Effect of Atmospheric Turbulence on Free Space Optical Multi-Carrier Code Division Multiple Access(MC-OCDMA)

T. A. Bhuiyan1 S.H.Choudhury1 A. Al-Rasheed1 , S.P. Majumder2

Department of Electrical and Electronics Engineering

Bangladesh University of Engineering and Technology Dhaka,Bangladesh

e-mail: (casillas1,samiulhayder1,asif1058781)@gmail.com spmajumder2@eee.buet.ac.bd

Abstract— In this paper, the effect of atmospheric turbulence on bit error probability in free-space multi-carrier optical CDMA (MC-OCDMA) scheme with Sequence Inverse Keyed (SIK) optical correlator receiver is analyzed. Here Intensity Modulation scheme is considered for transmission. The turbulence induced fading is described by the newly introduced gamma-gamma pdf[1] as a tractable mathematical model for atmospheric turbulence. Results are evaluated with Gold and Kasami code and it is shown that Gold sequence can be used for more efficient transmission than Kasami sequence in an atmospheric turbulence channel. Analysis also shows that, using two chips in each parallel path of MC-OCDMA transmitter rather than using single chip exhibits greater performance.

Keywords- MC-OCDMA; SIK; Corrilator Receiver; Intensity Modulation; Atmospheric Trbulence;Gamma-Gamma pdf; FSO; Gold; Kasami.

I. INTRODUCTION MulticarrierOptical Code Division Multiple Access (MC-OCDMA) is a multiplexing technique[1] where data bits are transmitted using multiple narrowband subcarriers with each subcarrier encoded with a phase offset of 0 or π based on a spreading code. In terms of asynchronous access, privacy, large bandwidth potential and security consideration, optical CDMA technique has received much popularity in fiber optic communication[2]. An MC-OCDMA is an upgraded system over Direct Sequence OCDMA where the later one is the direct spread of the signal by the pseudorandom codes. In order to replete the gap between the end user and fiber optic infrastructure, free space optical (FSO)[3] communication technology is introduced. FSO is a powerful and potential branch of optical communication of modern age[3]. In FSO, communication, optical transceivers communicate directly through the air to form point-to-point line-of-sight (LOS) links[3]. One major impediment of FSO communication is the atmospheric turbulence. It occurs due to the variations in the refractive index due to inhomogeneities in temperature and pressure fluctuations[4]. Atmospheric turbulence has been studied extensively and various theoretical models have been proposed to describe turbulence-induced image degradation and intensity fluctuations (i.e. channel

fading)[4]. The performance of an optical CDMA system in terrestrial fiber links are reported.[8] However, the path of OCDMA in a free space optical channel is yet to be reported. In this paper, an analytical formulation is presented to study the effect of atmospheric turbulence on bit error rate (BER) performance in MC-OCDMA scheme along with different code (i.e, Kasami & Gold sequence[7].

II. ATMOSPHERIC TURBULENCE CHANNEL MODEL To represent the FSO channel, it is very important to represent the scintillation[4]. Several probability density functions have been proposed for the intensity variation of the receiver of the optical link. Most prominent among the model is Raleigh model, log-normal model, gamma-gamma model etc. In gamma-gamma model the irradiance of the received optical wave is modeled as a product I=IxIy.. Where Ix arises from large scale turbulent eddies and Iy from small scale eddies. Specifically, gamma-gamma pdf is used to model both small and large scale fluctuations[6]. The influence of atmospheric turbulence channel described by gamma-gamma pdf [4],

(1)

Where, I is the signal intensity Ѓ(.) is tha gamma function, and Kα-β is the modified Bessel function of the second kind of order α-β. Here α and β are the effective number of small and large scale eddies of the scattering environment.

2010 12th International Conference on Computer Modelling and Simulation

978-0-7695-4016-0/10 $26.00 © 2010 IEEE

DOI 10.1109/UKSIM.2010.61

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2010 12th International Conference on Computer Modelling and Simulation

978-0-7695-4016-0/10 $26.00 © 2010 IEEE

DOI 10.1109/UKSIM.2010.108

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2010 12th International Conference on Computer Modelling and Simulation

978-0-7695-4016-0/10 $26.00 © 2010 IEEE

DOI 10.1109/UKSIM.2010.107

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These parameters can be directly related to atmospheric conditions according to [1],

1

)6/7(5/12

2

11)11.11(

49.0exp

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎟⎠

⎞⎜⎜⎝

⎛−

+=

x

x

σσα

1

)6/7(5/12

2

11)69.01(

51.0exp

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎟⎠

⎞⎜⎜⎝

⎛−

+=

x

x

σσβ

and the power affected by turbulence pdf is given by,

( ) ( )dIIfPIP ISS ∫= | (2)

The gamma-gamma model approaches for heavy turbulence the exponential distribution, whereas in less turbulence it is suitably approximated by a log-normal distribution[4].

III. SYSTEM MODEL The system model of the OCDMA is shown in figure 1. The narrowband subcarriers are generated using BPSK modulated signals, each at different frequencies which at baseband are at multiples of a harmonic frequency, 1/Tb. Consequently, the subcarriers are orthogonal to each other at baseband, and the component at each subcarrier may be filtered out by modulating the received signal with the frequency corresponding to the particular subcarrier of interest and integrating over a symbol duration. The orthogonality between subcarrier frequencies is maintained if the subcarrier frequencies are spaced apart by multiples of F/Tb, where F is an integer.

Fig 1: schematic block diagram for an optical MC-OCDMA transmitter

with Sequence Inversed Keyed (SIK)

The input data symbols, am[k], are assumed to be binary antipodal where k denotes the kth bit interval and m denotes

the mth user. In the analysis, it is assumed that am[k] takes on values of -1 and 1 with equal probability. The generation of an MC-CDMA signal can be described as follows. A single data symbol is replicated into N parallel copies. The ith branch (subcarrier) of the parallel stream is multiplied by a chip, cm[i] , from a PN code or some other orthogonal code of length N and then BPSK modulated to a subcarrier spaced apart from its neighboring subcarriers by F/Tb where F is an integer number. The transmitted signal consists of the sum of the outputs of these branches. This process yields a multicarrier signal with the subcarriers containing the PN-coded data symbol. It should be noted that, for the case of F = 1, the MC-OCDMA signal shares the same signal structure as OFDM. The analysis of OFDM has shown that the discrete-time version of the OFDM transmitter is simply a Discrete Fourier Transform (DFT). Thus, the transmitter model of MC-CDMA in Fig.1 may simply be replaced by an FFT operation for F = 1. In order to make the analysis simpler and more instructive, continuous-time receiver model is considered.

As illustrated in Fig. 1, the transmitted signal

corresponding to the kth data bit of the mth user is[3]

( ) [ ] ( )bTbb

cm

N

imm kTtpt

TFtfkaictS −⎟⎟

⎠

⎞⎜⎜⎝

⎛+=∑

−

=

ππ 22cos][1

0

(3) cm[0], cm[1], ... , cm[N-1] represents the spreading code of the mth user

Tbp = an unit amplitude pulse that is non-zero in the interval of [0, Tb].

Fig 2: Schematic block diagram for an optical MC-O(CDMA receiver with

Sequence Inversed Keyed (SIK)

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When there are M active users, the received signal is[3]

( ) [ ] ( )∑∑−

=

−

=

+⎟⎟⎠

⎞⎜⎜⎝

⎛+=

1

0

1

0

22cos][M

m bcm

N

imm tndtt

TFtfkaictS ππ

(4) Applying the receiver model of Fig. 2 to the received signal given in Eq.2 yields the following decision variable for the kth data symbol[3]

[ ] [ ]∑ ∑−

=

−

=

=1

0,0

1

01,0 )(

M

mmi

N

immR kadicIPv ρ

( )∫+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+×

b

b

Tk

kT bc tndtt

TFitf

)1(

22cos ππ

(5)

[ ] i

N

iiR dkaIPv ,0

1

0,000 )( ∑

−

=

= ρ

[ ] [ ] [ ] ( )tndicickaIPM

mmim

N

immR ∑∑

−

=

−

=

++1

11,,0

1

0

)( ρ

(6)

Here, the First term denotes the symbol of the intended

user and the second term is the Multi Access Interference (MAI). In case of MC-OCDMA, the MAI occurs with the other users code as well as inside the user data itself. If the codes are non orthogonal among users, then MAI degrades the performance. )(tn denotes the noise power

The variance of noise, )(tn is given by, shth NNn += (8) Nth is the receiver thermal noise which is given by,

Lrth RKTBN 4= (8) and Nsh is the Photodetector shot noise which is given by [5],

TqRKP

N rsh 4

2= (9)

where, k= Boltzmann constant. T= Receiver temperature (K) Br= Receiver bandwidth=1/T. RL= Load Resistance of the receiver PR= Received Power q= electron charge (1.6e-19) The signal to noise ratio of the correlator output can be obtained as,

0

2

NMAIUSNR

+= (10)

Hence Bit Error Rate of OCDMA transmission system is then given by[4]

⎟⎟⎠

⎞⎜⎜⎝

⎛=

221 SNRerfcBER (11)

Here Bit error rate is calculated using Gold and Kasami code.

IV. RESULTS AND DISCUSSIONS

Fig3: Bit Error Rate vs Received Power for different σx with no Multiple Access Interference (MAI)

Fig 3 shows the effect of atmospheric turbulence on bit error performance. Here the curves are for BER vs received power for different value of the variance (σx) of gamma-gamma pdf[1]. As the value of σx increases, the received

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power decreases. Here, the analysis is done only with Walsh code i.e. no multiple access interference. In the Fig 4 and Fig 5, non orthogonal codes[6] are incorporated. As the codes are non orthogonal, here MAI is present. Thus, Here BER vs Power is profiled with different valuo of σx. From these two curves, Power Penalty curve is drawn at the later part.

Fig: 4 BER vs Power for different σx using Gold sequence

Fig: 5 BER vs Power for different σx using Kasami sequence Fig 6 and 7 is the curve showing the Number of BER vs number of users using Gold and Kasami sequence respectively using different value of σx. Here, from the

curve, it is seen that, as the number of users increases,Gold sequence exhibits less Bit error rate than Kasami sequence. Here the comparison is done using 64 chip length.

Fig: 6 BER vs Number of users for different σx using Gold sequence

Fig: 7 BER vs Number of users for different σx using Kasami sequence

Fig 8 depicts the performance of MC-OCDMA. In each parallel path, one or two chip can be used to spread the bit slice at reduced bandwidth[8]. From the curve, it is seen that, using two chips is more power efficient than one chip. As one chip scheme causes more MAI than using two chips at each parallel path.

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Fig: 8 BER vs Received Power with Single and Double chip Scheme

Fig 9: Power Penalty Curve for Gold and Kasami Sequence

The Figure 9 is actually drawn from Figure 3, Figure 4 and Figure 5. This figure is the power penalty curve which determines how much power is needed for transmission in a turbulence channel for a particular Bit Error performance to

be achieved. Here, the BER is considered 10-4. This figure is profiled for different value of σx. It can be inferred from the analysis that for a desired Bit Error Rate signal can be transmitted at a lower power using Gold sequence than Kasami sequence in an Atmospheric Turbulence channel.

V. CONCLUSION Here, the performance of a free space optical CDMA

system influenced by atmospheric turbulence is evaluated. Gold sequence provides relatively efficient transmission than Kasami sequence in such kind of channel. Also, using two chips in each parallel path of multicarrier scheme exhibits less bit error rate than single chip scheme.

REFERENCES [1] S.Hara and R. Prasad, “Overview of Multicarrier cdma” IEEE

communications magazine December 1997 pp 126-133 [2] M.A. Santaro, “Asynchronous fiber optic local area network

using CDMA and optical correlation, “ Proc. IEEE, vol. 75 pp. 1336-1338, 1987

[3] V.W.S. chan “Free space optical communications”, IEEE/OSA J. Lightwave Technol., 124, (1998)

[4] M. A. Al-Habash, L.C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng.,40, 1554-1562 (2001)

[5] “Multi-Carrier CDMA in an Indoor Wireless Radio Channel”, by Nathan Yee and Jean-Paul Linnartz

[6] H.E. Nistazakis, G.S. Tombras, A.D. Tsigopoulos, E.A. Karagianni and M.E. Fafalios “Average Capacity of Wireless Optical Communication Systems over Gamma Gamma Atmospheric Turbulence Channels” IEEE Xplore. pp 1561-1564 August 2009.

[7] Tanveer Ahmed Bhuiyan,Samiul Hayder Choudhury, Asif Al - Rasheed, S.P. Majumder, “Performance Analysis of A Free-Space Optical Code Division Multiple Access Through Atmospheric Turbulence Channel,” Proceedings of ICCIT, World Academy of Science, Engineering and Technology, vol. 56, no. 55, pp. 283-286, ISSN 2070-3724, Aug. 2009.

[8] S. P. Majumder, Member, IEEE, Afreen Azhari, and F. M. Abbou,” Impact of Fiber Chromatic Dispersion onthe BER Performance of an Optical CDMA IM/DD Transmission System” IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 6, pp 1340-134 JUNE2005

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