# Nonlinear Effect and MAI Impact on SAC-OCDMA System Based on 2D Multi-Diagonal Code and Laser Array
## 1 Introduction  
Based on the nature of the optical source (i.e., coherent versus incoherent), the detection configuration scheme (i.e., coherent versus incoherent) and coding techniques (i.e., time/wavelength or amplitude/phase), optical code division multiplexing access (OCDMA) systems are either coherent or incoherent [1]. On the one hand, CDMA coherent systems use bipolar codes {-1,1} such as Maximum Length (ML) sequences and Walsh codes which are employed in wireless CDMA systems. On the other hand, CDMA incoherent systems employ unipolar codes {0,1} such as optical orthogonal codes (OOC) and prime codes [2]. Additionally, OCDMA systems are divided into three families; direct sequence OCDMA (DS-OCDMA) [3], time hopping OCDMA (TH-OCDMA) [4] and frequency hopping OCDMA (FH-OCDMA) [5]. OCDMA systems are also classified into two categories: synchronous and asynchronous [6]. Synchronous systems provide a high user capacity thatmakes them more complex, whereas asynchronous systems are less complex [7]. Moreover, OCDMA synchronous system provides a secure data transmission [8]. In literature, several works dealing with synchronous OCDMA systems are investigated based on one dimensional (1D) code and satisfying the zero cross-correlation (ZCC) feature. The ZCC feature is promising by improving system cardinality, while limiting interference [9; 10]. However, a specific coding family based on two-dimensional (2D) code namely multi-diagonal code (2D-MD) for spectral amplitude coding OCDMA (SAC- OCDMA), offers additional improvement to the system cardinality without the constraint of increasing the length of the 1D code [11]. Whereas, the previous 2D-MD proposed systems, using incoherent source and operating at low bit rates equal to 622 Mb/s, 1 Gb/s and 2.5 Gb/s, are studied in [12; 13; 14], respectively. Unfortunately, these bit rates do not satisfy the required user needs for different emergent applications and for the increasing demand in access network. In [14], authors developed the SNR expression of SAC-OCDMA system based on 2D-MD code while using LED source. However, in this work, we investigate a numerical analysis and a feasibility demonstration via simulation for SAC-OCDMA system utilizing the unique combination of a 2D-MD code and coherent light source. Laser sources are characterized by a narrowband spectral width and produce less chromatic dispersion compared to LED sources. Moreover, laser sources allow various types of modulation schemes, such as Frequency Shift Keying (FSK), Phase Shift Keying (PSK) and Quadrature Phase Shift Keying (QPSK) for high distance and data rate. Additionally, LED source is known as a cost-effective device. For instance, [PERSON] and al. [15] proposed a simulation model for SAC-OCDMA system based on two-dimensional Balanced Incomplete Block Design (2D-BIBD) codes for six users operating at 1 Gb/s and LED source. Additionally, authors in [16] demonstrated the feasibility of two-dimensional permutation vector codes (2D-PV) based on LED source and providing a BER less than \(10^{-9}\) for eight users operating at 2 Gb/s. However, due to the non-coherency of its broadband source, the Phase-Induced Intensity Noise (PINN) is a dominant factor which limits the system performance and the maximum achievable bit rate [17]. Furthermore, laser can allow other optimizations such as dispersion tolerance for high-speed transmission links and can be employed for high data rates up to 10 Gb/s [18]. The choice of the LED against laser source depends on the application, target performance and reliability requirement. For instance, LED is used mainly in fiber to the home (FTTH) and Local Area Network (LAN) [14], whereas laser source is employed in long-haul applications such as Metropolitan Area Network (MAN) [18]. In the state-of-the-art, many authors consider coherent source for SAC-OCDMA systems for various applications such as Passive Optical Network (PON) [18; 19; 20; 21], Free Space Optical (FSO) [22] and wireless optical networks [23].