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Farooqui and Saengudomlert EURASIP Journal onWireless Communications andNetworking 2013, 2013:138http://jwcn.eurasipjournals.com/content/2013/1/138

RESEARCH Open Access

Transmit power reduction through subcarrierselection for MC-CDMA-based indoor opticalwireless communications with IM/DDMuhammad Zubair Farooqui* and Poompat Saengudomlert

Abstract

This research addresses the issue of average transmit optical power reduction in multi-carrier code division multipleaccess (MC-CDMA)-based indoor optical wireless communications employing intensity modulation with directdetection. The problem is treated in a novel way by investigating pre- and post-equalization-based subcarrier selectionfor transmit power reduction in downlink transmissions. Analytical expressions are derived for upper bounds of therequired fixed DC bias for both cases. The fixed DC bias is used to reduce the system complexity on one hand and todevise optimal subcarrier selection criteria on the other. Simulation results based on the proposed subcarrier selectionreveal significant power reduction subject to the 10−4 bit error rate (BER) requirement for 10-Mbps 64-subcarrierMC-CDMA-based indoor optical wireless communication systems. In addition, the BER performance obtained frompre-equalization is shown to be no higher than that obtained from post-equalization for the same transmit power.

1 IntroductionMulti-carrier and multiple access communication tech-nologies like orthogonal frequency division multipleaccess (OFDMA) and multi-carrier code division mul-tiple access (MC-CDMA) have captured different vistasof communications not only for simple text data butalso for different types of multimedia requiring robusttransmissions. For 4G wireless systems [1] and beyond,optical wireless communication is considered as a linch-pin to serve as a complementary sibling of RF for systemimplementation in indoor environments. Although multi-carrier models, especially OFDM-based, have been muchinvestigated, relatively few work can be observed regard-ing the use of MC-CDMA for indoor optical wirelesscommunications.Recently optical wireless systems are reported to be

integrated with WiFi networks to provide ubiquitouscoverage systems for indoor applications [2]. In thesesystems, the optical spectrum provides an encouragingpotential as a complementary medium to the congestedradio spectrum. For such applications, intensity modu-lation (IM) can be applied to either infrared or visible

*Correspondence: [email protected] Field of Study, School of Engineering and Technology,Asian Institute of Technology (AIT), Klong Luang, Pathumthani 12120, Thailand

light. The key advantages of such optical wireless sys-tems are usage of flexible unlicensed spectrum, highdata rate support, energy efficiency, no electromagneticinterference, low-cost front ends, and inherent security.Major issues are eye and skin safety problems which canbe dealt with by limiting the average transmit opticalpower.The contributions of this research, which are not

reported previously to the best of the authors’ knowledge,are highlighted as follows:

1. Average transmit optical power reduction isaccomplished by subcarrier selection for the firsttime in MC-CDMA-based indoor optical wirelesscommunication systems employing intensitymodulation with direct detection (IM/DD).

2. Expressions for upper bounds of a fixed DC biasusing pre- and post-equalization-based subcarrierselection are analytically derived forMC-CDMA-based IM/DD system.

3. Optimal subcarrier selection algorithms thatminimizes the bit error rate (BER) for a fixedtransmit optical power are proposed for bothpre- and post-equalization.

© 2013 Farooqui and Saengudomlert; licensee Springer. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

Farooqui and Saengudomlert EURASIP Journal onWireless Communications and Networking 2013, 2013:138 of 14http://jwcn.eurasipjournals.com/content/2013/1/138

This paper is organized as follows. In Section 2, relevantworks are discussed. Section 3 presents the proposed sys-temmodel. Results and discussions are given in Section 4.Finally, conclusions are given in Section 5.

2 Related works2.1 Average transmit power issue inmulti-carrier optical

wireless communicationsOne major difference between an optical IM/DD chan-nel and a conventional radio/electrical channel is that thechannel input and output are signal intensities. This prop-erty has two major consequences - the input to the opticalchannel must be nonnegative, while the average transmitoptical power is proportional to the mean (first momentcontrary to second moment for electrical domain) of theinput to the channel [3]. The former requires that an opti-cal signal be unipolar, leading to the addition of a DC biasto the transmit signal. Despite the fact that the additionof symbol-by-symbol DC bias seems theoretically simple,it results in a significant increase in system implementa-tion complexity. Hence, using a fixed DC bias is practicallyattractive. The use of a DC bias results in a high trans-mit power whichmay be hazardous for eye and skin safety[4,5]. Moreover, this additional power does not increasethe SNR at the receiver at all [6]. Therefore, some appro-priate power reduction scheme is required so that theassociated DC bias does not lead to excessive transmitoptical power [7].The Infrared Data Association (IrDA), ANSI, and IEC

standards recommend to limit the transmit optical powerfor different applications to address eye and skin safetyproblems at length [8,9]. Hence, being equivalent in con-notation to the issue of peak-to-average power (PAPR)reduction in radio transmissions, transmit power reduc-tion is at the crux of researches in multi-carrier opticalwireless communications. While the issue has been inves-tigated for OFDM-based optical wireless systems, to thebest of the authors’ knowledge, any direction of reparationof this issue has not yet been reported for MC-CDMA-based optical wireless systems with IM/DD.For simple multi-carrier-based and OFDM-based

indoor optical wireless communications, the followingprominent solutions were put forth to address the issue ofaverage power reduction. Block coding was investigatedin [3] using symbol-by-symbol bias for power reduction.An approach based on optimized reserved subcarrierswas investigated in [10] . Clipped OFDMwas suggested in[7] instead of conventional DC bias for achieving powerreduction. The technique is claimed to have better powerefficiency when compared to the DC bias approach.According to [11], clipped OFDM attains some advan-tages over DC-biased OFDM but at the cost of sacrificinga reasonable chunk of the available signaling bandwidth.

The authors of [12] addressed the same issue by employ-ing in-band coding to use with symbol-by-symbol bias.A novel approach of using out-of-band subcarriers toreduce transmit power was proposed in [13]. The use ofthe selected mapping technique was investigated in [14]to achieve reduction in average transmit optical power. Asimple power allocation approach was suggested in [15] toachieve power reduction for a specific BER requirement.In [16], sparsity together with uncertainty principle wasused for average power reduction. The authors in [17]proposed the use of Hartley transform module instead ofinverse fast Fourier transform (IFFT) module to assurereal positive output, eliminating the need of addingDC bias and greatly enhancing the power efficiency inOFDM-based optical IM/DD systems. However, none ofthe works have been found reported for transmit powerreduction in MC-CDMA with IM/DD.

2.2 Optical wireless channelThe key distinction between a conventional electricalchannel and an IM/DD optical channel is that data aretransmitted through the optical channel in the form ofsignal intensity. Accordingly, an IM/DD optical wirelesssystem imposes the constraint that the transmitted sig-nal should be real-valued and nonnegative to appropri-ately drive the light source [18]. Moreover, there is nomulti-path fading due to a typically high ratio between aphotodetector area and an optical wavelength [8].From [8], the baseband model for an optical IM/DD

channel in a diffused configuration can be mathematicallyrepresented as

Y (t) = RX(t) ⊗ h(t) + N(t), (1)

where

h(t) = H(0)6a6

(t + a)7u(t), (2)

Y (t) is the output photocurrent of the photodetector, R isthe detector responsivity, and ⊗ is the convolution oper-ation. The IM/DD optical channel impulse response h(t)is dependent on the channel DC gain H(0) and a factora which further depends on the rms delay spread D suchthat a = 12

√1113D.

The prominent cause of noise is visible background light(fluorescent light, incandescent light, and sunlight), whichis independent of the nature of the signal and modeled asadditive white Gaussian noise (AWGN) [19], denoted byN(t). Finally, u(t) is the unit step Heaviside function.

2.3 MC-CDMAOwing to its high spectral efficiency, flexibility, andendurance to frequency-selective fading, MC-CDMA, anamalgam of OFDM and CDMA based on the principleof frequency domain spreading, has emerged as a strong

Farooqui and Saengudomlert EURASIP Journal onWireless Communications andNetworking 2013, 2013:138 of 14http://jwcn.eurasipjournals.com/content/2013/1/138

OFDM modulation

Cyclic prefix insertion

D/A conversion and passbandmodulation

DC bias insertion

Optical source

Transmit data symbols (weightedby1/Hn in case of pre-equalization)

Spreading infrequency domain

Transmitter

OFDM demodulation

Cyclic prefix removal(weighted by 1/Hn in case of post-equalization)

A/D conversion and demodulation

DC bias removal

Photodetector

Receive datasymbols

Despreading

Receiver

Optical IM/DDchannel

Figure 1MC-CDMA-based indoor wireless optical system with IM/DD.

candidate for future communication systems in recentyears. In the last decade, MC-CDMA has attracted lots ofinterests in the research community, especially for down-link applications, where frequency domain equalizationtechniques can be used to mitigate multi-access interfer-ence (MAI) that arises due to multi-path propagation. Nosignificant linear distortion is confronted in MC-CDMAbecause the symbol duration is much longer than the delayspread. MC-CDMA also offers flexible system designsince the length of orthogonal signatures distinguishingmultiple users from one another need not be equal to thenumber of subcarriers [20].The working of MC-CDMA is such that an individ-

ual user’s complex-valued data symbol is spread overOFDM subcarriers in the frequency domain using aspreading code. These symbols from different users aresummed in the frequency domain and then passed to theOFDM modulator to transform into the time domain. Acyclic prefix is appended to mitigate inter-symbol inter-ference with the result upconverted to the passband afterserial-to-parallel conversion. At the receiver side, cyclicprefix removal, FFT, and despreading are carried outrespectively.

2.4 EqualizationChannel equalization is a crucial phase in wirelesscommunication systems. Due to the frequency-selectivenature of wireless communication channels, spread spec-trum schemes suffer impairments in orthogonality, whichcan be restored using different equalization techniques.In essence, the exploitation of appropriate equalization

helps to efficiently combine different subcarriers’ sig-nals in order to optimize the system performance [21].Equalization requires the availability of channel esti-mates at the receiver or at the transmitter or at bothends depending upon the case of post-, pre- or com-bined equalization, respectively. Pre-equalization focuseson pre-compensating the predictable channel distortions.Conventionally, MAI mitigation in MC-CDMA systemsis carried out by single-user or multi-user detectionschemes (SUD or MUD) at the receiver [22]. Equalization

Table 1 Simulation parameters

Parameter Specification

Transmission bit rate 10 Mbps

Modulation QPSK

Number of subcarriers 64

Spreading sequences Walsh-Hadamard

Channel model As in (2) [8]

Equalization Single-tap frequency domain

pre- and post-equalization

Digital-to-analog converter (DAC) Rectangular pulse

H(0) (DC channel gain) −60 dB [8]

N0 (noise variance) 10−23 A2/Hz [8]

D (rms delay spread) 10 ns [8]

R (photodetector responsivity) 1 A/W [8]

Transmit power calculation As per multi-carrier optical

wireless communications


is preferred over SUD and MUD techniques in terms ofsystem complexity [23-25].Equalization may be linear or nonlinear [26]. Equal

gain combining, maximal ratio combining, orthogonal-ity restoring combining, and minimum mean squareerror techniques are some versions of linear equalizationemployed in MC-CDMA, where appropriate coefficientsare used as weighting factors for the signals from differentsubcarriers. Interference cancellation and maximum like-lihood detection are examples of nonlinear equalizationwhich provide performance improvement at a tradeoffwith receiver complexity [27]. The authors in [28] demon-strated the significant dependence of PAPR on the equal-ization technique and exploited equalization coefficientsfor PAPR reduction in MC-CMDA systems.

3 Proposed system3.1 MethodologyIn this research, we demonstrate how subcarrier selectioncan be exploited to achieve reduction in average transmitoptical power in MC-CDMA-based indoor optical wire-less communications with IM/DD.We propose subcarrierselection based on linear equalization, which is consid-ered to be the simplest and least expensive technique to beimplemented [26] tomitigate various impairments in con-ventional MC-CDMA systems. Along with taking advan-tage of these positive features of linear equalization, wederive upper bounds for obtaining fixed DC bias values forboth and pre- and post-equalization inMC-CDMA-basedindoor optical wireless communications with IM/DD.Based on these upper bounds, we devise subcarrier selec-tion criteria for both pre- and post-equalization imple-mentation.The subcarrier selection algorithms obtainedanalytically are used in the simulation to observe the

average transmit optical power reduction separately forboth cases.Optical wireless channels exhibit frequency-selective

nature at high data rates for multi-carrier signals. To usethe transmission bandwidth efficiently, subcarriers withbetter channel gains are used through an equalization-based criterion. For this, we investigate downlink opticalwireless transmissions with the data rates of 10 Mbps,which is considered moderate for optical wireless-basedindustrial applications [1,2]. The mentioned data trans-mission rate is used, keeping in view the two importantfactors in considering IR-based indoor optical wirelesssystems with diffused configuration. Firstly, the standardsframed by IrDA and IEEE for typical room sizes in indooroptical wireless systems are of the order of this range[9,29]. Secondly, the operating speed of currently avail-able commercial devices in the market is typically in thesame order as for our system. According to [30], thereare theoretical limits and practical constraints like suit-able optical sources and drive electronics in achievinghigh data rates for such systems. Data transmissions aresimulated separately using MATLAB (MathWorks Inc.,Natick, MA, USA), for pre- and post-equalization cases.The key parameters used for the selection of subcarri-ers are the channel gains of individual subcarriers. Sincechannel variations are slow in indoor environments, thechannel state information (CSI) derived at a particularinstant can be used for some subsequent time durationin indoor optical wireless systems. Subcarrier selectionfor MC-CDMA can be further advocated by the fact thatdifferent subcarriers contain information on the samedata symbol; therefore, noise-dominated subcarriers canbe discarded and signal energy can be reallocated tobetter subcarriers.

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 630

0.2

0.4

0.6

0.8

1

1.2

1.4 x 10−7

Subcarrier index

Cha

nnel

gai

ns (

mag

nitu

de)

Figure 2 Channel gains for 64 subcarriers at 10Mbps.


0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 6446

48

50

52

54

56

58

Number of active subcarriers (Na)

Q−

func

tion

argu

men

t

Figure 3 Q function argument vs. number of active subcarriers for the radio domain.

3.2 SystemmodelThe system model is specified by the following notations.For analysis, it is sufficient to focus on the transmission ofa single symbol from each user:

• L, number of active users• N, number of subcarriers• Ncp = γN , length of cyclic prefix where 0 ≤ γ ≤ 1• Na, set of active (selected) subcarrier indices• Na, number of active subcarriers indices, i.e.,

Na = |Na|• dl , data symbol from user l• cl,n, CDMA codeword component for user l on

subcarrier n ∈ Na

• T, MC-CDMA symbol period• fc, electronic carrier (passband) frequency• p(t), transmit pulse shape• B, fixed bias of nonnegative passband signal for IM• Amax, maximum amplitude of QPSK symbol• sb(t), baseband MC-CDMA signal• sp(t), passband MC-CDMA signal• sopt(t), transmit optical signal• Es, QPSK symbol energy• Hn, FFT of the discrete-time channel impulse

response with length N symbol periods(n ∈ {0, . . . ,N − 1})

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64−10

−5

0

5

10

15

20


Q−

func

tion

argu

men

t

Figure 4 Q function argument vs. number of active subcarriers for the optical wireless domain.


Table 2 Q function arguments for both domainsemploying post-equalization-basedsubcarrier selection

Radio domain Optical wireless domain

Naσ

√√√√ Es( ∑n∈Na

1/|Hn|2) Bpost

Lσ

√T

1+γ

√√√√ 1( ∑n∈Na

1/|Hn|2)

• Wn, complex AWGN values, which are iid circularlysymmetric complex Gaussian rv with variance σ 2

(the variance of a complex random variable is thesum of the variance of the real part and that of theimaginary part).

Each user’s binary data from the source is mappedonto complex-valued symbols dl and spread in the fre-quency domain using a user-specific Walsh-Hadamardspreading code. Each CDMA codeword is assumed to bebipolar with its components belonging to the set {1,−1}.However, for convenience, we assume that a codewordcomponent is equal to 0 on each inactive subcarrier. Forexample, out of eight subcarriers, if the first two and thelast two subcarriers are active for user 0 and if the CDMAcodeword for user 0 is (1,−1, 1,−1), then we write

(c00, c01, c

02, c

03, c

04, c

05, c

06, c

07) = (1,−1, 0, 0, 0, 0, 1,−1).

Hence, users are distinguished by their respective codesequences. Every chip of the spreading code represent-ing a fraction of the information symbol is transmittedthrough an active subcarrier. As described in Section 3.1,these active subcarriers are selected based on the CSI.Figure 1 illustrates the transmission system model. An

IFFT blockmodulates all QPSK data symbols correspond-ing to the total number of subcarriers. A cyclic prefix isinserted between each pair of successive symbols afterconverting them into a serial stream. Finally, the data

signal is converted from digital to analog after which afixed DC bias B is added to the signal to facilitate inten-sity modulation. When this signal travels through themedium, different subcarriers suffer different degradationand lose their mutual orthogonality. At the receiver, theDC bias is removed. After demodulation, each cyclic pre-fix is removed to obtain N-subcarrier components. TheN − Na components are discarded after FFT and theremaining Na components are despreaded to get eachrespective user-specific data symbol.The above model is used to derive upper bounds for

a fixed DC bias by employing pre-equalization and post-equalization schemes. For each case under investigation,CSI is assumed to be available at the transmitter or atthe receiver as per post- or pre-equalization requirements,respectively. Then these fixed biases, denoted by Bpostand Bpre, are employed in finding the optimal criteriafor subcarrier selection in both cases. The following twosubsections show the analytical models for both casesalong with the derivation of conservative bounds for fixedDC biases. In both cases, subcarrier selection is basedon maximizing the argument of the Q function in theBER expression, where the Q function is the comple-mentary cumulative distribution function of zero-meanunit-variance Gaussian random variable.

3.2.1 Post-equalization caseAt the transmitter, regardless of the number of active sub-carriers Na, the number of distinct symbols to be trans-mitted will always be N. The data symbols after the IFFToperation are represented as

Dk = 1√N

L−1∑l=0

N−1∑n=0

dl · cl,nej2πkn/N , k ∈{0, . . . ,N − 1} .

(3)

−2 1 4 7 10 13 16 19 22 25 28 31 3410

−5

10−4

10−3

10−2

10−1

100

Average transmit optical power (dBm)

BE

R

Na = Nc(L)= 2 [With subcarrier selection]

Na = N = 64 [Without subcarrier selection]

Figure 5 BER vs. transmit power with and without post-equalization-based subcarrier selection with two users.


16 18 20 22 24 26 28 30 32 34 36 3810

−5

10−4

10−3

10−2

10−1

100


BE

R



Figure 6 BER vs. transmit power with and without post-equalization-based subcarrier selection with 32 users.

The complex baseband transmitted signal is

sb(t) =N−1∑k=0

Dkp(t − kT/(1 + γ )N) (4)

where p(t) is the unit norm rectangular transmit pulseshape of width T/(1 + γ )N

p(t) ={√

(1+γ )NT t ∈ (0,T/((1 + γ )N)]

0, otherwise.(5)

Hence, the real passband MC-CDMA signal to be usedfor IM is

s(t) = Re

[ej2π fct

N−1∑k=0

Dkp(t − kt/(1 + γ )N)

], (6)

while the transmitted optical signal will be

sopt(t) = s(t) + Bpost. (7)

We focus on the transmission period of the kth pulse,i.e., p(t − kT/(1 + γ )N). The real signal amplitude from(5) and (6) is given by

s(t) =√

(1 + γ )NT

Re{Dkej2π fct

},

t ∈[k

T(1 + γ )N

, (k + 1)T

(1 + γ )N

].

For fc >> (1 + γ )N/T (i.e., several periods ofcarrier waveform during the pulse interval), which is

2 4 8 16 320

5

10

15

20

25

No. of Users (L)

Pow

er r

educ

tion

(dB

)

Figure 7 Power reduction for 2, 4, 8, 16, and 32 active users using post-equalization-based subcarrier selection.


typically the case, the minimum amplitude of s(t) in[k T

(1+γ )N , (k + 1) T(1+γ )N

]can be taken as

−√

(1 + γ )NT

∣∣∣Dkej2π fct∣∣∣ = −

√(1 + γ )N

T|Dk | .

It follows that the required bias during this interval is√(1+γ )N

T |Dk |, which can be bounded as

Bpost =√

(1 + γ )NT

|Dk |

=√

(1 + γ )NT

∣∣∣∣∣ 1√N

L−1∑l=0

N−1∑n=0

dl · cl,nej2πkn/N

∣∣∣∣∣=√1 + γ

T

∣∣∣∣∣L−1∑l=0

N−1∑n=0

dl · cl,nej2πkn/N

∣∣∣∣∣≤√1 + γ

T

L−1∑l=0

∣∣∣∣∣dlN−1∑n=0

cl,nej2πkn/N

∣∣∣∣∣≤√1 + γ

T

L−1∑l=0

|dl|∣∣∣∣∣N−1∑n=0

cl,nej2πkn/N

∣∣∣∣∣ . (8)

We are interested in the maximum negative value ofthe signal. Hence, we set |dl| ≤ Amax, which, in turn,depends upon the constellation configuration and theallocated subcarrier powers. Moreover, we set Cl,k =N−1∑n=0

cl,nej2πkn/N . So inequality (8) becomes

Bpost ≤√1 + γ

TAmax

L−1∑l=0

Cl,k .

To give an upper bound that is independent of k, i.e., fixedbias, the final expression is

Bpost ≤ maxk∈{0,1,...,N−1}

√1 + γ

TAmax

L−1∑l=0

Cl,k . (9)

Since only the data on the active subcarriers will be pro-cessed at the receiver

Cl,k =∣∣∣∣∣∣∑n∈Na

cl,nej2πkn/N

∣∣∣∣∣∣≤∑n∈Na

∣∣∣cl,nej2πkn/N∣∣∣ = Na, (10)

yielding an upper boundL−1∑l=0

Cl,k ≤ LNa. (11)

The expression in (10) imposes an upper bound on thevalue of Cl,k , thus yielding a conservative value of the DCbias. Thus, from (9) and (11), we get

Bpost ≤√1 + γ

TAmaxLNa. (12)

For the BER analysis, we shall focus on the equiva-lent baseband complex discrete-time system model. Thereceived signals at the OFDM receiver can be expressed asvector r = (r0, . . . , rN−1) such that

rn = Hnsn + Wn, (13)

where (H0, . . . ,HN−1) is the FFT of the discrete-timechannel impulse response (whose length is N symbolperiods), and Wns are complex AWGN values. In par-ticular, we assume that Wns are iid circularly symmetricGaussian random variables with variance σ 2 (when thenoise PSD is given by N0/2, we have σ 2 = N0/N). For

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64124

125

126

127

128

129

130

131

132

133

134


Q−

func

tion

argu

men

t

Figure 8 Q function argument vs. number of active subcarriers for the radio domain.


equalization as well as restoring the CDMA code orthog-onality, we apply one-tap equalization to obtain r′ =(r′0, . . . , r

′N−1

)such that

r′n = sn + Wn/Hn. (14)

From the equalized received signals, the QPSK symboldl can be obtained using the codeword cl, i.e., despread-ing. Let d̂l be the received signal after despreading. Inparticular,

d̂l = cTl r′ = Nadl +

N∑n=1

cl,nWn/Hn. (15)

For analyzing a user-specific performance, without loss ofgenerality, we consider the received signal of user 0 (d̂0).

d̂0 = Nad0 +N∑

n=1c0,nWn/Hn. (16)

For QPSK, the BER can be found from the receivedsymbol energy and the noise variance as

Received symbol energy = N2a Es

Noise variance = σ 2

⎛⎝∑

n∈Na

1/ |Hn|2⎞⎠

BERpost-eq = Q

⎛⎜⎜⎜⎜⎜⎝Naσ

√√√√√√Es( ∑

n∈Na

1/ |Hn|2)⎞⎟⎟⎟⎟⎟⎠ .

(17)

For QPSK, using Amax = √Es in (12), the BER in terms of

the DC bias is found to be

BERpost-eq = Q

⎛⎜⎝Bpost

Lσ

√T

1 + γ

√√√√ 1∑n∈Na

1/ |Hn|2

⎞⎟⎠

(18)

Subcarrier selection: post-equalization case. The BERexpression in (18) yields the following theorem that pro-vides a method to select active subcarriers. Let Nc(L)

denote the length of CDMA codewords required toaccommodate L users. Note that the value Nc(L) dependson the type of codewords used.

Theorem 1. Given that we use the DC bias in (12), theset of active subcarriers that yields the minimum BER isselected as follows:

1. The number of active subcarriers is Nc(L).

2. The selected active subcarriers are the Nc(L)

subcarriers with the highest gain magnitudes, i.e.,highest |Hn|s.

Proof. Minimize the BER expression in (18) over Nc(L) ≤Na ≤ N is equivalent to solving the following optimizationproblem:

maximize ξ =√√√√ 1∑

n∈Na

1/|Hn|2

subject to Nc(L) ≤ Na ≤ N

The value of ξ is decreasing withNa since |Hn|’s are alwayspositive. Consequently, the smallest possible value ofNa isoptimal. Since we need to use at leastNc(L) subcarriers, itfollows that Na = Nc(L). This proves part 1.Now, given that we must use Nc(L) subcarriers, the

best choice is to select the subcarriers with the highestmagnitude gains to maximize ξ . This proves part 2.

3.2.2 Pre-equalization caseWhen equalization is employed at the transmitter, everydata symbol is weighted by 1/Hn. Accordingly, the datasymbols after the IFFT operation are represented as

Dk = 1√N

L−1∑l=0

N−1∑n=0

dl · cl,nHn

ej2πkn/N . (19)

After a similar treatment as in the case of post-equalization, we get the fixed DC bias Bpre as follows

Bpre =√

(1 + γ )NT

|Dk | (20)

=√

(1 + γ )NT

∣∣∣∣∣ 1√N

L−1∑l=0

N−1∑n=0

dl · cl,nHn

ej2πkn/N

∣∣∣∣∣=√1 + γ

T

∣∣∣∣∣L−1∑l=0

N−1∑n=0

dl · cl,nHn

ej2πkn/N

∣∣∣∣∣≤√1 + γ

T

L−1∑l=0

∣∣∣∣∣dlN−1∑n=0

cl,nHn

ej2πkn/N

∣∣∣∣∣≤√1 + γ

T

L−1∑l=0

|dl|∣∣∣∣∣N−1∑n=0

cl,nHn

ej2πkn/N

∣∣∣∣∣ . (21)

We are interested in the maximum negative value ofthe signal. Hence, we set |dl| ≤ Amax, which, in turn,depends upon the constellation configuration and theallocated subcarrier power. Moreover, we set C′

l,k =∣∣∣∣N−1∑n=0

cl,nHn

ej2πkn/N∣∣∣∣. So inequality (21) becomes

Bpre ≤√1 + γ

TAmax

L−1∑l=0

C′l,k .


0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64−10

−5

0

5

10

15

20


Q−

func

tion

argu

men

t

Figure 9 Q function argument vs. number of active subcarriers for the optical wireless domain.

To give an upper bound that is independent of k, i.e.,fixed bias, the final expression is

Bpre ≤ maxk∈{0,1,...,N−1}

√1 + γ

TAmax

L−1∑l=0

C′l,k . (22)

Since only the data on the active subcarriers will beprocessed at the receiver, we can generalize in a similarfashion as in the case of post-equalization,

C′l,k =

∣∣∣∣∣∣∑n∈Na

cl,nHn

ej2πkn/N

∣∣∣∣∣∣≤∑n∈Na

∣∣∣∣cl,nHnej2πkn/N

∣∣∣∣ =∑n∈Na

1|Hn| , (23)

yielding an upper bound

L−1∑l=0

C′l,k ≤ L

∑n∈Na

1|Hn| . (24)

The expression in (23) imposes an upper bound on thevalue of C′

l,k , thus yielding a conservative value of the DCbias. Thus, from (22) and (24), we get

Bpre ≤√1 + γ

TAmaxL

∑n∈Na

1|Hn| . (25)

By proceeding in the similar fashion as in the caseof post-equalization and incorporating noise variance =σ 2Na, we get the BER expression as

BERpre-eq = Q(1σ

√EsNa

). (26)

Using (25) and incorporating Amax = √Es for QPSK,

the BER expressing in terms of the DC bias is

BERpre-eq = Q

⎛⎜⎝√

TNa1 + γ

Bpre

Lσ∑

n∈Na

1/|Hn|

⎞⎟⎠ . (27)

Subcarrier selection: pre-equalization case. The BERexpression in (27) yields the following theorem that pro-vides a method to select active subcarriers.

Theorem 2. Given that we use the DC bias in (25), theset of active subcarriers that yields the minimum BER isselected as follows:

1. The number of active subcarriers is Nc(L).2. The selected active subcarriers are the Nc(L)

subcarriers with the highest gain magnitudes i.e.,highest |Hn|s.

Proof. Minimizing the BER expression in (27) overNc(L) ≤ Na ≤ N is equivalent to solving the followingoptimization problem:

maximize κ =√Na∑

n∈Na

1/|Hn|

subject to Nc(L) ≤ Na ≤ N

Table 3 Q function arguments for both domainsemploying pre-equalization-based subcarrier selection

Radio domain Optical wireless domain

1σ

√EsNa

√TNa1+γ

BpreLσ

∑n∈Na

1/|Hn |


Since |Hn|s are smaller than 1 (i.e., signal attenuationtypically in the order of 10−7), κ decreases withNa. Conse-quently, the smallest possible value of Na is optimal. Sincewe need to use at least Nc(L) subcarriers, it follows thatNa = Nc(L). This proves part 1.Now, given that we must use Nc(L) subcarriers, the

best choice is to select the subcarriers with the highestmagnitude gains to maximize κ . This proves part 2.

3.3 Comparison betweenBERpost-eq and BERpre-eqFrom the previous discussions, we conclude that for bothpost-equalization and pre-equalization it is optimal toselect Nc(L) subcarriers with the highest |Hn|s. The nextquestion is whether post-equalization or pre-equalizationperforms better in terms of the BER for a given DC biasBpost = Bpre = B.The next theorem shows that pre-equalization always

performs no worse than post-equalization.

Theorem 3. Given that the DC biases in (12) and (25) areused for post-equalization and pre-equalization respec-tively, the corresponding BER for pre-equalization is nomore than the BER for post-equalization.

Proof. We first rewrite the post-equalization BER expres-sion of (18) as

BERpost-eq = Q

⎛⎜⎝ BLσ

√T

(1 + γ )Na

√√√√ Na∑n∈Na

1/|Hn|2

⎞⎟⎠ .

(28)

We proceed in a similar fashion from the pre-equalization BER expression of (27) to obtain

BERpre-eq = Q

⎛⎜⎝ BLσ

√T

(1 + γ )Na

Na∑n∈Na

1/|Hn|

⎞⎟⎠ . (29)

In (28) and (29), the first two factors in the arguments ofthe Q function are identical (denoted by α). Hence,

(28) =⇒ BERpost-eq = Q

⎛⎜⎝α

√√√√ Na∑n∈Na

1/|Hn|2

⎞⎟⎠

and(29) =⇒ BERpre-eq = Q

⎛⎜⎝α

Na∑n∈Na

1/|Hn|

⎞⎟⎠ .

From the direct consequence of the Cauchy-Schwarz

inequality

n∑i=0

xi

n ≤

√n∑

i=0x2i

n , the inequality Na∑n∈Na

1/|Hn| ≥√

Na∑n∈Na

1/|Hn|2 holds. It follows that BERpre-eq ≤ BERpost-eq.

4 Analytical and simulation results withdiscussions

Based on the system model of MC-CDMA-based indooroptical wireless communications and the simulationparameters shown in Table 1, the system is simulatedusing MATLAB for observing power reduction per-formance using optimal number of subcarriers (fromTheorem 1 and 2 developed in Section 3) with respect tousing all available subcarriers.For 10-Mbps 64-subcarrier system, the subcarriers’

channel gains are shown in Figure 2. The observed varia-tions in the channel gains can be exploited for subcarrierselection at high data rates of the same order. Besidesimproving the BER performance of the system, this factis used to reduce the DC bias and hence average transmitoptical power, as will be demonstrated in the subsequentgraphs.

4.1 Post-equalization-based subcarrier selectionFigures 3 and 4 show the analytical curves for the argu-ment of the Q function for 10 Mbps in the case of theradio domain and the optical wireless domain, respec-tively, when employing successively an increasing numberof active subcarriers (with decreasing channel gain mag-nitudes) in an MC-CDMA-based indoor optical wirelessIM/DD system with 64 subcarriers. The expressions forthe Q function arguments (derived in Section 3.2.1) forboth domains are shown in Table 2.It can be observed in Figure 3 that an optimal number

of active subcarriers exists in the range 1 < Na < Nfor the radio domain. The behavior is different for theoptical wireless domain where it is always better to havefewer active subcarriers, as can be observed in Figure 4.This reveals the fact that there is a fundamental differencein subcarrier selection between radio communicationsand optical wireless communications employing post-equalization. The optimal number of subcarriers to beemployed is consistent with Theorem 1 of Section 3.2.1.Considering the case of using all available subcarriers

as the baseline, investigation is made for average trans-mit optical power reduction subject to a BER require-ment of 10−4. The baseline of 10−4 is used because wefocus on uncoded transmissions. With error control cod-ing, which is typically used in practical systems, the BERcan be driven down by few order of magnitudes [31,32].Figures 5 and 6 show the simulation curves depictingBER performance and power reduction for the considered


0 3 6 9 12 15 18 21 24 27 3010

−4

10−3

10−2

10−1

100


BE

R



Figure 10 BER vs. transmit power with and without pre-equalization-based subcarrier selection two users.

system with and without subcarrier selection based onpost-equalization at the receiver for 2 and 32 users,respectively. The values of 2 and 32 users are considered tocheck the average transmit power for extreme cases. Sub-carrier selection in Theorem 1 is employed to choose outof the total of 64 subcarriers. A reduction of about 24 dBfor 2 users and about 10 dB for 32 users can be observedfrom the graph for a BER requirement of 10−4.Transmit optical power reduction for L = 2, 4, 8, 16, 32

active users using optimal number of subcarriers basedon Theorem 1 is next investigated. Simulation results forthe system under consideration, i.e., with 64 subcarri-ers and 10-Mbps data transmission rate, are shown inFigure 7. Each bar in the graph depicts the magnitudeof average transmit optical power reduction. It is evidentfrom the figure that although the power reduction mag-nitude decreases as the number of users increases, this

reduction is significant for up to a moderate number ofusers (wrt total number of subcarriers).

4.2 Pre-equalization-based subcarrier selectionFigures 8 and 9 show the analytical curves for the argu-ment of the Q function for 10-Mbps in case of the radiodomain and the optical wireless domain, respectively,when employing successively an increasing number ofactive subcarriers (with decreasing channel gain magni-tudes) in an MC-CDMA-based indoor optical wirelessIM/DD system with 64 subcarriers. These curves exhibitdifferent behaviors from those of post-equalization-basedsubcarrier selection. The expressions for the Q functionarguments (derived in Section 3.2.2) for both domains areshown in Table 3.Based on Figure 8, in radio communications employ-

ing subcarrier selection based on pre-equalization, a lower

15 17 19 21 23 25 27 29 31 33 3510

−4

10−3

10−2

10−1

100


BE

R



Figure 11 BER vs. transmit power with and without pre-equalization-based subcarrier selection with 32 users.


2 4 8 16 320

2

4

6

8

10

12

14

16

18

No. of Users (L)

Pow

er r

educ

tion

(dB

)

Figure 12 Power reduction for 2, 4, 8, 16, and 32 active users using pre-equalization-based subcarrier selection.

BER is obtained by employing more subcarriers for datatransmission. The case is exactly opposite for optical wire-less communications, as can be observed in Figure 9,where a lower BER results from using fewer active sub-carriers. This reveals the fact that there is a funda-mental difference in subcarrier selection between radiocommunications and optical wireless communicationsemploying pre-equalization. The optimal number of sub-carriers to be employed is consistent with Theorem 2 ofSection 3.2.2.Considering the case of using all available subcarriers

as the baseline, investigation is made for average trans-mit optical power reduction subject to a BER requirementof 10−4. Figures 10 and 11 show the simulation curvesdepicting BER performance and power reduction for thementioned system with and without subcarrier selectionbased on pre-equalization at the transmitter for 2 and 32users respectively. A reduction of 18 dB for 2 users and 8dB for 32 users can be observed from the graphs for a BERrequirement of 10−4.Similar to the case of post-equalization-based subcar-

rier selection, investigation is carried out to identify powerreduction for L = 2, 4, 8, 16, 32 MC-CDMA users forpre-equalization-based subcarrier selection according toTheorem2. It is clear from Figure 12 that the optical trans-mit power reduction decreases with the number of users.However, this reduction is significant for up to a moderatenumber of users.

5 ConclusionsWe proposed and investigated pre- and post-equalization-based subcarrier selection approaches as efficient modesof average transmit optical power reduction in an MC-CDMA-based indoor optical wireless communication

system with IM/DD. Based on these approaches, conser-vative expressions for fixed DC biases to be employed inthe system are derived. We then used the established DCbias expressions to construct optimal methods for choos-ing the number of active subcarriers for both pre- andpost-equalization.The simulation results validate the correctness of ana-

lytically found optimal criteria of subcarrier selection. Forup to a moderate number of users, as is the case in indooroptical wireless communication systems, the amount oftransmit power reduction can be significant. A typicaldata transmission rate of 10 Mbps with 64 subcarriersand QPSK modulation is used as an example case. Forpost-equalization-based subcarrier selection, reductionsranging from 10 to 24 dB are observed while 8 to 18 dB areobserved for pre-equalization-based subcarrier selectionwith the BER requirement of 10−4. Finally, analytical com-parison of both cases reveals that pre-equalization alwaysperforms no worse than post-equalization in terms of theBER for the same optical transmit power.

Competing interestsBoth authors declare that they have no competing interests.

AcknowledgmentsThe authors would like to pay gratitude to the Higher Education Commission(HEC), Pakistan, for supporting this research work and for the continuousencouragement in higher education.

Received: 12 June 2012 Accepted: 13 May 2013Published: 28 May 2013

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doi:10.1186/1687-1499-2013-138Cite this article as: Farooqui and Saengudomlert: Transmit power reductionthrough subcarrier selection for MC-CDMA-based indoor optical wirelesscommunications with IM/DD. EURASIP Journal on Wireless Communicationsand Networking 2013 2013:138.

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