We consider multi-input multi-output (MIMO) communications over multi-modefibers (MMFs). Current MMF standards, such as OM3 and OM4, use fibers withcore radii of 50\,$\mu$m, allowing hundreds of modes to propagate.Unfortunately, due to physical and computational complexity limitations, wecannot couple and detect hundreds of data streams. In order to circumventthis issue, two solutions were presented in the literature. The first is todesign new fibers with smaller radii so that they can support a desirednumber of modes. The second is to design multi-core fibers with a reasonablenumber of cores. However, both approaches are expensive as they necessitatethe replacement of installed fibers. In our work, we consider input-outputcoupling schemes that allow the user to couple and extract a reasonablenumber of signals from a fiber with many modes. This approach is particularlyattractive as it is scalable; i.e., the fibers do not have to be replacedevery time the number of transmitters or receivers is increased (which islikely to happen in the near future). In addition, fibers with large radiican support higher peak powers, relative to fibers with small radii, whilestill operating in the linear regime. However, the only concern is thatfibers with more modes suffer from increased mode-dependent losses (MDLs).Our work addresses this last concern.This thesis is divided into two parts. In the first part, we present achannel model that incorporates intermodal dispersion, chromatic dispersion,mode dependent losses, and mode coupling. We later extend this model toinclude the input and output couplers and provide an input-output couplingstrategy that leads to an increase in the overall capacity. This strategy canbe used whenever channel state information (CSI) is available at thetransmitter and the designer has full control over the couplers. We show thatthe capacity of an $N_t \timesN_t$ MIMO system over a fiber with $M\gg N_t$modes can approach the capacity of an $N$-mode fiber with no loss. Moreover,we present a statistical input-output coupling model in order to quantify theloss in capacity when CSI is not available at the transmitter or there is nocontrol over the input-output coupler. It turns out that the loss, relativeto $N_t$-mode fibers, is minimal (less than 0.5 dB) for a wide range ofsignal-to-noise ratios (SNRs) and a reasonable range of MDLs. This means thatthere is no real need to replace the already installed fibers and that our strategy isindeed a better approach to solving the above problem.In the second part, we explore reduced complexity maximum likelihood sequencedetection (MLSD) algorithms for single carrier MIMO systems. These algorithmscan be used for optical as well as wireless communications. We show that asphere decoding (SD)-like approach can be used to reduce the computationalcomplexity of the vector Viterbi algorithm (VVA), an extension to the Viterbialgorithm for MIMO systems. Our combined SD-VVA approach is attractivebecause it provides substantial computational savings while solving an exactMIMO MLSD problem. Our results show a $50\%$ reduction in complexmultiplications and real additions, relative to the full VVA, for a$2\times2$ MIMO system using $16$-QAM signal constellation and operating atan signal-to-noise ratio ($\SNR$) of $10$ dB. This figure is increased to$60\%$ when the $\SNR$ is increased to $15$ dB. We show that larger savingscan be achieved for larger MIMO systems and higher order signalconstellations. Finally, we show how our algorithm can be modified in orderto further reduce the complexity of VVA while still achieving close tooptimal performance.
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MIMO communications over multi-mode optical fibers
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