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26th NATIONAL RADIO SCIENCE CONFERENCE (NRSC2009)

<®J> March 17-19,2009, Faculty of Engineering, Future Univ., Egypt

Bandwidth and Power Efficiency of Various PPM Schemesfor Indoor Wireless Optical Communications

Nazmy Azzam', Moustafa H. Aly2 and A.K. AbouiSeoud3

1 Arab Academyfor Science, Technology and Maritime Transport, Alexandria, Egypt,(naz naz@vahoo ,com).

2 Arab Academyfor Science, Technology and Maritime Transport, Alexandria, Egypt, MemberGSA, ([email protected]).

3 Faculty ofEngineering, University ofAlexandria, Egypt, ([email protected]).

Abstract

Bandwidth and power efficiency of various pulse position modulation (PPM) schemes for wireless opticalcommunication (WaC) indoor applications are investigated. These schemes include traditional PPM, multiplePPM (MPPM), overlapping PPM (OPPM) and differential amplitude PPM (DAPPM). This study is unique inpresenting and evaluating bandwidth and power effici ency under wide range of design parameters such assymbol length, L, number of chips per symbol, n, number of chips forming the optical pulse, w, and ampl itudelevel , A. For the DAPPM scheme, the power efficiency with respect to the on-off keying (OaK) power isintroduced. A comparison among different modulation schemes is done . Relation with IrDA and IEEE 802.11standardization is clarified. DAPPM was found to be the best modulation schemes in terms of power andbandwidth requirements under careful design aspects (i.e. lowest bandwidth requirement B/Rb= 0.375, isachieved at L = 2, A = 8 and lowest power requirement , PDAPPMIPOOK= 0.013, is achieved at L = 32, A = 8).

1. Introduction

Recently, the need to access wireless local area networks from portable personal computers and mobiledevices has grown rapidly. Many of these networks have been designed to support multimedia with high data rates,thus the systems require a large bandwidth. Since radio communication systems have limited available bandwidths,a proposal to use indoor wireless optical communications (WaC) has received a wide interest [1]-[3]. The majoradvantages ofoptical systems are low-cost optical devices and virtually unlimited bandwidth.

An optical wireless channel is usually a non-directed link and can be categorized as either line-of-sight(LOS) or diffuse. A diffuse link is preferable because no alignment is required and it is more robust to shadowing.Normally , a diffuse link is corrupted by ambient light noise, high signal attenuation , and intersymbol interferencecaused by multipath dispersion. In addition, the average transmitted optical power is constrained by concerns ofpower consumption and eye safety regulations [1]-[3]. Furthermore, high capacitance in a large-area photodetectorlimits the receiver bandwidth. Consequently , a power-efficient and bandwidth-efficient modulation scheme isdesirable in an indoor optical wireless system [4].

Normally, an optical wireless system adopts a baseband modulation scheme, e.g. on-off keying (OaK) orpulse position modulation (PPM). To yield more efficiency in terms of power and bandwidth, a number ofmodulation techniques have been proposed which vary the number of chips per symbol, e.g. differential pulseposition modulation (DPPM), digital pulse interval modulation (DPIM), and dual header pulse interval modulation(DH-PIM). Multilevel modulation schemes were introduced to improve optical wireless system performance [2],[5].

The first contribution is based on investigating power and bandwidth requirements (used as an indicationfor efficiency performance) of different PPM schemes under wide range of design parameters. This is done to give

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a wider view on the performance of such schemes on different data rates and does not limit the performanceevaluation for such schemes to certain design parameters, data rates and conditions as in [5], [6]. The second isrelating the power of DAPPM to OOK for the first time. Finally, establishing a general comparison amongschemes in power and bandwidth requirements (efficiency) and relating results with today's IrDA and IEEE802.11 standards.

The paper is organized as follows: Section 2 gives the mathematical model including a review on theOaK as a benchmark for comparison among various PPM schemes on power efficiency. Section 3 presents thenumerical simulation results and discussion with a general comparison among different schemes and therelation with IrDA and IEEE 802.11 standards. This is followed, in Section 4, by the conclusion.

2. Mathematical Model

2.1. Introduction

The appropriate channel model for woe systems using intensity modulation depends on the intensity ofthe background light. In low background light, it is common to model the received signal as a Poisson process with arate As(t) + An where As(t) is proportional to the instantaneous optical power of the received signal and An isproportional to the power of the background light; when An is zero, the channel is quantum limited [6], [7]. However,in those applications where An is very large and the receiver employs a wideband photodetector, the photodetectorshot-noise is accurately modeled as an additive white Gaussian noise (AWGN) plus a d.c. offset, and it is often moreconvenient to use an AWGN model [6], [7].

Non-directed infrared radiation offers several advantages over radio as a medium for indoor wirelessnetworks, including an immense window of unregulated bandwidth, immunity to multipath fading (but not multipathdistortion) and a lack of interference from one room to another [1]-[3]. But, the background light in typical indoorenvironments is very intense; even after a narrow-band (10 nm) optical filter, An will be between 1011 and 1014

photons/s, depending on the proximity to a window [6]. Such high rates make the AWGN model extremelyaccurate. Furthermore, because the multipath propagation destroys spatial coherence, the effects of multipathpropagation can be characterized by a baseband linear model [2], [6]. This leads to the following equivalentbaseband channel model, the AWGN model, for wireless infrared communications using intensity modulation anddirect detection (IM-DD):

00

Y (t ) = IX ( T)h(t - T)dT+n(t ) (1)

where x(t) represents the instantaneous optical power of the transmitter, yet) represents the instantaneous current ofthe receiving photodetector, h(t) represents the multipath-induced temporal dispersion, and net) is the whiteGaussian noise with two-sided power spectral density No. The same model is used to model conventional radiochannels, where x(t) represents amplitude, and it must satisfy:

1 T

lim - Ix 2(t )dt ~ Po (2)t -s« 2T

-Twith Pothe average power constraint of the radio transmitter.

However, x(t) represents the optical power in our application. So, it must satisfy:1 T

X (t ) ~ 0 and lim - Ix (t )dt ~ Pt -s« 2T

-Twhere P is the average optical power constraint of the transmitter.

(3)

In this paper, the bandwidth efficiency is examined as well as the power efficiency of various modulationschemes under the constraints of (3). To isolate the effects of (3), one neglects the multipath dispersion, so that h(t)

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= 8(t) in (1). Nevertheless, bandwidth limitations of both h(t) and the receiver electronics are what motivates us toconsider bandwidth efficiency as an important parameter [2], [6].

2.2. On-off keying (OOK)

In this paper, this scheme will be used only as a benchmark to compare the power requirement of variousPPM schemes, noting that this technique is used widely in WOC [1]-[3]. One first reviews the classic problem ofdetermining the error probability for an L-ary modulation scheme in the presence of additive white Gaussian noise,assuming maximum-likelihood (ML) detection, and neglecting intersymbol interference [8]. The transmitter conveysinformation at a rate of R, bits/s by transmitting one of L non-negative signals {x.It), X2(t), ... , XL(t)} every T =

log2L/Rb sec, and the channel adds a white Gaussian noise with power spectrum No. To prevent intersymbolinterference, each signal is confined to the interval [0, T]. The signal set satisfies (3) with equality. Therefore, theaverage signal power is:

lIT- L(lim- fxJt)dt)=P (4)L i t -s« 2T -T

For example, an OOK transmitter emits a rectangular pulse of duration I/Rband of intensity 2P to signify aone bit, and no pulse to signify a zero bit. The bandwidth required by OOK is roughly Rb. To simplify analysis, onemakes the high-SNR assumption that the bit-error rate (BER) is dominated by the two nearest signals, so that [2],[6]:

(5)

where dmin is the minimum Euclidean distance between any pair of valid modulation signals, defined as [2], [6]:

dl~in == min f(x i (t) - X j (t ))2dt (6)1 :t:)

In fact, (5) is exact for OOK, at any time L = 2, exactly as [6]. So, the minimum distance between the twosignals in the OOK signal set and the BER, assuming ML detection, respectively, are:

dOOK = 2P / JR: (7)

BER =Q(P / JNoRb) (8)

The power required by OOK to achieve a given BER and the power required by any other modulationscheme to achieve the same BER are, respectively, [2], [6]:

POOK =JNoRbQ-I(BER) (9)

P == (dOOK Idmin)POOK (10)

These relations are used under the assumption that the SNR is high enough that (5) is accurate [2], [6].Therefore, in the remainder of the paper, the distance ratio dooK/dmin will be used to characterize the powerrequirements of any modulation scheme except for DAPPM which has special characteristics that will beinvestigated independently later.

2.3. Pulse position modulation (PPM)

In a pulse position modulation (PPM) scheme, each symbol interval of duration T {= log2(L/Rb)} ispartitioned into L sub-intervals, or chips, each at duration TIL, and the transmitter sends an optical pulse during one(and only one) of these chips. PPM is similar to L-ary FSK, in that all signals are orthogonal and have equal energy[6]. PPM can be viewed as the rate-log-L'L block code consisting of all binary L-tuples having unity Hammingweight. A PPM signal satisfying (3) is represented as:






(17)

(18)

L-I

x(t)==LPLckp(t -kT IL) (11)k=O

where [co,CI, .... , cL-d is the PPM code word, and p(t) is a rectangular pulse of duration TIL and unity height. All ofthe signals are equidistant [6]:

dl~in == min f(x i (t) -x j (t ))2dt == 2Lp 2log2L I R; (12)l *)

Therefore, the average power requirement for PPM is approximately [2], [6]:

PpPM / POOK =dOOK /drllin =~ (13)vLk%LThe bandwidth, B, required by the PPM scheme to achieve a bit rate of R, is approximately the inverse of

one chip duration. Then, one can write [2], [6]:

B PPM == L IT == LR b I log, L So,

LB PPM I u; == (14)

log2 L

2.4. Multiple pulse position modulation (MPPM)

In multiple PPM, each symbol interval of duration T (= log2LIRb) is partitioned into n chips, each ofduration Tin, and the transmitter sends an optical pulse during a weight w of these chips. The transmitted signal isgiven by:

n-I

x(t)==aLck¢(t-kT In) (15)k=O

where [co,CI, .... , cn-d is a binary n-tuple of weight w, where <D(t) = (n/T)o.5P(t) is a unit-energy rectangular pulse ofduration Tin. P(t) as described in previous section. The constant a is chosen so that the average optical power is P:

r;:;:; dOOK ~n log, La == (P Iw )"nT == (16)

2wThere are [n!/(w!e(n-w)!)] binary n-tuples of weight w, but it may be desirable to use only a fraction L of

these. For example, one may choose the code words to have a large minimum Hamming distance d. That is, one mayrestrict attention to an (n, d, w) constant weight code, which is a set of binary n-tuples having weight wandminimum Hamming distance d [2], [6].

For a given n, d, and w, let L ::s [n!/(w!e(n-w)!)] be the number of valid code words. The minimumHamming distance d must be 2:2, because it is impossible for two binary n-tuples of weight w to differ in only oneposition. If one admits all binary n-tuples of weight w, then L = [n!/(w!e(n-w)!)] and d =2. The bandwidth is roughlyn/T, the inverse of the chip duration. Hence, the bandwidth requirement is [2], [6]:

nB MPPM I R; ==--

log2 LBecause [<D(t-kT/n)] is an orthonormal set, (15) implies that the Euclidean distance between any two

MPPM waveforms Xi (t) and Xj (t) is [ae(dij)o.5] where dij is the Hamming distance between the corresponding binaryn-tuples. Thus, the minimum distance is dmin =ae(d)o.5, where d is the minimum Hamming distance and a as (16).The ratio of dOOK to dmingives the average power requirement for the MPPM scheme as [2], [6]:

2wPMPPM I POOK == I

Vnd log, L

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(19)

2.5. Overlapping pulse position modulation (L-OPPM)

The overlapping PPM (L-OPPM) is defined as a special case of MPPM, where the w ones are constrainedto be consecutive. In other words , each symbol interval of duration T (=logzLlRb) is divided into n chips, each ofduration T/n, and a rectangular pulse spanning w chips is transmitted, beginning at any of the first L (=n - w + I)chips. The motivation for constraining the w ones to be consecutive is the decreased bandwidth that results;unfortunately. This benefit is offset by the reduced alphabet size, since L drops from [n!/(w!o(n-w)!)] to (n - w + I).

This definition of L-OPPM is slightly more general than the usual definition in Ref. [7], because it allowsthe possibility that n/w is not an integer. One refers to the ratio u (=w/n) as the duty cycle [6]. One keeps in mindthat specifying L does not uniquely specify nand w. Thus, it takes two parameters to specify L-OPPM, either nandw or Land u, The bandwidth of L-OPPM is n/(wT) where T = 10gz(LlRb) . So, the bandwidth requirement is givenby [2], [6]:

B I R = n IwL - OPPM b I ( 1)ogz n -w +

The minimum Hamming distance, d, between OPPM code words is 2, so that the minimum Euclideandistance between received signals is:

dmin =Jia =(P Iw ).J2nTDividing dOOK by dmin yields the average power requirement for the L-OPPM scheme as:

P IP = 2wL -oPPM OOK 12 I ( 1)

" n ogz n -w +

2.6. Differential amplitude pulse position modulation (DAPPM)

(20)

(21)

DAPPM is an asynchronous modulation technique which is a combination of (pulse amplitude modulation)PAM and (differential PPM) DPPM. Therefore, the symbol length and the pulse amplitude are varied to representthe information being transmitted. A set ofDAPPM waveforms and difference w.r.t. DPPM is shown in Fig. I [5].

SO(I) S l it)

PeL t Pc

Tc 2Te

Setl ) 5 / 1)

'," ~:A1k-'(a) 5 , 1.1)

( b)

Figure 1. Symbol structure for M = 2 bits/symbol with (a) DPPM (L = 4) and (b) DAPPM (A = 2, L = 2) [51 .

A block ofM = 10gz(A x L) input bits is mapped to one of 2M distinct waveforms, each has one "on" chipwhose amplitude is selected from the set {1, ... , A}. The length of a DAPPM symbol varies from the set {1, .. . ,L}. Alternatively, the DAPPM encoder transforms an information symbol into a chip sequence according to aDAPPM coding rule. The transmitted DAPPM signal is then [5]:


Future University, Sib Compound, NewCairo, Egypt, March 17- 19,2009




(22)

(23)

x (t) = f bk •(Pc).P(t - kTc)k =-<fJ A

where bk is {O, 1, ... ,A}, pet) is a unit-amplitude rectangular pulse shape with a duration of one chip Tc, and P,represents the peak transmit power. The peak-to-average power ratio (PAPR) ofDAPPM is [5]:

PAPR=Pc =A(L+1)Pavg (A +1)

In a similar way for the previous PPM schemes, one can relate - for the first time - the peak power, PDAPPM,of DAPPM to POOK• To the best of our knowledge, this is done for the first time. First, the average power, Pavg, is tobe relat ed to POOK through the direct relations in [2], [5] and [6] as follows:

Pavg 1 r=x=P

OOK= 2M •V~ (24)

This will lead to the relation between peak power ofDAPPM and OOK power as :

P I P =A(L+1) ._1_. r=x=DAPPM OOK (A +1) 2M V~ (25)

The chip duration is Tc=2M/(L+ 1)Rb, where R, represents the data rate. Therefore, the required bandwidthofDAPPM is given by [5]:

(L +1)BDAPPM I s, = (26)

2MIt is evident to keep in mind that, in all previous PPM schemes, the value B/~ is used as an indication of

bandwidth efficiency.

3. Numerical Results and Discussion

3.1. Pulse position modulation (PPM)

Figures 2 and 3 present the bandwidth and power requirements of PPM under a wide range of the operatingsymbol length L. As one observes, increasing symbol length for PPM results in an increase in the bandwidthrequirement B/Rb (i.e. decreases the bandwidth efficiency and the allowable bit rate). However, this increasedecreases the required average power (i.e, enhances power efficiency). This situation assures the need of a goodcompromise to choose the most suitable symbol length taken into consideration that this technique is dominant foroperating today's IrDA standards [ 9], [10].

12 .------------------------,

10

4

S,., nbol liP llgth ( 0 1' "PM . L

1.2

"00I!o~

f- 0.8

;;f 0.6'-.;...t 0.4i:$0.. 0.2

4 16

Sym het leu grh foe-PPl\f, I.

32


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<@f>March 17-19,2009, Faculty of Engineering, Future Univ., Egypt

Figure 2. Bandwidth requirement for PPM Figure 3. Power requirement for PPM

For purpose of the following comparisons, largest bandwidth requirement point (worst point of bandwidthefficiency and allowable bit rate) is achieved at L= 64 with B/Rb=10.667 while the lowest corresponds to L= 2 withBlRb=2. The largest point for power requirement (worst for power efficiency) occurs at L = 2 with PPPM/POOK= Iwhich means that power required for PPM is exactly as the power required for POOK while the lowest is achieved at L =64 with PPPMIPOOK= 0.072.

3.2. Multiple pulse position modulation (MPPM)

As mentioned in Sec. 2.4 structure of MPPM is more complex than PPM by introducing number of chipsper symbol (n) and number of chips forms optical pulse (w). The power and bandwidth requirements areinvestigated at a wide range of these design parameters, in Figs. 4 and 5. This results in exploring newcharacteristics for the behavior under wider bit rates that is not investigated before, especially in Ref. [6], [7].

2.5 ,...----------------------,_ +_ w=2

--+- w=4.•. w=7__ w=12

II •

.,

..." .".. ,

-.... - ..._-.. - . -.-" ."."- " ... -.. - " ".-+- -+ - -+- - .. - -+--

i:~ 0.5o~

ao 2

~~ 1.5

~

.5~'"

- +- w=24.5 -- w=4

~ 4 .." w=7~

3.5 -- w=12~

.5 •g. 2.5~

'":: .:.. ~-e.~ 1.5 .... - _ .......--e •~~

0.5

4 10 14 18 20 25 30 35 40 45 4 10 14 18 20 25 30 35 40 45

Number of chips p (l>l' symbol for l\1PPl\l , II Numbe r of chips per sym bol fur l\lPP.M, II

Figure 4. Bandwidth requirement for MPPM Figure 5. Power requirement for MPPM

From Fig. 4, one observes that bandwidth requirement for MPPM has a different behavior depending on thevalue ofw. At w < 4, it seems that the bandwidth requirement increases dramatically with n. While, at larger values, w >4, the bandwidth requirement, B/Rb, starts large and then drops to a specific minimum point (with increasing n); afterthat, it takes the same behavior like that of the lower values of w. Taking the w = 7 curve, as an example, B/~ startswith large value at n=8 and drops until n=14 after that, B/Rb increases with n. This is mainly because of the nature ofL{= [n!/(w!o(n-w)!)]}, which acts as described when w > 4. From simulations, one can say that systems utilizinglarger w values require less bandwidth as n increases. Though, large bandwidth requirement reflects on lowbandwidth efficiency and low allowable bit rate.

Figure 5 presents the power requirement for the MPPM scheme. As n increases power requirementdecreases and hence enhances the power efficiency. This decrease and enhancement improve much with systemsutilizing lower w values. Again, a compromise between bandwidth and power for an MPPM system must be donesince a trade off between these values is a must noting that restrictions here are more complex than PPM due to thenature of both nand w. Under our studying ranges, the lowest bandwidth requirement, B/Rb=1.l21, is achieved at w= 12 and n = 25, while the largest one, B/Rb= 4.552, occurs at w = 2 and n = 45. Similarly, the lowest power,PMPPM/POOK= 0.134, is achieved at w=2 and n=45, while largest one, PMPPM/POOK= 2.021, occurs at w = 7 and n = 8.

3.3. Overlapping pulse position modulation (L-OPPM)

As mentioned in Sec. 2.5, L-OPPM is a special case of MPPM. Also, one needs to review the concept that LOPPM can be formed from different combinations ofn and w or a and L. For example, an 8-0PPM can arise from (w=I,n=8 and consequently a=I /8, L=8), (w=2, n=9 and a=2/9, L=8), (w=3, n=10 and a=3/1O, L=8) or (w=4, n=11 anda=4/1I, L=8) and so on. In this paper, we take the range w=I to w=6 which forms all possible combinations for 4OPPM, 8-0PPM, 16-0PPM and 32-0PPM to provide wider view on performance of such schemes on bandwidth and

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power requirement. Effect of duty cycle on both bandwidth and power requirement is also investigated (taking only 32OPPM as a case study). Figures 6 and 7 present the bandwidth and power requirement of different L-OPPMschemes.

7 2.5 r---------------------,

Number of chips fonns optical pulse for L-OPPM, W

Figure 6. Bandwidth requirement for L-OPPM

OL-~-"'--~--'--~---'-~--'--~~-"'--.....J

_+_ 4-0 PPM

-0- 8-0PPM. ... 16-0 PPM__32-0P P M

1 2 3 4 5 6

Number of chips forms opttcal pulse ror O P PM, W

Figure 7. Power requirement for L-OPPM

'"oo 2

1c,o~ 1.5

6

- +- 4-0PPM-.- 8-0PPM

• • . 16-0 PPM__ 32-0PPM

4

u=O.061

2

u=0.03 1

•

g 6~e 5c.5 4;..." 3::i 2::~ 1

Figure 6 states that the bandwidth requirement decreases with w (i.e. enhancing the bandwidth efficiency andallowable bit rate). This is associated by the increment of duty cycle II =w/n. Applying on 32-0PPM, one notices thatincreasing the value of II from 0.031 to 0.16 with increasing w from 1 to 6 will reduce bandwidth required five times.Also, simulation provides that as (L = n - w + 1) decreases, bandwidth requirement decreases. This is because of theconstraint that the w values must be consecutive in L-OPPM model [6].

On the other hand, increasing w with increment of duty cycle will result in increasing the power requirementof L-OPPM (Le. worst power efficiency of the scheme), Fig. 7. For the 32-0PPM as an example, increasing II from0.061 to 0.16 with increasing w from 1 to 6 will increase the power requirement by approximately six times. Resultsprovide us that as L (= n - w + 1) decreases, the power requirement increases.

Again, power and bandwidth requirements for this modulation scheme have different characteristics at thesame design parameters . So, a trade off should be done between these requirements to get a best performance. At thispoint of discussion, one can state that an effective comparison can be established between L-OPPM and MPPM sincethey are based on same design parameters and share some behavior under certain conditions. This part will beinvestigated independently later.

Under our studding ranges , the lowest bandwidth requirement, B/Rb= 0.75, is achieved at w = 6, n = 9(u = 0.667) for 4-0PPM and the largest one, B/Rb= 6.4, at w = I, n = 32 (n = 0.031) for 32-0PPM. Similarly , thelowest power requirement, P32-0PPM/POOK= 0.112, occurs at w = 1, n = 32 and the largest one, P4-0PPMIPOOK= 2, at w =6, n = 9.

3.4. Differential amplitude pulse position modulation (DAPPM)

For the DAPPM scheme, the effect of symbol length, L, and amplitude level, A, on the bandwidth andpower requirement is investigated, Figs. 8 and 9. We explore the effect of multiple amplitude level and hencethe advantage of combining PAM with DPPM.






32

- +- A=2__ A= 4

- + - A =8

168

-+--- . -.- -:-.~.

42

-,"-"-

"-"-

"-"-

"...<,. .....

<,<,

Sym bol length for DAPP M , L

Figure 9. Power requirement for DAPPM

0.6

~00 0.5

~e,

~ 0.4~~

0.3;:=.....= 0.2;.~

i:: 0.1~0~

0

•//

//

/ ~

// <1

,,".

_+_ A=2__ A=4

. + ·A=8

3r-- - - - - - - - - - - - - - - - ----,

2 4 8 16 32Symbol length for DAPPl\I, L

Figure 8. Bandwidth requirement for DAPPM

~ 2.5

Results obtained in Fig. 8 state that bandwidth requirement increase with the symbol length, L, of theDAPPM scheme. However, this increment in bandwidth requirement (lower bandwidth efficiency and allowable bitrate) can be reduced by adopting a wide variety of the amplitude, A, for the operating optical pulses. This gives anadvantage of combining PAM with DPPM. Comparing , at L = 32, when A = 8, the bandwidth is 70% of thebandwidth required when A = 2.

Figure 9 presents an opposite behavior to that observed for bandwidth requirement mainly with L. As Lincreases, power requirement decreases . This observation adds an additional advantage of combination with PAM.The advantage of using large values of A becomes less important as L increases as observed from Fig. 9, especially atL = 32 and more. On the other hand, when L is small (e.g. at L = 2), the power required at A = 8 is approximately33% ofthat required with A = 2 at the same value ofL.

As discussed before, using wide allowable amplitude levels for optical signals (A) provides advantages onboth power and bandwidth efficiency but we believe that will add a degree ofcomplexity to transmitter since differentamplitude levels are required to generate and may, in future, provide with codes. Again, a good compromise shouldbe done to choose a suitable operating symbol length since power and bandwidth requirements have oppositebehavior at the same L.

Under our studding ranges, the lowest bandwidth requirement, B/Rb= 0.375, is achieved at L = 2, A = 8 andthe largest one, B/Rb=2.75, at L = 32, A = 2. Similarly, the lowest power requirement, PDAPPM/PoOK= 0.013, isachieved at L = 32, A = 8 and the largest one, PDAPPM/PoOK= 0.5, occurs at L = 2, A = 2.

3.5. Comparison among different schemes

Because some schemes have common design aspects (e.g. DAPPM with PPM and MPPM with L-OPPM),the comparison can be divided into three major subsections; first between DAPPM and traditional PPM, secondbetween MPPM and L-OPPM and finally a general comparison includes all schemes.

For DAPPM and PPM schemes, one can observe that the two schemes share the property that the bandwidthrequirement increases with the symbol length (i.e. both bandwidth efficiency and allowable bit rate decrease). Thesimulation results are used as indicator for admitting that DAPPM is much bandwidth efficient than PPM in small orlarge values of L at any operating A values. This efficiency becomes more noticeable at large L values. Thisobservation can be applied on the power requirement also. As (L) increased both DAPPM and PPM require lesspower. However, power requirement for DAPPM is lower than that of PPM especially at large values of L. We haveto mention that bandwidth efficiency of DAPPM is larger than that efficient observed in power compared to PPMscheme.

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From results obtained for MPPM and L-OPPM, it is observed that the bandwidth requirement decrease withw. This is associated by the increment of a for the L-OPPM scheme. For the MPPM scheme, increasing n results inincreasing bandwidth requirement especially for low w values. The simulation provides that L-OPPM is more efficientthan MPPM for the same values ofn and w. This observation is in a fair agreement with theoretical background in [6],[7]. On the other hand, for power requirement, the power requirement increases with w in both L-OPPM and MPPMschemes. Again, this is associated by the increment of a for L-OPPM while for MPPM increasing n results indecreasing power requirement, especially for low w values.

Concentrating on the bandwidth and power requirement levels, one can state that, under careful designaspects, DAPPM has the lowest bandwidth and power requirement and hence best efficiencies. For bandwidthrequirement, DAPPM is followed by L-OPPM, MPPM and finally PPM which requires the largest bandwidth.Similarly, for power requirement DAPPM is followed by PPM, L-OPPM and finally MPPM which requires thelargest power compared to OOK scheme.

Another important remark is that the difference in power requirement among schemes under simulated widerange of different design parameters is not huge [i.e. 0.013 POOK to 2.021 POOK] as compared with the difference inbandwidth requirement [0.375 R, to 10.66 Rb]. So, a good design choice must be done especially when usingmodulation schemes like PPM which until now is the standard ofWOC indoor applications [9].

3.6. Relation with IrDA and IEEE 802.11 standards

There are presently two standardization bodies supporting worldwide standards for indoor wireless opticalcommunication systems: the IEEE 802.11 group, created in July 1990, and IrDA, created in June 1993. While thefocus of the IEEE 802.11 group is on the non-directed indoor optical wireless LANs, IrDA is mainly oriented toshort-range low bit-rate line-of-sight systems. However, in recent years, IrDA initiated a new project, calledAdvanced Infrared (AIr), whose main objective was to establish a new standard for non-directed optical wirelessLAN [9]-[11]. Both AIr and IEEE 802.11 specifications use the PPM scheme.

The IEEE 802.11 standard supports two data rates. In order to keep the same pulse duration at the two datarates (250 ns), two different PPM schemes are used: 16-PPM at 1 Mb/s and 4-PPM at 2 Mb/s. AIr uses 4-PPMmodulation at 4 Mb/s (i.e. with a pulse duration of 125 ns) [9]-[11].

From this work, one can understand the reason of using PPM for these standards since it has a very lowpower requirement which is a key factor for indoor WOC application. Also, one can suggest the DAPPM scheme asan alternative solution since it is more power efficient than PPM and much efficient in bandwidth requirement.Though, additional practical design aspects should be studied widely for DAPPM such as transmitter complexity,synchronization problem and coding design.

4. Conclusion

In this work power and bandwidth requirement for different PPM schemes were investigated. Study wasdone under wide range of design parameters to provide wide view on the behavior and characteristics of suchschemes. This study is useful for WOC designers since it provides them with knowledge that can help in overcomingdifficulties faced in indoor WOC network. A detailed and general comparison between schemes was done showingthat DAPPM scheme is the most power and bandwidth efficient one under careful design aspects. This is mainly dueadditional advantages added when combining DPPM with PAM. An overview on IrDA and IEEE 802.11 standardsis presented indicating the promising behavior ofDAPPM in replacing PPM.

References

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Raton: Auerbach Publications, 2008.






[3] S. Hranilovic, Wireless Optical Communication Systems, Boston: Springer Science, 2005.[4] S. Hranilovic and F. R. Kschischang, "Optical Intensity-Modulated Direct Detection Channels: Signal Space and

Lattice Codes," IEEE Trans. on Information Theory, vol. 49, pp. 1385-1399,2003.[5] U. Sethakaset and T. A. Gulliver, "Differential Amplitude Pulse-Position Modulation for Indoor Wireless

Optical Channels," IEEE Communication Society, vol. 3, pp. 1867-1871,2004.[6] H. Park and J.R. Barry, "Modulation Analysis for Wireless Infrared Communications," presented at IEEE

International Conference on Communications, ICC 95, Seattle, pp. 1182-1186,1995.[7] G. E. Atkin and K. S. Fung, "Coded Multipulse Modulation in Optical Communication System," IEEE Trans. on

Communications, vol. 42, pp. 574-582, 1994.[8] B. Sklar, Digital Communications Fundamentals and Applications, New Jersey: Prentice-Hall, 2001.[9] Infrared Data Association, http://www.irda.org., April 2006.[10] A. Tavares, R. Valadas, R. L. Aguiar, and A. O. Duarte, "Angle Diversity and Rate-Adaptive Transmission for

Indoor Wireless Optical Communications," IEEE Communications Magazine, pp. 64-73,2003.[11] B. H. Walke, S. Mangold, and L. Berlemann, IEEE 802 Wireless Systems, Protocols, Multi-hop Mesh/RelayingPerformance and Spectrum Coexistence. Chichester, West Sussex: John Wiley & Sons, 2006.


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