJO, 7−detectorDEPA, 1−detectorPADJO, 1−detector

400 lx illumination

Fig. 6. Peak radiation power to noise ratio (PPNR) required for a BER of10−3 in the large indoor environment using the minimum access area neededcover the room with 25-length OOC codes.

which is defined as pmax/σ2.1 Using the ”Fairness” criterion,the BER curves for all users are more similar than usingMin-BER criterion, as excepted. At a BER of 10−3, there isapproximately a 3 dB required transmitted power gap betweenthe best and worst-case users for Min-BER both in Cases 1 and2. Since the Min-BER method minimizes the average BER forall users, the average BER using Min-BER is slightly betterthan using ”Fairness”, by 1 dB. But when equal performanceis desired, the ”Fairness” method is preferable. Case 2 alwayshas a better BER than Case 1 because the users’ locationsmake better use of all lamps.

We compare the performance of the proposed CM-PAJOand our four decentralized algorithms with the multi-detectormodel. We test a large indoor environment described in Table Ito compare the CM-PAJO, PDM-PAJO, WDM-PAJO, PADJOand DEPA. The geometric position of the lamps and users areshown in Fig. 5. From the results in Fig. 6, the optimizedalgorithms do much better than DEPA in general showingthe advantage of resource optimization. CM-PAJO is theoptimal power allocation algorithm that can spend about 10dB less transmitted power than DEPA to achieve the sameBER performance. For decentralized algorithms, PDM-PAJOand WDM-PAJO only need 2 dB more power than the CM-PAJO to get the same BER. In addition, using 7 PDs can save

1Note that in VLC systems we use the transmitted power to receiver noiseratio as an SNR metric, instead of the normal received power to receiver noiseratio [13]–[15].

as much as 2 dB transmitted power for both centralized anddecentralized algorithms over single PD cases. If there is nobackground light, when the proposed VLC system satisfiesstandard in the room 400 lx illumination, 2 it can support upto 38 users when using the 7-detector CM-PAJO algorithm.

D. Computational Burden Comparison

The goal for seeking a decentralized power allocation al-gorithm is to reduce the computational burden of the cen-tralized algorithm, CM-PAJO, especially for a large indoorenvironment. To estimate the computational burden, we usethe maximum number of variables per thread (optimizationproblem size) as the metric. The variables to be calculated perthread are the power allocated from the LEDs to the users andthe combination weight of each detector, which are representedas pqk and µkv (defined in (4) and (6), respectively). The num-ber of variables in each thread is the size of the optimizationproblem, which implies the computational burden.

Since in CM-PAJO all lamps need to share the channelfeedback information from all the users and work together tosolve for the power allocation, there is only one optimizationthread. Therefore, the optimization problem size for CM-PAJOcan be derived as

ΛCM = (NQ + V )K. (16)

Since the proposed decentralized algorithms use parallelprocessing, the computational burden per thread for themis much lower than for CM-PAJO. The actual optimizationproblem size depends on the users’ positions in the indoorenvironment. In this paper, we consider the users to be uni-formly distributed in the indoor environment. The optimizationproblem size of the decentralized algorithms is also a functionof the access area a. In this paper, the access area of all lampsare assumed equal.

For DEPA, the transmitted power for each user is the same.Thus, the optimization problem size is smaller than the otherdecentralized algorithms because there is no need to calculatethe transmitted power for each user, only the combinationweight of the detectors. The optimization problem size ofDEPA can be calculated as

ΛDEPA =V K

N. (17)

Since for both PADJO and WDM-PAJO, the lamps all workindependently, and there is no channel information sharedamong the lamps, the optimization problem size of PADJOand WDM-PAJO can be assumed to be the same. Thus

ΛPADJO(a) = ΛWDM (a)

=πa

2N2am(NQ + V )K

≈ πa

2N2amΛCM ,

(18)

where am is the minimum access area so that all the indoorspace has coverage. The optimization problem size per thread

2400 lx is a standard illumination level for office spaces [18]. Theconversion between illuminance and power can be found in [19].

6

0 10 20 30 40 50100

101

102

103

104

105

Number of users

Opt

imiz

atio

n P

robl

em S

ize

CM−PAJOPDM−PAJOWDM−PAJOPADJODEPA

Fig. 7. Computational burden with the minimum access area in the largeindoor environment, 7 PDs per user.

of PDM-PAJO can be written as

ΛPDM (a) =πa

2Nam(NQ + V )K

≈ πa

2NamΛCM

= NΛWDM (a)

(19)

Numerical results on optimization problem size are shownin Fig. 7. With the help of parallel processing, the fourdecentralized algorithms have much lower computational bur-den than the CM-PAJO algorithm. As the number of usersincreases, the advantage of using a decentralized algorithmbecomes more obvious. PDM-PAJO and WDM-PAJO bothprovide a reasonable trade-off between BER performance andcomputational burden.

IV. PRACTICAL CONSIDERATIONS

In this section, several practical considerations such asshadowing effects, illumination requirements, dimming con-trol, beamwidth selection, and nonlinear effects of LEDs arediscussed.

A. Shadowing Effects

Shadowing is a common phenomenon that can be regardedas a kind of path loss as in RF communication systems [20].In our work, we assume that the shadowing effects in VLCsystems are caused by objects that block the light, as illustratedin Fig. 8. Since the light can be partially blocked, we define theshadowing effects as a power loss. We assume the shadowinglosses are generated from the one lamp that is closest to theuser. The shadowing loss coefficient for user k is denoted asαk ∈ [0, 1]. When αk = 0 the light is totally blocked, andwhen αk = 1 there is no shadowing for user k. In this work,we represent the power loss due to αk in dB.

To test the effects of shadowing on our system, we assume a4 users system in the small indoor environment, and only oneof them is affected by shadowing. In Fig. 9, the numericalresults show the data rate of the affected user normalizedto that of the non-shadowed case. In this paper, we designour algorithms to be adaptive, so the system reallocates thetransmitted power when the environment and users’ positions

Lamp

PD

Fig. 8. Semi-blocked LOS downlinks.

0 1 2 3 4 5 6

10−2

10−1

100

Shadowing effects (dB)

Nor

mal

ized

dat

a ra

te

Adaptive CM−PAJOCM−PAJO without shadowing info.Equal power allocationUser is only served by the closest lampNo shadowing

Fig. 9. Normalized data rate of the user that is blocked under differentshadowing conditions for a BER = 10−3. 4 users are in the small indoorenvironment, and a single detector is used with 7-length OOC codes.

change. Fig. 9 compares the adaptive CM-PAJO, the CM-PAJO without shadowing information, the equal power alloca-tion scheme, and the case that the affected user is only servedby the closest lamp. From the numerical results, althoughthe data rate of all the schemes decreases with increasingshadowing effects, the adaptive CM-PAJO has significantlybetter performance.

B. Illumination Requirements and Dimming Control

Dimming can be used to satisfy different illumination re-quirements for different purposes. The effective dimming leveldepends on the radiation power and the ratio of the OCDMAcode weight to the code length, η, which determines the powerutilization efficiency for illumination. In this work, we assumethe OCDMA codewords have been specified (not adaptive),and η is fixed. Thus, the dimming level can only be adjustedby changing the radiation power. The Illumination EngineeringSociety of North America provides some illumination levelstandards for indoor environments [18]. For example, theillumination level for an office building should be greaterthan 400 lx. For hotels and restaurants, 100 lx illuminationis enough.

To ensure the room is uniformly illuminated in space, weassume that there are Kv virtual users uniformly distributedin the room, and the virtual users need illumination only (nocommunications). Thus, the total number of users is Ktot =K +Kv , where K is the number of real users who need bothdata and illumination. Under this assumption, we can define

7

the illumination tolerance at user k as ∆k, and require that

|ηhTk pmaxdim + Pb − Preq| ≤ ∆k, (20)

where hk = (h1k1, h2k1, . . . , hNQk1)T . We denote hqk1

as the channel gain from LED q to the detector of us-er k that is pointed towards the ceiling. pmaxdim is thedimmed peak power vector, which can be represented aspmaxdim = γpmax = pmax(γ(1), γ(2), . . . , γ(NQ))T , where γ =

(γ(1), γ(2), . . . , γ(NQ)), and γ(q) is the dimming parameter forLED q. To satisfy the specific illumination requirements, thedimming parameters can be adjusted in the range of [0, 1] fordimming control. Thus, the peak power constraint for differentLEDs may be different. Pb and Preq represent the receivedpower from background light and the required illumination,respectively. The tolerance ∆k limits the difference betweenthe required illumination and the actual illumination.

To make sure the illumination throughout the room is asspatially constant as possible, the dimmed transmitted powerof each LED can be controlled to minimize the illuminationtolerance among all the users (real and virtual). Thus, theoptimal dimming parameters γ∗ can be found by

[γ∗] = arg minγ

maxk

∆k. (21)

Then, the dimmed peak power vector pmaxdim can be used asa peak power constraint for each LED, in either the central-ized or one of the decentralized power allocation algorithmsdescribed above.

The illumination tolerance can be used as a criterion toevaluate how uniformly an illumination can be provided bythe VLC system. Numerical results with different numbers ofuniformly distributed virtual users are shown in Fig. 10. Aswe expected, the more virtual users, the lower the illuminationtolerance, since more virtual users can represent the spacein the room more fully. However, more virtual users canintroduce more computational burden when we calculate theillumination tolerance. From these results, we conclude that16 uniformly distributed virtual users can fully represent theentire space in the small indoor environment. In this figure,since the peak power pmax can only provide 450 lx, anyillumination requirements over 450 lx can not be reached.Thus, the illumination tolerance increases as the requiredillumination increases.

The semiangle of the LEDs is another factor that affects thedimming control accuracy. In Fig. 11, the optimal illuminationtolerances for different semiangles are compared. For smallsemiangle LEDs (less than 15 degrees), the beam widthof the LEDs is too narrow, and all the area on the floorcannot be illuminated. Thus, some area on the floor wouldbe very dark, and other areas would be bright. Because ofthat, the illumination tolerance defined in (20) is large. Iflarge semiangle LEDs are used, the illumination area of eachLED is relatively large, but the intensity of the illuminationwould not be as high as in the small semiangle cases. Itis not easy to control the illumination level for a particulararea as accurately with large semiangle LEDs. Therefore, tomake sure the illumination distribution is uniform for differentrequirements, the semiangle of the LEDs can not be too large

300 350 400 450 500 550 6000

5

10

15

20

25

30

35

Required illumination (lx)

Opt

imal

(in

min

imal

sen

se) i

llum

inat

ion

tole

ranc

e (%

)

No virtual users9 virtual users16 virtual users36 virtual users 49 virtual users

Peak power constraint

Fig. 10. Optimal illumination tolerance under different illumination require-ments with 4 real users and virtual users in the small indoor environment.

5 10 15 20 25 30 35 406

8

10

12

14

16

18

20

22

Semiangle (degree)

Min

imum

illu

min

atio

n to

lera

nce

(%)

450 lx400 lx350 lx300 lx

Fig. 11. Minimum illumination tolerance under different illuminationrequirements for different LED’s semiangle in the small indoor environment;16 virtual users.

or too small. From the numerical results in Fig. 11, a 20-degree semiangle LED is the best choice for the proposedlamp model to have the lowest illumination tolerance if 16uniformly distributed virtual users are modeled in the smallroom.

We also take the background illumination (BI) in the indoorenvironment into account in the form of background power Pbin (20). If the illumination level in the room is assumed to befixed around 400 lx [18], the more background light there is,the less radiation power the LED lamps need to emit. Fig. 12shows the BER performance of the CM-PAJO algorithmunder different background light conditions. In this result, weassume the background light is uniformly distributed, and thebackground illumination on different PDs is the same.

If the background light comes from a window or anotherroom, our multiple PDs system has advantages over the singlePD case. Since the signal for a user is a linear combinationof the signals from different PDs, our algorithm can improvethe SINR by choosing the detectors’ weights. We can modelthe background light from a window as a point light sourceon a wall. We suppose the window is located on one wall ofthe small room at (0,2.8 2.8). Numerical results for this caseare shown in Table II. In this case, there are four randomly

8

7 8 9 10 11 12 1310

−8

10−7

10−6

10−5

10−4

10−3

10−2

Number of real users

BE

R

BI=0 lx BI=80 lx BI=100 lx

Fig. 12. BER performance for CM-PAJO under different background lightillumination conditions in the small indoor environment with 400 lx requiredillumination and 7-detector model, 4 users with 7-length OOC codes.

TABLE IIBER PERFORMANCE FOR CM-PAJO WITH 400 LX BACKGROUND LIGHT

FROM A WINDOW.

BER BI=0 lx BI=80 lx BI=100 lxPD number: 1 1.13e−4 5.73e−4 1.30e−3

PD number: 4 2.19e−5 2.39e−5 2.57e−5

PD number: 7 1.54e−5 1.67e−5 1.81e−5

distributed users, and the background light adds shot noise.The results indicate that our multi-detector system is robustagainst background light interference from a window by usingour MIMO technique.

C. Transmitted Power Quantization

Although we assume on-off CDMA coding and OOKmodulation, since each LED transmits the sum of the signalsmeant for the various users, the signal itself is no longer on-offpulsed.

The optical power from LEDs is driven by an input electricalsignal that carries information. Due to the structure of theLEDs and the principles of generating light, the relationbetween the output optical power and the input current canbe modeled as a nonlinear function. To diminish the effectof the nonlinearity of LEDs on our system, each LED can becomposed of an array of micro-LEDs (µLED), where each canonly be controlled as on or off [21]. To satisfy the illuminationrequirements for offices spaces, we assume that, for example,there are 14 × 14 µLEDs for each LED. Thus, the numberof quantization levels is 197. However, there is no need toquantize the transmitted power at such a high resolution.Therefore, these µLEDs can be clustered into different groups,where each group can be controlled to be on or off. Fig. 13shows a possible LED grouping scheme for 8 quantizationlevels. In this figure, the LEDs in the LED-array are dividedinto 7 groups with the same number of LEDs. Thus, there are8 levels of intensity that can be emitted, from level 0 to level7. For level 0, no group will be lit; for level 7, all the groupswill be switched on. A design trade-off needs to be found

ⅠⅡⅢ ⅣⅤⅥ Ⅶ Ⅷ ⅨⅩ Ⅺ Ⅻ XIII XⅣ

A

B

C

D

E

F

G

H

I

J

K

L

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

Group 7

M

N

Fig. 13. LED grouping scheme for 8 quantization levels

2 3 4 5 6 7 810

−6

10−5

10−4

10−3

10−2

10−1

Quantization levelB

ER

5 users4 users3 users2 users2 users, unquantized

Fig. 14. The average BER performance for different quantization levelswith 2, 3, 4 and 5 users using 7-length OOC codes in the small environment,semiangle is 30 degrees, no dimming control.

between the quantization errors and the structural complexity,which is outside the scope of this study.

Numerical results for the system performance for differentquantization levels are shown in Fig. 14. For this scenario, weconclude that 8 quantization levels are sufficient in our system.

V. CONCLUSION

In this paper, we present a multiuser MIMO indoor visiblelight communication system that is robust against shadowing,dimming, background radiation, and LED nonlinearity. Inthis system, a centralized power allocation scheme and fourdecentralized algorithms are proposed. To enhance the SINRfor each user, a multiple PDs model is employed at thereceiver. The BER performance and computational burden ofthe algorithms are analyzed. From the numerical results, ourproposed MIMO algorithm can support multiple users withhigh communication performance in both small and largeindoor environments within the illumination requirements.Compared to the centralized power allocation algorithms,the four proposed decentralized power allocation algorithmsall have much lower computational burden. Considering theBER performance of the centralized and all decentralizedalgorithms, PDM-PAJO and WDM-PAJO are the best choices.When some users are affected by shadowing, our proposedadaptive MIMO power allocation algorithms can reallocate thetransmitted power to reduce the shadowing effects. From thesimulation results, the data rate of the shadowed user using

9

adaptive CM-PAJO is about twice as high as the algorithmwithout knowing the shadowing information when the shad-owing loss coefficient αk is 3 dB. The algorithms proposed inthis paper can adjust the dimming parameters for each LED toaccommodate the illumination requirements. In addition, thenonlinearity of LEDs is also considered in this paper and canbe solved by using micro-LED arrays.

APPENDIX

We assume the MAI is dominant. In this appendix, we showthat for the receiver weights, the SINR is maximized if

∃ x, s.t. µkv =

1, v = x

0, ∀v 6= x. (22)

Maximizing the SINR for user k in (9) can be simplified tohave the following form:

arg maxµi

(∑Vi=1 µiAi

)2

(∑Vi=1 µiBi

)2 = arg maxµi

∑Vi=1 µiAi∑Vi=1 µiBi

, (23)

where Ai and Bi are the signal and MAI received from theith PD. It is obvious that Ai and Bi are both nonnegative. Toprove (22), it is sufficient to prove that

maxµi

∑Vi=1 µiAi∑Vi=1 µiBi

= maxi

AiBi

and µi ∈ 0, 1. (24)

We show this by induction. For the base case, when V = 1,

maxµi

∑Vi=1 µiAi∑Vi=1 µiBi

= maxµ1

µ1A1

µ1B1=A1

B1, where µ1 = 1. (25)

For the inductive case, it is given that

maxµi

∑Vi=1 µiAi∑Vi=1 µiBi

= maxµi

µiAiµiBi

=AxBx

, (26)

where µx = 1 and µi = 0 for i 6= x.If AV +1

BV +1≥ Ax

Bx, and from (26) we have∑V

i=1 µiAi∑Vi=1 µiBi

≤ AxBx≤ AV+1

BV+1

⇔ (

V∑i=1

µiAi +AV+1)BV+1 ≤ (

V∑i=1

µiBi +BV+1)AV+1

⇔ maxµi

∑V+1i=1 µiAi∑V+1i=1 µiBi

=AV+1

BV+1

(27)If AV +1

BV +1≤ Ax

Bx, from (26) we obtain

V∑i=1

µiAiBx +AV+1Bx ≤V∑i=1

µiBiAx +BV+1Ax

⇔ (

V∑i=1

µiAi +AV+1)Bx ≤ (

V∑i=1

µiBi +BV+1)Ax

⇔∑V+1i=1 µiAi∑V+1i=1 µiBi

≤ AxBx

(28)

Then, we conclude that ∃ x, s.t. µkv = 1 for v = x, andµkv = 0 for v 6= x.

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