Performance Comparison of Coherent versus Incoherent Direct Sequence Optical Code Division Multiple Access System

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1 Performance Comparison of Coherent versus Incoherent Direct Sequence Optical Code Division Multiple Access System Amel Farhat* a,d, Mourad Menif b, Catherine Lepers c, Houria Rezig a, Philipe Gallion d a Ecole Nationale d Ingénieurs de Tunis, SYSCOM, BP. 37, Le Belvédère, 100, Tunisie. b Ecole Supérieure des Communications, CIRTACOM, Cité Technologique des Communications, 083 Tunisie c Laboratoire PhLAM, CNRS UMR 853, Université de Lille, Villeneuve d Ascq, France d Institut TELECOM, TELECOM ParisTech, Ecole Nationale Supérieure des Télécommunications, 46 Rue Barrault Paris, France ABSTRACT In this paper, we consider the case of a Direct-Detection Direct Sequence Optical Code Division Multiple Access (DS- OCDMA) system using Superstructured Fiber Bragg Grating (S-FBG) as encoder/decoder to implement unipolar codes such as Prime Sequence (PS) and Extended Quadratic Codes (EQC) codes. We use the Importance Sampling (IS) technique, which is a variant of the known Monte-Carlo () method, to evaluate the Bit Error Rate (). We compare performances of the coherent and incoherent DS-OCDMA system and we validate our simulation results by experimental measure. Our simulation results depict a floor due the beat noise of the incoherent source. We show that increasing bit rate leads to a deterioration of the behavior and requiring an increase of the optical bandwidth of the signal. Keywords: DS-OCDMA, unipolar codes, coherent source, Monte Carlo, Importance Sampling, beat noise. 1. INTRODUCTION The Optical Code Division Multiple Access (OCDMA) technique has recently received substantial interest for the future generation of optical access networks. This could be explained by the enormous bandwidth offered by the optical fiber, the possibility of sharing the optical resources (source, fiber, etc ) over many users and the exploit of the Fiber Bragg Grating (FBG) technology for the encoding and decoding of transmitted data. The OCDMA is a multiple access technique which consists on assigning signature codes and provides simultaneous and asynchronous access to several users [1]. Many configurations of OCDMA systems have been proposed and studied depending on the code dimension. Direct Sequence (DS) [] and Frequency Encoding (FE) [3] OCDMA solutions use one-dimensional code respectively in time and frequency domain while Fast-Frequency Hopping (FFH) OCDMA system considers two dimensional time and wavelength codes [4]. The OCDMA systems can use either coherent (Laser, Super-Continuum Laser and Mode Locked Laser, etc ) or incoherent (LED, ASE from EDFA and SOA, etc ) optical sources. In order to reduce the Multiple Access Interference (MAI), the codes must have small cross-correlation [1]. Many classes of binary signature codes are suitable for OCDMA. Bipolar codes, composed with -1 and 1, have a strong autocorrelation peak and zero crosscorrelation function. However, the Direct-Detection OCDMA system can only manipulate unipolar codes composed with 0 and 1 [5]. This is due to the fact that the optical light intensity is a positive quantity. For the Direct-Detection DS-OCDMA system, many optical codes could be used such as Optical Orthogonal Codes (OOC), Prime Sequence (PS) codes, Quadratic Codes (QC) and Extended Quadratic Codes (EQC). For these codes the low cross-correlation property is usually achieved through the use of very long code sequences [1]. In [6], the PS codes have been shown to support many simultaneous users with short code length. But, they suffer from high cross-correlation level. In addition, the PS codes are shown to be significantly interest than OOC. However, the EQC and QC codes are shown to be less sensible to the Multipath Beat Noise (MBN) and MAI noise [7]. *farhat@enst.fr; phone ; fax ;

2 Many test beds have been done to evaluate OCDMA system performances. In [7], Fsaifes et al. implement a coherent DS-OCDMA system using periodic PS codes with superstructured FBGs having Full-Width at Half Maximum (FWHM) bandwidth 1.6 nm. It is shown that it is difficult to assure high precision control of the optical path within the FBG encoder and decoder. Indeed, the coherence impairments induce strong MBN which decreases the system performances. It was demonstrated in [8] that the same system, using aperiodic EQC codes, is less sensible to MBN. Ayotte et al. compare, in [9,10], coherent versus incoherent source for Spectral Amplitude Coding (SAC-OCDMA) and FFH-OCDMA systems. They demonstrated experimentally that coherent system offers better performances than the incoherent case. But for such systems, high performances are assured by using a multi-laser source instead of sharing the same incoherent source which affects the system cost. In addition, it is important to mention that the same optical bandwidth for the encoders and decoders was used for the two different optical sources configurations leading to the same spectral efficiency of the system. Indeed, incoherent system is more economical than coherent one and it provides comparable performances for the SAC-OCDMA configuration as mentioned in [11]. But, the limitation of the incoherent system was caused by the beating of the different optical frequencies of the signal bandwidth. This phenomenon was studied in [1] where a new Beat Noise (BN) term is considered. In order to optimize the system parameters, it is suitable to use simulations. Many simulation techniques could be used to determine system performances in term of Bit Error Rate () such as the Gaussian Approximation (GA) and Monte- Carlo () technique. But by considering the noise s variance, essentially for the MAI variance, the GA overestimates the real performances. In fact, it considers that all the users are active to determine the average over all the crosscorrelation between different codes for different chips delay [4]. While technique, which is a statistical method used to model the real system, requires a large number of samples to estimate very low values of. In order to decrease the number of simulations involved in estimation, it is possible to use the Importance Sampling (IS) technique. It consists on increasing the number of errors in an artificial way by biasing the input distribution of the noise [13]. The objective of the IS technique is to consider the events from distribution tails more frequently. This modification in the distribution is later corrected by weighting the samples [14]. In Section of the paper, we present the DS-OCDMA system and validate the Importance Sampling technique with Monte-Carlo one s. In section 3, we compare the performance of coherent and incoherent DS-OCDMA system and we validate our simulation results by experimental measure. Thermal Noise (TN), Shot Noise (SN), Dark current Noise (DN) and BN are considered in this analysis in addition to the MAI. Finally, conclusions and perspectives are given in section 4..1 DS-OCDMA system description. SYSTEM AND SIMULATION MODELLING Figure 1 shows the block diagram of the DS-OCDMA system. The transmitter is composed of an optical source, which can be a Laser (for the coherent DS-OCDMA system) or LED (for incoherent DS-OCDMA system), sending a 50 ps, which representing the chip time (Tc), pulse train at the data repetition rate. The generated pulses are modulated afterward by the user s data and encoded by superstructured FBGs separated by sections of optical fiber with variable length, through a three-port circulator. L 1- Bit Data R 1 R R 3 Decoder time L -3 Short light pulse L 1- Encoder L code Unipolar signal Network Photo detector Decision circuit Fig. 1. Architecture of a DS-OCDMA system The FBGs will temporally slice the incoming optical signal into a pulse train where the positions of the pulses are determined by the ON OFF-keying spreading codeword assigned to each transmitter. To get the same reflected power

3 from the different FBGs, each one will presents a different reflection rate, to compensate the incident wave depletion during its propagation through the FBGs [7]. The reflected pulse trains coming from different users are combined and transmitted to the network. Many optical codes could be implemented using such arrangement. Among them, the unipolar codes characterized by 3 parameters (L, w, N) with L the code length, w its weight i.e. number of chips with 1 in the code and N is the multiplexing capacity. In our simulations, we have consider a Direct-Detection DS-OCDMA system using PS and EQC codes with weight p = 3, where p is a prime number. In this case the length of PS and EQC codes are respectively p and p(p-1). At the receiver, the incoming encoded data is decoded after removing the time spreading and gathering all chip energy into a single pulse. The optical pulse is converted into electrical signal by a photodetector. The electrical signal is then integrated over one chip Tc. The decision circuit compares the received power to a threshold in order to extract the transmitted data. More details on the experimental setup are reported in [7].. Modeling of simulation The performances of the DS-OCDMA system could be estimated by several techniques. To simplify the analysis, most of the previous works use the Gaussian Approximation (GA) to calculate the probability of error. However, this analysis is only valid for the case with a large number of users [1]. Assuming the interfering users are statistically independent, the MAI variance is determined by [4]: ( ) = k 1 MAI (1) with k is the number of interfering users and is the average over all cross-correlation between different pairs codes. Therefore, the Signal to Interference Ratio can be estimated by: p SIR = MAI with p is the weight of the code. Thus, the probability of error, without considering the other sources of noises, is given by: P e = Q( SIR). (3) Since the number of interferers, used in our simulations, is small (N=3) and we did not know which codes will be active at any given time, the GA will overestimates the real system performances. In order to avoid the GA s drawback, we can use Monte-Carlo () technique. It is a statistical technique allowing the modeling of a real digital communication system in order to measure its performances [14]. After encoding/decoding process, the binary data pass through a block decision and then the emitted and received sequences are compared. The simulation counts the number of errors. It achieves realistic estimates of performances of optical communication systems. However, for high performances systems, this technique requires a large number of simulation trials to estimate the in a reasonable interval of confidence [15]. Therefore, huge simulation run time is required to evaluate low values. The error probability for communication system can be defined as: 1 P (4) e = P D ( 1/0)( r) + P( 0/1)( r) D 1 0 with P (1/0), P (0/1) are the conditional probability distribution under statistical binary hypotheses H i (H 0 space is transmitted and H 1 mark is transmitted), r i the random sample and D i is the region of decision for H i. In simulation, the error probability is estimated as the ratio of the number of errors seen to the number of samples considered [15]. ()

4 P = 1 N N i= 1 ( r ) with I(r i )=1 if i th bit is error and I(r i )=0 if the i th bit is correct, and N represents the number of samples. The variance of the estimator is defined by: I i ( 1 ) P P e e = (6) N As technique is impractical for simulating optical detection system [15], it is possible to use Importance Sampling (IS) method. The IS is a modified technique used in simulation to determine low probability events without needing a huge number of samples. The main idea of the method is to consider the events from important regions more frequently [14]. The IS technique consist on modifying the probability density function (PDF) f of the input random process. The new distribution f * is a Gaussian PDF with a zero mean and a new variance defined in [14]. The IS estimator is given by rewriting the error probability in (4) as [15]: IS 1 P (7) * * = P( / 0) w( r H 0 ) + P( 0 /1) w( r H1), D 1 D 1 0 where P * (1/0), P * (0/1) are respectively the modified conditional probability distribution in place of P (1/0) and P (0/1 ) and w(r/h i ) is the weight associated with the random sample r i that is generated with equal probability from the modified densities P * under H i, i=0, 1. Therefore, the IS estimator has a variance given by: where the quantity W is defined in [15]..3 Importance Sampling Validation W Pe IS =, (8) N IS To simulate IS technique, we have to choose the source noise. And then, we have to change its statistic by increasing its variance. In the OCDMA system, the MAI and the BN are considered as the main degradation. As the number of interferers is small (w=3), the variance of MAI can not be consider. For this reason, we have simulated interferers data. In our simulations, we choose the BN to apply IS technique. To calculate the modified BN variance, we use the parameter α which has a value in the interval [0 1[. with BN is the original BN variance. BN =, 1 α In order to optimize curves, the parameter α has to be carefully chosen. Fig. shows variation of versus α for a coherent DS-OCDMA system using PS codes. The FBGs used to implement the encoders/decoders are superstructured with different reflectivity rate and having a FWHM bandwidth Δλ=1.6 nm representing the optical bandwidth B o used in our simulation. We assume that all noise sources generated in the receiver such as TN, DN, SN and BN are Gaussian and represented with its variances. We have used a random of 1000 bit sequence. We note that for α < 0.85, we have an improvement in the performances. But for α>0.85, we have a degradation in the performances. We conclude that better performances are attained for α opt equal to To show the advantage of IS over technique, it is possible to evaluate their performances for the same number of samples. Fig. 3 illustrates the performances versus the received power for the coherent DS-OCDMA system. We use a random 1000 bit sequence. Simulations result show that with simulations, we get a of 10-3 however IS method reaches a lower than The gain offered by the use of the IS technique is significantly important even with small length of the bit sequence. This result confirms that technique is enabling to get high performance with (5) (9)

5 small number of samples. In the rest of our work, we use IS technique to compare performances of coherent and incoherent DS-OCDMA system α Fig.. Optimization of parameter alpha for Importance Sampling technique 10 - IS Fig. 3. Validation Monte Carlo and Importance Sampling techniques 3. COMPARISON BETWEEN COHERENT AND INCOHERENT DS-OCDMA SYSTEM In order to compare performances of coherent versus incoherent DS-OCDMA system, we suppose that all noises (TN, SN, DN and BN) are present at the receiver. For the coherent DS-OCDMA system, the signal-spontaneous beat term (ssp) and the spontaneous-spontaneous beat term (sp-sp) are considered. Their variances are respectively given by: Be s sp = GI si sp, (10) B 1 = I B o ( Bo Be ), e sp sp sp (11) Bo

6 where G is the optical amplifier gain, I s and I sp are the photo-currents generated respectively by the signal and the spontaneous emission at the output of the optical amplifier, B e refers to the electrical filter bandwidth. With the incoherent source, a third noise term, called signal-signal beat noise (s-s), must be added to represent the noise generated by beating of the signal ASE at different frequencies of the optical bandwidth [1]. The variance of this noise is defined by: s s 1 = Be ( ) ( Bo Be ) GI. (1) sp Fig. 4 gives the performances for both coherent and incoherent DS-OCDMA system using the PS codes for bit rate of.5gbps, optical bandwidth of 1.6 nm and 0 dbm amplifier gain. We notice that for low level power, the performances are the same for both coherent and incoherent system. In fact in this case, the thermal noise is the major contributor [1]. But for high level power, coherent system outperforms the incoherent one. Indeed, the performances of the incoherent DS-OCDMA system are limited by the beat noise caused by the beat signal-signal noise for the incoherent optical sources. B o 10 - Incoh. source coh. source Fig. 4. Comparison between coherent versus incoherent DS-OCDMA system Coh. source(simulation) Coh. source(measure) Incoh. source(simulation) Fig. 5. Comparison between coherent versus incoherent DS-OCDMA system

7 Fig. 5 presents performances of both coherent and incoherent DS-OCDMA system using the EQC codes for bit rate of.5 Gbps, optical bandwidth of 1.6 nm and 0 dbm amplifier gain. For the coherent case, we compare the result of simulations with the experimental result obtained in [7]. This comparison depicts some discrepancy between simulation and experimental results (~4 db for.5 Gbps at ). This could be explained by the fact that we did not consider the MBN related to the design of the encoder/decoder together with the coherence of the system. Simulations curve with o mark show that this phenomenon is not observed in the incoherent system. In addition, For the high level power, the signal-signal beat noise is dominant and B o <<B e, so the Signal to Noise Ratio (SNR) expression will be [1]: B SNR 0 (13) B e is fixed to 0.7 times the bit rate. Equation (13) confirms that the performances of the incoherent optical communication systems are limited by the ratio B o /B e. To improve this ratio, we have to increase the useful optical bandwidth. We can also decrease the bit rate. B e Gbps.5Gbps Fig. 6. Performances of incoherent DS-OCDMA system for Bo=0.4nm 10 - M=0 M=40 M= Fig. 7. performances for incoherent DS-OCDMA for different values of M. Bit rate =1.5Gbps

8 We present in Fig. 6 performances for incoherent DS-OCDMA system with EQC codes for the optical bandwidth B o =0.4 nm and at the bit rates 1.5 Gbps and.5 Gbps. We show that increasing the bit rate so the electrical bandwidth and maintaining the optical bandwidth leads to decreasing the performances of the system. In Fig. 7, we fixed the bit rate at 1.5 Gbps and we varied the parameter M (M=0, 40, 80) by varied the optical bandwidth and simulated the performances. As we can see, the performances of the incoherent system are improved with large values of M. In fact, if we increase the M value the SNR will be much better (Eq.13) and as a result the error bit rates drop. So the value of M gives the floor. 4. CONCLUSION AND RECOMMANDATIONS To reach good performances precise laser positioning must be assured. And as it is difficult to control the laser shift, we suggest using the incoherent source due to its low complexity and cost. In our work, we have confirmed that the choice of the optical source can have important impact on the beat noise. A floor was shown in the incoherent DS-OCDMA system case. The effect of beat noise can be significantly reduced by the use of FEC. To avoid the drawbacks of laser source wavelength fluctuation on the spectral response of the superstructured FBG encoder/decoder, we suggest the use of a super-gaussian FBG. Indeed, they offer a better reflection spectrum and a good rejection of the side-lobes which improve system performances. REFERENCES [1] [] [3] [4] [5] [6] [7] [8] [9] [10] [11] [1] [13] [14] [15] Chen J. and Yang G., "CDMA Fiber-Optic Systems with Optical Hard Limiters," J. Light Techno. 19, (001). Prucnal P.R., Santoro M.A. and Fan T.R, "Spread Spectrum Fiber-Optic Local Area Network Using Optical Processing," J. Light. Techno. 4(5), (1986). Zaccarin D. and Kavehrad M., "An Optical CDMA System Based on Spectral Encoding of LED,"IEEE Photonics Tech. Letters, 4(4), (1993). Fathallah H., Rusch L. A., "Robust Optical FFH-CDMA Communications: Coding in Place of Frequency and Temperature Controls," J. Light. Techno. 17, (1999). Kwong W. C., Perrier P.A. and Prucnal P.R., "Performance Comparison of Asynchronous and Synchronous Code Division Multiple Access Techniques for Fiber Optic Local Area Networks," IEEE Trans. Com. 39(11), (1991). Zhang, J.-G., Picchi, G., "Tunable prime-code encoder/decoder for all-optical CDMA applications," Elec. Lett 9, (1993). Fsaifes I., Lepers C., Lourdiane M., Gallion P., V. Beugin et P. Guignard, "Source coherence impairments in a direct detection direct sequence optical code division multiple access system," App. Opt. 46, (007). Fsaifes I., Lepers C., R. Gabet, M. Douay, Gallion P., "Implementation of aperiodic codes using superstructured fiber Bragg gratings in coherent DS-OCDMA system," OSA, (007). Ayotte S., Rusch L. A., "A Comparison of Optical Sources for Spectral Amplitude Coding OCDMA," LEOS, (006). Ayotte S., Rusch L. A., "Experimental Comparison of Coherent Versus Incoherent Sources in a Four-User λ-t CDMA System at 1.5 Gb/s,", IEEE Photonics Technology Letters 17, (11), (005). Smith E.D.J, Blaikie R.J and Taylor D.P., "Performance Enhancement of Spectral Amplitude Coding Optical CDMA Using Pulse-Position Modulation," IEEE Trans. Com. 46(9), (1998). Mathlouthi W., Menif M., and Rusch L. A., "Beat noise effects on spectrum-sliced WDM," Proc. SPIE 560, (003). Shanmugam K.S. and Balaban P., "Modified Monte Carlo simulation technique for the evaluation of error rate in digital communication," IEEE Trans. 8, (1980). Lu D. and Yao K., "Improved Importance sampling technique for efficient simulation of digital communication systems," IEEE Selected Areas in com. 6, (1988). Mandayam N. B. and Aazhang B., "Importance Sampling for analysis of direct detection optical communications systems," IEEE Trans. 43(/3/4), (1995).