carrier allocation combined with independent component...

Carrier allocation combined withindependent component analysis formultiple-input-multiple-output visiblelight communication

Fangqing JiangHonggui DengFang YangKaicheng ZhuCongxu Zhu

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Carrier allocation combined with independentcomponent analysis for multiple-input-multiple-outputvisible light communication

Fangqing Jiang,a Honggui Deng,a,b,* Fang Yang,a Kaicheng Zhu,a and Congxu Zhuc

aCentral South University, School of Physics and Electronics, Lushan South Road, Changsha 410083, ChinabXinjiang Nonferrous Central South University Joint Research Institute, Urumqi 830000, ChinacCentral South University, School of Information Science and Engineering, Lushan South Road, Changsha 410083, China

Abstract. We present a scheme based on precoding carrier allocation and independent component analysis(ICA) for indoor multiple-input-multiple-output (MIMO) visible light communication (VLC). In order to improve thereliability of the ICA algorithm for the mixed signal separation, at the sending end, frequency doubled-carriersare employed to module the parallel data which ensure that the modulated signals are independent of eachother. The ICA algorithm is applied to separate the mixed signal at the receiving end directly without the require-ment of the channel information. Simulation results show that this indoor MIMO VLC scheme can achieveexcellent performance. When the signal-to-noise ratio is equal to 14 dB, the bit error ratio (BER) reachesthe level of 10−5. So, the communication performance is superior to that of the commonly used schemesbased on the channel estimation. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License.Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.OE.53.2.026103]

Keywords: multiple-input-multiple-output visible light communication; carrier allocation; independent component analysis.

Paper 131565 received Oct. 16, 2013; revised manuscript received Dec. 14, 2013; accepted for publication Jan. 13, 2014; publishedonline Feb. 13, 2014.

1 IntroductionVisible light communication (VLC) system will be requiredto be capable of supporting up to hundreds of megabits persecond or even multigigabit high-speed packet data transmis-sion in the future. Multiple-input–multiple-output (MIMO)can make full use of space resources, maximizing spectrumutilization, and power efficiency. So, MIMO wireless trans-mission technology is the key to the future VLC. MIMOindoor VLC system, transmitting signals through multilightsources, has higher capacity and transmission rate than thesingle input-single output (SISO) system. On the one hand,MIMO indoor VLC can meet the lighting requirements. Onthe other hand, it can overcome the shadow effect in com-munication system and increase the communication distance.

In MIMOVLC system, the channel is divided into variousseparate subchannels. Multiple users modulation, precoding,and adaptive equalization techniques are often employed toovercome the mutual interference between each subchannel.1

All of the above work is based on the channel state informa-tion (CSI) under the predictable premise. However, in theactual case, to accurately estimate the channel informationis almost impossible. Also, the estimation of the channelitself will introduce large error so that the bit error rateincreases.

In order to restore the source signal at the receiving end,many studies have been proposed based on the estimation ofchannel parameters. Predistortion coding, zero on-off keying(OOK) modulation and synchronous OFDMmodulation2 aretaken at the sending end to overcome inter-carrier interfer-ence. At the receiving end, by means of adaptive equalization

to extract the signal,3 and so on. In order to accurately esti-mate the CSI, we need to use a lot of training sequences con-stantly which will waste lots of bit rate and then reduce thesignal transmission rate also increase the noise.4 Therefore,this paper proposes an MIMOVLC system scheme in whichprecoding subcarrier allocation modulation is employed attransmitters and through the independent component analy-sis (ICA) algorithm separation mixed signals at receiver.This scheme improves the independence of each modulatedsignals and do not rely on the channel estimation.

2 MIMO Indoor VLC ModelIn indoor VLC system, a typical MIMO VLC system can beexpressed as the model shown in Fig. 1. When every light-emitting diode (LED) source sends signal at the same time,the received signals at receiver comprise signals receiveddirectly and reflected optical signals, for the reason of multi-path transmission of light. The solid arrows indicate thedirect transmission path, whereas the dotted arrows indicatethe reflection path. The total number of LED light sourcesand different direction receiving antennas are assumed tobe K and L, respectively, in this system.

Because every LED light reaches the receiving endthrough different path and a single LED light can alsohave multiple transmission paths, the multipath effect of vis-ible light signal transmission is obviously. Therefore, a singleLED light signal transmission process in this communicationsystem can be expressed as

RðnÞ ¼ XðnÞ þXNi¼1

aiXðn − tiÞ þ NðnÞ; i ¼ 1; 2; : : : ; N;

(1)*Address all correspondence to: Honggui Deng, E-mail: [email protected]

Optical Engineering 026103-1 February 2014 • Vol. 53(2)

Optical Engineering 53(2), 026103 (February 2014)


http://dx.doi.org/10.1117/1.OE.53.2.026103

http://dx.doi.org/10.1117/1.OE.53.2.026103

http://dx.doi.org/10.1117/1.OE.53.2.026103

http://dx.doi.org/10.1117/1.OE.53.2.026103

http://dx.doi.org/10.1117/1.OE.53.2.026103

http://dx.doi.org/10.1117/1.OE.53.2.026103

where XðnÞ, YðnÞ, ai, ti, and NðnÞ represent the LED trans-mission signal, the received signal, the coefficients, the delaytime, and Gaussian background noise, respectively. N is thereflecting times of the received signal, researches show thatthe three times reflected signal is negligible.5 Therefore, wetake N ¼ 2, ai is the strength coefficient of the reflectiondelay signal and 0 < ai < 1.

Figure 1 shows the system of K LED light sources (signalsources) transmit simultaneously and Eq. (1) can be regardedas the case of one LED light path in this system. When the Ksources transmit signals simultaneously, the K receivingantennas would receive the mixed signals from the Ksources. So, in this case, the system can be expressed inthe matrix form, as Eqs. (2) or (3):

R ¼ HX þ N; (2)

equivalent to0B@

r1...

rk

1CA ¼

0B@

h11 · · · h1k... . .

. ...

hk1 · · · hkk

1CA

0B@

x1...

xk

1CAþ

0B@

n1...

nk

1CA: (3)

where R, H, X, and N in Eq. (2) denotes the received signalmatrix, the channel matrix, source signal matrix, andGaussian noise matrix, respectively. In Eq. (3), ri is the sig-nal received by the i’th receiving antenna, xi is the i’thsource transmitted signal, hij denotes the channel betweenthe i’th transmitting antenna and the j’th receiving antenna,and ni is the Gaussian noise.

In order to recover X from the received signal R, previousstudies are based on the estimation of channel H. But, theprocess of channel estimation will generate large errorand take a lot of time. From Eqs. (2) and (3), we can seethat this signal process have the same form with ICA signalprocess. So, we can restore the source signals by ICA algo-rithm when the source signals satisfy the independent prin-ciple. The ICA algorithm is to find a separation matrixWT toseparate the received signal. The details are as follows:

Y ¼ WTR ¼ WTHX þWTN. (4)

Let E ¼ WTH, Z ¼ WTN in Eq. (4), so

Y ¼ EX þ Z; (5)

where Y is the restored signal and E ¼ WTH, Z ¼ WTN.The ICA algorithm is designed to make E tend to a unitmatrix and Z tend to a zero matrix, thus

Y ¼ X þ Z: (6)

3 System DesignThis section proposes the MIMO VLC scheme which isbased on the precoding carrier allocation and ICA algorithm.At the sending end, the preprocessed data are sent into mod-ulators separately and modulated by different carriers. Atthe receiving end, ICA algorithm is used to separate themixed-signal and demodulate without CSI.

3.1 Precoding Carrier Allocation Modulation

ICA is based on the basic principle of statistical independ-ence, which is the key to achieve the ICA algorithm. In prac-tice, the independence between variables in ICA algorithmis often measured by non-Gauss difference, nonlinear irrel-evance, and mutual information.6

The modulated signals have a strong correlation and smallnon-Gauss difference in traditional MIMO VLC systemwhose carrier frequencies are the same. Therefore, traditionalMIMO VLC scheme is not conducive to apply ICA algo-rithm to separate the mixed signals. Based on this, we pro-pose the carrier allocation modulation to strengthen theindependence between each modulated signal. The intensitymodulation and direct detection (IM/DD) method is welladopted to achieve the VLC, so we need not worry aboutthe problem of limited bandwidth. Meanwhile, in order torestore the phase of source signal, add prefix “1” as thephase identification to bytes allocated data. The block dia-gram of the sending end is shown in Fig. 2.

We know that the independence between two signals isthe basic principle to achieve the ICA algorithm, and inthis paper, nonlinear irrelevance is adopted to measure theindependence of signals. Random variable X is nonlinearirrelevant to Y when their arbitrary continuous functionmeet the relationship shown in Eq. (7), it is concludedthat X and Y are mutually independent7

Fig. 1 Multiple-input-multiple-output (MIMO) indoor visible light com-munication (VLC) system model.

Fig. 2 Sending end block diagram of the MIMO VLC system.


Jiang et al.: Carrier allocation combined with independent component analysis. . .


E½fðXÞgðYÞ� ¼ E½fðXÞ�E½gðXÞ�: (7)

In Eq. (7), f and g are the arbitrary continuous functions.In practice, nonlinear irrelevance-based ICA algorithm useEq. (8) as the nonlinear irrelevance criterion which is a suf-ficient condition of Eq. (7). A common situation is to set Xi

and Yj as odd function with mean zeros,8 such as Xi ¼ X,Yj ¼ Y3

E½XiYj� ¼ 0: (8)

In order to make the ICA algorithm work effective inseparating the mixed modulated signals, we hope that themodulated signals are meet the nonlinear irrelevancewhich is shown above at the sending end. When phase-shift-keying (2PSK) modulation is applied in this MIMOvisible communication system, the modulated signal at then’th sending end can be expressed as

cosð2πfntþ snÞ; (9)

where fn is the carrier frequency and sn is the phase depend-ents on the modulating signal. It is easy to prove that themodulated signals would meet the nonlinear irrelevance cri-terion expressed by Eq. (8) when the carrier frequency ateach sending end is allocated by Eq. (10) and a reasonablesetting of i and j. Therefore, when the carriers are allocatedby Eq. (10), the modulated signals meet the independentprinciple and the requirement of ICA algorithm is met

fn ¼ n · f; n ¼ 1; 2; : : : (10)

In a practical system, we add prefix “1” to the paralleleddata to produce the preprocessed data. As Fig. 2 shows,binary-PSK (BPSK) modulation based on the carrier alloca-tion is used to modulate the preprocessed data at the sendingend. Let f2 ¼ f1þ Δf, Fig. 3 shows the correlation coef-ficient between two modulated signals vary with Δf.

In Fig. 3, the abscissa from 0 to 500 means theΔf rangingfrom 0 times f1 to 5 times f1. As shown in Fig. 3, when thefrequency difference Δf is 0 (f2 ¼ f1), the two modulatedsignals have the strongest correlation. With frequency

difference increasing, the correlation coefficient shows adecreasing trend, and the correlation coefficient close to 0when f2 ≥ 2f1. When Δf ¼ n · f1, n ¼ 1; 2; : : : , the cor-relation coefficient between two modulated signals is 0.Further, nonlinear irrelevance is adopted to measure the inde-pendence of signals in ICA algorithm, and then we can usethe nonlinear irrelevance to measure the independence of sig-nals. Therefore, when the carriers are allocated according toEq. (10), the modulated signals are independent of each otherand meet the independence principle of ICA algorithm. So,the carrier allocation modulation can reduce the correlationbetween each modulated signal and improve the separationperformance of received mixed signal in ICA algorithm. Infact, the carrier allocation modulation can also reduce theintercell interference of MIMO VLC.9

3.2 Use ICA to Separate the Received Signals

The modulated signals X turn into the observed signals(received signals) R at the receiving end after being transmit-ted through the wireless channel, R is the mixing of X.Because the modulated signals X modulated by the proposedcarrier allocation modulation are independent of each other,we can use ICA algorithm to separate the observed signalwithout estimating the CSI to get the separated signalY. In this paper, FastICA algorithm is applied. FastICAalgorithm is designed to find a direction to make WTRðY ¼WTRÞ has the maximum non-Gaussian.10 Non-Gaussian canbe measured by entropy which is shown below:

NgðYÞ ¼ fE½gðYÞ� − E½gðYGaussÞ�g2; (11)

where YGauss is the Gauss random and YGauss has the samevariance with Y, Hð·Þ represents the differential entropy ofrandom variable.

In order to derive the FastICA algorithm, we must firstensure that the maximum approximation of negative entropyof WTR can be obtained by optimizing EfGðWTRÞg.According to Kuhn-Tucker, under the constraint ofEfðWTRÞ2g ¼ kWk2 ¼ 1, the optimal value of EfGðWTRÞgcan be obtained on the condition of

EfRgðWTRÞg þ βW ¼ 0; (12)

where β ¼ EfWT0RgðWT

0RÞg is a constant value, W0 is theoptimization value of W. We use Newton iteration to solveEq. (12). Let F denote the left part of Eq. (12), we can obtainthe Jacobian matrix JFðWÞ asJFðWÞ ¼ EfRRTg 0ðWTRÞg − βI: (13)

The data R is preprocessed as

EfRRTg ¼ I: (14)

And then

EfRRTg 0ðWTRÞg ≈ EfRRTg · Efg 0ðWTRÞg¼ Efg 0ðWTRÞgI: (15)

Thus Jacobi matrix turns into a diagonal matrix, and itsinversion can be easily found to yield an approximateNewton iteration formula:

0 50 100 150 200 250 300 350 400 450 500-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Frequency difference df

Cor

rela

tion

coef

ficen

t

Fig. 3 Correlation varies with frequency difference Δf .




W� ¼ W − ½EfRgðWTRÞg − βW�∕½Efg 0ðWTRÞg − β�;W ¼ W�∕kW�k; (16)

where W� is the new value of W, β ¼ EfWTRgðWTRÞg.Normalization can improve the stability of solution, aftersimplifying it we can obtain the iterative formula ofFastICA algorithm as

W� ¼ EfRgðWTRÞg − Efg 0ðWTRÞgW; W ¼ W�∕kW�k:(17)

So, the iterative algorithm shown in Eq. (17) can find a WT

such that R has the maximum non-Gaussian, and the treatedY is the restored signal of X.

4 System SimulationIn order to verify the feasibility of the proposed scheme, thesimulation experiments are implemented as follows. In thesimulation, precoded and carrier allocation modulation areadopted at the sending end, and ICA algorithm is appliedto separate the observed mixing signal at the receivingend. At the same time, carriers of the same frequency areused to modulate the signals as a comparison with the pro-posed modulation scheme. Because of the Rayleigh fadingcharacteristic of the VLC channel, the Rayleigh fading chan-nel is assumed in the simulation.11

In the simulation, there are four sending and receivingnodes assumed in the MIMO VLC system, that is K ¼ 4,

L ¼ 4. The modulated signals are sent into the channeland superposed with signal-to-noise ratioðSNRÞ ¼ 20 dBwhite Gauss noise. Using ICA algorithm to separate themixed signal received from the four receiving nodes.Figure 4 shows the simulation process of the proposed com-munication scheme based on the carrier allocation combinedwith ICA. As a contrast, Fig. 5 shows the simulation processof the communication scheme based on the same frequencycarrier-based modulation combined with ICA.

In Fig. 4, the first part shows the four modulated signalsbased on the carrier allocation 2PSK modulation, and themixed signals are shown in the second part, whereas therestored signals are shown in the third part. In Fig. 5,the first part shows the four modulated signals based onthe same frequency carrier 2PSK modulation, and themixed signals are shown in the second part, whereas therestored signals are shown in the third part. The modulatedsignals based on the carrier allocation modulation are inde-pendent of each other and meet the independence principleof ICA algorithm. Although the same frequency carriermodulation based modulated signals have strong correlation,and they do not satisfy the independence principle of ICAalgorithm. So, as shown in Fig. 4(c), the proposed MIMOVLC scheme can restore the modulated signals at the receiv-ing end for just change the phase and amplitude of the sourcesignal. By comparison, Fig. 5(c) shows that the comparisonscheme cannot restore the modulated signals.

Because of each sending end witha different carrier fre-quency, we can distinguish the various restored signals.

Fig. 4 Simulation of carrier allocation combined with independent component analysis (ICA)–basedsystem. (a) The modulated signals, (b) the mixed signals, and (c) the separated signals.




Precoding data can find the change of phase amplitude.Based on this, the proposed MIMO VCL scheme basedon the carrier allocation and ICA can be effectively imple-mented in the unknown CSI case.

5 Analysis of System PerformanceThe modulated signals modulated by carrier allocation based2PSK modulation at the sending end solved the independ-ence requirement of ICA algorithm, makes it possible touse ICA algorithm in MIMO VLC systems without CSI.In order to verify the performance of the proposed MIMOVLC scheme, 2PSK and 2 × 2 MIMO VLC system areadopted to investigate the SNR and bit error ratio (BER) per-formance. The effect of the proposed system on the SNR andBER of the restored signal is studied and compared with thedetection method based on the channel estimation.

5.1 SNR Performance of the Proposed SystemScheme

Because the degree of non-Gaussian is measured by high-order cumulant and the high-order cumulant of Gaussian ran-dom variable is 0, ICA algorithm can theoretically removeGaussian noise. Therefore, we expect that the separated sig-nals have a higher SNR than the received signal. The effectof signal separation process on the SNR is shown in Table 1.

Where Rs represents the SNR of the received signal, Dsrepresents the SNR of the separated signal, the separated sig-nal is restored from the received signal by ICA algorithm. Asshown in Table 1, the SNR of the separated signal improvedwhen the SNR of the received signal is low. Although the

received signal at higher SNR, the SNR of the separated sig-nal is decreased a little. Therefore, the proposed scheme canimprove system performance at low SNR environment, andalso close to the ideal requirement at high SNR environment.

5.2 BER Performance of the Proposed SystemScheme

In order to study the BER performance of the proposed com-munication scheme, 2 × 2 MIMOVLC system is adopted asthe simulation system. 2PSK modulation based on the carrierallocation is used in each sending end. ICA algorithm is usedto restore modulated signal from the received signal, whereasMMSE and ZF are the comparison schemes under the sameconditions to restore the modulated signal.12 The BER ofeach scheme is shown in Fig. 6, the abscissa representsthe SNR of the received signal.

In Fig. 6, the black line represents the theoretical BER of2PSK modulation in SISO VLC system and the other threecurves represent the BER of the above three signal process-ing schemes, respectively, in 2 × 2 MIMO VLC system.When the SNR ≤ 0 dB, the BER of the proposed scheme

Fig. 5 Simulation of the same frequency carrier modulation combined with ICA based system. (a) Themodulated signals, (b) the mixed signals, (c) the separated signals.

Table 1 The effect of signal separation process on signal-to-noiseratio.

Rs (dB) −6 −4 −2 0 2 4 6 8 10 12 14

Ds (dB) −2.7 −2.4 −1.1 0.04 1.9 3.2 4.5 6.2 7.5 8.7 9.7




is slightly lower than the two comparison schemes, and all ofthem are close to theoretical BER of the 2PSK modulation.With the SNR increasing, the BER of the proposed schemedecreases significantly, and its BER reaches the level of onemillionth when SNR ¼ 14 dB. In contrast, the BER of theMMSE and ZF based scheme which dependent on CSIestimation greater than 0.0001 under SNR ¼ 14 dB anddecrease slowly with the increasing SNR. So, the proposedcommunication scheme has a better BER performance thanthe method based on CSI estimate like MMSE or ZF.

6 ConclusionIt is difficult to precisely estimate the channel in practicalMIMO VLC system. Sometimes there is no CSI availableat all. Under such conditions, those CSI-based algorithmswould not work or work with poor efficiency. In thispaper, we propose an indoor MIMOVLC scheme based pre-coding carrier allocation and ICA. Carrier allocation ensuresthat the modulated signals are independent of each othersuch that the application of ICA to separate the mixed modu-lated signal is possible. Simulation results show that the pro-posed MIMOVLC scheme can be implemented successfullywithout CSI, and both SNR performance and BER perfor-mance have reached a good level.

AcknowledgmentsThis work was supported by the Natural Science Foundation ofHunan project ring-resonator-spectroscopic-based detection

mechanism and methods of gas pollution, ProjectNo. 14JJ2013 and Natural Science Foundation of Xinjiangproject Detection theory and methods of gas pollution,Project No. 2013211A035.

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8. A. Hyvärinen, J. Karhunen, and E. Oja, Independent ComponentAnalysis, pp. 239–262, John Wiley (2001).

9. H.-S. Kim et al., “Mitigation of inter-cell interference utilizing carrierallocation in visible light communication system,” IEEE Commun.Lett. 16(4), 526–529 (2012).

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Fangqing Jiang is a postgraduate student at Institute of Physics andElectronics in Central South University. His research interests includevisible communication, information theory, source coding, and signalprocessing.

Honggui Deng is a professor and vice president at the School ofPhysics and Electronics at Central South University. His researchinterests include communication, information theory, source coding,and signal processing.

Fang Yang is a postgraduate student at the Institute of Physics andElectronics at Central South University. Her research interests dealwith wireless communication.

Biographies of other authors are not available.

-6 -4 -2 0 2 4 6 8 10 12 1410-7

10-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BE

RBER for BPSK modulation with MIMO

MIMO, ZF, (Tx=2, Rx=2)MIMO, MMSE, (Tx=2, Rx=2)MIMO, ICA, (Tx=2, Rx=2)SISO, 2PSK performance theory

Fig. 6 Bit error ratio performance.




http://dx.doi.org/10.1109/JSAC.2009.091215

http://dx.doi.org/10.1109/JSAC.2009.091215

http://dx.doi.org/10.1109/LPT.2008.926030

http://dx.doi.org/10.1109/LCOM.2006.224413

http://dx.doi.org/10.1109/LCOMM.2011.010411.101945



http://dx.doi.org/10.1109/TCOMM.2003.813259

carrier allocation combined with independent component...

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