Multiple-Input Multiple-Output (MIMO) for multimode optical fiber communication channels
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This thesis evaluates the benefits of Multiple Input Multiple Output (MIMO) techniques on the capacity of Multimode Fiber (MMF) links. Optical MMF MIMO systems take advantage of the spatial diversity present in the multiple propagating paths in multimode fibers. By using multiple lasers at the input facet of the fiber and multiple photodetectors at the output, we show that the capacity of the link is improved from the single device link, hence demonstrating the usefulness of MIMO in such optical systems. An initial simulation of butt-coupling a Vertical Cavity Surface Emitting Laser (VCSEL) to multimode fiber reveals that the placement position of the laser axis with respect to the fiber axis is critical in exciting a large number of modes. More specifically, we show that there exists a tradeoff between total power coupled into the fiber and the number of modes launched. We then consider a mathematical description of the fiber channel and use it to simulate the capacity of a 1x1, 2x2, and 3x3 MIMO links over a statistical ensemble of channel realizations. This simulation reveals that a 2x2 system is capable of approximately a 50% increase in capacity over the 1x1 case while the 3x3 system is capable of approximately an 80% increase. Moreover, we show that the choice of the placement positions on the facets of the fiber affects the channel capacity, thereby implying that an optimal device position exists. We find the optimal device geometry by an exhaustive search and compare the capacities for the optimal geometry and that of a suboptimal one. A capacity tolerance study is then developed that considers perturbations about the optimal device locations and shows that the capacity of a rotated laser plane is over 90% of the capacity of the original device locations. A second perturbation study considers lateral offsets and shows that systems with a higher number of devices show good tolerance with poorer lateral tolerances for systems with less devices. When small lasers and a large grid of possible device locations are used, an exhaustive search for the optimal device location becomes computationally infeasible. We show that the problem of searching for the optimal detector locations while holding the laser positions fixed is submodular. This property allows a greedy algorithm to select the device positions at a small fraction of the computational complexity, however, only guaranteeing that the capacity of the resulting configuration is greater than a (1 - e^-1) fraction of the optimal configuration. We use this technique to compare the exhaustive search and the greedy search for coarse grids, and then exclusively use the greedy algorithm to select a device configuration for a fine grid whereby an exhaustive search is computationally infeasible.