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1 | \documentclass[a4paper,12pt,twocolumn]{article} |
2 | \usepackage{authblk} | |
3 | \usepackage{siunitx} | |
4 | \sisetup{group-digits=false} | |
5 | \title{\SI{100}{GbE} Passive Optical Access Networks\\Technical Milestone Report} | |
6 | \author{Adrian I.~Lam\vspace{-1em}\\Supervised by Dr.~Seb Savory} | |
7 | \date{16 January 2019} | |
8 | ||
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16 | pdftitle={Technical Milestone Report}, | |
17 | pdfauthor={ail30}, | |
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82 | ||
83 | \begin{document} | |
84 | \maketitle | |
85 | ||
86 | \begin{abstract} | |
87 | This project aims at evaluating methods of achieving a \SI{100}{Gb/s} | |
88 | Ethernet passive optical access network. An optical link based on | |
89 | coherent receivers will be considered, and a computer model | |
90 | will be built using \MATLAB{} to simulate various physical effects | |
91 | in the optical fibre. Digital signal processing techniques will be | |
92 | employed to correct for these effects and demodulate the transmitted | |
93 | symbols. Currently, all relevant linear effects have been successfully | |
94 | simulated and compensated for, while non-linear effects have not been | |
95 | completed yet. After the model is complete, different designs of the | |
96 | network, such as using different modulation schemes or multiplexing | |
97 | methods, can be simulated and their performance compared, and the | |
98 | feasibility to use them in an access network will be discussed. | |
99 | The results may also be verified through off-line processing of | |
100 | real measured data. | |
101 | \end{abstract} | |
102 | ||
103 | \section{Introduction and Motivation} | |
104 | A passive optical network (PON) is a point-to-multipoint system | |
105 | where data for all users of the network, modulated onto an | |
106 | optical signal, leaves the optical line terminal at the service | |
107 | provider, and is carried along a fibre feeder, then split | |
108 | by an unpowered beam splitter, without any routing or selection, | |
109 | to separate distribution fibres reaching the optical network units | |
110 | of the users~\cite[\S6.1]{PONintro}. This design allows high-speed | |
111 | communication for a large number of consumers, with relatively low cost | |
112 | for each user~\cite{NGPON2-1}, and is currently typically employed | |
113 | in a fibre-to-the-home setting~\cite{ponroadmap}. | |
114 | ||
115 | Fibre-to-the-home applications are already well-served by the | |
116 | currently mature implementation of \SI{1}{Gb/s} PONs, which may | |
117 | make higher speed PON seem unnecessary. However, there are many more | |
118 | future applications that could potentially benefit from a | |
119 | \SI{100}{Gb/s} PON. By designing future PON specifications to be | |
120 | compatible with existing fibre installations, less installation | |
121 | costs will be incurred, allowing the mixing of | |
122 | more applications onto the same network, thus increasing | |
123 | revenues for service providers. In addition, as more and more | |
124 | people rely on mobile networks for their daily communication | |
125 | and entertainment needs, mobile operators are looking to increase | |
126 | the density in cell sites, making PONs a good candidate to deliver | |
127 | the cell data backhaul. As the 5G mobile standard develops, PONs | |
128 | may even be useful in the fronthaul, where | |
129 | radio signals were sampled and relayed, | |
130 | through a PON, to a centralized | |
131 | location for digital signal processing (DSP), seen as a way to | |
132 | reduce costs~\cite{ponroadmap}. | |
133 | ||
134 | The use of coherent receivers in a high-speed PON is considered. | |
135 | In contrast to direct detection receivers, both the real and imaginary | |
136 | parts of each polarization of the received electrical field can be | |
137 | detected separately | |
138 | in a coherent receiver. This makes complex modulation schemes such | |
139 | as phase-shift keying (PSK) or quadrature amplitude modulation | |
140 | (QAM) possible, and combined with polarization-division multiplexing (PDM), | |
141 | makes very high data rates possible~\cite[\S5.6]{foc},~\cite{savorydigital}. | |
142 | ||
143 | In this project, a model to simulate the various physical effects in | |
144 | an optical channel is to be built. DSP will | |
145 | then be used to attempt to correct for these effects to recover the | |
146 | original signal. Using this model, different options for achieving a | |
147 | \SI{100}{Gb/s} PON will be compared. The response of a real channel | |
148 | will then be measured and, using the DSP techniques investigated, | |
149 | processed offline to verify the model and the correction methods. | |
150 | Feasibility of employing these techniques in a commercial PON setting | |
151 | will also be discussed. | |
152 | ||
153 | The current progress in developing the simulation model is detailed | |
154 | in \Cref{sec:simmodel}, with future plans listed in | |
155 | \Cref{sec:future}. | |
156 | ||
157 | \section{The Simulation Model} \label{sec:simmodel} | |
158 | ||
159 | \begin{figure*}[tb] | |
160 | \centering | |
161 | \begin{tikzpicture} | |
162 | \small | |
163 | \bXInput[$x_n$]{input} | |
164 | \bXBlocL[3]{p}{\makecell[c]{Pulse shaping\\$p(t)$}}{input} | |
165 | ||
166 | \bXBloc[3]{sim1}{Fibre-optic link}{p} | |
167 | \bXLink[$x(t)$]{p}{sim1} | |
168 | ||
169 | \bXSumb*[6]{AWGN}{sim1} | |
170 | \bXLink{sim1}{AWGN} | |
171 | \path (AWGN) ++(0,-1) node (noise) {$n(t)$}; | |
172 | \bXLink{noise}{AWGN} | |
173 | ||
174 | \bXOutput[3]{y}{AWGN} | |
175 | \bXLink[$y(t)$]{AWGN}{y} | |
176 | \end{tikzpicture} | |
177 | ||
178 | \begin{tikzpicture} | |
179 | \small | |
180 | \bXInput{yt} | |
181 | \bXBloc[3]{q}{\makecell[c]{Matched filter\\$q(t)=p(-t)$}}{yt} | |
182 | \bXLink[$y(t)$]{yt}{q} | |
183 | \bXBloc[3]{sampler}{\makecell[c]{Sample\\$T_s=1/R_\text{sym}$}}{q} | |
184 | \bXLink[$r(t)$]{q}{sampler} | |
185 | \bXBloc[3]{sim2}{\makecell[c]{Channel\\equalization}}{sampler} | |
186 | \bXLink[$r_n$]{sampler}{sim2} | |
187 | \bXBlocL[3]{decision}{Decision}{sim2} | |
188 | \bXOutput[2.5]{xhatn}{decision} | |
189 | \bXLink{decision}{xhatn} | |
190 | \path (xhatn) ++(0.3,0) node {$\hat{x}_n$}; | |
191 | \end{tikzpicture} | |
192 | \caption{Block diagram of the | |
193 | simulation model.} | |
194 | \label{fig:model} | |
195 | \end{figure*} | |
196 | ||
197 | \Cref{fig:model} shows the current basic model, | |
198 | involving a transmitter with a root-raised | |
199 | cosine pulse shaping filter, processed to simulate the various | |
200 | physical effects, then | |
201 | transmitted through an additive white | |
202 | Gaussian noise (AWGN) channel to a receiver with a matched filter. | |
203 | The received signal is then sampled and DSP is used to correct for | |
204 | the physical effects in the electrical domain. The demodulated signal | |
205 | is then compared to the original pseudorandom data, to obtain a | |
206 | measurement of the bit-error rate (BER) using a Monte-Carlo approach. | |
207 | Currently, the main modulation scheme considered is quadrature | |
208 | phase-shift keying (QPSK), with Gray coding. | |
209 | ||
210 | The effects considered are enumerated below. The results of the | |
211 | methods used to correct for the effects are compared to the ideal | |
212 | AWGN channel. | |
213 | ||
214 | \subsection{Chromatic Dispersion} \label{sec:CD} | |
215 | Chromatic dispersion (CD) is the effect of the group speed of light varying | |
216 | with the wavelength of the optical signal~\cite[\S2.7.3]{foc}. It can be | |
217 | modelled as a linear system, with transfer function in the Fourier | |
218 | domain | |
219 | \[ | |
220 | G(z, \omega) = \exp\left( -\imj \frac{D\lambda^2 z}{4\pi c} \omega^2\right) | |
221 | \] or with impulse response in the time domain | |
222 | \begin{equation} | |
223 | g(z, t) = \sqrt{\frac{c}{\imj D \lambda^2 z}} | |
224 | \exp\left( \imj \frac{\pi c}{D\lambda^2 z} t^2\right) | |
225 | \label{eq:CDimpresp} | |
226 | \end{equation} | |
227 | with $z$ being the transmitted distance, $c$ the speed of light | |
228 | in vacuum, $\lambda$ the wavelength in vacuum, and $D$ the dispersion | |
229 | parameter of the fibre~\cite{savorydigital}. For all simulations | |
230 | below, $D=\SI{17}{ps/(nm.km)}$. | |
231 | ||
232 | Using this model, constellation diagrams were obtained and | |
233 | shown in \Cref{fig:CDconst}. It can be seen that over long | |
234 | distances, CD would make demodulation very difficult, and as | |
235 | such, it is necessary to compensate for this effect. Current | |
236 | systems use dispersion compensating fibres, but DSP may be applied | |
237 | instead to reduce cost~\cite{savorydigital}. It is noted that | |
238 | by inverting the sign of $D$ in | |
239 | \Cref{eq:CDimpresp}, the impulse response of the dispersion compensating | |
240 | filter is obtained, and with truncation and discretization, | |
241 | can be implemented as a simple tapped delay line~\cite{savorydigital}. | |
242 | ||
243 | \begin{figure}[htb] | |
244 | \centering | |
245 | \begin{subfigure}[t]{0.22\textwidth} | |
246 | \includegraphics[width=\textwidth]{cd_qpsk_noiseless_Dz17_new.eps} | |
247 | \caption{$z=\SI{1}{km}$.} | |
248 | \end{subfigure} | |
249 | \begin{subfigure}[t]{0.22\textwidth} | |
250 | \includegraphics[width=\textwidth]{cd_qpsk_noiseless_Dz85_new.eps} | |
251 | \caption{$z=\SI{5}{km}$.} | |
252 | \end{subfigure} | |
253 | \caption{QPSK constellation after chromatic dispersion, | |
254 | without AWGN.} | |
255 | \label{fig:CDconst} | |
256 | \end{figure} | |
257 | ||
258 | \Cref{fig:CDCompz200} shows the dispersion compensating filter in | |
259 | action. The resulting BER very closely resembles that of the ideal | |
260 | AWGN, thus verifying the implementation. | |
261 | ||
262 | \begin{figure}[htb] | |
263 | \centering | |
264 | \includegraphics[width=.44\textwidth]{CDCompz200.eps} | |
265 | \caption{QPSK signal with simulated chromatic dispersion and | |
266 | CD compensation, over an AWGN channel, with | |
267 | $z=\SI{200}{km}$.} | |
268 | \label{fig:CDCompz200} | |
269 | \end{figure} | |
270 | ||
271 | \subsection{Adaptive Equalizer} | |
272 | Adaptive equalizers can be used to correct for time-varying effects, | |
273 | an example of which is polarization dependent effects. | |
274 | \cite{savorydigital} discusses the implementation of adaptive | |
275 | equalization to PDM signals. | |
276 | This has yet to be implemented in the simulation model. | |
277 | ||
278 | On the other hand, an implementation for a single polarization | |
279 | state has been done. This would be useful for correcting for | |
280 | fluctuations to the environment~\cite[\S11.6.1]{foc}, | |
281 | not simulated in the model, but would be present in real life. | |
282 | In addition, | |
283 | it was observed that the CD compensating filter discussed | |
284 | in \Cref{sec:CD} does not perform very well over short | |
285 | distances, as can be seen in \Cref{fig:CDCompz2}, due to | |
286 | truncation of the non-causal infinite-length impulse response. | |
287 | Adaptive equalization was attempted to correct for this effect | |
288 | as well. | |
289 | ||
290 | Two types of equalizing algorithms are typically considered, namely | |
291 | the constant modulus algorithm (CMA) and the decision-directed | |
292 | least mean square (DD-LMS) algorithm~\cite[\S11.6.1]{foc}. | |
293 | CMA has been implemented due to its | |
294 | simplicity. If time permits, DD-LMS can also be attempted. | |
295 | ||
296 | The CMA relies on the fact that for PSK signals, the transmitted | |
297 | symbols all have unit amplitude. As a result, it attempts to minimize | |
298 | the distance between the signal and the unit circle. | |
299 | \Cref{fig:adaptBefAft} illustrates the adaptive nature of the algorithm. | |
300 | \Cref{fig:CDCompz2} demonstrates the success of the CMA, bringing | |
301 | the performance curve back to the theoretical values. | |
302 | ||
303 | \begin{figure}[htb] | |
304 | \centering | |
305 | \includegraphics[width=.44\textwidth]{CDCompz2.eps} | |
306 | \caption{QPSK signal with CD, CD compensation, and CMA adaptive | |
307 | equalizer, over an AWGN channel, with $z=\SI{2}{km}$.} | |
308 | \label{fig:CDCompz2} | |
309 | \end{figure} | |
310 | ||
311 | \begin{figure}[htb] | |
312 | \centering | |
313 | \begin{subfigure}[t]{.22\textwidth} | |
314 | \centering | |
315 | \includegraphics[width=\textwidth]{adaptBefore.eps} | |
316 | \caption{Symbols 1 to 500.} | |
317 | \end{subfigure}% | |
318 | \begin{subfigure}[t]{.22\textwidth} | |
319 | \centering | |
320 | \includegraphics[width=\textwidth]{adaptAfter.eps} | |
321 | \caption{Symbols 2001 to~2500.} | |
322 | \end{subfigure} | |
323 | \caption{Constellations showing the adaptive behaviour of | |
324 | the CMA.} | |
325 | \label{fig:adaptBefAft} | |
326 | \end{figure} | |
327 | ||
328 | \subsection{Phase Noise Correction} | |
329 | Lasers used in the transmitter and the receiver local oscillator | |
330 | have a linewidth $\Delta\nu$ over which random frequency deviations | |
331 | occur, resulting in a phase noise in the signal. When discretized, | |
332 | the phase noise $\phi[k]$ can be modelled as a one-dimensional | |
333 | Gaussian random walk, | |
334 | \begin{gather*} | |
335 | \phi[k] = \phi[k-1] + \Delta\phi_k \\ | |
336 | \qq*{where} \Delta\phi_k | |
337 | \mathrel{\overset{\makebox[0pt]{\mbox{\normalfont\tiny\sffamily i.i.d.}}}{\sim}} | |
338 | \mathcal{N}(0, 2\pi \Delta\nu T_s) | |
339 | \quad\text{for all }k, | |
340 | \end{gather*} | |
341 | with $T_s$ being the sampling period~\cite[\S11.3]{foc}. | |
342 | ||
343 | The effect of phase noise can be most easily understood from a plot | |
344 | of the constellation, as shown in \Cref{fig:phaseNoiseCircle}. | |
345 | Demodulation is | |
346 | impossible without any correction. Fortunately there are various | |
347 | techniques to mitigate this issue, and two of them are discussed | |
348 | below. | |
349 | ||
350 | \subsubsection{Differential PSK} | |
351 | In a normal PSK scheme, information is modulated as the | |
352 | phase of each transmitted symbol. In contrast, in differential PSK (DPSK), | |
353 | information is modulated as the \emph{difference} in phase between | |
354 | two consecutive symbols~\cite[\S7.3.2]{ccsm}. | |
355 | It can mitigate the effect of phase noise | |
356 | if the linewidth is small (such that $\Delta\phi_k$ is sufficiently | |
357 | smaller than, for example, $\pi/4$ for QPSK). Phase noise would then | |
358 | have little influence to the phase difference between consecutive | |
359 | symbols. | |
360 | ||
361 | It was however noted that in DPSK, the demodulator is affected | |
362 | ``twice'' by phase noise. This increases the noise variance, | |
363 | making bit errors more likely~\cite[\S7.3.2]{ccsm}. | |
364 | This can be seen (among other results) in \Cref{fig:phasenoise_ult}. | |
365 | This translates to | |
366 | a SNR penalty compared to the normal PSK scheme. At a BER of | |
367 | $10^{-3}$, the penalty is about \SI{2.5}{dB}. | |
368 | ||
369 | \subsubsection{Block phase noise estimation} | |
370 | The phase noise can also be estimated assuming the total phase noise | |
371 | over a small number of symbols is small. The Viterbi-Viterbi algorithm | |
372 | used is best illustrated by an example. Consider a QPSK scheme. At the | |
373 | receiver, the received signal $r[k]$ is given by | |
374 | \[ | |
375 | r[k] = \exp\left( \imj \phi[k] + \imj \frac{\pi}{4} + | |
376 | \imj \frac{d[k]\pi}{2} \right) + n[k] | |
377 | \] | |
378 | where $\phi[k]$ is the unknown phase of the $k$th symbol, | |
379 | $d[k] \in \{0, 1, 2, 3\}$ is the transmitted data, and | |
380 | $n[k]$ is AWGN. Taking the signal to the 4th power eliminates | |
381 | $d[k]$ from the expression, resulting in | |
382 | \begin{equation} | |
383 | r[k]^4 = \exp\left( \imj 4\phi[k] + \imj \pi\right) + n'[k] | |
384 | \label{eq:rk4} | |
385 | \end{equation} | |
386 | where $n'[k]$ are the terms involving $n[k]$. It can be shown | |
387 | that $n'[k]$ has zero mean, thus if $\phi[k]$ does not vary | |
388 | much over a small range of $k$, then its value can be estimated | |
389 | by averaging over that range (thus eliminating $n'[k]$)~\cite[\S11.5]{foc}. | |
390 | \Cref{fig:viterbiphest} shows the algorithm | |
391 | estimating the phase of a noisy signal. | |
392 | ||
393 | With a phase estimation method available, the effect of phase noise | |
394 | can be undone simply by adding a reversed phase shift. | |
395 | ||
396 | \begin{figure}[htb] | |
397 | \centering | |
398 | \begin{subfigure}[t]{.22\textwidth} | |
399 | \centering | |
400 | \includegraphics[width=\textwidth]{phaseNoiseCircle.eps} | |
401 | \caption{Phase noise randomly rotating the constellation.} | |
402 | \label{fig:phaseNoiseCircle} | |
403 | \end{subfigure}% | |
404 | \begin{subfigure}[t]{.22\textwidth} | |
405 | \centering | |
406 | \includegraphics[width=\textwidth]{phaseEst.eps} | |
407 | \caption{Example of the Viterbi-Viterbi algorithm | |
408 | estimating phase noise.} | |
409 | \label{fig:viterbiphest} | |
410 | \end{subfigure} | |
411 | \caption{Phase noise, and how it affects the received symbols.} | |
412 | \end{figure} | |
413 | ||
414 | However, at larger linewidths, phase estimation may make mistakes. | |
415 | This is due to the ambiguity in \Cref{eq:rk4}, where in QPSK an | |
416 | additional phase increase of $\pi/2$ gives the same solution, | |
417 | and phase noise makes unambiguous phase unwrapping impossible. | |
418 | This is known as a \emph{cycle slip}~\cite{taylorphest}, and | |
419 | is illustrated in \Cref{fig:cycleslip}. | |
420 | ||
421 | The result of a particular run of the simulation is shown in | |
422 | \Cref{fig:phasenoise_ult}. | |
423 | It can be seen that when cycle slips do not occur, the resulting | |
424 | BER is much closer to the theoretical AWGN channel compared to | |
425 | DPSK. However, if a cycle slip occurs, all the subsequent symbols | |
426 | will be demodulated incorrectly~\cite{taylorphest}, | |
427 | giving very poor performance. | |
428 | ||
429 | To eliminate the effect of cycle slips, principles from DPSK | |
430 | can be incorporated into the phase estimation method, but instead | |
431 | of differentially modulating the \emph{symbols}, the source | |
432 | \emph{bit stream} is differentially \emph{encoded}. This is known | |
433 | as \emph{differentially encoded} PSK (DEPSK). At the receiver, the | |
434 | symbols are corrected after phase estimation (as above), and then | |
435 | demodulated like conventional PSK, before differentially decoding | |
436 | the bits. While this method transforms a single bit error into | |
437 | a pair of bit errors~\cite{taylorphest}, it has a smaller SNR | |
438 | penalty than DPSK~\cite[Ch.~13]{matlabcomm}, since the | |
439 | noise variance | |
440 | is not increased like it is in DPSK. \Cref{fig:phasenoise_ult} also | |
441 | shows the result of DEPSK, which is immune to cycle slips, with | |
442 | a smaller SNR penalty than DPSK. Many forward error correction | |
443 | codes can effectively correct for short bursts of bit errors, | |
444 | thus further reducing the penalty~\cite{taylorphest}, however | |
445 | this will not be investigated in this project. | |
446 | ||
447 | \begin{figure}[htb] | |
448 | \centering | |
449 | %\begin{subfigure}[t]{.22\textwidth} | |
450 | %\centering | |
451 | \includegraphics[width=.3\textwidth]{cycleslip.eps} | |
452 | \caption{A cycle slip.} | |
453 | \label{fig:cycleslip} | |
454 | %\end{subfigure}% | |
455 | %\begin{subfigure}[t]{.22\textwidth} | |
456 | % \centering | |
457 | % \includegraphics[width=\textwidth]{adaptAfter.eps} | |
458 | % \caption{Symbols 2001 to~2500.} | |
459 | %\end{subfigure} | |
460 | %\caption{Constellations showing the adaptive behaviour of | |
461 | %the CMA.} | |
462 | \end{figure} | |
463 | ||
464 | \begin{figure}[htb] | |
465 | \centering | |
466 | \includegraphics[width=.44\textwidth]{phasenoise_ult.eps} | |
467 | \caption{Performance of various methods under a phase noise | |
468 | of \SI{10}{MHz}, on a particular run of the simulation.} | |
469 | \label{fig:phasenoise_ult} | |
470 | \end{figure} | |
471 | ||
472 | ||
473 | \subsection{Non-linearity: Kerr Effect} | |
474 | Kerr effect is one of the non-linear effects investigated in this | |
475 | project. Kerr effect describes the change in refractive index of | |
476 | a material as the optical power of the incident beam changes. | |
477 | The result is a phase shift proportional to the optical power | |
478 | (i.e.~the square of the electric field, hence | |
479 | non-linear)~\cite[\S10.2]{foc},~\cite[\S6.2.2]{nfo}. | |
480 | To numerically simulate this effect together with other linear effects, | |
481 | the \emph{split-step Fourier method} is used. In brief, the fibre | |
482 | length is divided into many small bits. The signal is first transformed | |
483 | to the Fourier domain, and chromatic dispersion is applied | |
484 | (as in \Cref{sec:CD}). The signal is then transformed back to the time | |
485 | domain and its power is calculated. From this, the corresponding | |
486 | phase shift due to Kerr effect can be applied. This process repeats | |
487 | until the total simulated length reaches the desired transmission | |
488 | distance~\cite[\S2.4.1, App.~B]{nfo}. | |
489 | ||
490 | Currently, the general structure of the split-step Fourier method | |
491 | has been coded, but there are small problems that require fixing, | |
492 | and as such results are yet to be included in this report. However, | |
493 | the general shape of the resulting curve matches existing | |
494 | literature~\cite{savory100Gbps}, | |
495 | so there should be little difficulty in having it completed soon. | |
496 | ||
497 | \section{Future Plan and Timeline} \label{sec:future} | |
498 | After completing the simulation for Kerr effect, the most important | |
499 | task would be to integrate all the effects into a single simulation | |
500 | program, to prepare for the final model to evaluate different | |
501 | transmission schemes. | |
502 | Afterwards, it was planned to have a more realistic | |
503 | model of the noise -- the AWGN channel would be replaced with | |
504 | a combination of thermal noise (which can be modelled as | |
505 | AWGN)~\cite[\S8.1.1]{aoe} | |
506 | and shot noise. Finally, PDM and wavelength-division | |
507 | multiplexing would | |
508 | be implemented to have a ``complete'' model. To have sufficient | |
509 | time for the remaining parts of the project, it was planned to have | |
510 | this completed by week 3 of Lent term, i.e.\ about one week for | |
511 | each of the three tasks. | |
512 | ||
513 | A few different designs of the network will be evaluated and compared, | |
514 | and the suitability to use in a PON will be discussed. Running the | |
515 | simulation a few times with different parameters should not take | |
516 | too much time, but discussing real-life feasibility may involve | |
517 | more review of current literature, so an estimate of 2 weeks is | |
518 | reserved for this. | |
519 | ||
520 | The final three weeks of Lent will be spent obtaining experimental | |
521 | data and verifying simulation results, to make further adjustments | |
522 | to the model if necessary, and to prepare | |
523 | for the final report and presentation. | |
524 | ||
525 | It is expected that most of the Easter vacation would be spent preparing | |
526 | for the examinations. Work on the final report and presentation would | |
527 | resume after that, which should be enough time to meet the deadline | |
528 | in week 5 of Easter term. | |
529 | ||
530 | \begin{thebibliography}{10} | |
531 | \bibitem{PONintro} | |
532 | C.C.K.~Chan, | |
533 | ``Protection architectures for passive optical networks,'' in | |
534 | \textit{Passive Optical Networks: Principles and Practice}, | |
535 | C.F.~Lam, Ed. | |
536 | Burlington, MA: Academic Press, 2007, pp.~243-266. | |
537 | \bibitem{NGPON2-1} | |
538 | J.S.~Wey \textit{et al.}, | |
539 | ``Physical layer aspects of NG-PON2 standards -- Part 1: | |
540 | optical link design,'' | |
541 | \textit{J.~Opt.\ Commun.\ Netw.}, vol.~8, no.~1, pp.~33-42, 2016. | |
542 | doi:10.1364/JOCN.8.000033 | |
543 | \bibitem{ponroadmap} | |
544 | D.~Nesset, ``PON Roadmap,'' | |
545 | \textit{J.~Opt.\ Commun.\ Netw.}, vol.~9, no.~1, pp.~A71-A76, 2017. | |
546 | doi:10.1364/\allowbreak JOCN.9.000A71 | |
547 | \bibitem{foc} | |
548 | S.~Kumar and M.J.~Deen, | |
549 | \textit{Fiber Optic Communications: Fundamentals and Applications}. | |
550 | Chichester, UK: Wiley, 2014. | |
551 | \bibitem{savorydigital} | |
552 | S.J.~Savory, ``Digital filters for coherent optical receivers,'' | |
553 | \textit{Opt.\ Express}, vol.~16, no.~2, pp.~804-817, 2008. | |
554 | doi:10.1364/OE.16.000804 | |
555 | \bibitem{ccsm} | |
556 | J.G.~Proakis and M.~Salehi, | |
557 | \textit{Contemporary Communication Systems Using \MATLAB}. | |
558 | Pacific Grove, CA: Brooks/Cole, 2000. | |
559 | \bibitem{taylorphest} | |
560 | M.G.~Taylor, ``Phase estimation methods for optical coherent | |
561 | detection using digital signal processing,'' | |
562 | \textit{J.~Lightwave Technol.}, vol.~27, no.~7, pp.~901-914, 2009. | |
563 | doi:10.1109/JLT.2008.927778 | |
564 | \bibitem{matlabcomm} | |
565 | The MathWorks, Inc., | |
566 | \textit{Communications Toolbox\textnormal{\texttrademark{}} User's Guide} | |
567 | (R2018b), | |
568 | 2018. [Online]. Available: | |
569 | \url{https://www.mathworks.com/help/pdf_doc/comm/comm.pdf}. | |
570 | [Accessed: Jan.~9, 2019]. | |
571 | \bibitem{nfo} | |
572 | G.P.~Agrawal, | |
573 | \textit{Nonlinear Fiber Optics}, 5th ed. | |
574 | Oxford, UK: Academic Press, 2013. | |
575 | \bibitem{savory100Gbps} | |
576 | Md.S.~Faruk, D.J.~Ives, and S.J.~Savory, | |
577 | ``Technology requirements for an Alamouti-coded \SI{100}{Gb/s} | |
578 | digital coherent receiver using $3\times3$ couplers for | |
579 | passive optical networks,'' | |
580 | \textit{IEEE Photon.\ J.}, vol.~10, no.~1, 2018. | |
581 | doi:10.1109/JPHOT.2017.2788191 | |
582 | \bibitem{aoe} | |
583 | P.~Horowitz and W.~Hill, | |
584 | \textit{The Art of Electronics}, 3rd ed. | |
585 | New York: Cambridge University Press, 2015. | |
586 | \end{thebibliography} | |
587 | ||
588 | \end{document} |