--- /dev/null
+\documentclass[a4paper,12pt,twocolumn]{article}
+\usepackage{authblk}
+\usepackage{siunitx}
+\sisetup{group-digits=false}
+\title{\SI{100}{GbE} Passive Optical Access Networks\\Technical Milestone Report}
+\author{Adrian I.~Lam\vspace{-1em}\\Supervised by Dr.~Seb Savory}
+\date{16 January 2019}
+
+% Generic formatting packages
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage{microtype}
+\usepackage[margin=2.5cm]{geometry}
+\usepackage{hyperref}
+\hypersetup{unicode=true,
+ pdftitle={Technical Milestone Report},
+ pdfauthor={ail30},
+ pdfborder={0 0 0},
+ breaklinks=true}
+\usepackage{parskip}
+\usepackage[title]{appendix}
+
+\usepackage[compact,small]{titlesec}
+%\titlespacing{\section}{0pt}{0pt}{0pt}
+%\titlespacing{\subsection}{0pt}{0pt}{0pt}
+\usepackage{titling}
+\setlength{\droptitle}{-8ex}
+
+\setlength{\columnsep}{0.5cm}
+
+% Math typesetting packages
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{physics}
+\newcommand*{\imj}{\mathrm{j}}
+
+% Convenient referencing packages
+\usepackage{cleveref}
+\crefname{appsec}{Appendix}{Appendices}
+
+% Graphics-related packages
+\usepackage[justification=centering,margin=0.5cm,font=small]{caption}
+\usepackage{subcaption}
+\usepackage{graphicx}
+\usepackage{rotating}
+
+\usepackage{blox}
+\usepackage{makecell}
+
+% code listings
+\usepackage{upquote}
+\usepackage{courier}
+\usepackage{listings}
+\makeatletter
+\lstset{
+ basicstyle=\ttfamily\lst@ifdisplaystyle\footnotesize\fi,
+ keywordstyle=\bfseries,
+ showstringspaces=false,
+ numbers=left
+}
+\makeatother
+
+% URL formatting, from <http://tex.stackexchange.com/a/194418>
+\DeclareUrlCommand{\angleurl}{\def\UrlLeft{<}\def\UrlRight{>}\urlstyle{tt}}
+\makeatletter
+\DeclareRobustCommand*{\url}{\hyper@normalise\angleurl@}
+\newcommand*{\angleurl@}[1]{\hyper@linkurl{\angleurl{#1}}{#1}}
+\makeatother
+
+\newcommand*{\MATLAB}{MATLAB\textsuperscript{\textnormal{\textregistered{}}}}
+
+\renewcommand\floatpagefraction{.9}
+\renewcommand\dblfloatpagefraction{.9} % for two column documents
+\renewcommand\topfraction{.9}
+\renewcommand\dbltopfraction{.9} % for two column documents
+\renewcommand\bottomfraction{.9}
+\renewcommand\textfraction{.1}
+\setcounter{totalnumber}{50}
+\setcounter{topnumber}{50}
+\setcounter{bottomnumber}{50}
+
+
+\begin{document}
+\maketitle
+
+\begin{abstract}
+ This project aims at evaluating methods of achieving a \SI{100}{Gb/s}
+ Ethernet passive optical access network. An optical link based on
+ coherent receivers will be considered, and a computer model
+ will be built using \MATLAB{} to simulate various physical effects
+ in the optical fibre. Digital signal processing techniques will be
+ employed to correct for these effects and demodulate the transmitted
+ symbols. Currently, all relevant linear effects have been successfully
+ simulated and compensated for, while non-linear effects have not been
+ completed yet. After the model is complete, different designs of the
+ network, such as using different modulation schemes or multiplexing
+ methods, can be simulated and their performance compared, and the
+ feasibility to use them in an access network will be discussed.
+ The results may also be verified through off-line processing of
+ real measured data.
+\end{abstract}
+
+\section{Introduction and Motivation}
+A passive optical network (PON) is a point-to-multipoint system
+where data for all users of the network, modulated onto an
+optical signal, leaves the optical line terminal at the service
+provider, and is carried along a fibre feeder, then split
+by an unpowered beam splitter, without any routing or selection,
+to separate distribution fibres reaching the optical network units
+of the users~\cite[\S6.1]{PONintro}. This design allows high-speed
+communication for a large number of consumers, with relatively low cost
+for each user~\cite{NGPON2-1}, and is currently typically employed
+in a fibre-to-the-home setting~\cite{ponroadmap}.
+
+Fibre-to-the-home applications are already well-served by the
+currently mature implementation of \SI{1}{Gb/s} PONs, which may
+make higher speed PON seem unnecessary. However, there are many more
+future applications that could potentially benefit from a
+\SI{100}{Gb/s} PON. By designing future PON specifications to be
+compatible with existing fibre installations, less installation
+costs will be incurred, allowing the mixing of
+more applications onto the same network, thus increasing
+revenues for service providers. In addition, as more and more
+people rely on mobile networks for their daily communication
+and entertainment needs, mobile operators are looking to increase
+the density in cell sites, making PONs a good candidate to deliver
+the cell data backhaul. As the 5G mobile standard develops, PONs
+may even be useful in the fronthaul, where
+radio signals were sampled and relayed,
+through a PON, to a centralized
+location for digital signal processing (DSP), seen as a way to
+reduce costs~\cite{ponroadmap}.
+
+The use of coherent receivers in a high-speed PON is considered.
+In contrast to direct detection receivers, both the real and imaginary
+parts of each polarization of the received electrical field can be
+detected separately
+in a coherent receiver. This makes complex modulation schemes such
+as phase-shift keying (PSK) or quadrature amplitude modulation
+(QAM) possible, and combined with polarization-division multiplexing (PDM),
+makes very high data rates possible~\cite[\S5.6]{foc},~\cite{savorydigital}.
+
+In this project, a model to simulate the various physical effects in
+an optical channel is to be built. DSP will
+then be used to attempt to correct for these effects to recover the
+original signal. Using this model, different options for achieving a
+\SI{100}{Gb/s} PON will be compared. The response of a real channel
+will then be measured and, using the DSP techniques investigated,
+processed offline to verify the model and the correction methods.
+Feasibility of employing these techniques in a commercial PON setting
+will also be discussed.
+
+The current progress in developing the simulation model is detailed
+in \Cref{sec:simmodel}, with future plans listed in
+\Cref{sec:future}.
+
+\section{The Simulation Model} \label{sec:simmodel}
+
+\begin{figure*}[tb]
+ \centering
+ \begin{tikzpicture}
+ \small
+ \bXInput[$x_n$]{input}
+ \bXBlocL[3]{p}{\makecell[c]{Pulse shaping\\$p(t)$}}{input}
+
+ \bXBloc[3]{sim1}{Fibre-optic link}{p}
+ \bXLink[$x(t)$]{p}{sim1}
+
+ \bXSumb*[6]{AWGN}{sim1}
+ \bXLink{sim1}{AWGN}
+ \path (AWGN) ++(0,-1) node (noise) {$n(t)$};
+ \bXLink{noise}{AWGN}
+
+ \bXOutput[3]{y}{AWGN}
+ \bXLink[$y(t)$]{AWGN}{y}
+ \end{tikzpicture}
+
+ \begin{tikzpicture}
+ \small
+ \bXInput{yt}
+ \bXBloc[3]{q}{\makecell[c]{Matched filter\\$q(t)=p(-t)$}}{yt}
+ \bXLink[$y(t)$]{yt}{q}
+ \bXBloc[3]{sampler}{\makecell[c]{Sample\\$T_s=1/R_\text{sym}$}}{q}
+ \bXLink[$r(t)$]{q}{sampler}
+ \bXBloc[3]{sim2}{\makecell[c]{Channel\\equalization}}{sampler}
+ \bXLink[$r_n$]{sampler}{sim2}
+ \bXBlocL[3]{decision}{Decision}{sim2}
+ \bXOutput[2.5]{xhatn}{decision}
+ \bXLink{decision}{xhatn}
+ \path (xhatn) ++(0.3,0) node {$\hat{x}_n$};
+ \end{tikzpicture}
+ \caption{Block diagram of the
+ simulation model.}
+ \label{fig:model}
+\end{figure*}
+
+\Cref{fig:model} shows the current basic model,
+involving a transmitter with a root-raised
+cosine pulse shaping filter, processed to simulate the various
+physical effects, then
+transmitted through an additive white
+Gaussian noise (AWGN) channel to a receiver with a matched filter.
+The received signal is then sampled and DSP is used to correct for
+the physical effects in the electrical domain. The demodulated signal
+is then compared to the original pseudorandom data, to obtain a
+measurement of the bit-error rate (BER) using a Monte-Carlo approach.
+Currently, the main modulation scheme considered is quadrature
+phase-shift keying (QPSK), with Gray coding.
+
+The effects considered are enumerated below. The results of the
+methods used to correct for the effects are compared to the ideal
+AWGN channel.
+
+\subsection{Chromatic Dispersion} \label{sec:CD}
+Chromatic dispersion (CD) is the effect of the group speed of light varying
+with the wavelength of the optical signal~\cite[\S2.7.3]{foc}. It can be
+modelled as a linear system, with transfer function in the Fourier
+domain
+\[
+G(z, \omega) = \exp\left( -\imj \frac{D\lambda^2 z}{4\pi c} \omega^2\right)
+\] or with impulse response in the time domain
+\begin{equation}
+g(z, t) = \sqrt{\frac{c}{\imj D \lambda^2 z}}
+\exp\left( \imj \frac{\pi c}{D\lambda^2 z} t^2\right)
+\label{eq:CDimpresp}
+\end{equation}
+with $z$ being the transmitted distance, $c$ the speed of light
+in vacuum, $\lambda$ the wavelength in vacuum, and $D$ the dispersion
+parameter of the fibre~\cite{savorydigital}. For all simulations
+below, $D=\SI{17}{ps/(nm.km)}$.
+
+Using this model, constellation diagrams were obtained and
+shown in \Cref{fig:CDconst}. It can be seen that over long
+distances, CD would make demodulation very difficult, and as
+such, it is necessary to compensate for this effect. Current
+systems use dispersion compensating fibres, but DSP may be applied
+instead to reduce cost~\cite{savorydigital}. It is noted that
+by inverting the sign of $D$ in
+\Cref{eq:CDimpresp}, the impulse response of the dispersion compensating
+filter is obtained, and with truncation and discretization,
+can be implemented as a simple tapped delay line~\cite{savorydigital}.
+
+\begin{figure}[htb]
+ \centering
+ \begin{subfigure}[t]{0.22\textwidth}
+ \includegraphics[width=\textwidth]{cd_qpsk_noiseless_Dz17_new.eps}
+ \caption{$z=\SI{1}{km}$.}
+ \end{subfigure}
+ \begin{subfigure}[t]{0.22\textwidth}
+ \includegraphics[width=\textwidth]{cd_qpsk_noiseless_Dz85_new.eps}
+ \caption{$z=\SI{5}{km}$.}
+ \end{subfigure}
+ \caption{QPSK constellation after chromatic dispersion,
+ without AWGN.}
+ \label{fig:CDconst}
+\end{figure}
+
+\Cref{fig:CDCompz200} shows the dispersion compensating filter in
+action. The resulting BER very closely resembles that of the ideal
+AWGN, thus verifying the implementation.
+
+\begin{figure}[htb]
+ \centering
+ \includegraphics[width=.44\textwidth]{CDCompz200.eps}
+ \caption{QPSK signal with simulated chromatic dispersion and
+ CD compensation, over an AWGN channel, with
+ $z=\SI{200}{km}$.}
+ \label{fig:CDCompz200}
+\end{figure}
+
+\subsection{Adaptive Equalizer}
+Adaptive equalizers can be used to correct for time-varying effects,
+an example of which is polarization dependent effects.
+\cite{savorydigital} discusses the implementation of adaptive
+equalization to PDM signals.
+This has yet to be implemented in the simulation model.
+
+On the other hand, an implementation for a single polarization
+state has been done. This would be useful for correcting for
+fluctuations to the environment~\cite[\S11.6.1]{foc},
+not simulated in the model, but would be present in real life.
+In addition,
+it was observed that the CD compensating filter discussed
+in \Cref{sec:CD} does not perform very well over short
+distances, as can be seen in \Cref{fig:CDCompz2}, due to
+truncation of the non-causal infinite-length impulse response.
+Adaptive equalization was attempted to correct for this effect
+as well.
+
+Two types of equalizing algorithms are typically considered, namely
+the constant modulus algorithm (CMA) and the decision-directed
+least mean square (DD-LMS) algorithm~\cite[\S11.6.1]{foc}.
+CMA has been implemented due to its
+simplicity. If time permits, DD-LMS can also be attempted.
+
+The CMA relies on the fact that for PSK signals, the transmitted
+symbols all have unit amplitude. As a result, it attempts to minimize
+the distance between the signal and the unit circle.
+\Cref{fig:adaptBefAft} illustrates the adaptive nature of the algorithm.
+\Cref{fig:CDCompz2} demonstrates the success of the CMA, bringing
+the performance curve back to the theoretical values.
+
+\begin{figure}[htb]
+ \centering
+ \includegraphics[width=.44\textwidth]{CDCompz2.eps}
+ \caption{QPSK signal with CD, CD compensation, and CMA adaptive
+ equalizer, over an AWGN channel, with $z=\SI{2}{km}$.}
+ \label{fig:CDCompz2}
+\end{figure}
+
+\begin{figure}[htb]
+ \centering
+ \begin{subfigure}[t]{.22\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{adaptBefore.eps}
+ \caption{Symbols 1 to 500.}
+ \end{subfigure}%
+ \begin{subfigure}[t]{.22\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{adaptAfter.eps}
+ \caption{Symbols 2001 to~2500.}
+ \end{subfigure}
+ \caption{Constellations showing the adaptive behaviour of
+ the CMA.}
+ \label{fig:adaptBefAft}
+\end{figure}
+
+\subsection{Phase Noise Correction}
+Lasers used in the transmitter and the receiver local oscillator
+have a linewidth $\Delta\nu$ over which random frequency deviations
+occur, resulting in a phase noise in the signal. When discretized,
+the phase noise $\phi[k]$ can be modelled as a one-dimensional
+Gaussian random walk,
+\begin{gather*}
+\phi[k] = \phi[k-1] + \Delta\phi_k \\
+\qq*{where} \Delta\phi_k
+\mathrel{\overset{\makebox[0pt]{\mbox{\normalfont\tiny\sffamily i.i.d.}}}{\sim}}
+\mathcal{N}(0, 2\pi \Delta\nu T_s)
+\quad\text{for all }k,
+\end{gather*}
+with $T_s$ being the sampling period~\cite[\S11.3]{foc}.
+
+The effect of phase noise can be most easily understood from a plot
+of the constellation, as shown in \Cref{fig:phaseNoiseCircle}.
+Demodulation is
+impossible without any correction. Fortunately there are various
+techniques to mitigate this issue, and two of them are discussed
+below.
+
+\subsubsection{Differential PSK}
+In a normal PSK scheme, information is modulated as the
+phase of each transmitted symbol. In contrast, in differential PSK (DPSK),
+information is modulated as the \emph{difference} in phase between
+two consecutive symbols~\cite[\S7.3.2]{ccsm}.
+It can mitigate the effect of phase noise
+if the linewidth is small (such that $\Delta\phi_k$ is sufficiently
+smaller than, for example, $\pi/4$ for QPSK). Phase noise would then
+have little influence to the phase difference between consecutive
+symbols.
+
+It was however noted that in DPSK, the demodulator is affected
+``twice'' by phase noise. This increases the noise variance,
+making bit errors more likely~\cite[\S7.3.2]{ccsm}.
+This can be seen (among other results) in \Cref{fig:phasenoise_ult}.
+This translates to
+a SNR penalty compared to the normal PSK scheme. At a BER of
+$10^{-3}$, the penalty is about \SI{2.5}{dB}.
+
+\subsubsection{Block phase noise estimation}
+The phase noise can also be estimated assuming the total phase noise
+over a small number of symbols is small. The Viterbi-Viterbi algorithm
+used is best illustrated by an example. Consider a QPSK scheme. At the
+receiver, the received signal $r[k]$ is given by
+\[
+r[k] = \exp\left( \imj \phi[k] + \imj \frac{\pi}{4} +
+\imj \frac{d[k]\pi}{2} \right) + n[k]
+\]
+where $\phi[k]$ is the unknown phase of the $k$th symbol,
+$d[k] \in \{0, 1, 2, 3\}$ is the transmitted data, and
+$n[k]$ is AWGN. Taking the signal to the 4th power eliminates
+$d[k]$ from the expression, resulting in
+\begin{equation}
+ r[k]^4 = \exp\left( \imj 4\phi[k] + \imj \pi\right) + n'[k]
+ \label{eq:rk4}
+\end{equation}
+where $n'[k]$ are the terms involving $n[k]$. It can be shown
+that $n'[k]$ has zero mean, thus if $\phi[k]$ does not vary
+much over a small range of $k$, then its value can be estimated
+by averaging over that range (thus eliminating $n'[k]$)~\cite[\S11.5]{foc}.
+\Cref{fig:viterbiphest} shows the algorithm
+estimating the phase of a noisy signal.
+
+With a phase estimation method available, the effect of phase noise
+can be undone simply by adding a reversed phase shift.
+
+\begin{figure}[htb]
+ \centering
+ \begin{subfigure}[t]{.22\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{phaseNoiseCircle.eps}
+ \caption{Phase noise randomly rotating the constellation.}
+ \label{fig:phaseNoiseCircle}
+ \end{subfigure}%
+ \begin{subfigure}[t]{.22\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{phaseEst.eps}
+ \caption{Example of the Viterbi-Viterbi algorithm
+ estimating phase noise.}
+ \label{fig:viterbiphest}
+ \end{subfigure}
+ \caption{Phase noise, and how it affects the received symbols.}
+\end{figure}
+
+However, at larger linewidths, phase estimation may make mistakes.
+This is due to the ambiguity in \Cref{eq:rk4}, where in QPSK an
+additional phase increase of $\pi/2$ gives the same solution,
+and phase noise makes unambiguous phase unwrapping impossible.
+This is known as a \emph{cycle slip}~\cite{taylorphest}, and
+is illustrated in \Cref{fig:cycleslip}.
+
+The result of a particular run of the simulation is shown in
+\Cref{fig:phasenoise_ult}.
+It can be seen that when cycle slips do not occur, the resulting
+BER is much closer to the theoretical AWGN channel compared to
+DPSK. However, if a cycle slip occurs, all the subsequent symbols
+will be demodulated incorrectly~\cite{taylorphest},
+giving very poor performance.
+
+To eliminate the effect of cycle slips, principles from DPSK
+can be incorporated into the phase estimation method, but instead
+of differentially modulating the \emph{symbols}, the source
+\emph{bit stream} is differentially \emph{encoded}. This is known
+as \emph{differentially encoded} PSK (DEPSK). At the receiver, the
+symbols are corrected after phase estimation (as above), and then
+demodulated like conventional PSK, before differentially decoding
+the bits. While this method transforms a single bit error into
+a pair of bit errors~\cite{taylorphest}, it has a smaller SNR
+penalty than DPSK~\cite[Ch.~13]{matlabcomm}, since the
+noise variance
+is not increased like it is in DPSK. \Cref{fig:phasenoise_ult} also
+shows the result of DEPSK, which is immune to cycle slips, with
+a smaller SNR penalty than DPSK. Many forward error correction
+codes can effectively correct for short bursts of bit errors,
+thus further reducing the penalty~\cite{taylorphest}, however
+this will not be investigated in this project.
+
+\begin{figure}[htb]
+ \centering
+ %\begin{subfigure}[t]{.22\textwidth}
+ %\centering
+ \includegraphics[width=.3\textwidth]{cycleslip.eps}
+ \caption{A cycle slip.}
+ \label{fig:cycleslip}
+ %\end{subfigure}%
+ %\begin{subfigure}[t]{.22\textwidth}
+ % \centering
+ % \includegraphics[width=\textwidth]{adaptAfter.eps}
+ % \caption{Symbols 2001 to~2500.}
+ %\end{subfigure}
+ %\caption{Constellations showing the adaptive behaviour of
+ %the CMA.}
+\end{figure}
+
+\begin{figure}[htb]
+ \centering
+ \includegraphics[width=.44\textwidth]{phasenoise_ult.eps}
+ \caption{Performance of various methods under a phase noise
+ of \SI{10}{MHz}, on a particular run of the simulation.}
+ \label{fig:phasenoise_ult}
+\end{figure}
+
+
+\subsection{Non-linearity: Kerr Effect}
+Kerr effect is one of the non-linear effects investigated in this
+project. Kerr effect describes the change in refractive index of
+a material as the optical power of the incident beam changes.
+The result is a phase shift proportional to the optical power
+(i.e.~the square of the electric field, hence
+non-linear)~\cite[\S10.2]{foc},~\cite[\S6.2.2]{nfo}.
+To numerically simulate this effect together with other linear effects,
+the \emph{split-step Fourier method} is used. In brief, the fibre
+length is divided into many small bits. The signal is first transformed
+to the Fourier domain, and chromatic dispersion is applied
+(as in \Cref{sec:CD}). The signal is then transformed back to the time
+domain and its power is calculated. From this, the corresponding
+phase shift due to Kerr effect can be applied. This process repeats
+until the total simulated length reaches the desired transmission
+distance~\cite[\S2.4.1, App.~B]{nfo}.
+
+Currently, the general structure of the split-step Fourier method
+has been coded, but there are small problems that require fixing,
+and as such results are yet to be included in this report. However,
+the general shape of the resulting curve matches existing
+literature~\cite{savory100Gbps},
+so there should be little difficulty in having it completed soon.
+
+\section{Future Plan and Timeline} \label{sec:future}
+After completing the simulation for Kerr effect, the most important
+task would be to integrate all the effects into a single simulation
+program, to prepare for the final model to evaluate different
+transmission schemes.
+Afterwards, it was planned to have a more realistic
+model of the noise -- the AWGN channel would be replaced with
+a combination of thermal noise (which can be modelled as
+AWGN)~\cite[\S8.1.1]{aoe}
+and shot noise. Finally, PDM and wavelength-division
+multiplexing would
+be implemented to have a ``complete'' model. To have sufficient
+time for the remaining parts of the project, it was planned to have
+this completed by week 3 of Lent term, i.e.\ about one week for
+each of the three tasks.
+
+A few different designs of the network will be evaluated and compared,
+and the suitability to use in a PON will be discussed. Running the
+simulation a few times with different parameters should not take
+too much time, but discussing real-life feasibility may involve
+more review of current literature, so an estimate of 2 weeks is
+reserved for this.
+
+The final three weeks of Lent will be spent obtaining experimental
+data and verifying simulation results, to make further adjustments
+to the model if necessary, and to prepare
+for the final report and presentation.
+
+It is expected that most of the Easter vacation would be spent preparing
+for the examinations. Work on the final report and presentation would
+resume after that, which should be enough time to meet the deadline
+in week 5 of Easter term.
+
+\begin{thebibliography}{10}
+\bibitem{PONintro}
+ C.C.K.~Chan,
+ ``Protection architectures for passive optical networks,'' in
+ \textit{Passive Optical Networks: Principles and Practice},
+ C.F.~Lam, Ed.
+ Burlington, MA: Academic Press, 2007, pp.~243-266.
+\bibitem{NGPON2-1}
+ J.S.~Wey \textit{et al.},
+ ``Physical layer aspects of NG-PON2 standards -- Part 1:
+ optical link design,''
+ \textit{J.~Opt.\ Commun.\ Netw.}, vol.~8, no.~1, pp.~33-42, 2016.
+ doi:10.1364/JOCN.8.000033
+\bibitem{ponroadmap}
+ D.~Nesset, ``PON Roadmap,''
+ \textit{J.~Opt.\ Commun.\ Netw.}, vol.~9, no.~1, pp.~A71-A76, 2017.
+ doi:10.1364/\allowbreak JOCN.9.000A71
+\bibitem{foc}
+ S.~Kumar and M.J.~Deen,
+ \textit{Fiber Optic Communications: Fundamentals and Applications}.
+ Chichester, UK: Wiley, 2014.
+\bibitem{savorydigital}
+ S.J.~Savory, ``Digital filters for coherent optical receivers,''
+ \textit{Opt.\ Express}, vol.~16, no.~2, pp.~804-817, 2008.
+ doi:10.1364/OE.16.000804
+\bibitem{ccsm}
+ J.G.~Proakis and M.~Salehi,
+ \textit{Contemporary Communication Systems Using \MATLAB}.
+ Pacific Grove, CA: Brooks/Cole, 2000.
+\bibitem{taylorphest}
+ M.G.~Taylor, ``Phase estimation methods for optical coherent
+ detection using digital signal processing,''
+ \textit{J.~Lightwave Technol.}, vol.~27, no.~7, pp.~901-914, 2009.
+ doi:10.1109/JLT.2008.927778
+\bibitem{matlabcomm}
+ The MathWorks, Inc.,
+ \textit{Communications Toolbox\textnormal{\texttrademark{}} User's Guide}
+ (R2018b),
+ 2018. [Online]. Available:
+ \url{https://www.mathworks.com/help/pdf_doc/comm/comm.pdf}.
+ [Accessed: Jan.~9, 2019].
+\bibitem{nfo}
+ G.P.~Agrawal,
+ \textit{Nonlinear Fiber Optics}, 5th ed.
+ Oxford, UK: Academic Press, 2013.
+\bibitem{savory100Gbps}
+ Md.S.~Faruk, D.J.~Ives, and S.J.~Savory,
+ ``Technology requirements for an Alamouti-coded \SI{100}{Gb/s}
+ digital coherent receiver using $3\times3$ couplers for
+ passive optical networks,''
+ \textit{IEEE Photon.\ J.}, vol.~10, no.~1, 2018.
+ doi:10.1109/JPHOT.2017.2788191
+\bibitem{aoe}
+ P.~Horowitz and W.~Hill,
+ \textit{The Art of Electronics}, 3rd ed.
+ New York: Cambridge University Press, 2015.
+\end{thebibliography}
+
+\end{document}
projects / 4yp.git / blobdiff