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\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{2.5}{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}

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\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}
