Power Control for Optical Wireless Cdma Network

8/8/2019 Power Control for Optical Wireless Cdma Network

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Published in IET Communications

Received on 22nd July 2009

Revised on 21st February 2010

doi: 10.1049/iet-com.2009.0465

ISSN 1751-8628

Analysis of power control for indoor opticalwireless code-division multiple accessnetworks using onoff keying and binary

pulse position modulationS. Khazraei M.R. Pakravan A. Aminzadeh-GohariOptical Communications and Data Networks Research Lab, Advanced Communications Research Institute, Electrical

Engineering Department, Sharif University of Technology, Tehran 11365-9363, Iran

E-mail: [email protected]

Abstract: Wireless infrared optical code-division multiple access (W-OCDMA) is a new developing technique with

many useful applications. Noting the limitation on power consumption and eye-safety requirements, wireless

optical systems are power limited. Therefore control and efficient use of optical power is a key issue in

analysis and design of these systems. Also, multi-user interference is the major source of impairment in these

systems and power control is required to control and reduce this interference. Power control and the

inevitable errors in its algorithms play an important role in design and implementation of these systems. In

this article the authors study the uplink performance of W-OCDMA networks employing onoff keying (OOK)

and binary pulse position modulation (BPPM) schemes without any power control algorithm. The performance

improvement as a result of using perfect power control is calculated. Then, the impact of imperfect power

control that is the result of channel estimation error is analysed. The results clearly illustrate that deploying a

proper and accurate power control algorithm can increase network capacity and reduce network average

power consumption. The authors show that systems with non-ideal power control still perform considerably

better than no-power controlled systems.

1 Introduction

Indoor wireless infrared communication systems have beenthe subject of considerable research and developmentactivities during recent years [121]. It is believed that

wireless infrared networks receive more attention wheresecurity is an issue or using radio band would not beeconomical or practical because of bandwidth regulation orelectromagnetic interferences [1, 2].

Analysis of various aspects of wireless indoor infraredcommunication systems and local area networks (LAN) hasbeen presented in the literature [38]. Applying spread

spectrum techniques to infrared networks has received moreattention recently [917]; Ghaffari et al. studied the digitaldesign concepts and structure in a typical code-division

multiple access (CDMA)-based infrared network prototype

considering the practical aspects of system implementation.The results of various stages of the proposed wireless opticalCDMA (OCDMA) LAN strongly indicate the viability andthe importance of such networks in certain applications [13].

In this paper, we consider the performance analysis for theuplink of indoor wireless infrared networks employing opticalorthogonal codes (OOC) [22]. It has been shown that usingOOCs can provide a suitable modulation and multiple accessalgorithm in fibre-optic communication systems [22, 23].However, applying this technique to wireless opticalcommunication raises many important and interesting

questions [1017], some of which are analysed in thispaper. The scenario of interest for propagation channel inthis paper is a diffused system [1] that connects several

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portable nodes to a central fixed node or base station (BS) [8] which provides backbone connectivity through the wiredinfrastructure of the building.

The importance of power control in wireless infrared

optical CDMA (W-OCDMA) networks is because ofthree important facts. First and foremost, is the multi-userinterference at the receiver, which can dramatically affectthe system performance. High dynamic range in receivedpower just like traditional wireless CDMA networksnecessitates the implementation of appropriate powercontrol mechanisms in the transmitters. Second, theamount and pattern of optical power radiated from atransmitter should meet eye-safety standards. That requirescareful control of emitted optical power from eachtransmitter [1]. Last but not least, power limitations ofmobile wireless systems puts severe restrictions on theirpossible radiated optical power levels. The objective of this

paper is to analyse the power control issues in the uplink ofan OOC-based indoor diffused infrared network. Theanalysis has been done in two different scenarios todemonstrate the important effects of power controlimplementation. In the first scenario, the system is analysedassuming no power control mechanism in the uplinkdirection. Results demonstrate the system deficiencies andthe need for a power control algorithm for both OOK andbinary pulse position modulation (BPPM) schemes. In thesecond scenario, a power controlled system is analysed in

which all users estimate their uplink channel path loss andcorrespondingly send sufficient uplink power to ensure

equal received power level from all transmitters at the basestation. However, the imperfect channel estimation by usersduring the power control process causes an undesired errorin the power control algorithm. This makes it impossible toensure exact parity of received powers at the base station;the limitations caused by this error on the performance iscalculated and demonstrated as well. Furthermore, we havecompared the performance of the network using on offkeying (OOK) and BPPM modulation schemes each of

which is shown to have some advantages and drawbacks [24];for instance, employing OOK improves the bandwidthefficiency of the system (i.e. it can achieve higher bit rates)

while BPPM improves the power efficiency, in other wordsthe network is more robust regarding the amount ofreceived noise and it can perform better when thetransmission power is low. However, it is concluded thatboth OOK and BPPM schemes dramatically suffer fromnearfar problem as stated above.

The rest of this paper is organised as follows. Section 2describes the indoor infrared CDMA system modelincluding signalling, channel model and noise sources.Section 3 provides analytically, in both scenarios, the BERperformance of the system as well as average powerconsumption. Section 4 derives some numericalcomparisons for two strategies while the conclusions arepresented in Section 5.

2 Infrared CDMA system model

The indoor infrared system is assumed to be deployed using acellular architecture that consists of a few base stations placedat the centre of each cell. Base stations act as a bridge betweenthe users in wireless environment and the wired backbone

infrastructure. Transceivers use OCC [22] as the multipleaccess method. The system is assumed to use a set of OOCsequences with length Lc and weight K having minimumauto- and cross-correlation (la lc 1) to minimiseinterference [23]. A unique code should be assigned toeach user for transmission. Two modulation schemes areconsidered: OOK and BPPM. In OOK the user sends itsunique OOC signature for data bit 1 and sends nothingfor data bit 0. In BPPM the duration of each chip, isdivided into two equal sub-chip parts. Transmission of Kmarked sub-chips, all in the first part of the divided chiptimes, represents the data bit 0 whereas the data bit 1 is

represented by choosing the second K sub-chip times [25]. This pattern is therefore called chip-level BPPM that hasmore uniform power distribution in comparison with bit-levelBPPM. For both cases the number of associated users in eachcell (M+ 1) is limited to Nmax = (Lc 1)/K(K 1) [22].Furthermore, if the irradiance of the received signal is Ir (W/cm2), the average received power can be expressed byPr = (K/2Lc)irAd, where Ad is the area of detector[10].

2.1 Channel model

Diffuse infrared links are known to be the most robust linkconfiguration in wireless infrared communication systems[1]. However, they provide a challenging environment forsystem designers because of their high path loss and longdelay spreads [36]. One of the most important parametersthat affects the performance of infrared systems is thechannel path loss that is the gain of the channel transferfunction H( f) at f 0 which is used to evaluate therelation between transmitted and received average power tobe Pr = H0Pt. To compute the path loss of a diffusechannel, as a first-order approximation, only the firstbounce off the ceiling can be considered [1].

To simplify and evaluate the channel path loss, it isassumed that both transmitter and receiver are pointedstraight upward and transmitter emits a Lambertianpattern. It has been shown in this case that the numericaland experimental evaluation of path loss can be found as afunction of r (horizontal separation between transmitterand receiver) in [1, 3]. To simplify the calculations, H0(r)is approximated from the one-bounce curve by a function10logH0(r) = a0 + a1r+ a2r2 + a3r3 + a4r4 in whicha0 a4 are chosen so that the fitted curve minimises themean square difference between the logarithm of main dataand fitted data. In the fitted curve, which is derived from

the above equation and used for path loss calculations, the values for the a0 to a4 coefficients are: 53.555, 1.559,0.412, 20.04 and 0.0011, respectively [14].

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2.2 Photon counting characteristicsand noise sources

The infrared medium has its own drawbacks. Random natureof number of photons and other noise sources are inevitablein wireless optical systems.

2.2.1 Photon counting statistical characteristics:In infrared communication systems the signal detection isdone by a photodetector, having quantum efficiency of h,

which is the probability that an incoming photon releases anelectron in the photodetector [26]. Therefore the number ofphotoelectrons at the output of the photodetector is aPoisson process which can be approximated by a Gaussianprocess in many cases [26]. If the intensity of received powerto a photodetector with the quantum efficiency h and thearea of Ad is given by Ir, the mean number of photoelectroncount at the output of the photodetector in t seconds will be

mr = hAdIrt/hv, where n is frequency of light and h isPlanks constant [25].

2.2.2 Ambient light noise: In many applications,infrared links operate in the presence of intense infraredand visible background light. Although receivedbackground light can be minimised by optical filtering, itstill adds shot noise, which is usually the limiting noisesource in a well-designed receiver. Owing to its highintensity, this shot noise can be modelled as white,independent of Gaussian noise [1]. Therefore the meannumber of photon counts produced by ambient background

noise at the output of photodetector in t seconds will bemb = hAdIbt/hn, where Ib is the intensity of radiatedambient light. Infrared data association (IrDA) links shouldoperate at BER of 1026 when the maximum intensity ofradiated ambient light is limited to Ib 490 mW/cm

2 [27].

2.2.3 Photodetector dark current noise:Photodetectors dark current (id) has been shown to be aGaussian process and the mean number of photon countproduced by this source in t seconds can be expressed bymd = idt/e where e is the electron charge [1].

2.2.4 Gaussian thermal noise: When little or noambient light is present, the dominant noise source will bethe receivers preamplifier noise. In a well-designedpractical system, this rarely happens and the system ismostly dominated by ambient light noise.

2.3 Transmitter and receiver

Fig. 1 shows the block diagram of transmission and detectionarchitecture. The system uses OOK or BPPM intensitymodulation at the transmitter and direct detection at thereceiver. Duration of each chip is Tc = Tb/Lc, where Lc isthe code length and Tb is the bit duration. At the receiver,the desired signal along with the noise and interferencefrom all other M active users (interferers) is detected. Thereceivers structure is assumed to be based on correlationdetection. It should be noted that one of the system designobjectives here is to design a high-performance uplinkminimising the interference as well as the average powerconsumption of the network.

3 Performance analysis ofwireless optical CDMA uplink

In this part we derive analytical formulation for the uplinkperformance of the introduced wireless optical CDMAnetwork for both OOK and BPPM modulations in thetwo presented scenarios. First, when there is no control onthe users transmitted power and then assuming an

Figure 1 Infrared CDMA system architecture block diagrama Employing OOK modulation and detectionb Employing chip-level BPPM detection diagram



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imperfect power control algorithm defined for transmission.A simplifying assumption is to consider signals of differentusers to be chip synchronous. This represents a pessimisticcase and gives an upper bound to the bit error rate (BER)of the real chip-asynchronous system [22]. Additionally,the average power consumption of the active users in each

cell is derived in the above cases.

3.1 Upper bound BER analysis nocontrol on transmission power

3.1.1 OOK modulation scheme: Since we usecorrelation receiver, interference pattern is not importantand just number of interferers should be taken intoaccount. In OOC with minimum auto- and cross-correlation, two code words cannot overlap at more thanone pulse position. Therefore the probability that two code

words overlap at one pulse position is q K2/2Lc where

factor 1/2 accounts for the probability that interfering userhas sent one. Assuming M interfering users, the BER ofthe desired users detected information can be expressedas [28]

PE =Ml=0

Ml

ql(1 q)MlPE(l) (1)

where PE(l) is the probability of error when there exists linterferes in the system.

If the position vector of linterferers is considered to be r,

that is, ri is the distance of ith user from the base station(placed at the center of the cell), the value of PE(l) can beobtained by averaging the conditional probability PE(l|r)

with respect to r

PE(l) =

r

PE(l|r)fr(r) dr (2)

Since the position of each user is independent of the others;dr= li=1 dri and correspondingly fr(r) = li=1 f(ri),

where f(r) is the probability distribution function (PDF) ofhorizontal separation distance between each user and base

station. f(r) is the probability of user existence in a thinring with thickness of dr. Assuming the distribution of allusers over the area of the cell is uniform, f(r) can be easilyexpressed by: f(r) = 2r/r2cell. Mention that rcell is theradius of the cell. So that integration of f(r) over rbecomes 1.

As discussed in Section 2.2, using Gaussian approximationfor photon detection in [25, 26], PE(l|r) can be written as

PE(l|r) =1

2PE(l|r, 0) +

1

2PE(l|r, 1)

= 0.5 Q Th R0sR0

+ 0.5 Q R1 Th

sR1

(3)

Rj=0 o r 1 and s2Rj

(the mean and variance of received photoncount) can be expressed as (j is the information bittransmitted by the desired user)

Rj=

Kmr j

+KmbKmd

+l

i=1mi

s2Rj

= Rj + Ks2T(4)

The number of photoelectrons at the output of thephotodetector is the sum of Gaussian variables(photoelectrons from different sources). Therefore the finaldecision variable is also a Gaussian variable with mean and

variance equal to the sum of means and variances of eachvariable. Decision variable is composed ofK pulse positionsconsisting desired signal, noise and sum of interferencesfrom other users. mr is the mean received photon count ofthe desired user, mb is the mean photon count of ambientlight noise, s2T is the variance of the electron countproduced by thermal circuit noise and md representsphotodetector dark current noise. Introduced equations inSection 2 completely determine mr, mb and md. Furthermore,mi is the mean photon count produced by ith interferer

which is a function ofri, path loss and transmission power.

By replacing Pr = (K/2Lc)IrAd in mr = hAdIrTb/hnLc,we will have mr = 2hPr/KhnRb, mb = hAdIbTc/hn

md =idTc

e , mi =2hPr,iKhnRb

(5)

Pr,i is the power that base station receives from ith user andcan be expressed as Pr,i = H0(ri)Pt. Rb is the transmitterbit rate and Tc is chip duration in seconds. Notice that Pr,iis the average received power. By dividing Pr,i to code

weight (and applying other coefficients), average number ofphotons in every chip is obtained. Finally, the errorprobability of detected information can be derived usingequations (1)(5).

3.1.2 BPPM scheme: For the case of BPPM even theusers transmitting information bit 0 should be consideredin the interference pattern. Consider the number ofinterfering pulses in the first and second sub-chips as l0and l1. Following the same methodology of (1) and (2) thebit error probability can be obtained using

PE =Ml0=0

Ml0l1=0

M!

l0!l1!(M l0 l1)!

ql0+l1 (1 2q)Ml0l1PE(l0 , l1) (6)

l0 and l1 users cause interference sending information bit 0

and 1 respectively among M users. This follows atrinomial distribution with parameters M (total number ofpossible interferers) and q= q1 = q2 = K2/2Lc.



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As illustrated in Fig. 1 the decision about the received datafor BPPM is completed by comparing two decision variablesU0 and U1. Since the probability of transmitting 0 and 1 isequal, considering symmetry we have

PE(l0, l1)

=PE(l0, l1

|0)

=PE(l0, l1

|1)

= P(U0 , U1|l0, l1,0) (7)

To finalise the computation, we have to consider the locationvectors of interfering users r0 and r1, where r0,i and r1,j arethe position of ith first sub-chip interfering user (of l0) andjth second sub-chip interfering user (of l1), respectively. Therefore the error probability of P(U0 , U1|l0, l1,0) canbe obtained by averaging P(U0 , U1|l0, l1,0, r0, r1) withrespect to r0 and r1

PE(l0, l1) = P(U0 , U1|l0, l1,0)

= r0 , r1

P(U0 , U1|l0, l1,0, r0, r1)

fr0

(r0)f

r1(r

1) dr

0dr

1(8)

where f(r) is the PDF of users distribution in the area whichis described in the previous section. Finally we have

P(U0 , U1|l0, l1,0, r0, r1) = P(x. 0|r0, r1) (9)

where x is a Gaussian random variable with mean andvariances equal to

mx = Kmr l0i=1

mi +l0+l1

i=l0+1mi

s2x = Kmr +

l0i=1

mi +l0+l1

i=l0+1mi + 2K(mb + md + s2T)

(10)

mr, mi, mb and md are determined using (5). However, forBPPM, chip time is different from what is stated forOOK; in other words, as Fig. 1 predicts the chip rate of aBPPM system operating at the same bit rate with OOK, is

twice the OOK system. If two systems are considered tohave the same chip rate, OOK can achieve twice the bitrate of BPPM enabled network. In this article, we assumethe same chip rate for both systems, so that both systemsuse equal amount of system resources, for examplebandwidth. For the case of same bit rates, BPPM needstwice bandwidth. If we assume that the uplink directchannel does not degrade at higher frequencies, bothsystems can be considered to be equal. However, in reality,the channel frequency response degrades at higherfrequencies and that has an impact on system performance.

Furthermore, in BPPM, two decision variables arecompared together, as provided in (8), which leads to aninteresting phenomenon in the system design. Calculation

of the optimum threshold for OOK would be a difficulttask because of the inaccuracy in estimating the propersignal value in noisy environments. For the case of BPPMno threshold calculation is required at the receiver;therefore the results do not suffer from possible errors ofoptimum threshold computation. Additionally, (10)

predicts that the mean of the noise is cancelled whencomparing decision variables in detection process and givesbetter performance and robustness in noisy environments.

These advantages of the BPPM system come at the cost ofadditional bandwidth requirement of this modulationscheme.

3.2 Upper bound BER analysis powercontrolled network

Power control is required for all realistic CDMA systems,mainly because of what is known as the nearfar problem,

that is, users far from the base station experience greaterpath loss than users that are near the base station.Optimum power control is achieved when all users aredecoded with the same signal-to-interference ratio (SIR),that is, the users signals all arrive at the base station withapproximately the same power. Otherwise, a user with ahigh SIR dominates the BER performance of the system [29].

The power control algorithms are generally based on thechannel estimation in portable users or base station, thus ifthere is a perfect power control algorithm with no errors,finding the BER performance is straightforward asdescribed in [22, 28, 30]. In the ideal uplink power controlscenario, the transmission power of all users is set to asuitable value to assure the received power of all users atthe base station is fixed to a desired predefined value (Pr,d).

Therefore the user located at the edge of the cell emits themaximum transmission power of all users (Pt,max) which isrelated to Pr,d by Pr,d = Pt,maxH0(Rcell).

Unfortunately, because of large ambient light noise, andother sources of noise or interference, there will be an errorin estimation that causes power control error (PCE). PCEcan be considered to follow a lognormal distribution [29,31]. The impact of PCE on the system performance should

therefore be investigated.

Performance evaluation of a system with PCE is similar toprevious calculation; in which because of the consideredlognormal distribution of PCE, the received power fromith user (Pr,i) is given by

Pr,i = Pr,dexi, where xi N(0, s2PCE) (11)

Therefore the desired received mean photon count ofith userwill be

mr,i = mr,dexi

, where xi N(0, s2

PCE) (12)

where Pr,d is the desired power received from all users,



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including ith user (if there is no estimation error) and mr,d isthe desired mean photon count (for which a proper BER isobtained). Mention that xi is a random variable whoserandomness is because of error in estimation of power ineach receiver and its variation would depend on the updatefrequency of the much slower power measurement process.

Therefore xi has a much slower rate of variation comparedto system bit rate.

3.2.1 OOK modulation scheme: Since interferingusers are not distinguishable in correlation receiver, wedefine PE(l|X) the conditional error probability of PE(l) ifthe PCE for every interfering user (xi) is known to be the

vectorX. Hence PE(l) can be easily derived as follows

PE(l) =X

PE(l|X)fX(X) dX (13)

where dX = li=0 dxi and fX(X) = li=0 f(xi) = el

l

=0

xi

.

Therefore using the same methodology in (3) andconsidering Gaussian approximation for photon detection,PE(l|X) is clearly extracted as follows

PE(l|X) =1

2PE(l|X, 0) +

1

2PE(l|X, 1)

= 0.5 Q Th R0sR0

+ 0.5 Q R1 Th

sR1

(14)

Finally, the values of Rj and s2Rj can be expressed as

Rj = Kjex0 +li=1

exi

mr,d + Kmb + Kmd

s2Rj

= Rj + Ks2T(15)

In this case mb, md and s2

T can be found directly, using (5),whereas mr,d is determined by replacingPrbyPr,d in (5). It isrequired to note that the value of Pr,d should be adjusted bythe power control algorithm to obtain the desired BER, forexample, 1026. Furthermore, Pr,d is related and limited by

the maximum possible transmission power of an infraredsource (Pt,max); in other words the user located at the edgeof the cell is permitted to emit Pt,max while the powercontrol algorithm forces all closer users to decrease theirtransmission power with respect to their path loss.

3.2.2 BPPM scheme: To compute the error probabilityfor BPPM power controlled network, (6) and (7) are validand using the same methodology of obtaining (13) we caneasily compute PE(l0, l1) as follows

PE(l0, l1) = P(U0 , U1|l0, l1,0)

=X

P(U0 , U1|l0, l1,0, X)fX(X) dX (16)

Similar to (9) the above equation can be reduced using thefollowing form

P(U0 , U1|l0, l1,0, X) = P(y. 0|X, 0) (17)

where y is a Gaussian random variable with mean and

variances equal to

my = Kex0 l0i=0

exi +l0+l1

i=l0+1exi

mr,d

s2

y = Kex0 +l0i=0

exi +l0+l1

i=l0+1exi

mr,d

+ 2K(mb + md + s2T)

(18)

Finally, mb, md and s2

T can be found directly, using (5) and

mr,d is determined by replacing

Pr by

Pr,d in(5) as well.

3.3 Average power consumption

Power efficiency is considered to be an important factor indesigning any energy limited network, because sourcepower limitations of mobile wireless systems puts majorrestrictions on their possible radiated power levels for longtime. Hence, deriving the average power consumptionshould be considered for such networks beside the analysisof their performance.

3.3.1 Basic structure employing no power

control: In the first scenario, there is no control ontransmission power of the users and it is logical to assumeall users consume the same energy to transmit at the samepower (Pt) independently. Using (3) (5) for OOKmodulation and equivalently (6)(10) for BPPM, the only

way to acquire desired error probability is to change Pt forall users; hence, the average power consumption of eachuser is equal to the required transmission power to achievethe desired BER. Although the error probability for allusers located within the cell area is less (better) than theuser(s) located on the edge of the cell (i.e. worst-case user),it is mandatory to adjust the transmission power of all users

to attain desired BER for the worst-case user(s). It has tobe noted that in this case the average power consumption isnot related to the distribution of users in the cell.

3.3.2 Power controlled network: The average powerconsumption of users in the power controlled network canbe calculated using the location vector (r) and the PCE

vector (X) both of which are (M+ 1)-dimensional becauseof a desired user plus M interferers. ConsideringPr,d = H0(ri)Pt and using (11), the transmission power forthe ith user is as follows

Pr,d = Pt,iH0(ri), where xi N(0, s2

PCE) (19)

This leads to the following equation for the transmission



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power of the ith user

Pt,i = Pr,dexiL0(ri), where L0(ri) =1

H0(ri)(20)

Regardless of how power control algorithm works, from (12)to (15) we know how much power is required at base station(Pr,d) to achieve acceptable BER. Using (20), the requiredtransmit power of each user can be obtained. It should benoted that in the uplink, received signals from all usersexperience the same SINR because they are all detected byone photodetector at the base.

As we know the users are distributed independently on thecell area and their PCE is independent of each other, too.

Therefore the average power consumption is expressed byaveraging of (20) over position and PCE variance, which

leads to

Pav =ri

xi

Pr,dexiL(ri)

12p

sPCE

ex2i/s

2PCE

2riRcell2

dxi dri

=Rcell

0

Pr,dL(ri)

xi

12p

sPCE

ex2i/s

2PCE dxi

f(ri) dri

= Pr,des2PCE/2

Rcell0

L(rt)f(rt) drt (21)

where f(r) = 2r/r2cell. Additionally, for the ideal powercontrolled network, finding the average power consumptionis straightforward and is written as follows

Pav = Pr,dRcell

0

L(ri)f(ri) dri (22)

It is important to note that there are two factors that affectaverage power consumption in (21), first and obvious one is

es2

PCE/2 that directly increases the average powerconsumption and the power control error variance.However, one should note that the desired received powerat the receiver (Pr,d) in (21) is highly affected by PCE toachieve a desired error probability as well. To elaborate thiseffect consider, for instance, an ideal power controllednetwork that works having BER 1029 and consequentlyits average power consumption is given by (22). Now if inthis case PCE is added to the network, BER increases, forexample, to 1026 while average power consumption isincreased by es

2PCE/2. However, it is clear that in order to

compare the two cases the power control algorithm should

increase the desired received power (Pr,d) for the latter caseto attain BER 1029 which consequently increase theaverage power consumption to a higher value.

4 Numerical results

In this part we present some numerical result on performanceof the introduced cases and scenarios using the previouslypresented analytical evaluations. We also present MonteCarlo simulations to verify the numerical results. We

assume an infrared CDMA system with Rb 2 Mbps andRb 1 Mbps per user for OOK and BPPM cases,respectively. These bit rates are chosen to allocate equalbandwidth to the two analysed schemes. Furthermore, theOOC code words with length Lc 256 and weight K 5(which result in Nmax 12) is considered for computations.

The system is assumed to operate atl 850 nm and thecell radius is fixed to 4 m. Photodetectors efficiency, areaand dark current are assumed to be h 0.77, Ad 1 cm

2

and id 160 nA, respectively, as in [1, 11, 21]. Although,background light irradiance can be as strong asIb 10 000 mW/cm

2 because of direct sunlight without

optical filtering in the field of view of the receiver, theIrDA standard places the limit of Ib 490 mW/cm2 on the

background light for the operation of an infrared receiver[27]. This amount of background light is the equivalent ofdirect sun in the field of view of the receiver with adeveloped unexposed film such as a long-pass optical filter[11]. In all cases, optimum threshold is assumed for OOKdetection system [10, 30].

Fig. 2 illustrates the nearfar problem in a basic OOCwireless infrared network without power control employingOOK or BPPM schemes using (2) and (8). In this figure

the effect of users position (r

) on BER is plotted for fiveactive interfering users (M 5). This figure clearlydemonstrates the need for control on transmission power.

As an example when user is located at the radius of 1.5 mor more, BER is worse than 1024 for Pt 5 mW andtherefore users at distance over 1.5 m cannot properlyconnect to base. It can be seen that the performance of thenetwork for both OOK and BPPM degrades rapidly as theuser moves towards the boundary of the cell, in fact evenif a user changes its position a few centimetres, itsperformance might degrade or improve about ten times.

This demonstrates that the users who are located near thebase station obtain much better BER than required,

whereas the data from farther users cannot be detected witha desired BER. The designer should consider the far usersto have satisfactory performance but much power will be

wasted because of over design for near users. Also, in thiscase the transmission power is the only parameter toimprove the networks performance, however, as Fig. 2illustrates clearly, the effect of change in transmissionpower has its minimum effect just when it is needed themost, that is when the user is at the edge of the cell. Forexample, for a user of OOK system at a distance of 1 mfrom the source, increasing the transmit power from 5 mWto 50 mW improves the performance from around 1024 to

less than 1029

whereas the same amount of increasedpower for a user at r 3 m changes the BER from 1021

to 1022 approximately. Furthermore, although BPPM



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performs better at lower transmission powers than OOKbecause of mean noise cancellation in detection, bothmodulation schemes show the same weakness when thenetwork becomes interference limited at large rvalues.

Now let us find out whether code parameters can improvesystem performance or not. Fig. 3 depicts BER against codelength for different transmission powers. There are fiveinterfering users, the desired user is located at the middleof the cell (r= Rcell/2), and code weight is kept fixed. It isseen that larger codes can have a slight better performance.But can we increase code length to improve performance tothe desired value? The answer is NO! Because optical

wireless system is a band limited system. Channelfrequency response will degrade when using largebandwidth. So the designer selects code length as long aspossible (limited by channel) to have better performanceand looks for other solutions to improve system output.

Some other performance degradation issues of the network without control on the transmission power are shown inFig. 4 which is also obtained from (2) and (8). The upperbound of BER against number of uniformly distributedinterfering users for several values of transmission power isplotted in Fig. 4a for a user located at the middle of thecell. Transmission power is controlled through (6)considering appropriate channel loss.

It is apparent form Fig. 4a that increasing the number ofinterfering users degrades the link performance because ofthe increase of multiple access interference (MAI). It is also

clear that dependence of performance on the number ofusers is less for lower transmission powers because of noisedomination and less interference. It can also be seen fromFig. 4b that when the system is MAI limited, increasingthe transmission power of all users does not solve theproblem. For example, there is little BER improvement ingoing from 40 mW of transmit power per user to 100 mWof transmit power. Moreover, as stated above and obviouslydemonstrated in Fig. 4b, BPPM gives better performancein lower transmission powers where the system is noiselimited, nevertheless, increasing the transmission powerfades BPPM strength over OOK because MAI dominates.

Finally, Fig. 5 shows the effect of cell radius on BER forseveral values of uplink transmission power when there is

Figure 3 Effect of code length on BER for different

transmission powers

Figure 2 System performance against the users distance from base station (r) for several transmission power ranges

Results are presented for a case with M 5 interfering users



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no power control. Users are assumed to be uniformlydistributed over cell area. Cell radius impacts f(r) in (2)and (8). This curve can be used to obtain an appropriaterange of coverage for a given target BER value and uplinktransmission power level. For example, for a target BER of

1023

, a cell radius of around 2.2 m can be achieved iftransmit power is set to 50 mW. It is clear that low targetvalues of BER (less than 1024) cannot be achieved even by

decreasing cell radius, or increasing transmission powerconfirming the previous stated system behaviour. Thisclarifies the importance of power control for properoperation of the system.

The performance results of the power controlled networkusing (13) and (16) are depicted in Figs. 6 and 7. In thiscase the limiting factor is the maximum allowed

Figure 4 Performance degradation issue of a non-power controlled network

a BER against the number of interferers (M ), user is placed at the half cell radius, Rcell 4 mb BER against transmission power in the same situation



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transmission power that should be set to a proper value whereall users in the cell (including users at the edge) attainappropriate BER. Users located closer to the edgeexperience higher path loss and therefore should transmithigher power in comparison to other users in the cell.Regardless of how power control algorithm operates, themaximum allowed transmission power is directly related todesired received power at the base station withPr,d H0(Rcell)Pt,max, which means all in-cell users havebeen forced to reduce their transmission power so that thereceived power of all users at BS is equal to the ones at theedge (sending Pt,max).

Fig. 6a illustrates the effect of maximum transmissionpower (Pt,max) on the error performance of network whenthe power control procedure is assumed to be ideal usingperfect channel estimation (s2PCE = 0). This figure showsthat employing power control greatly enhances the systemperformance. It should be noted that as this figure shows

for both OOK and BPPM, when M is less than codeweight, that is, M, 5, MAI is negligible and BER can bereduced as much as desired by increasing the transmissionpower to overcome noise sources. Perfect power control isan idealistic assumption because channel estimation issubject to estimation error and that impacts theperformance of the power control algorithm. Analysis ofthe impact of power control error on system performancehas also been performed using Monte Carlo simulations.

The results of simulation are very close to the analyticalresults and are presented in Fig. 6a.

The effect of PCE on BER is shown in Fig. 6b for a casewhere the maximum transmission power of a node is set to50 mW. It can be seen that power control can considerably

enhance the system performance in comparison to whatFig. 2 (curves with Pt 50 mW) stated in worst case(worst-case happens when user is placed in the farthestposition from centre), considering points with fiveinterferers in Fig. 6b. Moreover, the capturing effect andnearfar problem (Fig. 2) is solved in this scenario and allthe users disregarding to their location achieve the sameBER as predicted in Fig. 6b. Estimation errors (higher

values of PCE, i.e. sPCE or call it s) degrade thisperformance as it can be seen in this figure, but even withs 0.5 results are better than the case of no powercontrol. Fig. 6 also demonstrates the improvement onsystem capacity when using power control. For example toachieve BER 2 1024, system can tolerate only oneinterferer when PCE is high (s 0.5), but eight users(seven active interferers) can coexist in the system whenPCE is low (s 0.05). One of the interesting observationsfrom the results of this figures is that, even though BPPMperforms much better than OOK in lower PCE, for

example s 0.25, it starts to lose its attitude for highererrors in power control algorithm and gives unacceptableperformance as PCE increases. This is verified by Fig. 7 in

which the performance degradation of both OOK andBPPM modulation schemes is plotted against s fordifferent number of interfering users and two differentPt,max values. As predicted by Fig. 6, Fig. 7a states thatBPPM performs better than OOK when the system is

working near ideal power control scheme; however,increasing the amount of PCE leads the performance ofBPPM to degrade faster than OOK until it gets worse forlarger amount of error in estimation. The cross point varies

for different number of interfering users. In BPPMdecision is based on comparing two decision variables, bothof which suffer from power control error, so the total

Figure 5 BER against cells radius (Rcell ) for M 5 and different values of transmission power



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variance of error is actually doubled in BPPM. This leads tosharper performance degradation in BPPM over OOK. Theperformance degradation of BPPM over OOK starts soonerif we increase the maximum allowed transmission power

which is illustrated by Fig. 7b. In high transmission power,where the effect of noise is cancelled and interference is the

limiting factor, performances of BPPM and OOK are closeto each other. So power control error makes BPPM to have worse performance than OOK in comparison to low

transmission powers (in low transmission power, BPPMperforms better than OOK).

Mention that obtaining the right threshold level for OOKrequires relatively accurate levels of received power estimation

which is exactly what is required for a good power control

algorithm. Fig. 8 shows the effect of threshold on OOKBER for different PCE. Each curve has an optimum pointin which BER is at its minimum value. It can be seen that

Figure 6 Performance evaluation of a power controlled network

a BER against maximum transmission power in ideal power control case for various values of Mb BER against number of interferers (M ) for several values of PCE varianceMaximum transmission power is set to 50 mW



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when PCE is high, BER is less susceptible to threshold

selection. It means that in a situation where we have errorin estimating received power, although threshold cannot beaccurately obtained, system performance is less susceptibleto threshold value selection. So we expect OOK to performbetter than BPPM when PCE is high.

Finally, it is essential to find out the average powerconsumption of the systems for possible errors in powercontrol procedure employing OOK and BPPM. In Fig. 9Pav is plotted againsts for a system achieving BER 10

24.Each point in this figure is obtained through (21) using thefollowing procedure: A plot of BER against Pr,d for different

values ofs should be provided using (14) and (16) forOOK and BPPM, respectively. The required Pr,d forBER 1024 and for a specific s is extracted from that plot.

Figure 7 BER of a non-ideal power control algorithm against PCE for different number of interfering users (M)

a Maximum transmission power is set to Pt,max 50 mWb Pt,max 100 mW

Figure 8 BER against threshold for different values of PCE

Threshold is expressed as the percentage of maximum received level



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This Pr,d is used in (21) to calculate average powerconsumption for the specified s.

UsingFig. 9, one can determine the maximum acceptableerror in power control algorithm to design a power efficientnetwork. In other words, the trade-off between design

complexity of the power control loop and energyconsumption of nodes can be addressed and numericallycalculated by such plots. For example to design a BPPMsystem with average power consumption less than 30 mW,PCE should be kept less than 0.15. Designing aninaccurate power control loop, results in higher averagepower consumption to achieve BER of 1024. Furthermore,Fig. 9 confirms that PPM appropriately enhances theaverage power consumption of the network in lowerdeficiencies in power control algorithm while this behaviourrapidly diminishes when PCE is increased and OOKbecomes the first choice to decrease average power

consumption of users.

5 Conclusions

In this paper we analysed the performance of an opticalCDMA wireless LAN with and without control ontransmission power. The system uses OOC with minimumauto- and cross-correlation as an implementation ofCDMA concept. Both OOK and BPPM modulationschemes are employed. Intense background light and othernoise sources are considered. In a wireless infrared medium

with line of sight, path loss is the main issue; therefore

power control becomes the main concern to reduceinterference between users, each using a specific signaturesequence. It is proposed and proved by numerical results

that these systems have to employ some form of powercontrol with proper accuracy level in their uplink toenhance their performance for both BPPM and OOKmodulation schemes. Analytical equations and results wereincluded to evaluate and emphasise the advantages ofpower control on the system performance which are

generally overcoming near far effect and decreasing averagetransmission power. Since error in power controlalgorithms is inevitable, we focused on PCE to see howPCE impacts system performance. Analytical evaluation ofimperfect power control and numerical results for somespecial cases were presented. Results show that the use ofpower control, even with channel estimation errors can stillsignificantly enhance the performance of the uplinkchannel in these systems while the effect of power controlerror is quite different for PPM and OOK schemes. Theresults demonstrated that PPM performs better than OOKin a typical non-power control enabled network as well as a

power controlled network with lower errors in channelestimation. But power control error has a larger effect onPPM than on OOK and as a result OOK can beconsidered optimal when the system suffers from largeamounts of error in its power control process. As stated inthe paper, it should be noted that although OOK showsbetter robustness in some cases, the main practicaldisadvantage of this modulation scheme is its requirementfor an adaptive optimal threshold level to achieve the bestperformance.

The success of OCDMA will definitely rest upon

maturing technologies but more importantly it depends onfinding the right application where OCDMA features willstand out when compared to other multiple access

Figure 9 Average power consumption of the network (Pav ) againsts to achieve BER 1024

, for different number of

interfering users (M)



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techniques. We have highlighted and discussed such anapplication in this paper and reported some analytical andnumerical computations to overcome some basicinefficiencies.

6 Acknowledgment This paper was presented in part at the IEEE 25thInternational Performance Computing and CommunicationConference, Phoenix, AR., USA, April 2006 and in part atthe IEEE International Conference on Telecommunications,Penang, Malaysia, May 2007.

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Power Control for Optical Wireless Cdma Network

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