Precoder for Multimode Optical Fiber Under a Low Modal Coupling Assumption

High speed and bandwidth applications have become more popular and available within recent years, shifting network traffic from voice-based to data-based traffic. Fiber optic communications have made increased network capacity substantially and made such growth possible. However, it is expected within the next 5 years that the capacity of classic single-mode optical fiber systems will be reached. Several groups have attempted to enhance single-mode fiber capacity via increased modulation constellation points or adopting coherent detection, but such techniques are only temporary solutions to the capacity crunch problem. Conversely, many groups are turning toward revolutionizing lightwave systems by adapting multimode fibers for long-haul applications, where multiple modes carry several bit streams down the fiber and leave the potential to increase capacity substantially.
Despite the opportunity for large capacity gains, multimode fiber performance is inherently hindered by modal dispersion and modal coupling. The several modes in the fiber travel at different speeds and, therefore, do not reach the receiver at the same time, which causes intersymbol interference and the system to be described as frequency selective in nature. Additionally, modal coupling causes power transfer between modes and worsens performance to unacceptable levels. Several groups have attempted to utilize multimode fiber potential via post-processing methods or transmission of select modes of the fiber with moderate success. However, little work has been done in precoding, which would eliminate the need for expensive coherent reception and maximize channel performance. Precoding requires the adoption of a Mach-Zehnder modulation, an inexpensive option to improve multimode fiber performance.
In this thesis, the concept of precoding was explored for a three mode low coupling system through an iterative training scheme that sends coefficients back to the transmitter. By sending specific training sequences through the transmission channel, the magnitude and phase information of the system can be exploited and subsequently used to develop a precoder that is nearly identical to the inverse of the transmission matrix. Particularly when additive white Gaussian noise is present and at low SNRs, we propose that several realizations of an estimate of the inverted channel matrix are generated and subsequently averaged in order to create a generalized precoder.
We demonstrate that the precoder produced is an accurate reproduction of the inverted channel matrix, which is the ideal precoder. The maximum mean squared error found between coefficients was relatively low, with most precoder coefficient errors hovering in the order of tenths of error. Additionally, we demonstrate that precoding in the low coupling regime improves performance greatly, particularly with regards to the secondary modes of the system, and is tolerant to modal crosstalk as the number of iterations increases. However, as the amount of modal coupling increases and the channel becomes frequency selective, the precoder becomes less effective.
We conclude that the precoder developed thrives when operated on multimode fibers with low coupling, which describes a system that is frequency flat, and reproduces an accurate estimate of the ideal precoder. Concepts for a precoder for the high coupling scenario are discussed and left as future work.