Positioning for Visible Light CommunicationSystem Exploiting Multipath Reflections

Hamid Hosseinianfar⇤, Mohammad Noshad† and Maite Brandt-Pearce‡⇤‡Charles L. Brown Department of Electrical and Computer Engineering,

University of Virginia, Charlottesville, VA 22904.†VLNCOMM LLC, Charlottesville, VA 22904

Email: ⇤hh9af@virginia.edu, †noshad@vlncomm.com, ‡mb-p@virginia.edu

Abstract—In this paper, we introduce a new uplink visiblelight indoor positioning system that estimates the position of theusers in the network-side of a visible light communications (VLC)system. This technique takes advantage of the diffuse componentsof the uplink channel impulse response for positioning, whichhas been considered as a destructive noise in existing visiblelight communication positioning literature. Exploiting the line ofsight (LOS) component, the most significant diffusive componentof the channel (the second power peak (SPP)), and the delaytime between LOS and SPP, we present a proof of conceptanalysis for positioning using fixed reference points, i.e. uplinkphotodetectors (PDs). Simulation results show the root meansquare (RMS) positioning accuracy of 25 cm and 5 cm for oneand 4 PDs scenarios, respectively.

Index Terms—Visible light indoor positioning, visible lightcommunications (VLC), multipath reflections.

I. INTRODUCTION

Ubiquitous use of light-emitting diodes (LEDs) alongsidetheir fast modulation capability paves the way for introducingnew indoor services such as internet of things, visible lightcommunications (VLC) and positioning through lighting. Incomparison with radio-frequency (RF) indoor networks, visi-ble light communication systems are considered as a viableapproach for indoor wireless data access providing highersecurity and larger multiuser capacity [1]. Indoor positioningis difficult to achieve because the signals from GPS satellitescan be blocked in indoor areas and underground facilities.VLC systems can provide centimeter accuracy in findingthe location [2]. Various positioning algorithms have beenproposed using visible light signals that demonstrate higheraccuracy compared to conventional RF techniques [3], [4].

The main approaches for estimating the users’ locationin visible light positioning systems generally rely on threefeatures of the received signals: time of arrival (TOA), angleof arrival (AOA), and received signal strength (RSS). RSS-based techniques use the intensity of the signal to estimate thedistance from the transmitter to the receiver. These techniqueshave the potential to achieve a high accuracy in visiblelight positioning systems because of the strong line of sight(LOS) signals, which are often not available in RF systems.However, the accuracy of the RRS techniques that rely on LOSsignals is limited due to the shadowing and multi-path effects,which make the relationship between the distance and RSSunpredictable [2], [5], [6]. In TOA-based systems, the position

of the receiver is estimated by measuring the arrival time ofthe signal from different transmitters, and hence, it requiresperfect synchronization between the transmitters, which canlimit the application of these systems. Theoretical limits havebeen presented on the accuracy of the TOA-based [4] and RSS-based [7] positioning techniques. TOA and RSS locate usersusing triangulation, trilateration, and/or fingerprinting and ingeneral, require at least two LEDs when the height of theuser is known, and three LEDs when it is unknown. AOAhas been used with imaging receivers to locate the users bymeasuring the angle at which the line-of-sight (LOS) signalfrom the transmitter is received. Shadowing can interrupt theperformance of this type of positioning system. AOA-basedtechniques can estimate the user’s location using one imagingreceiver when the height of the user is known and two imagingreceivers when it is not [2].

In this paper, we propose a new positioning technique forindoor visible light systems that uses the characteristics of thechannel impulse response to locate users. This method exploitsthe multipath signals to get a better estimate of the user’sposition rather than considering them as noise. While most ofthe research on visible light positioning has concentrated ondownlink and user-side positioning, the proposed algorithm isdeveloped for the infrared (IR) uplink of a VLC system. Thislocalization algorithm provides the network the informationneeded for communications purposes, such as resource alloca-tion and hand-off where the network monitors the number andposition of the users. For this purpose, less complex algorithmsare preferred over more accurate ones. In the proposed algo-rithm, one reference point, i.e., one uplink receiver, suffices forestimating the user’s position. However, adding more referencepoints enhances the positioning accuracy.

The rest of the paper is organized as follows. In Section II,the system model and measurement scenario are discussed.The positioning algorithm is presented in Section III. Thenumerical results are presented and discussed in Section IV.Finally, the paper is concluded in Section V.

II. SYSTEM DESCRIPTION

A. Fingerprint Definition

In a typical visible light communication system, thereare usually multiple white LED fixtures on the ceiling thattransmits downlink data and multiple infrared photo-detectors

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Fig. 1. System configuration for visible light communication uplink system

(PDs) that capture uplink signals as shown in Fig. 1. In thispaper we propose a technique to find the position of the usersusing only one transmitter-receiver pair. We further, extend thisalgorithm to multiple receivers for the sake of accuracy. Theidea in this work is to use the channel impulse response of theuplink channel to locate the user, and map the characteristicsof the impulse response to the location of the user. Fig. 2illustrates the room configuration considered for the proposeduplink positioning system. In this model, a PD is assumed tobe installed on the ceiling at the point (x(r), y(r), h(r)) facingvertically downwards, and the user at coordinates (x, y, h) isassumed to have an infrared LED transmitter that is facingvertically upwards.

To develop the proposed positioning algorithm, we firstdivide the indoor area into a grid and then create a databaseof the channel impulse responses for different positions of theuser on the grid, Ck = (xk, yk), k 2 {1, 2, . . . , MN}, fora known height h. We consider an N ⇥ M grid, as shownin Fig. 2. We focus on the main features of the impulseresponse, which give sufficient information about the userlocation. For the proof of concept, we consider the LOSpeak power PLOS , the second power peak (SPP) term PSPP ,i.e., the first peak of the diffuse term, and the arrival timedifference between these two components �⌧ . The vectorSk = [PLOS , PSPP ,�⌧ ] , k 2 {1, 2, . . . , MN}, representsthe constellation vector corresponding to the kth point on themeasurement grid for one PD. For the multiple PDs scenario,the feature space is simply expanded to Q ⇥ 3 dimensions,where Q is the number of PDs.

B. Channel Model

In indoor environments, the channel response of opticalwireless systems includes both LOS and diffuse componentsthat are caused by multipath reflections. For simplicity, in oursimulation we consider only the first bounce of the channel’sdiffuse components. This approximation has a small errorsince the first bounce is the strongest component of the diffusepart. In addition, considering that the paths with more bounces

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Fig. 3. Impulse response of the channel for different locations of thetransmitter when the receiver is located at (150 cm, 150 cm, 300 cm) andthe simulation parameters are as in Table I.

have larger delays, neglecting the paths with more than onereflection does not have significant impact on the second powerpeak [8]. The impulse response is captured in simulationthrough ray tracing, presented in [9]. Fig. 3 illustrates theimpulse response for three different user locations. For a fixedIR receiver position on the ceiling, each point of the room hasa unique channel response and the LOS peak power, SPP, andtheir time delay can uniquely characterize the user’s position.Table I presents the simulation parameters considered for thiswork.

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TABLE ISIMULATION PARAMETERS OF RAY TRACING CHANNEL MODEL [9].

Transmitter Parameters ValueHeight 0.85 mWavelength 950 nmLambertian Mode (m) 1LED transmit power, PT 10 mWReceiver Parameters ValueSurface area of the PD, APD 1 cm2

Height 3 mField of View (Half Angle) 70�

Wall reflectance coefficient, ⇢ 0.8Reflecting element area, Aref 2 cmRoom Parameters ValueRoom Size 5 ⇥ 5 ⇥ 3 m3

III. POSITIONING ALGORITHM

In this section, we describe our indoor positioning algo-rithm. Given that the transmitter sends an ideal delta function�(t), the received signal is the channel impulse response withadditive white Gaussian noise (AWGN) that can be defined as

v(✓, t) = h(✓, t) + n(t) (1)

where h(✓, t) is the corresponding channel impulse responseand n(t) is AWGN. In this algorithm, the user’s position isestimated using features captured from v(✓, t): the receivedpeak power from LOS, and SPP components of the impulseresponse, and the time delay between LOS and SPP compo-nents. These three observations can be expressed as

v1(✓) = PLOS(✓) + n1,

v2(✓) = PSPP(✓) + n2,

v3(✓) = �⌧(✓) + n3. (2)

where ✓ = (x, y) is the two dimensional coordinates of theuser to be estimated, and n1 and n2 are independent Gaussiannoises with variance �2. n3 is the time delay noise betweenLOS and SPP which is modeled as a Gaussian noise withvariance �2

⌧ and assumed independent from n1 and n2. LetV (✓) = [v1(✓), v2(✓), v3(✓)]T be the observation vector.

A. Calculation of Time Jitter Noise �2⌧ for Peak Detector

In real applications, the observation components defined in(2) are the output of a peak detector. The variance �2 ofpeak amplitude noises, namely, n1 and n2, are the same asthe received signal variance. However, the variance of timedelay noise n3, the time jitter noise of a peak detector, is afunction of �2. To figure out the relation between the timejitter and amplitude noise, we can simplify the problem tothe relation of amplitude noise and time noise of the zerocrossing, when the amplitude noise distribution is Gaussian.The first derivative of the received signal in (1), v0(t)

.= @v(✓,t)

@tcrosses zero at the times near the LOS and SPP peaks, with thesame amplitude noise variance. At these zero crossing times,

the function v0(t) can be approximated as linear with constantslope � = dv0(t)/dt|v0(t)=0. Thus, the amplitude noise canbe translated to jitter noise n3. This linear approximation isaccurate for high SNR scenarios. Considering this approxima-tion, the distribution of the jitter noise remains Gaussian. Thecorresponding noise variance can be written

�2⌧ =

�2

�2. (3)

In this paper, we use �2 = 30, based on our numerical results.

B. Maximum Likelihood EstimationMaximum likelihood estimation is employed for position-

ing, where the algorithm looks for the constellation pointSk(✓) = [PLOS(✓), PSPP(✓),�⌧(✓)], k 2 {1, . . . , MN} thathas the minimum Euclidean distance to the observation vectorV (✓) 2 observation plane. ✓ 2 room plane corresponding tothis constellation point is considered as the estimated location.Fig. 4 illustrates an example of mapping between some regionclose to V (✓) in the observation plane onto the room plane.The decision regions are depicted based on the minimumEuclidean distance criterion. In this example, ✓ = Ci is theestimated location since V (✓) is located in the Si decisionregion (see Fig. 4).

C. Calculation of the Positioning ErrorConsidering the minimum distance algorithm, the probabil-

ity of choosing Si(✓) given the position of ✓ is denoted by

✏j = Pr{Sj=i(✓)|✓}, (4)

where

i = arg mini

���V (✓) � Si(✓)���2

i 2 {1, 2, . . . , NM} (5)

is the index of the selected center point, Si(✓). The root meansquare (RMS) positioning error can be calculated as

dRMS =

vuuutE✓

8<:

N⇥MX

j=1

|✓ � Cj |2 ✏j

9=; (6)

where E✓{·} denotes the expectation over different locations✓.

Due to the complex shapes of the decision regions, aderivation of the exact value of ✏j is not trivial. In this case,a reasonable approach, especially for high SNR scenarios, isto calculate a lower-bound (LB) on the estimation error [10].To that end, we consider only ✏j’s that correspond to the twoclosest center points to the observation point, V (✓). Then, (4)evaluated at these center points can be rewritten

✏i = Q(

qLT (i)·⌃�1·L(i)

2 ),

✏i0 = 1 � Q(

qLT (i)·⌃�1·L(i)

2 ).(7)

where L(i) is the distance vector between V (✓) and theboundary between the two closest center points, named i andi0 (see Fig. 4). The covariance matrix can be defined as

⌃ = diag(�2,�2,�2⌧ ). (8)

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Pi Pj

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Observation Plane

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Fig. 4. Mapping the room plane onto the observation plane. The Si, Si0 , andSk are three typical observation points, close together in observation spaceand, the Ci, Ci0 , and Ck are corresponding center points in the room plane.

The �2 and �2⌧ are the variances of the noises on the obser-

vation vector defined in (2). For the multiple PDs scenario,the observation space vectors are simply expanded to Q ⇥ 3dimensions by concatenating the corresponding vectors fromdifferent PDs. In this case, ⌃ is the 3Q⇥3Q covariance matrixformed by values of �2 and �2

⌧ in the appropriate places onthe diagonal.

IV. NUMERICAL RESULTS

In order to model the multipath signals in a typical room,simulations are done in an empty cubicle of size 5⇥5⇥3 m3.Table I summarizes the parameters used in the simulations. Inthese simulations, we assume the single PD to be located atpoint (1.5, 1.5, 3) on the ceiling. For multiple PDs scenarios,the other PDs are located at points (3.5, 1.5, 3), (1.5, 3.5, 3),and (3.5, 3.5, 3). The transmitter is assumed to be at 85 cmfrom the floor.

Fig. 5 demonstrates the contour plots for the three obser-vation components, namely, PLOS, PSPP and �⌧ . Based onpreviously presented positioning methods, like trilateration,given enough power measurements (three in trilateration), theuser position can be estimated to be at the intersection pointof power observation contour plots. As an intuition for theproposed algorithm, here the user position can be estimatedas the intersection of three observation contours PLOS, PSPP ,and �⌧ .

Fig. 6-(a), and (b) illustrate the constellation points inthe room plane and in the corresponding observation plane,based on two observations components, PLOS and PSPP . Thecorresponding points in both planes are denoted with markersof the same size and color. As shown in Fig. 6-(b), themapping to the observation plane maintains the same roomplane pattern, i.e., almost all the point on the observation planeare surrounded by the mapping of its corresponding neighborsin the room plane. Hence, maximum likelihood estimation,i.e., the minimum Euclidean distance in the observation plane,leads to the closest measurement point on the room plane.Adding the third observation component, �⌧ , we can see in

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Fig. 5. Contour plots in room space: a) LOS component of received power(dB), b) SPP component of received power (dB), c) Time delay between theLOS and SPP components (ns).

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Fig. 6-(c) that the distances between the points are increased,which brings higher positioning accuracy.

In order to determine the estimation error, we run a MonteCarlo (MC) simulation by randomly choosing the location ofthe user and estimating the closest grid point on the roomplane using the proposed algorithm. The RMS positioningerror is a representation of the probability of choosing aconstellation point by the algorithm and the mapping costof that decision. However, given that the algorithm tries tofind the closet grid point, the larger the grid step size, theworse the absolute positioning accuracy becomes, and yetthe lower the probability of mapping to some far bin inthe room. Therefore, there is a trade off between the roomplane absolute grid accuracy and the cost of wrong mapping.Figs. 7-(a) and 7-(b) demonstrate the RMS positioning errorsfor the 2 and 3 observations algorithms, respectively. For adifferent number of PDs, the MC simulations converge to theLB results (calculated in section III-C) at high SNR, whichverifies the simulation results. Deploying more PDs leadsto higher accuracy level: for 4 PDs we reach the minimumerror that is inevitable due to quantization on a grid. Asexpected, for the same SNR and number of PDs, the 3observations algorithm provides better accuracy compared tothe 2 observations algorithm.

Fig. 8 shows the RMS positioning error versus grid stepfor a high SNR scenario. There is a nearly linear relationbetween accuracy and the grid step size for all multiple PDsscenarios. In addition, for a larger number of PDs, the RMSerror gets closer to the RMS quantization error, where theestimated location is mapped to the closest grid point in theroom, in the high SNR case.

A. Addressing Practical Challenges

The performance of the proposed algorithm tightly dependson the channel model. Therefore, the features extracted fromthe impulse response are different for real indoor spaces con-taining furnishings, surfaces with different reflection factors,specular reflections from windows, etc. In real scenarios, it isonly a matter of defining the fingerprint database: the actualimpulse response can be learned once for a specific grid, andthen the algorithm can be deployed. The other practical con-cern has to do with the shadowing effect, which is inevitablewhen there are moving users and/or objects in the room. Inthis case, installing multiple PDs on the ceiling can address theproblem. Tracking the movement path of the users can increasethe accuracy of the proposed algorithm by limiting the numberof constellation points for the user’s location. The positioningerror can also be reduced by redesigning the grid in theroom plane and optimizing the observation constellation usingirregular points in the room, and more regular constellationsin the observation space.

V. CONCLUSION

In this paper, an infrared uplink positioning algorithm isproposed that takes advantage of the user location informationembedded in the multipath reflections. Using the LOS, SPP

Fig. 6. a) Anchor points in room plane, b) Corresponding fingerprints inobservation plane for two observations, PLOS and PSPP , c) Correspondingfingerprints in observation plane for three observations, PLOS, PSPP , and�⌧ .

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Fig. 7. RMS distance error for a grid step of 14 cm and multiple PDsscenarios: a) Two observations, b) Three observations.

and the time delay between these two components, a databaseof room fingerprints on a grid is created. The performance ofthe maximum likelihood estimation algorithm is evaluated forseveral different grid steps and multiple PDs scenarios. Theresults show a RMS positioning error of 5 cm using 4 PDs, aSNR of 50 dB, and grid step of 14 cm.

VI. ACKNOWLEDGEMENT

This work was funded by the National Science Founda-tion (NSF) through the STTR program, under award number1521387.

REFERENCES

[1] M. Noshad and M. Brandt-Pearce, “Can visible light communicationsprovide Gb/s service?” arXiv:1308.3217, Aug. 2013.

[2] W. Zhang and M. Kavehrad, “Comparison of VLC-based indoor posi-tioning techniques,” in Proc. SPIE, 2013, pp. 86 450M–86 450M.

[3] J. Armstrong, Y. Sekercioglu, and A. Neild, “Visible light positioning:A roadmap for international standardization,” IEEE Commun. Mag.,vol. 51, no. 12, pp. 68–73, Dec. 2013.

[4] T. Q. Wang, Y. A. Sekercioglu, A. Neild, and J. Armstrong, “Positionaccuracy of time-of-arrival based ranging using visible light with appli-cation in indoor localization systems,” Lightwave Technology, Journalof, vol. 31, no. 20, pp. 3302–3308, 2013.

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Fig. 8. RMS distance error for SNR= 50 dB and multiple PDs scenarios:a) Two observations, b) Three observations.

[5] X. Zhang, J. Duan, Y. Fu, and A. Shi, “Theoretical accuracy analysis ofindoor visible light communication positioning system based on receivedsignal strength indicator,” Journal of Lightwave Technology, vol. 32,no. 21, pp. 3578–3584, 2014.

[6] A. Sahin, Y. S. Eroglu, I. Guvenc, N. Pala, and M. Yuksel, “Hybrid3-D Localization for Visible Light Communication Systems,” Journalof Lightwave Technology, vol. 33, no. 22, pp. 4589–4599, 2015.

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

[8] W. Gu, M. Aminikashani, and M. Kavehrad, “Impact of multipath re-flections on the performance of indoor visible light positioning systems,”arXiv preprint arXiv:1505.07534, 2015.

[9] K. Lee, H. Park, and J. R. Barry, “Indoor channel characteristics forvisible light communications,” IEEE Commun. Lett, vol. 15, no. 2, pp.217–219, 2011.

[10] J. G. Proakis, Intersymbol interference in digital communication systems.Wiley Online Library, 2001.

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