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12 % pdflatex -jobname presentation+notes ./presentation.tex && \
13 % pdfnup --nup 1x4 --no-landscape --a4paper presentation+notes.pdf
15 \title[100 GbE PON
]{100 GbE Passive Optical Access Networks
}
16 \author[A.~Lam (ail30)
]{Adrian Lam (ail30)
}
17 \institute[]{Supervised by: Dr.~Seb Savory
}
18 \date[M
2018]{Michaelmas
2018}
26 \usepackage{multimedia
}
28 \hypersetup{colorlinks,linkcolor=,urlcolor=magenta
} % https://tex.stackexchange.com/a/13424
36 \frame{\titlepage} % 15s
39 \frametitle{What is a passive optical network (PON)?
}
41 \item Point-to-multipoint
42 \item Unpowered beam splitter
43 \item ``Everything sent to everyone''
47 \includegraphics[height=
0.5\paperheight]{PON.png
}\\
48 \tiny Image credit: Riick
\textasciitilde commonswiki, ``PON vs AON.png''.
49 CC BY-SA
3.0.
\url{https://commons.wikimedia.org/wiki/File:PON_vs_AON.png
}. Cropped.
54 A passive optical network, or PON, is typically used in a
55 fibre-to-the-home setting. Optical signal from the network provider
56 is split, without amplification or selection, to all users in the same
57 network. The ONT here which sits somewhere in your home will select
58 the data related to you.
63 \frametitle{Need for high-speed (
\SI{100}{Gb/s
}) PON
}
65 \item Fibre-to-the-home?
66 \item Well-served by
\SI{1}{Gb/s
} PON, mature (mass deployment $>$
1 decade)
68 \item Reuse existing fibres in other applications
69 %%\item Business users
72 \item Increase density in cell sites $
\rightarrow$ PON to deliver
74 \item Possible
5G fronthaul: radio receivers sample RF signals and relay
75 them to centralized location for processing
80 * Typical usage of PON is in FTTH. However, gigabit PONs are already
81 quite sufficient and mature with low cost hardware.
83 * The motivation to go up to
100 Gb/s is to share other applications along existing
84 fibres, to reduce the cost of installing new fibres.
86 %% For example, business users.
87 A particularly interesting application is in mobile networks.
88 As people get more addicted to their smart phones, mobile network
89 operators would need to increase the density in cell sites, making
90 PON a good candidate to deliver the cell site backhaul.
92 As
5G mobile develops, PON may also be useful in the fronthaul.
93 RF receivers relay the signals back to a centralized location
94 for processing, which is seen as a way to reduce operating costs.
99 \frametitle{Direct detection vs coherent receivers
}
102 Direct detection receiver
104 \item Single photodiode with amplifier
105 \item Rx current $
\propto$ received optical power (Phase information lost)
106 \item On-off keying (mainly)
111 \item $
\propto$ real and imaginary parts of received electrical
113 \item Polarization-division multiplexing
114 \item Phase-shift keying, quadrature amplitude modulation
118 \fbox{\includegraphics[height=
.3\paperheight,clip,trim=
40mm
167mm
40mm
55mm
]{coherentRx.pdf
}} \\
119 {\tiny Image credit: Seb J.~Savory, ``Digital filters for coherent
120 optical receivers,''
2008.
}
124 To achieve a high data rate, coherent receivers are to be used.
125 This is different from the direct detection receivers which you may
126 have come across last year in
3B6, where the receiver photocurrent
127 is proportional to the optical power. In a coherent receiver, as illustrated
128 by this example here,
%the light, after passing through a single-mode fibre,
129 %is first split by polarization,
130 %and then the real and imaginary parts of each polarization are detected
131 both the real and imaginary parts of two orthogonal polarizations are detected.
132 This allows different modulation schemes, similar to
133 radio transmissions, such as PSK and QAM.
138 \frametitle{Aims of this project
}
140 \item Build simulation models for optical networks with coherent receivers
141 \item Use DSP to correct for fibre effects
142 \item Simulate different options for achieving
\SI{100}{Gb/s
}
143 \item Experimentally validate simulation results
144 \item Evaluate feasibility to use in PONs
147 In this project, simulation models for optical networks will be
148 built using MATLAB, with digital signal processing to correct
149 for fibre effects. Different options for achieving the target
150 data rate of
100 Gb/s will be simulated and compared, and
151 later experimentally validated. The results will be evaluated
152 in terms of suitability to use in a PON.
157 \frametitle{Simulations performed thus far
}
158 QPSK with symbol rate
\SI{25}{GBd
} over AWGN channel
161 \item Chromatic dispersion
162 \item Adaptive equalizer
163 \item Phase noise (laser linewidth)
169 \bXInput[$x_n$
]{input
}
170 \bXBlocL[3]{p
}{\makecell[c
]{Pulse shaping\\$p(t)$
}}{input
}
172 \bXLink[$x(t)$
]{p
}{AWGN
}
173 \path (AWGN) ++(
0,-
1) node (noise)
{$n(t)$
};
175 \bXBloc[3]{sim1
}{?
}{AWGN
}
177 \bXOutput[3]{y
}{sim1
}
178 \bXLink[$y(t)$
]{sim1
}{y
}
186 \bXBloc[3]{q
}{\makecell[c
]{Matched filter\\$q(t)=p(-t)$
}}{yt
}
187 \bXLink[$y(t)$
]{yt
}{q
}
188 \bXBloc[3]{sampler
}{\makecell[c
]{Sample\\$T_s=
1/R_
\text{sym
}$
}}{q
}
189 \bXLink[$r(t)$
]{q
}{sampler
}
190 \bXBloc[3]{sim2
}{$?'$
}{sampler
}
191 \bXLink[$r_n$
]{sampler
}{sim2
}
192 \bXBlocL[3]{decision
}{Decision
}{sim2
}
193 \bXOutput[3]{xhatn
}{decision
}
194 \bXLink{decision
}{xhatn
}
195 \path (xhatn) ++(
0.2,
0) node
{$
\hat{x
}_n$
};
200 The overall model has this structure, with root-raised cosine
202 The channel is modelled as
203 additive white Gaussian noise, followed by the simulated physical effect.
205 On the receiver side, after analog-to-digital conversion, the
206 received complex symbols $r_n$ are further processed to compensate
207 for channel effects before decision and demodulation.
209 Currently I have based by simulations on a quadriphase-shift keying
210 modulation scheme with
211 $
25\times 10^
9$ symbols per second. QPSK gives two bits per symbol,
212 giving
50 Gb/s. Adding in polarization-division multiplexing,
213 which I haven't done yet, would reach the target of
100 Gb/s.
218 \frametitle{Chromatic dispersion
}
219 \onslide<
1->
{\begin{itemize
}
220 \item Group speed of light varies with wavelength
221 \item Modelled as linear system, impulse response:
223 g(z, t) =
\sqrt{\frac{c
}{\mathrm{j
} D
\lambda^
2 z
}}
224 \exp{\left(
\mathrm{j
} \frac{\pi c
}{D
\lambda^
2 z
} t^
2\right)
}
229 \includegraphics<
2>
[height=
0.4\paperheight]{chromaticDispersionTest.eps
}
230 \includegraphics<
3-
4>
[width=
4cm
]{qpsk_clean.eps
}
231 \includegraphics<
3>
[width=
4cm
]{cd_qpsk_noiseless_Dz17.eps
}
232 \includegraphics<
4>
[width=
4cm
]{cd_qpsk_noiseless_Dz85.eps
}
237 * The first effect investigated was chromatic dispersion.
238 This effect occurs as a result of the speed of light being
239 slightly different at different wavelengths, and lasers have a
240 wavelength band that, although small, still makes a large impact
243 Literature has shown that chromatic dispersion can be modelled
244 as a linear system, with D being the dispersion coefficient and
245 z the distance travelled.
247 * In direct detection receivers, this effect can be seen as a pulse-
248 broadening effect. However, in coherent receivers, we are more interested
249 in the changes to the complex constellation symbols.
251 * Here is a result of a simulation with
17 ps/(nm km) dispersion, with
252 1 kilometre of fibre, in the absence of any additive noise.
253 You can still cleanly decode the symbols without much difficulty.
255 But when we go slightly longer to
5 km...
259 So clearly the receiver needs to do something to mitigate the effects
260 of chromatic dispersion. A linear filter can be used. How do we design
261 this filter? Well, we know the impulse response of the dispersion
262 model, so if we invert the sign of D here...
267 \frametitle{Chromatic dispersion compensation
}
269 g_
\text{c
}(z, t) =
\sqrt{\frac{c
}{\mathrm{j
} (-D)
\lambda^
2 z
}}
270 \exp{\left(
\mathrm{j
} \frac{\pi c
}{(-D)
\lambda^
2 z
} t^
2\right)
}
274 \includegraphics<
2>
[height=
.6\paperheight]{cd_qpsk_Dz3400.eps
}
275 \includegraphics<
3>
[height=
.6\paperheight]{cd_qpsk_Dz34.eps
}
280 * We get the impulse response of the dispersion compensating filter.
282 * Additive noise was added back to the channel, and a million bits were
283 sent through the channel.
284 This is a plot of the bit-error rate, or the probability of decoding
285 a bit incorrectly, against a measure of the signal-to-noise ratio,
286 at a simulated transmission distance of
200 km.
287 We can see that while the magenta curve, that is without any compensation,
288 doesn't do any better than chance,
289 The red curve, which is the simulation result of
290 the compensating filter, does a very good job at approaching the
291 theoretical blue curve of an ideal AWGN channel.
293 * An interesting behaviour was observed when the transmission distance
294 was reduced, in this case, to
2km. We can see that the compensation
295 filter actually does worse, which is counter-intuitive.
297 a reduced number of filter taps when converting this continuous-time
298 filter to a discrete-time filter. We can, of course, add an extra filter
299 to try to correct for this, which brings us to the next topic:
304 \frametitle{Adaptive equalizer
}
306 \item Error of previous symbol fed back to change filter tap weights
307 \item Can correct for static and time-varying effects
308 \item Constant modulus algorithm (CMA)
309 \item For PSK, magnitude of transmitted symbols is constant (unity)
310 \item Error signal is distance of received signal from unit circle
314 Adaptive equalization. Here, the error of the previous symbol is used
315 to update the filter taps, which can correct for static as well as
316 slowly varying effects. In the following simulations, the constant
317 modulus algorithm was implemented. This relies on the fact that, while
318 the receiver doesn't know what symbol was transmitted, it knows, for
319 PSK, that the symbols must lie on a unit circle. The distance from the
320 received signal to the unit circle is thus used as a measure of error.
325 \frametitle{Adaptive equalizer: convergence
}
327 \foreach \x in
{1,
2,
3,
4,
5,
6,
7,
8,
9} {%,10,11,12} {%
328 \includegraphics<
\x>
[height=
0.75\paperheight]{adaptEqAni_
\x.eps
}%
331 \includegraphics<
10>
[height=
0.75\paperheight]{CD+CMA_fin.eps
}
335 * Here is an animation of how the adaptive equalizer converges,
336 again with a small dispersion but without additive noise.
337 %At first it doesn't do much, and the symbols are still quite
339 Initially the symbols are quite widely spread,
340 but as the algorithm runs, /just click through the slides/
342 we can see the equalizer brings the symbols close to
4 single points.
344 * The overall effect can be seen with additive noise added back in,
345 here with the green curve very closely agreeing with the theoretical
351 \frametitle{Laser phase noise
}
353 \item Laser linewidth: deviations from the nominal wavelength
354 \item Instantaneous change in wavelength (frequency) $
\rightarrow$
356 \item $
\phi[k
]$ modelled as
\textit{one-dimensional Gaussian random walk
}
358 \phi[k
] =
\phi[k-
1] +
\Delta\phi
361 \text{where
}\quad\Delta\phi \sim \mathcal{N
}(
0,
2 \pi \Delta\nu T_s)
365 \includegraphics[height=
.5\paperheight]{../phasenoise_linewidths.eps
}
369 The next effect investigated was laser phase noise. This arises as the
370 true laser wavelength is a slight deviation from the nominal central
371 wavelength within the linewidth.
372 This instantaneous change in wavelength can be modelled as
373 a phase shift. Literature suggests a one-dimensional Gaussian
374 walk model, where each sample of the phase differs
375 from the previous sample with a random delta phi drawn from a Gaussian
376 distribution, with zero mean and whose variance is proportional to both the linewidth
377 delta nu and the sampling time $T_s$.
382 \frametitle{Laser phase noise
}
384 \item Rotates symbol constellation
385 \item Problematic, e.g.~for QPSK, rotation by $
\pi/
2$ gives another
386 constellation with all symbols decoded wrongly
389 \includegraphics[height=
.6\paperheight]{../phasenoise_rotation.eps
}
393 The effect of phase noise is a rotation of the constellation symbols
394 by an arbitrary amount, which is very problematic for PSK modulation
395 as this would mean completely incorrect decoding.
400 \frametitle{Laser phase noise: solutions
}
402 \begin{column
}{0.5\textwidth}
404 \item Differential PSK
405 \item Information encoded as the difference in phase with previous
407 \item Difference in phase noise between consecutive symbols small
408 \item \SI{2.5}{dB
} penalty at $
\text{BER
} =
10^
{-
3}$
411 \begin{column
}{0.5\textwidth}
413 \item Estimate phase noise by Viterbi-Viterbi algorithm
414 \item Taking average over a small block of samples
418 \includegraphics[height=
.5\paperheight]{../phasenoise_estimation.eps
}
424 We will consider two methods to mitigate this effect. The first is to
425 use a differential PSK scheme, where the information is encoded not as
426 the absolute phase, but as a difference in phase with the previous
427 symbol. This works relying on the assumption that the phase noise between
428 two consecutive symbols is sufficiently smaller than
90 degrees.
429 However, by considering two
430 symbols together, the effect of phase noise is enhanced,
431 translating to a penalty in the signal-to-noise ratio.
433 Another method is to estimate the amount of phase noise in each symbol
434 and to rotate the symbols back by the estimated amount.
435 The Viterbi-Viterbi algorithm, very briefly,
436 works by taking an average over
437 a block of samples to estimate the average phase noise in that block.
442 \frametitle{Cycle slips
}
444 \begin{column
}[t
]{0.5\textwidth}
446 \item<
1-> At large linewidths, Viterbi-Viterbi algorithm can
448 \item<
1-> For QPSK the phase estimate can be off by $
\pi/
2$
449 \item<
1-> All subsequent symbols will be decoded incorrectly\\
[1em
]
450 \item<
3-> Solution: Differential encoding
455 \begin{column
}[t
]{0.5\textwidth}
457 \includegraphics<
1>
[width=
\textwidth]{../cycleslip.eps
}
459 \includegraphics<
2-
3>
[width=
\textwidth]{../phasenoise_ult_sansDE.eps
}
461 \includegraphics<
4>
[width=
\textwidth]{../phasenoise_ult.eps
}
465 This estimation algorithm does not always work though. Sometimes, due to noise,
466 a cycle slip would occur, which results in a systematic error of
90 degrees.
467 This means that all the following symbols would actually be decoded
470 * We can see in this simulation result that, when a cycle slip does not
471 occur, the performance is much closer to the ideal curve than using
472 differential PSK, but when it does occur the result is disastrous.
474 Can we get the best of both worlds, with a small penalty but without
477 * The answer is yes, with a differential *encoding*. Note that this is
478 different from differential PSK. Differential encoding is an operation
479 on the bits, and the receiver would perform differential decoding
480 on the bits *after* choosing the closest constellation symbols.
481 Whereas in DPSK the receiver evaluates the difference in phase between
482 the received samples directly, before converting them to bits.
484 * The result is this cyan curve, with a smaller penalty than DPSK, and
485 not affected by cycle slips.
490 \frametitle{What next?
}
492 \item Integrating CD and phase noise into a single system
493 \item Adaptive equalizer
496 \item Decision-directed algorithms
497 \item Training sequences
500 \item Polarization-division multiplexing
502 \item Polarization mode dispersion
503 \item Adaptive equalizer
505 \item Non-linear effects
508 That's all I have done as of now. Looking forward, simulations
509 would need to integrate both effects into a single channel.
510 Further investigations into adaptive equalizers can also be done.
511 %For example, their convergence with different number of taps or
512 %with different convergence parameters, and also different algorithms
513 For example, the use of decision-directed algorithms,
514 %%such as decision-directed algorithms,
515 and to train the equalizer
516 with pre-known sequences, to increase accuracy at the cost of losing
519 Other modulation schemes can also be investigated, such as
521 It would require careful alterations to existing implementations,
522 for example with the constant modulus algorithm, but can reduce the
523 required symbol rate.
525 The simulations performed only considered a single polarization.
526 Further investigations should be done to send data through one more
527 polarization, and the resulting effect of polarization mode dispersion
528 needs to be addressed. Adaptive equalizers for PDM signals also need
531 Finally, non-linear fibre effects can also be considered.
533 All these should hopefully be done before mid-Lent, leaving sufficient
534 time for experimental measurements.
536 That's all I've got. Thank you.
541 \setbeamercolor{background canvas
}{bg=black
}
542 \setbeamertemplate{navigation symbols
}{}
543 \begin{frame
}[plain,noframenumbering
]{}
547 \begin{frame
}[noframenumbering
]
548 \frametitle{Viterbi-Viterbi algorithm
}
549 Assume $
\hat{\phi}\;
\approx\;
\phi[1] \approx \phi[2] \approx \cdots \approx \phi[N
]$
551 r
[k
] &=
\exp\left(
\mathrm j
\phi[k
] +
\mathrm j
\frac \pi 4 +
\mathrm j
552 \frac {d
[k
] \pi} 2\right) + n
[k
] \\
553 r
[k
]^
4 &=
\exp\left(
\mathrm j
4 \phi[k
] +
\mathrm j
\pi\right) + n'
[k
]
555 \sum_{k=
1}^
{N
} r
[k
]^
4 &
\approx N
\exp\left(
\mathrm j
4 \hat{\phi} +
\mathrm j
\pi\right) + n''\\
[1.5em
]
556 \hat{\phi} &
\approx \frac14 \arg\left( -
\sum_{k=
1}^
{N
} r
[k
]^
4 \right)