--- /dev/null
+% presentation
+%\documentclass{beamer}
+%\setbeameroption{hide notes}
+% notes
+\documentclass[handout]{beamer}
+%\usepackage{pgfpages}
+\setbeameroption{show only notes}
+\setbeamercolor{note page}{bg=white}
+\setbeamercolor{note title}{bg=white}
+\setbeamertemplate{note page}{\vspace{1em}\insertnote}
+% To compile, run
+% pdflatex -jobname presentation+notes ./presentation.tex && \
+% pdfnup --nup 1x4 --no-landscape --a4paper presentation+notes.pdf
+
+\title[100 GbE PON]{100 GbE Passive Optical Access Networks}
+\author[A.~Lam (ail30)]{Adrian Lam (ail30)}
+\institute[]{Supervised by: Dr.~Seb Savory}
+\date[M 2018]{Michaelmas 2018}
+
+\usetheme{Madrid}
+\usepackage{lmodern}
+\usepackage{amsmath}
+\usepackage{siunitx}
+\usepackage{graphicx}
+\usepackage{epstopdf}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\hypersetup{colorlinks,linkcolor=,urlcolor=magenta} % https://tex.stackexchange.com/a/13424
+\usepackage{pgffor}
+\usepackage{pdfpages}
+\usepackage{blox}
+\usepackage{makecell}
+
+\begin{document}
+
+\frame{\titlepage} % 15s
+
+\begin{frame}
+ \frametitle{What is a passive optical network (PON)?}
+ \begin{itemize}
+ \item Point-to-multipoint
+ \item Unpowered beam splitter
+ \item ``Everything sent to everyone''
+ \end{itemize}
+
+ {\centering%
+ \includegraphics[height=0.5\paperheight]{PON.png}\\
+ \tiny Image credit: Riick\textasciitilde commonswiki, ``PON vs AON.png''.
+ CC BY-SA 3.0. \url{https://commons.wikimedia.org/wiki/File:PON_vs_AON.png}. Cropped.
+
+ }
+
+\note{
+ A passive optical network, or PON, is typically used in a
+fibre-to-the-home setting. Optical signal from the network provider
+is split, without amplification or selection, to all users in the same
+network. The ONT here which sits somewhere in your home will select
+the data related to you.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Need for high-speed (\SI{100}{Gb/s}) PON}
+ \begin{itemize}
+ \item Fibre-to-the-home?
+ \item Well-served by \SI{1}{Gb/s} PON, mature (mass deployment $>$ 1 decade)
+ \pause
+ \item Reuse existing fibres in other applications
+ %%\item Business users
+ \item Mobile
+ \begin{itemize}
+ \item Increase density in cell sites $\rightarrow$ PON to deliver
+ backhaul
+ \item Possible 5G fronthaul: radio receivers sample RF signals and relay
+ them to centralized location for processing
+ \end{itemize}
+ \end{itemize}
+
+ \note{
+ * Typical usage of PON is in FTTH. However, gigabit PONs are already
+ quite sufficient and mature with low cost hardware.
+
+ * The motivation to go up to 100 Gb/s is to share other applications along existing
+ fibres, to reduce the cost of installing new fibres.
+
+%% For example, business users.
+ A particularly interesting application is in mobile networks.
+ As people get more addicted to their smart phones, mobile network
+ operators would need to increase the density in cell sites, making
+ PON a good candidate to deliver the cell site backhaul.
+
+ As 5G mobile develops, PON may also be useful in the fronthaul.
+ RF receivers relay the signals back to a centralized location
+ for processing, which is seen as a way to reduce operating costs.
+ }
+\end{frame}
+
+\begin{frame}
+ \frametitle{Direct detection vs coherent receivers}
+ \begin{itemize}
+ \item
+ Direct detection receiver
+ \begin{itemize}
+ \item Single photodiode with amplifier
+ \item Rx current $\propto$ received optical power (Phase information lost)
+ \item On-off keying (mainly)
+ \end{itemize}
+ \item
+ Coherent receiver
+ \begin{itemize}
+ \item $\propto$ real and imaginary parts of received electrical
+ field
+ \item Polarization-division multiplexing
+ \item Phase-shift keying, quadrature amplitude modulation
+ \end{itemize}
+ \end{itemize}
+ {\centering%
+ \fbox{\includegraphics[height=.3\paperheight,clip,trim=40mm 167mm 40mm 55mm]{coherentRx.pdf}} \\
+ {\tiny Image credit: Seb J.~Savory, ``Digital filters for coherent
+ optical receivers,'' 2008.}
+
+ }
+ \note{
+ To achieve a high data rate, coherent receivers are to be used.
+This is different from the direct detection receivers which you may
+have come across last year in 3B6, where the receiver photocurrent
+is proportional to the optical power. In a coherent receiver, as illustrated
+by this example here, %the light, after passing through a single-mode fibre,
+%is first split by polarization,
+%and then the real and imaginary parts of each polarization are detected
+both the real and imaginary parts of two orthogonal polarizations are detected.
+This allows different modulation schemes, similar to
+radio transmissions, such as PSK and QAM.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Aims of this project}
+ \begin{itemize}
+ \item Build simulation models for optical networks with coherent receivers
+ \item Use DSP to correct for fibre effects
+ \item Simulate different options for achieving \SI{100}{Gb/s}
+ \item Experimentally validate simulation results
+ \item Evaluate feasibility to use in PONs
+ \end{itemize}
+ \note{
+ In this project, simulation models for optical networks will be
+ built using MATLAB, with digital signal processing to correct
+ for fibre effects. Different options for achieving the target
+ data rate of 100 Gb/s will be simulated and compared, and
+ later experimentally validated. The results will be evaluated
+ in terms of suitability to use in a PON.
+ }
+\end{frame}
+
+\begin{frame}
+ \frametitle{Simulations performed thus far}
+ QPSK with symbol rate \SI{25}{GBd} over AWGN channel
+
+ \begin{itemize}
+ \item Chromatic dispersion
+ \item Adaptive equalizer
+ \item Phase noise (laser linewidth)
+ \end{itemize}
+
+ {\centering%
+ \begin{tikzpicture}
+ \scriptsize
+ \bXInput[$x_n$]{input}
+ \bXBlocL[3]{p}{\makecell[c]{Pulse shaping\\$p(t)$}}{input}
+ \bXSumb*[9]{AWGN}{p}
+ \bXLink[$x(t)$]{p}{AWGN}
+ \path (AWGN) ++(0,-1) node (noise) {$n(t)$};
+ \bXLink{noise}{AWGN}
+ \bXBloc[3]{sim1}{?}{AWGN}
+ \bXLink{AWGN}{sim1}
+ \bXOutput[3]{y}{sim1}
+ \bXLink[$y(t)$]{sim1}{y}
+ \end{tikzpicture}
+
+ \addvspace{1em}
+
+ \begin{tikzpicture}
+ \scriptsize
+ \bXInput{yt}
+ \bXBloc[3]{q}{\makecell[c]{Matched filter\\$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)$]{q}{sampler}
+ \bXBloc[3]{sim2}{$?'$}{sampler}
+ \bXLink[$r_n$]{sampler}{sim2}
+ \bXBlocL[3]{decision}{Decision}{sim2}
+ \bXOutput[3]{xhatn}{decision}
+ \bXLink{decision}{xhatn}
+ \path (xhatn) ++(0.2,0) node {$\hat{x}_n$};
+ \end{tikzpicture}
+
+ }
+ \note{
+ The overall model has this structure, with root-raised cosine
+ pulses used.
+ The channel is modelled as
+ additive white Gaussian noise, followed by the simulated physical effect.
+
+ On the receiver side, after analog-to-digital conversion, the
+ received complex symbols $r_n$ are further processed to compensate
+ for channel effects before decision and demodulation.
+
+Currently I have based by simulations on a quadriphase-shift keying
+modulation scheme with
+$25\times 10^9$ symbols per second. QPSK gives two bits per symbol,
+giving 50 Gb/s. Adding in polarization-division multiplexing,
+which I haven't done yet, would reach the target of 100 Gb/s.
+}
+\end{frame}
+
+\begin{frame}[t]
+ \frametitle{Chromatic dispersion}
+ \onslide<1->{\begin{itemize}
+ \item Group speed of light varies with wavelength
+ \item Modelled as linear system, impulse response:
+ \[
+ g(z, t) = \sqrt{\frac{c}{\mathrm{j} D \lambda^2 z}}
+ \exp{\left(\mathrm{j} \frac{\pi c}{D \lambda^2 z} t^2\right)}
+ \]
+ \end{itemize}}
+
+ {\centering%
+ \includegraphics<2>[height=0.4\paperheight]{chromaticDispersionTest.eps}
+ \includegraphics<3-4>[width=4cm]{qpsk_clean.eps}
+ \includegraphics<3>[width=4cm]{cd_qpsk_noiseless_Dz17.eps}
+ \includegraphics<4>[width=4cm]{cd_qpsk_noiseless_Dz85.eps}
+
+ }
+
+ \note{
+* The first effect investigated was chromatic dispersion.
+This effect occurs as a result of the speed of light being
+slightly different at different wavelengths, and lasers have a
+wavelength band that, although small, still makes a large impact
+over long distances.
+
+Literature has shown that chromatic dispersion can be modelled
+as a linear system, with D being the dispersion coefficient and
+z the distance travelled.
+
+* In direct detection receivers, this effect can be seen as a pulse-
+broadening effect. However, in coherent receivers, we are more interested
+in the changes to the complex constellation symbols.
+
+* Here is a result of a simulation with 17 ps/(nm km) dispersion, with
+1 kilometre of fibre, in the absence of any additive noise.
+You can still cleanly decode the symbols without much difficulty.
+
+But when we go slightly longer to 5 km...
+
+* we get this mess.
+
+So clearly the receiver needs to do something to mitigate the effects
+of chromatic dispersion. A linear filter can be used. How do we design
+this filter? Well, we know the impulse response of the dispersion
+model, so if we invert the sign of D here...
+}
+\end{frame}
+
+\begin{frame}[t]
+ \frametitle{Chromatic dispersion compensation}
+ \[
+ g_\text{c}(z, t) = \sqrt{\frac{c}{\mathrm{j} (-D) \lambda^2 z}}
+ \exp{\left(\mathrm{j} \frac{\pi c}{(-D) \lambda^2 z} t^2\right)}
+ \]
+
+ {\centering%
+ \includegraphics<2>[height=.6\paperheight]{cd_qpsk_Dz3400.eps}
+ \includegraphics<3>[height=.6\paperheight]{cd_qpsk_Dz34.eps}
+
+ }
+
+\note{
+* We get the impulse response of the dispersion compensating filter.
+
+* Additive noise was added back to the channel, and a million bits were
+sent through the channel.
+This is a plot of the bit-error rate, or the probability of decoding
+a bit incorrectly, against a measure of the signal-to-noise ratio,
+at a simulated transmission distance of 200 km.
+We can see that while the magenta curve, that is without any compensation,
+doesn't do any better than chance,
+The red curve, which is the simulation result of
+the compensating filter, does a very good job at approaching the
+theoretical blue curve of an ideal AWGN channel.
+
+* An interesting behaviour was observed when the transmission distance
+was reduced, in this case, to 2km. We can see that the compensation
+filter actually does worse, which is counter-intuitive.
+This is due to
+a reduced number of filter taps when converting this continuous-time
+filter to a discrete-time filter. We can, of course, add an extra filter
+to try to correct for this, which brings us to the next topic:
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Adaptive equalizer}
+ \begin{itemize}
+ \item Error of previous symbol fed back to change filter tap weights
+ \item Can correct for static and time-varying effects
+ \item Constant modulus algorithm (CMA)
+ \item For PSK, magnitude of transmitted symbols is constant (unity)
+ \item Error signal is distance of received signal from unit circle
+ \end{itemize}
+
+\note{
+Adaptive equalization. Here, the error of the previous symbol is used
+to update the filter taps, which can correct for static as well as
+slowly varying effects. In the following simulations, the constant
+modulus algorithm was implemented. This relies on the fact that, while
+the receiver doesn't know what symbol was transmitted, it knows, for
+PSK, that the symbols must lie on a unit circle. The distance from the
+received signal to the unit circle is thus used as a measure of error.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Adaptive equalizer: convergence}
+ {\centering%
+ \foreach \x in {1,2,3,4,5,6,7,8,9} {%,10,11,12} {%
+ \includegraphics<\x>[height=0.75\paperheight]{adaptEqAni_\x.eps}%
+ }
+
+ \includegraphics<10>[height=0.75\paperheight]{CD+CMA_fin.eps}
+
+ }
+ \note{
+* Here is an animation of how the adaptive equalizer converges,
+again with a small dispersion but without additive noise.
+%At first it doesn't do much, and the symbols are still quite
+%widely spread.
+Initially the symbols are quite widely spread,
+but as the algorithm runs, /just click through the slides/
+
+we can see the equalizer brings the symbols close to 4 single points.
+
+* The overall effect can be seen with additive noise added back in,
+here with the green curve very closely agreeing with the theoretical
+blue curve.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Laser phase noise}
+ \begin{itemize}
+ \item Laser linewidth: deviations from the nominal wavelength
+ \item Instantaneous change in wavelength (frequency) $\rightarrow$
+ change in phase
+ \item $\phi[k]$ modelled as \textit{one-dimensional Gaussian random walk}
+ \[
+ \phi[k] = \phi[k-1] + \Delta\phi
+ \]
+ \[
+ \text{where}\quad\Delta\phi \sim \mathcal{N}(0, 2 \pi \Delta\nu T_s)
+ \]
+ \end{itemize}
+ {\centering%
+ \includegraphics[height=.5\paperheight]{../phasenoise_linewidths.eps}
+
+ }
+\note{
+ The next effect investigated was laser phase noise. This arises as the
+ true laser wavelength is a slight deviation from the nominal central
+ wavelength within the linewidth.
+ This instantaneous change in wavelength can be modelled as
+ a phase shift. Literature suggests a one-dimensional Gaussian
+ walk model, where each sample of the phase differs
+from the previous sample with a random delta phi drawn from a Gaussian
+distribution, with zero mean and whose variance is proportional to both the linewidth
+delta nu and the sampling time $T_s$.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Laser phase noise}
+ \begin{itemize}
+ \item Rotates symbol constellation
+ \item Problematic, e.g.~for QPSK, rotation by $\pi/2$ gives another
+ constellation with all symbols decoded wrongly
+ \end{itemize}
+ {\centering%
+ \includegraphics[height=.6\paperheight]{../phasenoise_rotation.eps}
+
+ }
+\note{
+The effect of phase noise is a rotation of the constellation symbols
+by an arbitrary amount, which is very problematic for PSK modulation
+as this would mean completely incorrect decoding.
+}
+\end{frame}
+
+\begin{frame}[t]
+ \frametitle{Laser phase noise: solutions}
+ \begin{columns}[t]
+ \begin{column}{0.5\textwidth}
+ \begin{itemize}
+ \item Differential PSK
+ \item Information encoded as the difference in phase with previous
+ symbol
+ \item Difference in phase noise between consecutive symbols small
+ \item \SI{2}{dB} penalty at $\text{BER} = 10^{-3}$
+ \end{itemize}
+ \end{column}
+ \begin{column}{0.5\textwidth}
+ \begin{itemize}
+ \item Estimate phase noise by Viterbi-Viterbi algorithm
+ \item Taking average over a small block of samples
+ \end{itemize}
+
+ {\centering%
+ \includegraphics[height=.5\paperheight]{../phasenoise_estimation.eps}
+
+ }
+ \end{column}
+ \end{columns}
+\note{
+We will consider two methods to mitigate this effect. The first is to
+use a differential PSK scheme, where the information is encoded not as
+the absolute phase, but as a difference in phase with the previous
+symbol. This works relying on the assumption that the phase noise between
+two consecutive symbols is sufficiently smaller than 90 degrees.
+However, by considering two
+symbols together, the effect of phase noise is enhanced,
+translating to a penalty in the signal-to-noise ratio.
+
+Another method is to estimate the amount of phase noise in each symbol
+and to rotate the symbols back by the estimated amount.
+The Viterbi-Viterbi algorithm, very briefly,
+works by taking an average over
+a block of samples to estimate the average phase noise in that block.
+}
+\end{frame}
+
+\begin{frame}[t]
+ \frametitle{Cycle slips}
+ \begin{columns}[t]
+ \begin{column}[t]{0.5\textwidth}
+ \begin{itemize}
+ \item<1-> At large linewidths, Viterbi-Viterbi algorithm can
+ make mistakes
+ \item<1-> For QPSK the phase estimate can be off by $pi/2$
+ \item<1-> All subsequent symbols will be decoded incorrectly\\[1em]
+ \item<3-> Solution: Differential encoding
+ \end{itemize}
+
+ \end{column}
+
+ \begin{column}[t]{0.5\textwidth}
+
+ \includegraphics<1>[width=\textwidth]{../cycleslip.eps}
+
+ \includegraphics<2-3>[width=\textwidth]{../phasenoise_ult_sansDE.eps}
+
+ \includegraphics<4>[width=\textwidth]{../phasenoise_ult.eps}
+ \end{column}
+ \end{columns}
+\note{
+ This estimation algorithm does not always work though. Sometimes, due to noise,
+a cycle slip would occur, which results in a systematic error of 90 degrees.
+This means that all the following symbols would actually be decoded
+incorrectly.
+
+* We can see in this simulation result that, when a cycle slip does not
+occur, the performance is much closer to the ideal curve than using
+differential PSK, but when it does occur the result is disastrous.
+
+Can we get the best of both worlds, with a small penalty but without
+any cycle slips?
+
+* The answer is yes, with a differential *encoding*. Note that this is
+different from differential PSK. Differential encoding is an operation
+on the bits, and the receiver would perform differential decoding
+on the bits *after* choosing the closest constellation symbols.
+Whereas in DPSK the receiver evaluates the difference in phase between
+the received samples directly, before converting them to bits.
+
+* The result is this cyan curve, with a smaller penalty than DPSK, and
+not affected by cycle slips.
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{What next?}
+ \begin{itemize}
+ \item Integrating CD and phase noise into a single system
+ \item Adaptive equalizer
+ \begin{itemize}
+ %%\item Convergence
+ \item Decision-directed algorithms
+ \item Training sequences
+ \end{itemize}
+ \item QAM
+ \item Polarization-division multiplexing
+ \begin{itemize}
+ \item Polarization mode dispersion
+ \item Adaptive equalizer
+ \end{itemize}
+ \item Non-linear effects
+ \end{itemize}
+\note{
+ That's all I have done as of now. Looking forward, simulations
+would need to integrate both effects into a single channel.
+Further investigations into adaptive equalizers can also be done.
+%For example, their convergence with different number of taps or
+%with different convergence parameters, and also different algorithms
+For example, the use of decision-directed algorithms,
+%%such as decision-directed algorithms,
+and to train the equalizer
+with pre-known sequences, to increase accuracy at the cost of losing
+some data rate.
+
+Other modulation schemes can also be investigated, such as
+higher-order QAM.
+It would require careful alterations to existing implementations,
+for example with the constant modulus algorithm, but can reduce the
+required symbol rate.
+
+The simulations performed only considered a single polarization.
+Further investigations should be done to send data through one more
+polarization, and the resulting effect of polarization mode dispersion
+needs to be addressed. Adaptive equalizers for PDM signals also need
+to be revised.
+
+Finally, non-linear fibre effects can also be considered.
+
+All these should hopefully be done before mid-Lent, leaving sufficient
+time for experimental measurements.
+
+That's all I've got. Thank you.
+}
+\end{frame}
+
+\bgroup
+\setbeamercolor{background canvas}{bg=black}
+\setbeamertemplate{navigation symbols}{}
+\begin{frame}[plain,noframenumbering]{}
+\end{frame}
+\egroup
+
+\begin{frame}[noframenumbering]
+ \frametitle{Viterbi-Viterbi algorithm}
+ Assume $\hat{\phi}\;\approx\; \phi[1] \approx \phi[2] \approx \cdots \approx \phi[N]$
+ \begin{align*}
+ r[k] &= \exp\left(\mathrm j \phi[k] + \mathrm j \frac \pi 4 + \mathrm j
+ \frac {d[k] \pi} 2\right) + n[k] \\
+ r[k]^4 &= \exp\left(\mathrm j 4 \phi[k] + \mathrm j \pi\right) + n'[k]
+ \\
+ \sum_{k=1}^{N} r[k]^4 &\approx N \exp\left(\mathrm j 4 \hat{\phi} + \mathrm j \pi\right) + n''\\[1.5em]
+ \hat{\phi} &\approx \frac14 \arg\left( -\sum_{k=1}^{N} r[k]^4 \right)
+ \end{align*}
+\end{frame}
+
+\end{document}
projects / 4yp.git / blobdiff