Multilevel Modulation and Channel Codes forTerrestrial FSO links

S.Sheikh Muhammad *, E. Leitgeb*,O.Koudelkat*Institute of Broadband Communications,tInstitute of Communication Networks and Satellite Communications,

TU Graz, Inffeldgasse 12, 8010 Graz, Austriasmsajid@sbox.tugraz.at, leitgeb@inw.tugraz.at, koudelka@tugraz.at

Abstract- The basic aim of this work is to enhancethe performance of the existing terrestrial FSO links byintroducing a well suited modulation and channel codingscheme. Selecting an appropriate modulation and codingscheme for the FSO systems requires thorough knowledgeof the behavior of the FSO systems under differentconditions and the objectives that need to be achieved outof the modulation mechanism. Since modulation for theFSO systems are primarily targeted at achieving higheraverage optical power, so that the penetration of the lightwaves through the adverse weather conditions can beincreased. Thus, the power efficiency of the scheme remainsthe deciding criteria in the selection of the modulationformat. The choice of the modulation and coding formathas to be based on measurements and simulation ofthe performance of FSO systems under nonfavourableatmospheric conditions. An effort is also being made tosimulate the atmospheric free space optical channel to getmore insight into the problem.

Keywords: Free Space Optics (FSO), Modulation, Chan-nel Coding, FSO channel modeling, atmospheric impair-ments.

I. INTRODUCTIONFree space optical communications (FSO) has gained

importance in recent times due to a variety of applicationsin the field of telecommunications. FSO applications spanover a wide range from satellite links to robotics andgenerates interest for several distinct markets. FSO is be-coming famous both as a preferable last mile solution andas a supplement to the more conventional RF links [1],[2]; and this has given rise to the need of investigations inmechanisms to enhance the performance of the systems.The free-space, direct detection, optical intensity-modulated channel offers the modem designer interestingnew challenges. Most practical FSO systems use lightemitting diodes (LED) or laser diodes as transmittersand PIN photodiode or avalanche photodiodes (APD)as receivers forming a relevantly simple communicationsystem. These devices modulate and detect solely theintensity of the carrier, not its phase, which impliesthat all transmitted signal intensities are non-negative.Furthermore, biological safety considerations (eye safety)constrain the average radiated optical power, therebyconstraining the average signal amplitude. Conventionalsignal space models and coded modulation techniquesfor electrical channels cannot be directly applied to thischannel [3].

Historically, optical intensity channels have been mod-eled as Poisson counting channels, and the model remains

a valid assumption for basic investigations in FSO aswell. The literature is replete with channel capacity re-sults for the photon-counting channel. In the absence ofbackground noise, the capacity of such channels is infinite[4], [5]; and M-ary Pulse Position Modulation (PPM)can achieve arbitrarily small probability of error for anytransmission rate. McEliece demonstrated that schemesbased on photon counting in discrete intervals requirean exponential increase in bandwidth as a function ofthe rate (in nats per photon) for reliable communication[6]. The most prominent modulation formats for wirelessoptical links are binary level PPM and on-off keying(OOK). Shiu and Kahn developed lattice codes for freespace optical intensity channels by constructing higherdimensional modulation schemes from a series of onedimensional constituent OOK constellations [7].In this paper, we present the channel modeling effortfor the terrestrial FSO channel based on photon countingand simulations of the channel. Section III of the paperprovides the results of investigations in appropriate mod-ulation schemes for FSO and the next section deals withthe channel codes to be combined with the modulationformat to provide better gains.

II. CHANNEL MODELINGTo get more insight into the problem, a better under-

standing of the characteristics of terrestrial FSO channelis necessary. Modeling the channel for terrestrial FSO isa problem of considerable complexity due to the varietyof impairments possible and the disagreement over themathematical modeling of the various phenomena. FSOlinks are impaired by absorption and scattering of lightby earths atmosphere. The atmosphere interacts with thelight due to its composition, which normally consists ofa variety of different molecular species and small sus-pended particles called aerosols. This interaction producesa variety of phenomena: frequency selective attenuation,absorption, scattering and scintillation. In addition, sun-light can affect FSO performance when the sun is co-linear with the free space optical link. An effort is beingmade to simulate these effects as accurately as possibleso that the resultant channel model may later be used asa test-bed for the verification of the selected modulatorand channel coder [8]. Investigations into the capacity ofoptical intensity channels have focussed on channels inwhich the dominant noise source is quantum in nature.In these channels, the transmitted optical intensity is

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constant in discrete time intervals and the received signalis modeled by a poisson-distributed count of the numberof received photons in each discrete interval. In order, tounderstand the theoretical framework of optical channels,this photon counting channel has been utilized and thedevelopment of an efficient modulation and coding formathas been based on the mathematical analysis of thischannel model, and to bring the work nearer to reality theterrestrial free space optical channel has been simulatedwith an effort to keep it as close to the real environmentas possible.

A. Photon Counting ChannelWe assume a photon counting communication system

as the basic model for investigating the behavior of thechannel. For this purpose, we built up a model in a waythat the time interval during which communication takesplace is divided into many sub-intervals ("slots"), eachof duration to seconds. The transmitter is a laser whichis pulsed during each time slot; it may be pulsed witha different intensity in each slot. At the receiver is aphoton counter which accurately counts the number ofphotons received during each time slot. We denoted byxi the expected number of photons received during theith time slot; xi will be the intensity of the ith pulse.We assume that no noise photon exists and because ofthe poisson nature of photon arrivals, the probability thatexactly k photons will be received during a slot in whichthe laser was pulsed with intensity x is e k, thus wecan summarize this discrete memoryless channel by theconditional probability

kP(klx) = -x(1)

The channel described by the above equation is calledthe photon channel and has been extensively used in re-search on optical communication channel design [6]. Thephoton channel is the appropriate model when applied tooptical channels in which the receiver intensity is low,such as the fiber optic and the free space optical channel.Photons are detected by the photon counter with theprobability of their detection depending on the energy inthe electric field. For a given electric field energy E, theprobability of the number of photons detected over a giventime T has a poisson distribution

P,(j) = jnie, j =0, 1, 2, (2)

Here n = n(E) is the mean number of photons detectedin the counting time t. It is equal to the expected fieldenergy in time t divided by hf. Note that

P,(O) = e (3)

is the probability that no photons are detected. Thenumber n is called the poisson parameter.

In [5], Pierce argued that if one uses photon count-ing techniques for communication at optical frequencies,channel capacity is hf nats/photon where f is the photoncenter frequency and T is the noise temperature (h is

Plancks constant, k is Boltzmanns constant). Later, it wasalso observed that techniques of linear amplification yielda capacity of I nat/photon. However, channel capacity isan absolute limit on performance and only tells us what ispossible using arbitrarily complex encoding and decodingstrategies [9].B. Terrestrial Free Space Optical Channel

The terrestrial free space optical channel representsone of the most challenging environments to model andsimulate. A significant effort in this regard was made byM.Achour [10], [11]; but still much more is desired. Achannel model has been developed to look more deeplyinto the issues of modulation and coding and at presentthis model simulates the major attenuators for the FSOlinks namely fog, rain and snow besides providing theflexibility to introduce different levels of turbulence basedon the turbulence coefficient [8]. The simulation was triedto be setup in a way to keep as many parameters variableas possible, to give the model a very general outlook.

1) Fog Attenuation: The theoretical background of fogattenuation for light based on Mie Scattering can be foundin detail in literature [12], [13]. Several models existwhich allow to calculate specific attenuation for differentoptical wavelength based on visibility data. The two mostwidely used models are the Kim and the Kruse model,they have been implemented and the resultant attenuationcurves are shown. At very high attenuations the Kimmodel is the better choice.

Fig. 1. Fog Attenuation curves

2) Rain and Snow Attenuation: Rain is also an impor-tant attenuator for optical signals and has been modeledusing the best known relations. The attenuation due tosnow fall has been modeled based on dry and wet snow,the simulated attenuations are shown in Fig. 2.

3) Scintillation: Randomly distributed cells are formedunder the influence of thermal turbulence inside thepropagation medium; the wave fronts vary causing thefocussing and de-focusing of the beam. Such fluctuationsof the signal are called scintillations. The intensity andspeed of the fluctuations increase with wave frequency.Based on the refractive index structure parameter Cn2, thescintillation losses have been modeled for low, mediumand high turbulence and are depicted in Fig. 3.

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signal. The response of the photodiode is the integrationof tens of thousands of wavelength of incident light. Usingincoherent, diffuse light sources (for eye safety reasons),only the intensity of the optical signal can be determined,which must remain positive [15].

Let x(t) denote the intensity of the transmitted opti-cal signal and let ry(t) be the photodetector current atthe receiver, where the constant r is the photodetectorresponsivity. When the intervening channel has impulseresponse h(t), y(t) is given by

y(t) = J x(r)h(t --r)d(r) + n(t) (4)

Fig. 2. Attenuation due to dry and wet snowThe input x(t) represents power, not amplitude and

this leads to two unusual constraints on the transmittedsignal; firstly, x(t) must be positive, and secondly, theaverage amplitude of xr(t) is limited. If the average of thetransmitted light wave is constrained to a value which wedenote by R, then the input x(t) of the baseband channelmust satisfy

x (t) > 0

li Io2 TX (t)dt < R

Fig. 3. Scintillation losses

A Graphical User Interface for the channel model hasbeen developed to provide the user the convenience ofhandling the simulation setup on his own. This channelmodel directly provides availability and reliability predic-tion for terrestrial FSO. In the next steps, it will be usedto test the performance of the modulation and channelcoding schemes mentioned in this paper.

III. MODULATION SCHEMES

Most of the FSO systems being currently used employthe intensity modulation with direct detection scheme(IM/DD), and the performance of the FSO systems ishampered by varying atmospheric conditions. Previousinvestigations [14] have shown that deep fog is the mostsevere deterrent, as the light penetration through fogreduces considerably, and thus intuitively it appears thatthe penetration of light can be improved by concentratingmore power into lesser areas. This indicates towards theutilization of power efficient modulation schemes.The transmission of information using optical intensity

channels differs significantly from the conventional RFchannel. Unlike the RF technologies, where the carrieramplitude and phase are varied, wireless infrared relieson the intensity modulation of a terahertz range optical

The first constraint implies that any modulation schemefor an optical intensity channel must have a DC compo-

nent which transmits no information but consumes energy

[16].These special requirements for the optical intensity

channel prevents applying the wealth of modulationanalysis available for the conventional channel to theFSO application. Different binary schemes like the on-offkeying (OOK), two pulse-position modulation (2-PPM)and subcarrier binary phase shift keying (BPSK) havebeen compared, based on their power efficiency, measuredby the average optical power required to achieve a givenBER at a given bit rate. It has been noticed that 2-PPMhas the same power requirements as OOK, whereas BPSKsuffers a 1.5 dB optical power penalty [1]. For a givenoptical power Pt, the receiver SNR can be improved bytransmitting a waveform X(t) having a high peak-to-average ratio, such as L-PPM. We note that the opticalpath loss of the channel is H(0) = f° h(t)d(t), andthe received optical power is P = H(O)Pt [17].

A. Pulse Position Modulation

Most modulation schemes for data transmission on

landline or wireless optical channels rely on binary levelsto transmit data. Schemes such as on-off keying and pulseposition modulation depend on the use of two levels totransmit data. Multilevel modulation schemes can providebetter bandwidth and power efficiencies because of theirmore complex signal constellations. Schemes such as

L-PAM and QAM achieve higher bandwidth efficiencyat the expense of decreased power efficiency. L-levelPPM is a fundamentally different modulation schemethat achieves high power efficiency at the expense of

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reduced bandwidth efficiency [16]. Digital Pulse PositionModulation (PPM) is widely used in intensity-modulatedoptical communication systems, such as fibre optic andsatellite systems, primarily because of its high average-power efficiency [5], [6]. The abundance of bandwidth inthese applications makes the poor bandwidth efficiency ofPPM of little concern, the FSO environment representsa very similar situation, and PPM with its significantlybetter power efficiency seems the appropriate choice.

Talking in terms of our photon communication channel,if we take a block of M counting times t and use pulseposition modulation, we can find how large Al can beso that the probability of error will still be low. We canhave an error if there is a noise photon during one of theM - 1 time intervals when the shutter is closed. Theremaybe no noise photons in these intervals, but we mayfail to receive a signal photon when the shutter is open.This corresponds to an erasure, in which no photons at allare received. It is well known that, in an erasure channel,the erasure lowers the capacity in bits/second, but onlyby the probability of an erasure. So it is reasonable thatwe can ignore the probability of erasure in computing thecapacity in bits per photon. This is assumed true and thecapacity in bits per photon is then

C = log2M (7)

Here M is the largest number of intervals for which theprobability of receiving a noise photon in some intervalduring which the shutter was closed is small.

In a pulse-position modulation scheme, each symbolinterval of duration

T = log2 k (8)

is partitioned into L subintervals, or chips, each ofduration T, and the transmitter sends an optical pulseduring one and only one of these chips. PPM is similar toL - ary FSK, in that all signals are orthogonal and haveequal energy. PPM can be viewed as the rate - log2 LLblock code consisting of all binary L - tuples havingunity hamming weight. A PPM signal can be written as

L-1 kTx(t) = LP , Ckp(t - L) (9)

k=O

where [co, c1, C2.. CL-1] is the PPM codeword, andwhere p(t) is a regular pulse of duration T and unityheight. All of the signals are equidistant, with:

dmin = min,jj J(xi(t) - xj(t))2dt = 2LP2 log2 L

(10)therefore, the average power requirement is approxi-

mately:

PPPM/POOK = dOOK/dmin L og2L (11)

From the above equation, we say that, for any Lgreater than 2, PPM requires less optical power thanOOK. In principle, the optical power requirement can bemade arbitrarily small by making L suitably large, at theexpense of bandwidth, the bandwidth required by PPM toachieve a bit rate of Rb is approximately the inverse ofone chip duration, B = L/T= LlORL [18].PPM is an orthogonal modulation technique and can be

viewed as a simple nonlinear block code; specifically, therate log2 L block code consisting of the set of L-binaryLL-tuples with unity hamming weight [19]. It has beenshown in [16] and can be seen through (11) that 2-PPMhas same power efficiency as OOK but requires twicethe bandwidth and 4-PPM requires 3.8 dB less opticalpower, and as L increases from 4 to 16, the bandwidthrequirement doubles, while the sensitivity increases from3 dB better than OOK to 7.5 dB better than OOK, andclearly increasing L improves the power efficiency formultilevel PPM.

IV. EFFICIENT CHANNEL CODESThe channel capacity of the photon channel was dis-

cussed earlier, and it is a general rule that the closerone approaches channel capacity, the more complex andcostly the needed coding strategies become. In the case ofphoton communication, however, coding problems seemto become more serious much sooner than usual, and foran unexpected reason. It is not the noise temperature,but the nature of the photon-counting process itself, thatcauses the most serious problems; so that even in thelimiting case T = 0, when capacity is in principleinfinite, it seems unlikely that a signalling efficiency ofeven 10 nats/photon can be achieved practically. This isbecause, as the signalling rate increases one encountersan explosive increase in bandwidth expansion.

A. Channel Codes for Pulse Position ModulationIn [5], Pierce suggested the use of Pulse Position

Modulation (PPM) for optical communications. In PPM,a fixed integer q > 2 is selected, and the transmissioninterval is divided into consecutive blocks of q slots each.In each such block the laser is pulsed in exactly one ofthe q slots at a fixed intensity. Each of these q patterns canbe regarded as a letter in the sender's alphabet. In codedPPM, the idea is to regard the q - letter transmissionalphabet as the input alphabet of a discrete memorylesschannel with q + 1 output letters, the (q + 1)st letteris regarded as the erasure symbol. In order to achievebetter performance, appropriate channel codes need tobe combined with PPM. Three strong possibilities forchannel coding exists with PPM namely Reed Solomoncodes [6], Turbo Codes [20], [21] and Trellis codedmodulation [22].

1) Reed Solomon Codes: A PPM signalling schemeseems to lend itself naturally to a Reed Solomon code,whose alphabet size can be easily matched to the PPMorder. This result in a one-to-one correspondence betweenRS code symbols and PPM symbols. Using a maximumcount or threshold hard decision rule, a single PPM error

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translates directly into a single RS-code symbol error. Or,by using threshold or 6 - max demodulation, an erasuremay be declared based on the soft counts in a PPMsymbol. This is sometimes referred to as soft decisionRS coding. Since every RS code is a maximum distancecode, it appears that no more powerful code could befound for this application.

2) Turbo Codes . There have been proposals forcombining Turbo codes with PPM [20], [21] primarilybecause of their higher coding gains and their ability toutilize soft outputs, but for the FSO applications it isenvisaged that the gains achieved by Turbo codes maynot justify the increase in the complexity and the delayrequirements inherent to them, and moreover, its alwaysthought better to be utilizing hard decision demodulatorsin FSO applications. A relevantly innovative scheme isproposed where through the quantization of APD/PINoutput voltage levels, soft decisions can be generated;which can then be used for the Turbo decoding and thiswill lead towards significant coding gains. However, itsstill an open question as to how Turbo codes may performin combination with higher level PPM on a terrestrial FSOchannel and only further investigations can prove withcertainty their supremacy.

3) Trellis Coded Modulation: Since PPM is an or-thogonal multipulse modulation scheme, the Euclideandistance between any pair of symbols is the same, andtrellis coded modulation which is designed to maximizethe minimum Euclidean distance between allowed signalsequences may provide performance enhancement onmultipath intersymbol interference (ISI) effected channels[22] , but it will not be of much benefit in a FSO envi-ronment which does not suffer from multipath problems.

Thus, all in all, the choice is really between ReedSolomon Codes and Turbo Codes as the most suitablefor FSO application and their combination with multilevelPPM should yield significant performance enhancement.Reed Solomon codes are well known channel codes andare extremely efficient at correcting erasures and wellestablished encoding and decoding procedures exist forthem. Similarly, Turbo codes have gained considerableimportance due to their high coding gains and utilizationof iterative decoding mechanism in them.The optimal PPM order for FSO applications can be

256 and the rate (255,128) RS code can be a goodchoice to be combined with 256 - ary PPM. Hence,one of the possible modulation and coding scheme to beutilized in FSO systems is believed as RS-coded PPM.Still an open question is the selection of the PPM orderin combination with Turbo codes to yield desired results.

V. CONCLUSIONS

This paper summarizes the preliminary research resultsfor providing a suitable modulation and channel codingformat for the FSO systems. This is the first of its kindattempt to introduce the well established principles ofpower efficient modulation and channel coding in the FSO

with substantial coding gains to combat fog and otherattenuators which limit the performance of the technology.We are now, in the process of developing hardware andsoftware modules to test the performance of these ideas ona real world environment and the results will be publishedin due course of time.

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environment; and these investigations indicate that the useof these schemes will eventually lead to better systems

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