OSA/ANIC/IPR/Sensors/SL/SOF/SPPCom/2011
ATuB5.pdf
Influence of the MAI Distribution over the BER Evaluation in a Multirate, Multiclass OOC-OCDMA System Thiago R. Raddo, Anderson L. Sanches, José Valdemir dos Reis, Jr., Ben-Hur V. Borges, Member, OSA Electrical Engineering Department, São Carlos School of Engineering, University of São Paulo, 13566-590 São Carlos, Brazil
[email protected];
[email protected];
[email protected];
[email protected]
Abstract: We propose a BER expression based on binomial distribution for a multirate OCDMA system. We compare it with a Poisson assumption for MAI and show the later underestimates the number of users for a given BER. OCIS codes: (060.2330) Fiber Optic Communications; (060.4510) Optical Communications
1. Introduction Optical Code Division Multiple Access (OCDMA) constitutes a potential candidate for the next generation of optical access networks. New multimedia applications such as high-data capacity, high-definition television (HDTV), e-learning, telemedicine, video-on-demand (VoD), etc., are experiencing a fast growth in the last few years. As a result, capability of supporting multimedia and differentiated-quality of service (QoS) transmission will be essential for future optical networks [1]. In most OCDMA systems, the effect of multiple-access interference (MAI) is considered to be the principal degrading factor of the system, since it is the main noise source [2]. Further, many probability distributions for the analyses of MAI have been used for multirate, multiclass-based OCDMA networks. In this paper, to the best of our knowledge, we show for the first time that bit error rate (BER) calculation in a multimedia scenario can be overestimated by many orders of magnitude depending on the assumed distribution for the MAI and the number of simultaneous users. Since the output interference of any OCDMA system is considered to be binomially distributed [3-5], we compare the BER of multi-weight, multi-length optical orthogonal codesbased system (MWML-OOCs) [3] using both binomial and Poisson assumption for the MAI. Approximating the multiclass MAI by a Poisson distribution is useful to simplify the performance analysis of some specific multimedia scenarios with acceptable accuracy. In addition, we show that for a multirate scenario with a low number of users both distributions, and consequently the BER, diverge rather than converge. Moreover, with the simulation results we estimate how many simultaneous users should be on the system so that Poisson distribution can be used to closely approximate binomial distribution. 2. Multirate System Description and BER Evaluation We consider a strict MWML-OOC system [3] capable of achieving multiple rates and differentiated QoS through both different code lengths L1≤L2≤…≤Lj≤…≤LJ and arbitrary code weights Wj respectively. The total number of users U in the J-class system is , where Uj is the number of users in each class j ϵ {1, 2,…,J}. Without loss of generality, we assume that the desired user is the first user in the desired class j' and Uj = Uj' - 1 when j = j'. Also, the chip duration of all classes is the same and is given by Tc = Tj / Lj, where Tj is the bit period. Further, we consider a chip synchronous scenario, which reflects the worse possible case for the system analysis [5]. Thus, assuming the MAI has a binomial distribution, considering both an equiprobable data, and MAI as the only degrading factor of the system, we have derived a new expression for the BER. The performance analysis of this expression is compared with the one based on Poisson distribution provided in [3, eq. 24]. 3. Simulation Results The validation of the proposed BER expression assuming a multiclass MAI binomially distributed is shown in Fig. 1, where we have assumed a MWML-OOC system [3] with three different users' classes. The code length, weight, and number of users for the three classes are, respectively, L1 = 500, W1 = 7, and U1 = 4 (diamonds), L2 = 1000, W2 = 5, and U2 = 20 (squares), and L3 = 1500, W3 = 3, and U3 = 20 (circles). As can be seen, our results agree quite well with those obtained in [3, please refer to Fig. 7] which was obtained using the Monte Carlo simulation method. This figure also shows that both results are better than those obtained with a Poisson distribution for the MAI [3].
OSA/ANIC/IPR/Sensors/SL/SOF/SPPCom/2011
ATuB5.pdf
Fig 1. BER as a function of simultaneous users for a three classes MWML-OOC system. The MAI distributions are Poisson (solid lines) and binomial (dotted lines).
Fig 2. BER for the lowest rate users’ class with L3 = 2000, W3=13, and U3 =4. The number of users in the second class is varied from 6 to 120. The MAI distributions are Poisson (solid line) and binomial (dotted line).
Next, we consider a three classes MWML-OOC system with L1 = 500, W1 = 7, and U1 = 4 for the highest rate class, L2 = 1500, W2 = 3, and U2 = 120 for the medium rate class, and L3 = 2000, W3 = 13, and U3 = 4 for the lowest rate class. Fig. 2 shows the BER performance comparison between the two distributions, but only for the lowest rate users’ class. One can observe from this figure that as the number of simultaneous users decreases, the BER curve with binomial distribution (dotted line) drops more rapidly than that obtained with Poisson distribution (solid line). The difference between both approaches becomes more dramatic particularly if an error-free scenario is desirable (BER
