# Nonlinear Effect and MAI Impact on SAC-OCDMA System Based on 2D Multi-Diagonal Code and Laser Array
## 1 Introduction
This paper aims to employ coherent source in a PON context to improve the SAC-OCDMA system performance in terms of allowed user bit rate and maximum system reach. A novel architecture based on 2D-MD SAC-OCDMA codes for LR-PON is proposed with a coherent optical source, an external Mach-Zehnder modulator, spectral/temporal coding and spectral direct detection (SDD). In addition, we investigate the system performance in terms of the maximum achievable bit rate, Q-factor and eye diagram analysis using a computer simulator tool. Firstly, we study the feasibility of a SAC-OCDMA system based on 2D-MD in LR-PON. Secondly, we determine the maximum reachability of the system in terms of fiber length. Finally, we investigate the impact of linear effects (i.e., fiber loss, group velocity dispersion and differential group delay) and non-linear effects (i.e., Kerr effect, self-phase modulation and stimulated Raman scattering) of the optical channel on the system performance when increasing the bit rate. Recall that the bit rate is correlated to the nonlinear effects in optical communication systems. Therefore, when the bit rate increases, the nonlinear effects caused by the optical channel will increase as well leading to a degradation of the system performance [24]. On the one hand, in this paper we focus on determining the maximum bit rate that results in a Q-factor higher than the limit corresponding to a bit error rate (BER) of \(10^{-9}\), when nonlinear effects due to optical channel are considered. On the other hand, a simulation setup is proposedto study the impact of Multiple Access Interference (MAI) and nonlinear effects while increasing the number of network subscribers. For a single user, we demonstrate that the proposed system can reach up to 55 Gb/s and 40 Gb/s when first, and second (as well as third) order dispersion are considered as frequency parameters, respectively. In addition, the simulation setup shows four connected users operating at an aggregate bit rate of 20 Gb/s over 50 km of single-mode fiber (SMF) link while considering linear and nonlinear effects. Furthermore, the nonlinear effects are considered by enabling the Kerr effect (i.e., \(\gamma\)) in the simulator, the self-phase modulation (SPM) and the stimulated Raman scattering (SRS) at a bit rate of 5 Gb/s per user. To the best of our knowledge, this is the first time to demonstrate the feasibility of a 2D-MD SAC-OCDMA system in LR-PON context by considering optical coherent source noise, group velocity dispersion (GVD), differential group delay (DGD), SPM, SRS effects and photo detector noise. The received electrical eye diagrams reveal an aggregate bit rate of 20 Gb/s dispatched equally among four users over 50 km of SMF length that had never been reached before compared to similar systems in PON configuration. This paper is organized as follows. Section 2 presents the system description for LR-PON. Section 3 deals with the SAC-OCDMA encoder and decoder model in which 2D-MD codes are exhibited. Section 4 discusses the system performance analysis in terms of SNR, BER and Q-Factor. Simulation results and discussion are investigated, in Section 5, as function of bit rate, optical channel nonlinear coefficient and fiber length. Finally, some conclusions are drawn in Section 6.