Channel Capacity of MIMO FSO System under Strong Turbulent Condition

Transcription

1 International Journal o Electrical & Computer Sciences IJECS-IJENS Vol: No: 0 Channel Capacity o IO FSO System under Strong Turbulent Condition Bobby Barua # and Dalia Barua # # Assistant Proessor, Department o EEE, Ahsanullah University o Science and Technology, Dhaka, Bangladesh #.Sc. Student, Institute o ICT, Bangladesh University o Engineering and Technology, Dhaka, Bangladesh bobby@aust.edu Abstract Free Space Optics (FSO) or optical wireless communication is a promising solution or the need to very high data rate point-to-point communication. In FSO communication links, atmospheric turbulence causes luctuations in both the intensity and the phase o the received light signal, impairing link perormance. This intensity luctuation, also known as scintillation is one o the most important actors that degrade the perormance o an FSO communication link even under the clear sky condition. This paper investigates the use o multiple lasers and multiple apertures to mitigate the eects o scintillation. Also an analytical approach is presented to evaluate the channel capacity o a ree space optical link using Q-ary optical PP under strong atmospheric turbulent condition. In this view, we propose design rules or optimal channel capacity o the system. Index Term Free space optics (FSO), pulse position modulation (PP), probability o density unction (PDF), channel capacity, I. INTODUCTION Free Space Optical (FSO) communication is a telecommunication technology that uses light propagating in ree space to transmit data between two points. FSO communication links have some distinct advantages over conventional microwave and optical iber communication systems by virtue o their high carrier requencies that permit large capacity, enhanced security, high data rate and so on. Such links are suitable or Gb/s rates over distances in the range o 5 km. However, a number o limitations due to atmospheric turbulence make it diicult to achieve the desired level o perormance [, ]. Atmospheric turbulence-induced ading is one o the main impairments aecting FSO communications.optical signal propagation in ree space is aected by atmospheric turbulence and pointing errors, which ade the signal at the receiver and deteriorate the link perormance. The reliability o an FSO communication system is greatly inluenced by the atmospheric conditions. The beam scattering caused by og and haze can signiicantly reduced the received optical signal level. Again heavy og causes attenuation greater than 300 db/km, thus limits the link length to < 00m. ain and snow aect mainly the radio and microwave requencies but their eects are not deleterious or FSO systems. However FSO can encounter signiicant losses in a clear sky condition due to inhomogeneities in temperature and pressure [3, 4]. So the scintillation severely limits the reliability o FSO links as it deteriorates the signal intensity at the receiver and can even result in complete loss o communication links. The eect o scintillation is more severe or small aperture receivers [5,6]. Several communication techniques to mitigate turbulence-induced intensity luctuations. These techniques are applicable in the regime in which the receiver aperture is smaller than the correlation length o the ading, and the observation interval is shorter than the correlation time o the ading. To enable the transmission under strong the atmospheric turbulence the use o the multi-laser multi-detector (LD) concept has been reported in e. [7,8]. Speciically, we envision separate lasers, assumed to be intensity-modulated only, together with photodetectors (PDs), assumed to be ideal noncoherent (direct-detection) receivers. The sources and detectors are physically situated so that the ading experienced between source detector pairs is statistically independent, and thus, diversity beneits can accrue rom the multiple-input multiple-output (IO) channel [9]. Channel capacity is the maximum achievable data rate that can be reliably communicated between the transmitter and the receiver [0]. In this paper, we develop an analytical approach to evaluate the channel capacity under strong turbulence with Q-ary PP. The developed scheme allows aggregation o F/microwave signals and a conversion to the optical domain in a very natural way and may be a good candidate or hybrid F/microwave-FSO systems. The symbol error probability (SEP) are evaluated with ading in the presence o background radiation. In the determination o SEP it is also assumed that p.i.n. photodiodes are used, and the channel is modeled using Gamma-Gamma distribution or strong turbulence. To determine the channel capacity we employed the concept proposed by Fang Xu in [], although in a dierent context (or multi amplitude/multi phase signaling) IJECS-IJENS April 0 IJENS

2 International Journal o Electrical & Computer Sciences IJECS-IJENS Vol: No: 0 Source Channels Transmitter Transmitter eceiver eceiver Users L PP apper Transmitter ilter & Driver ampliier Processor Transmitter eceiver N L Atmospheric Turbulence Channel Fig.. Atmospheric optical IO system with Q-ary PP II. SYSTE ODEL Fig. depicts a block diagram o the physical system under study. laser sources, all pointed toward a distant array o N PDs, are intensity-modulated by an inormation source The laser beam-widths are narrow, but suiciently wide to illuminate the entire PD array. For example, i the hal-power beam-width is 0 mrads, the hal-power spot size at distance km has diameter 0 m. The N optical path pairs may experience ading, and we designate Anm as the amplitude o the path gain (ield strength multiplier) rom m source to detector. A Q-ary PP scheme transmits L=logQ bits per symbol, providing high power eiciency. The total transmitted power Ptot is ixed and independent o the number o lasers so that emitted power per laser is Ptot/. This technique improves the tolerance to atmospheric turbulence, because dierent Q-ary PP symbols experience dierent atmospheric turbulence conditions. At the receiver the received signal r(t) ater optical/electrical conversion is: r( t) h( t) I n( t) () where I 0 is the average transmitted light intensity, I is the corresponding received intensity in an ON PP slot, h is the channel ading coeicient and n is the receiver noise. 0 quantum eiciency. Also a single-channel link analysis is included to suggest typical link parameters. Though the transmission rate is rather lexible, we have in mind systems sending in the range o 00 b/s. Here we consider the chosen parameters rate 00 b/s, the expected number o detected photoelectrons per slot is on the order o 300 in either binary or quaternary PP. Though this is more than adequate or the desired perormance with the ideal photon-counting model, ading and other parameter choices could make this number much smaller. III. CHANNEL ODELING To characterize the FSO channel rom a communication theory perspective, it is useul to give a statistical representation o the scintillation. The reliability o the communication link can be determined i we use a good probabilistic model or the turbulence. Several probability density unctions (PDFs) have been proposed or the intensity variations at the receiver o an optical link. Al- Habash et al. [7] proposed a statistical model that actorizes the irradiance as the product o two independent random processes each with a Gamma PDF. The PDF o the intensity luctuation is given by [7] ( )/ ( ) ( ) ( I) I K( ) ( I), I 0 ( ) ( ) () The aggregate optical ield is detected by each PD, assuming an ideal photon counting model with typical I is the signal intensity, Г(.) is the gamma unction, and K is the modiied Bessel unction o the second kind IJECS-IJENS April 0 IJENS

3 International Journal o Electrical & Computer Sciences IJECS-IJENS Vol: No: 0 3. and are PDF parameters describing the scintillation experienced by plane waves, and in the case o zero-inner scale are given by [9] where the integral is interpreted as an N-dimensional integral. Since the Anm variables are assumed independent, the above averaging leads to 0.49 exp /5 7/6 (. ) (3) w wi w i ( ) t( Q, w, i) e ( a) da i l0 N s ( i l ) a l w A i i 0 (8) 0.5 exp /5 5/6 ( 0.69 ) (4) I the channel is under log-normal ading, the probability o zero count in slot at detector n is given by [], n Pr Ts a mn nm h Q P allz 0 slot, A e (9) n where σ is the ytov variance given by[4] I the path gains are independently distributed and identical, the average symbol error is given by [4], σ =.3C n k 7/6 L /6 (5) k = distance, and Cn is the reractive index structure parameter, which we assume to be constant or horizontal paths. IV. THEOETICAL ANALYSIS OF EO POBABILITY First, we assume the channel gain o every laser-detector pair is ixed over a symbol duration. Letting amn denote the amplitude ading on the path rom laser m to photodetector n, we deine the channel gain matrix as A with element [a nm, n =,,N, m =, ]. The probability o symbol error conditioned on the ading variables is P sa ww i w wi s anm ( il) l n m ( ) t( Q, w, i) e (6) i i l0 i To extend the analysis o non-ading link and no background radiation case to the case o link ading, we can simply average the (conditional) symbol error probability o (7), with respect to the joint ading distribution o the Anm variables. We emphasize that this produces the symbol error probability averaged over ades. Formally, we ind by evaluating PS A A( a) da (7) E N a s h Q A A( a) da e A( a) da Q (0) In case o gamma-gamma ading, the probability o zero count in slot at detector n is n Pr Ts a mn nm h Q P allz 0 slot, A e () n I the path gains are independently distributed and identical, the average symbol error becomes E N a s h Q A ( I) di e ( I ) di Q V. CHANNEL CAPACITY () We consider in this paper the case o terrestrial multipleinput multiple-output (IO) channel with FSO systems used over ranges up to several kilometers. In such systems, photon counting is not easible in practice. In act, the received photon lux is important and we can detect the received signal based on the beam intensity directly. Here, we consider the channel capacity or dierent value o Q or intensity-based signal detection. The channel capacity is the maximum o the mutual inormation I(X; Y) between the channel input X and output Y, with respect to the probability mass unction o X: IJECS-IJENS April 0 IJENS

4 International Journal o Electrical & Computer Sciences IJECS-IJENS Vol: No: 0 4 PX ( x) C max I X ; Y (3) We assume equiprobable symbols or PP. Without loss o generality, let us assume that the irst slot is ON and the others are OFF. We denote this symbol by x and and N are no. o transmitter and receiver respectively. In addition, let us denote by x k a PP symbol with the k th slot ON. Then the channel capacity YX C YX y x log dy Q Q k Y X y x k Q y x N (4) (I) S.I=3.0 VI. ESULTS AND DISCUSSION Following the analytical approach presented in section IV and V we evaluate the symbol error probability result and estimate the channel capacity o a IO FSO link with Q-ary PP and direct detection scheme under strong turbulence conditions. For the convenience o the readers the parameters used or computation in this paper are shown in table I. Table I System Parameters used or computation Parameter Name Value Bit ate, B r 00 bps odulation Q-PP Order o PP, Q, 4, 8,.. Channel Type Gamma-gamma Scintillation Index, S.I. 3.0 Symbol energy with -70dBJ background noise ytov Variance, x Symbol Energy, E s 0-6 Joules Quantum eiciency, η 0.5 The simulations are perormed using matlab, the inluence o scintillation is modeled assuming Gamma-Gamma distribution, and an ideal photon counting receiver is employed Value o (I) Fig.. Probability o Distribution Function or Gamma-Gamma. The plot o the probability density unction in Fig. or gamma gamma cases with typical value o scintillation index (S.I) and turbulence strength ading varying with and N 0-0 IO,=,N= IO,=,N= IO,=4,N=4 IO,=8,N= Esdb Fig. 3. SEP with varying both and N, or gamma-gamma ading with S.I. =3. Q= and no background noise IJECS-IJENS April 0 IJENS

5 International Journal o Electrical & Computer Sciences IJECS-IJENS Vol: No: 0 5 that p.i.n. photodetectors are employed, and evaluate how much we can approach this theoretical limit employing dierent value o Q. We discussed the impact o bitsymbol mapping on the channel capacity as well as on the perormance o the receiver. The analysis shows the beneicial eects rom a diversity standpoint o multiple sources and detectors, and transmit diversity is achieved here without additional special coding. Fig. 4. SEP Channel capacity or dierent number o lasers (), photodetectors (N) and number o slots (Q) in strong turbulence regime (σ =3.0). In particular, notice the gamma-gamma model has a much higher density in the high amplitude region, leading to a more severe impact on system perormance. The SEP are shown in Fig. 3 or several combinations o transmitter and receiver under aded condition. The symbol energy due to background light is set to -70 dbj or system. It is ound that, or IO coniguration, the system provides better perormance also noticed that, SEP improves as the numbers o lasers and photodetectors are increased and in the presence o background light the SEP decreases as the order o the Q-ary PP scheme increases. Fig.4 shows the channel capacity or dierent combination o transmitter and receiver. Here we evaluate the channel capacity or the case o an additive white Gaussian noise (AWGN) channel. That is to say, we consider the presence o atmospheric turbulence and set the channel ading coeicient to three. From the plots in Fig.4 we ound that the perormance o the channel will improve i we increase the number o transmitter and receiver with proper combination o Q. EFEENCES [] L.C. Andrews,.L. Phillips, Laser Beam Propagation through andom edia, SPIE Optical Engineering Press, Bellingham, WA, 005. []. Uysal, J.Li,. YU, Error rate perormance analysis o coded ree-space optical links over gamma gamma atmospheric turbulence channels, IEEE Transactions on Wireless Communications 5(6), 006, pp [3] N. Cvijetic, S.G. Wilson, and Brandt- Pearce., eceiver optimization in turbulent ree-space optical IO Channels with APDs and Q-ary PP, IEEE photon tehnol.lett.8, (006) [4] J. Strohbehn, Ed. Laser Beam Propagation in the Atmosphere New York: Springer, 978. [5] L. C. Andrews,. L. Phillips, C. Y. Hopen,. A. Al- Habash, Theory o optical scintillation, J. Opt. Soc. Am. A 6, (999). [6] S.G. Wilson,. Brands-Pearce, Q. Cao, and J.J.H. Leveque,III, Free-Space optical IO transmission with Q- ary PP, IEEE Trans. Commun.53,40-4(005) [7] G. Ochse, Optical Detection Theory or Laser Applications. NewYork: Wiley- Interscience, 00. [8] B. Saleh, Photoelectron Statistics. Berlin, Germany: Springer- Verlag,978. [9].A. Al-Habash, L.C. Andrews, and. L. Phillips, Optical Engineering 40,pp (00). [0] C. E. Shannon, A mathematical theory o communication, Bell Syst. Tech. J., vol. 7, pp , Jul./Oct [] F. Xu,.A. Khalighi an S. Bourennane, Pulse Position odulation or FSO Systems:Capacity and Channel Coding 0th International Conerence on Telecommunications - ConTEL 009 pp.3-38 (009). VII. CONCLUSIONS We have analyzed an optical IO system employing QPP across sources with direct detection Gamma gamma model or strong turbulent condition. We determine the channel capacity o this scheme assuming IJECS-IJENS April 0 IJENS