## Abstract

Several fiber-fault monitoring schemes based on traditional OTDR technique have been proposed for monitoring fiber links in passive optical networks (PONs). However, in a tree-topology PON, it is difficult for network managers to distinguish which fiber link the fault occurs in. Thus, some schemes based on an optical coding technique have been proposed to overcome the optical time-domain reflectometry disadvantages in monitoring point-to-multipoint networks. In this paper, we develop a mathematical model for an optical 2D coding-monitoring system in PONs which includes three modules: detection pulse generator, optical encoding and transmission, and optical decoding and fault identification. We also analyze the correlation distance expression and interference probability with partial overlap between any two 2D codes. In addition, we derive close-form expressions for ${P}_{D}$ (detection probability) and ${P}_{\mathrm{FA}}$ (false-alarm probability) by analyzing the target signal, interference, and all possible noises, which are used to calculate optimal decision probability. The system performance in terms of signal-to-noise ratio, signal-to-interference ratio (SIR), and the optimal decision probability are investigated with different system parameters such as client separation distance, network size, transmitted pulse width, and transmitted pulse power. The extensive simulation results show that the optimal transmitted pulse width is ${T}_{C}\approx 1\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{ns}$ and the SIR is to a lower bound of $\sim 21\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{dB}$. It is concluded that suitable system variables can be chosen optimally to facilitate the optimal decision.

© 2016 Optical Society of America

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