Regular ArticlesPerformance analysis of mode division multiplexing system in presence of nonlinear phase noise
Introduction
Optical fiber communication (OFC) is the mainstay of transporting the demanded information over the world [1]. The maximum communicable capacity over single-mode fiber (SMF) has elevated several orders of magnitudes when various multiplexing technologies have been implemented, namely optical time-division multiplexing, wavelength division multiplexing (WDM), orthogonal frequency division multiplexing (OFDM) and others [2], [3]. The transmission capacity in OFC systems is noticeably expanded, and it is expected to increase since the anticipated demand supported by the creation of additional data transportations and high definition video facilities [2], [4]. The unlimited increase in the capacity demand in long haul OFC leads to a point of almost reaching the nonlinear capacity limit of SMF. To increase the capacity of SMF, spatial division multiplexing (SDM) systems have been introduced to utilize the unused area of the fiber. SDM system, which uses several spatial paths in multimode and/or multi-core fibers, has been introduced as a favorable solution to overcome the capacity problem in SMF transmission systems [5], [6], [7]. Because traditional multimode fibers are not suitable for long-distance MDM transmission, the FMF is developed to support a small number of spatial modes at relatively small differential mode delay (DMD) [8]. MDM systems based-FMF have attracted wide attention because of its ability to transmit an ultrahigh information rate [9], [10], [11]. Using fibers supporting multi-spatial modes, MDM is expected to be the most powerful technique to increase capacity per fiber, where the capacity scales with the number of modes in the absence of mode-dependent loss (MDL), mode-dependent gain (MDG) or nonlinear effects between modes [12], [13], [14], [15]. To improve the fibers that support multiple spatial modes, optical amplifiers that can be operated on multimode, spatial mode multiplexers (SMUXs) and spatial mode demultiplexers (SDEMUXs) have been developed, too [15].
In fact, transmission over FMFs can produce new impairments that addressed to reach their full capacity [16], [17], including; linear mode coupling, DMD, and inter-modal nonlinear coupling [18]. In addition, the fiber nonlinearity effects such as SPM, XPM and FWM phenomena can induce nonlinear distortion which can reduce the performance of optical fiber transmission systems that use phase-modulated signals, such as mQAM [19], [20]. Amplified spontaneous emission (ASE) that originated from inline amplifiers is a major source of random noise. The nonlinear distortion and ASE can interact inside the optical amplifier to produce random NLPN that reduces the signal quality and limits the transmission distance [21], [22], [23], [24].
Several researchers have focused on the detrimental impact of MDL [25] and introduced a digital signal processing solution to enhance system performance and improve the channel capacity [26]. Other researchers have studied the influence of linear mode coupling on the nonlinear impairments [18; 27]. They showed that the power transfer between the mode channels may lead to increase nonlinear distortions [27] and an intermediate coupling is required to minimize nonlinear noise in coupled FMF [18]. Some works are focused on the derivation of the nonlinear propagation equations for SDM systems [17], [28]. Nonlinear propagation equations satisfied by the bit stream transmitted through each optical mode or core in the presence of fiber dispersion, birefringence, and nonlinearity have been derived [28]. While a generalized multimode nonlinear Schrödinger equation (NLSE) describing the propagation of ultrashort pulses in multimode optical fibers or waveguides based on a full vectorial mode expansion have been presented [17]. Other researches work on enhancing the design of FMF itself to obtain the required results such as designing a low mode-crosstalk FMF [29] and tune the DMD by controlling the graded-index fiber core [30].
For our knowledge, most previous works have focused on characterizing and studying FMF parameters and their influence on the performance of MDM systems for short distances without considering the interaction of ASE noise with SPM, XPM, and FWM phenomena. In this research work, we derive an analytical model, which estimates nonlinear phase noises induced by nonlinear fiber impairments and their interactions with amplifiers noise in multi-span mQAM MDM transmission systems. This analytical model enables the expectation of NLPN variation induced by SPM, XPM, and FWM in a quantitative manner versus mode power and transmission distance. The validity of our developed analytical model is assessed by comparing the analytical results with numerical results. It found that both results agree well with each other. The results are obtained for single-, two-, and six-mode transmission to demonstrate the impact of SPM, XPM, and FWM on the NLPN in the long haul 4QAM MDM system. The results reveal that the XPM highly affects the system performance, specifically, when degenerated modes are synchronously transmitted. Moreover, the NLPN induced by FWM insignificantly influences on the MDM system.
The rest of this paper is organized as follows: in Section 2, an analytical model that describes the nonlinear propagation of optical signals in FMF is developed and the NLPN induced by Kerr nonlinearities is derived. The general setup of the 4QAM MDM system and the design of FMF are described in Section 3. The analytical and numerical results are demonstrated and discussed in Section 4. Finally, conclusions are given in Section 5.
Section snippets
Analytical modeling of MDM system
In this section, a simplified analytical model is developed for estimating the NLPN in the long haul MDM system that produced by Kerr nonlinearities and their interaction with amplifiers noise. Nonlinear effects can be significant in long haul MDM systems, especially, when the number of modes is increased. Generalized coupled multimode nonlinear Schrödinger equations can describe the transmission of the mode superposition in silica glass fiber in the time domain as [27], [28], [31]:
Setup of mQAM-MDM transmission system
The general structure of the long haul MDM transmission system is shown in Fig. 1. It mainly consists of N-independent optical transmitters, SMUX, multi-span FMF link, SDEMUX, N-independent coherent receivers with multiple-input multiple-output (MIMO) digital signal processing (DSP). Each transmitter comprises a laser diode and an mQAM modulator. The generated data by pseudo-random binary sequence is mapped as in-phase (I) and quadrature-phase (Q) components. Then, I- and Q- components are
Results and discussion
In this section, the impact of fiber nonlinearity on the 4QAM MDM system is studied. The influence of mode power on the NLPN is demonstrated. Furthermore, an error vector magnitude (EVM) as a function of launched power with and without dispersion compensation is numerically examined. The effect of transmission distance on EVM is also predicted numerically. To evaluate NLPN by our analytical model, a multi-span MDM transmission system that supports six spatial modes is considered. Each spatial
Conclusions
In this work, analytical calculations for estimating NLPN in mQAM MDM systems based on SI-FMF have been derived. NLPNs due to SPM, XPM, and FWM and their interactions with ASE noise in the 4QAM MDM system have been examined. The effect of mode power on the total NLPN and EVM has been estimated for single-, two-, and six-mode transmissions. The results reveal that LP21a and LP21b spatial modes are superior among other modes when they travel alone or together with other modes due to their large
CRediT authorship contribution statement
Esraa K. Hamed: Data curation, Visualization, Investigation, Writing - original draft, Software. Mohammed A. Munshid: Supervision, Resources. Jassim K. Hmood: Conceptualization, Methodology, Writing - review & editing, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The Authors thank Laser and Optoelectronics Engineering Department, University of Technology, Iraq.
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