Access Networks
Burst-mode Electronic Equalization for Future Optical
Academic year 2019-2020
Master of Science in Electrical Engineering - main subject Electronic Circuits and Systems Master's dissertation submitted in order to obtain the academic degree of
Counsellors: Dr. ir. Gertjan Coudyzer, Prof. dr. ir. Johan Bauwelinck Supervisors: Prof. dr. Xin Yin, Dr. ir. Peter Ossieur
Student number: 01500081
Access Networks
Burst-mode Electronic Equalization for Future Optical
Academic year 2019-2020
Master of Science in Electrical Engineering - main subject Electronic Circuits and Systems Master's dissertation submitted in order to obtain the academic degree of
Counsellors: Dr. ir. Gertjan Coudyzer, Prof. dr. ir. Johan Bauwelinck Supervisors: Prof. dr. Xin Yin, Dr. ir. Peter Ossieur
Student number: 01500081
Preface
As I am getting closer to finishing this Master’s dissertation, I am also getting closer to finishing this part of my education here at Ghent University. I started here, 5 years ago, a fresh-out-of high school teen, with little electronics experience. It is hard to fathom just how much I have learned over these past 5 years. I am grateful for the opportunity to have learned so much from the present knowledge here at Ghent University, in electronics and non-electronics related topics. Every lecture, project, exam or field trip, has made me into the engineer I will be, when I graduate.
I would like to thank all professors and staff of Ghent University for making this such an informative and pleasant time. In particular I would like to thank prof. dr. ir. Johan Bauwelinck, dr. ir. Peter Ossieur and prof. dr. Xin Yin for the guidance in this thesis and the opportunity to continue my career here in the form of a PhD at this department. Special thanks go to dr. ir. Gertjan Coudyzer for the very elaborate guidance and help during this thesis, which was definitely required to reach this final result. To all my friends here at the engineering faculty and over the entire Ghent University, I want to say thank you, for making these last 5 years of my life unforgettable. Being a student in such a vibrant and beautiful city, truly is the time of one’s life.
Finally, to my parents and my sister, I want to express the greatest gratitude for making my home a pleasant working environment during corona virus quarantine and for keeping my mood up, in these particular times.
Admission to loan
The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In all cases of other use, the copyright terms have to be respected, in particular with regard to the obligation to state explicitly the source when quoting results from this master dissertation.
Borre Van Lombergen May, 2020
Burst-mode Electronic Equalization for Future
Optical Access Networks
By Borre Van Lombergen
Student number: 01500081
Supervisors: prof. dr. Xin Yin, dr. ir. Peter Ossieur
Counsellors: dr. ir. Gertjan Coudyzer, prof. dr. ir. Johan Bauwelinck
Master’s dissertation submitted in order to obtain the academic degree of Master of Science in Electrical Engineering - main subject Electronic Circuits and Systems
Academic year 2019-2020
Summary
The research and standardization being done for 25G TDM PON for bitrates of 25G and beyond brings with it the need for high speed burst-mode receivers at the optical line terminal (OLT) of the passive optical network (PON). A vital component here is the burst-mode equalizer, used to compensate for the distortion introduced by the channel, which becomes significant at bitrates of 25G and beyond. This thesis presents a new fully analog burst-mode equalization architecture, potentially to be leveraged for 25G TDM PON. First, a simple model of the equalization structure is designed and the potential implementation of a fully analog weight update algorithm is researched. Based on this result, a new architecture is discussed. The architecture is based on sample and hold circuits that implement the FFE delay line and that make it possible to implement the weight calculation algorithm in a fully analog way on chip. The burst-mode capabilities of this new architecture are then verified, after which the total equalization structure is discussed and performance for a typical 25G TDM PON is studied. Finally the imple-mentation of this equalization architecture is researched. The sample and hold circuits, that are essential to the functionality of the equalizer are partially designed and their per-formance is assessed in a complete equalization structure. The potential implementation options of other essential blocks in this equalization structure are then briefly discussed as well.
Keywords
Analog integrated circuits, optical fiber communication, passive optical networks (PONs), burst-mode equalization, high-speed electronics, integrated circuit design, time division multiple access (TDMA), time division multiplexing
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Burst-mode Electronic Equalization for Future
Optical Access Networks
Borre Van Lombergen
Supervisors: Prof. dr. Xin Yin, dr. ir. Peter Ossieur
Counsellors: dr. ir. Gertjan Coudyzer, prof. dr. ir. Johan Bauwelinck
Abstract— The research and standardization being done for 25G TDM PON for bitrates of 25G and beyond brings with it the need for high speed burst-mode receivers at the optical line terminal (OLT) of the passive optical network (PON). A vital component here is the burst-mode equalizer, used to compensate for the distortion introduced by the channel, which becomes significant at bitrates of 25G and beyond. This thesis presents a new fully analog burst-mode equalization architecture, potentially to be leveraged for 25G TDM PON. First, a simple model of the equalization structure is designed and the potential implementation of a fully analog weight update algorithm is researched. Based on this result, a new architecture is discussed. The architecture is based on sample and hold circuits that implement the FFE delay line and that make it possible to implement the weight calculation algorithm in a fully analog way on chip. The burst-mode capabilities of this new architecture are then verified, after which the total equalization structure is discussed and performance for a typical 25G TDM PON is studied. Finally the implementation of this equalization architecture is researched. The sample and hold circuits, that are essential to the functionality of the equalizer are partially designed and their performance is assessed in a complete equalization structure. The potential implementation options of other essential blocks in this equalization structure are then briefly discussed as well.
Index Terms–Analog integrated circuits, optical fiber communi-cation, passive optical networks (PONs), burst-mode equalization, high-speed electronics, integrated circuit design, time division multiple access (TDMA), time division multiplexing.
I. INTRODUCTION
Over the last two decades, the world has seen an evolution from the third generation wireless network (3G) to the currently employed fourth generation (4G) and the currently under development fifth generation (5G) network. This evolution has brought a dramatic increase in the total internet traffic. This increase is set to continue in the foreseeable future as 5G networks will implement massive device connectivity and increased traffic in general [1]. To accommodate for these rapid increases, intelligent designs of the access networks have to be done. These high data rates have caused a shift from coaxial and twisted pair copper cables towards optical fibers for very high speed communication, as for high data rates the transmission properties, such as distortion and attenuation, of copper cables are less optimal than optical fibers. Using optical fibers, signals can be transmitted up to higher rates at lower attenuation and distortion. When moving towards data rates of 25 Gb/s or even 50 Gb/s however, optical fibers also exhibit severe distortion, mainly caused by optical dispersion in the fiber [2] [3]. In order to continue increasing data rates, this distortion has to be compensated for. For this purpose, electronic equalization is done for electronic dispersion compensation (EDC). Because optical fibers and equipment are expensive, special cost efficient access network structures called passive optical networks
Fig. 1: General PON structure
In a tree-like structure a shared fiber arrives at a central office and is split up for different customers. Although reducing cost, this increases complexity as access schemes are required for multiple access from the customers. This is done in burst mode (TDMA) [5] operation , which puts stringent requirements on the to be designed hardware [6] [7]. The EDC circuit hence also has to operate in burst mode [8], meaning that it needs to be able to switch between channels very quickly. This calls for a EDC circuit that converges very quickly and does not require a lot of training bits.
II. PASSIVEOPTICALNETWORKS
TDM PONS [4] were first invented in the late 1980s. The first official PON standard that was published was Asynchronous Transfer Mode (ATM) PON that could provide 622 Mbits/s of downstream bandwidth and 155 Mbit/s of upstream traffic. This ATM PON or APON evolved into BPON for broadband PON. Mass deployment of this BPON started in 2003. The ongoing increase of required data rates had been started. EPON, which could offer 1 Gb/s symmetrically in upstream and in downstream was employed in 2004, followed by GPON, offering 2.488 Gb/s downstream and 1.248 Gb/s upstream in 2008. At this time research was being done for extending EPON and GPON towards 10 Gb/s, which was standardized in 2010. After this, it was quiet for a while around possible future improvements in PON data rates. 10G PONs are currently in the process of being employed around the world. The last few years research on this topic has started to surface again with research being done for potential 25G, 50G and even 100G PONs [9] and its challenges. In 2016, standardization process for 25G TDM PON [10] was started by the IEEE P802.3ca task force. This evolution is graphically represented in Figure 2 [9].
The success of 25G PON will greatly depend on its ability to supply the improved data rate (2,5 times higher than 10G PON), with a small incremental cost. Keeping the incremental cost low for 25G PON, relies on several techniques [4]. Firstly, O-band wavelengths will be used. In the O-band the standard telecom optical fiber (ITU-T G.652), exhibits its zero dispersion wavelength (1330 nm), significantly decreasing the effect of chromatic dispersion in
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Fig. 2: Evolution PON standards
Fig. 3: Model of optical communication system
potential dispersion performance improvement, possible with higher level modulation schemes, the increased cost and power that these higher level modulation schemes come with make NRZ modulation still the preferred modulation for 25G PON. As was the case for 10G PON, 25G PON will still leverage direct modulated lasers (DML) (also called Distributed feedback laser: DFB), instead of electroabsorption modulated lasers. The lowered cost and power consumption of DMLs are here chosen, over the improved dispersion characteristic of EMLs.
Standardization of the 25G TDM PON [10] started in 2016 and is expected to be published in 2020. 50G PON could also be realized by using these 25G PONS by wavelength-stacking two 25G TDMA PONs on top of each other. When moving towards higher data rates of 25 Gb/s and beyond optical dispersion in the deployed fibers becomes significant, proving the need for burst mode equalization for these data rates.
III. MODELING OFFIBERLINK
The data transmission over a potential 25G TDM PON system is modeled using VPIphotonics. This is done in order to better assess the distortion of the designed equalizer, using more realistic data signals. The model of this PON system is constructed to be simple, yet accurate enough such that a good assessment can be made. Since 25G TDM PON might still leverage DFB [4], a 1mW DFB laser is used. It was previously explained that future 25G TDM PONS will continue to work in O-band [4], for lower dispersion properties. The modeling will be verified for O-band and C-band. More significant distortion should arise in the C-band. This paper presents the O-band results. A pseudorandom bit sequence (PRBS) is coded into a NRZ modulation scheme with rise and fall times of 0.4Tb. The
OOK modulator modulates this NRZ data waveform onto the laser. This is done using a Mach-Zehnder modulator. A variable length fiber is used to model the dispersion and distortion that arises in the fiber. The fiber is given 16ps
nm.km dispersion. For this purpose the
non-linearity of this fiber was made negligible, since the goal of the equalizer is to minimize this dispersion. At the receiver side a PIN photodiode is used to detect the signal coming from the optical fiber. This contributes to overall noise performance by adding noise having 10.10−14√A
(Hz) noise spectral density. Finally a TIA having a
cut-off frequency of3f = 18.75GHz, a noise bandwidth of 0.8f = 20
(a) 20 km fiber (b) 30 km fiber
Fig. 4: Eye diagrams of extracted waveforms, O-band
Fig. 5: BERs for extracted waveforms
of this TIA is chosen such that the output is again re-scaled to a -1V to 1V range for 1 mW laser power.
The simulated O-band waveform eyediagrams are shown in Figure 4 for 20 km of fiber and 30 km of fiber used. The fiber is given no attenuation, hence the optical receive power is equal to the transmit power. The eyes are thus for 1mW receive power. The indicated BERs are for an ideally found sampling point and decision level. An arbitrary sampling point (nTb) and decision level 0 results in the
BER curve in Figure 5. This figure shows the BER in function of the laser power. Decreasing the laser power reduces the SNR, as the noise of the system will be the same. This causes more bit errors. Note that 100 000 bits have been used to simulate this. This means that where BER = 0, it actually means that BER< 1
100000 = 10−5.
This limited amount of bits simulated also does not necessarily give accurate BERs. The trends are however correct and this is what is of main importance in this design now. This figure also already shows the BERs of the equalized results. The improvement is clear. The sidenote that BER = 0 is in fact BER < 10−5is even more important
here.
IV. MODEL OFEQUALIZER
A. Digital LMS
Using these extracted waveforms, equalization structures are re-searched. The decision was made to design a 7-tap FFE Tb
2
frac-tionally spaced equalizer (Figure 6). This is a generally used topol-ogy with a proven performance [11]. These equalized waveforms, including BERs can be seen in Figure 7. The improvement over
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(a) 20 km fiber (b) 30 km of fiber
Fig. 7: Eye diagram of equalized waveforms, O-band
(a) 20 km fiber (b) 30 km fiber
Fig. 8: Eye diagram of equalized waveforms, analog LMS, O-band
the unequalized case, indicated in Figure 5 is clear. For O-band communication, this gives error-free (BER < 10−5) communication
up to at least 30 km for 1mW receive power.
B. Analog LMS
The effect of implementing the LMS algorithm in a fully analog way is studied. For this, the LMS algorithm is slightly adapted. The steps to be taken are:
• Multiply the error signal with the respective taps. • Update weights according to:
Wk(t) = µAN AR0te(u)x(u− kT )du [12]. In order to obtain
the same update rate, choose µDIG= µAN ATb.
These simulated results can be seen in Figure 8. A new affect occurs however. This effect is clear when comparing Figure 7b and Figure 8b. The analog equalizer creates a smaller vertical eye opening. The digital LMS algorithm samples the error and tap values at times nTb.
Based on these values, the weights are updated. The algorithm thus only minimizes the product xi(t)e(t)(xi(t)indicating tap i) at times
nTb. This results in an eye that is specifically opened at times nTb,
which is optimal for communication purposes. The LMS algorithm however, does not sample the incoming signals. The product xi(t)e(t)
is integrated, hence this total product will be minimized. This results in a waveform that is in total more equal to the desired waveform, but that will have a larger error on the specific sampling times. The other figures also show this effect. This is an undesired effect for digital communication purposes. To verify this, a table is created that compares the RMS error values of the equalized waveforms and the reference waveform achieved with both algorithms.
TABLE I: RMS error comparison digital versus analog LMS
digital LMS analog LMS 20 km 0.0986 0.0876 25 km 0.2294 0.1218 30 km 0.4764 0.1559
It can be seen that the RMS error is lower for the analog LMS algorithm. As explained however, this is not particularly the desired
Fig. 9: Sample and hold delay line implementation
vertical eye opening. This result is indicated on Table II. As the level of distortion increases, the analog LMS algorithm gets a smaller vertical eye opening than the digital LMS algorithm. This is not the desired property for digital communication purposes. A smaller eye opening leaves less margin for certain noise perturbations on the symbols. For small vertical eye openings, a small amount of noise could shift a symbol over the decision boundary, causing a wrongly detected symbol. For a larger vertical eye opening, that same amount of noise would keep the sample in its decision region, hence keeping correct decision. Because of this a fully analog LMS algorithm implementation is not the best option.
TABLE II: Vertical eye opening comparison digital versus analog LMS
digital LMS analog LMS 20 km 1.5707 1.3252 25 km 1.5880 0.9251 30 km 1.1841 0.3393
C. 25G Sample and Hold Equalizer
The same result as the digital LMS algorithm can be achieved by placing analog sample and hold (SH) circuits in front of the integration in the analog LMS algorithm. These SH circuits sample the product xi(t)e(t) at times nTb. By doing this, the algorithm
minimizes this value again and hence the same result as the digital LMS algorithm is obtained. Using such SH structures here could hence make a fully analog implementation of the equalizer + LMS structure possible, while keeping the performance of a digitally implemented LMS.
The SH circuits can also be re-used to implement the delay line of the FFE as well (represented in Figure 9). This removes the need for the design of analog active delay cells [13], which can be cumbersome. Here the delay line is split up into two branches. Because the output and LMS algorithm both work at 25G, this gives the same result as using one 50G delay line chain.
D. 12.5G Sample and Hold Equalizer
In order to lower requirements on the SH circuits, 12.5G SH circuits can be designed instead of 25G SH circuit. This requires an update of the delay line structure into the structure depicted in Figure 10. The total burst-mode equalizer structure now requires updating. Because the taps are 12.5G samples now, the equalizer consists of two separate FFEs (sharing the SH delay line) and outputs two separate waveforms: y1(t) and y2(t), respectively holding the
equalized samples at times 2nTband (2n + 1)Tb.
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Fig. 10: 12.5G delay line structure
(a) y1 O-band (b) y2O-band
Fig. 11: Eye diagram of equalized waveforms, 20 km
the correct linear combination of 12.5G sampled tap signals and the error signals (e1(t) and e2(t), respectively ref(t) − y1(t) and
ref (t)−y2(t)delayed over Tb). For W1((n+1)2Tb) = W1(2nTb)+
∆W1(n), the linear combination is given.
∆W1(n) = µ(d1(n2Tb)e2(n2Tb) + d2(n2Tb)e1(n2Tb)) (1)
This algorithm makes it possible to obtain the same weights as a 25G LMS system would, using a 12.5G algorithm. The equalized eyes of the full system can be seen in Figure 11 and Figure 12. The way the two separate output signals result in equalized samples is clear on the figures. The final overview of the complete structure is represented in Figure 13. The extra delay Tb for e2(t) is needed for the LMS
algorithm. The two FFEs (y1(t)and y2(t)) require the same weights,
hence only one LMS block is required.
(a) y1 O-band (b) y2O-band
Fig. 13: Total burst mode equalizer structure
Fig. 14: BER curve, effect of omitting SH in LMS
E. Effect of Omitting SH Blocks in LMS
Omitting all the sample and hold blocks in the LMS algorithm would be a very cost-efficient improvement, in case the performance reduction introduced by this, would not be too significant. In this case e1(t)and e2(t)(Figure 13) need to be sampled at times 2nTb
and (2n + 1)Tb respectively. This introduces two sample and hold
circuits for the errors, but omits eight sample and hold circuits in the LMS algorithm.
The effect of this is shown in Figure 14. This figure compares the BER curves for the scenario where the SHs are omitted versus the scenario where they are still present in the LMS block. It is seen (as expected) that this causes a deterioration of the BER curve. Equalization is however still present and the performance of this might suffice for digital communication purposes, since the deterioration does not seem too significant at first glance. The BER curve for the fully analog equalizer is also plotted here. It is also seen on this plot that this scenario still gives the worst performance. For the analog LMS, errors start occurring for higher receive powers than for the other equalizers. It is seen that for very low receive powers, the BER of the no SH in LMS equalizer is higher than for the analog LMS equalizer. This however only occurs for receive powers that result in BERs that are too high for communication purposes. It is concluded from this that omitting the additional sampling blocks in the LMS block might be a good way of reducing implementation cost, while keeping the performance satisfactorily.
F. Gear Shifting LMS
The burst-mode property of the equalizer translates into the need for high convergence-speed training of the equalizer. In this case 1000 bits are used for the training. The update factor µ is adapted over the course of the training algorithm. A large value of µ initially gets a quick approximate value. Then the value is decreased
step-5
Fig. 15: Track and hold amplifier
This technique is called Gear Shifting LMS [15]. In this paper µ was chosen to be: µ(n) = 0.15 0≤ n < 125 0.06 125≤ n < 500 0.024 500≤ n < 750 0.00384 750≤ n < 1000 (2) Even though this choice was made relatively arbitrary, this works here, so these values are used here.
V. CIRCUITLEVELIMPLEMENTATION
The SH circuits are essential to the functioning of this equalization architecture. For this reason the specific implementation of this is researched, as well as their functioning in the total equalizer structure.
A. The Track and Hold Amplifier
The functionality of a sample and hold amplifier is achieved by cascading two out of phase track and hold amplifiers. The structure that is used for this is shown in Figure 15 [16]. This structure has two phases: a track phase and a hold phase.
• In the track phase, all current of ItailT HC flows through Q2
and Q4. Q1and Q3are in cut-off. This ensures emitter follower
functioning for transistor Q5. The capacitor CHis charged and
Vout−≈ Vin+.
• In the hold phase, all current flows through Q1 and Q3. This
causes an extra current contribution through Rc and hence an
extra voltage drop RcItailT HC over the resistor. This extra
voltage drop causes transistor Q5 to go in cut-off, isolating
Vout− from Vin+. No current flows and the charge is held on
capacitor CH, ensuring hold functionality.
The capacitor CH is very influential in the circuit. In the track state,
it determines the dominant pole of the emitter follower: vout
vin
= gmRL
1 + gmRL+ sCHRL (3)
Q2 and Q4 form a cascode here, causing RL in this system to
be high. This increases the accuracy of the follower (DC gain =
gmRL
1+gmRL) but this does lower the pole fp=
1
2πRLCH. This effect is
shown in Figure 16. The bandwidth for a 90 fF, 210 fF and 480 fF capacitor is respectively approximately 44 GHz, 29 GHz and 15 GHz in simulation. From this it can be seen that that this capacitor can not be chosen too large in order to still achieve accurate tracking. In the hold stage, a larger capacitor value is desired, as a small value will
Fig. 16: Track state frequency characteristic
Fig. 17: 12.5G sample and hold circuit result
forms the most important trade-off in the circuit. The capacitor value is chosen to be 210 fF . In order to improve sampling accuracy, the capacitor value for the first track and hold amplifier in the chain is chosen to be 90 fF .
B. Sample and Hold Circuit
A snippet of a 12.5G sampled signal is shown of Figure 17. Here the sampled value is compared to the ideally sampled value. Despite the fact that some distortion arises, there is a clear sampling functionality present. A limited amount of distortion, caused by the SH circuit itself, is not necessarily detrimental to the performance of the equalizer. The sampled value is used in the FFE and in the LMS algorithm. Since both circuits use the same distorted sampled value, a small amount of distortion will not necessarily reduce the equalization capacity of the system.
The performance of these sample and hold circuits in the total system is verified. The SH circuits in the delay line, in the additional Tb delay for the error signal (just one track and hold) and in the
LMS algorithm are all replaced by their circuit level implementations. The obtained eye diagrams can be seen in Figure 19. The non-ideal SH circuits, cause a deviation from the typical shape in Figure 11 and Figure 12. The same characteristic, being the opened eye with large vertical and horizontal eye opening does return however. It is clear that equalization is done. It can also be seen in Figure 18 that convergence is achieved, within the 1000 training bits. It was studied before that omitting the sample and hold circuits in the LMS block could be a potential cost-decreasing option for this equalizer, while keeping sufficient performance. It was expected here that inaccuracies in the sample and hold circuit would be more problematic in this case. The waveform eye diagrams obtained with this method are plotted in Figure 20. The eyes are clearly still opened and equalization is achieved. Visually, this eye is very similar to the eye obtained in Figure 19. For higher distortion a larger difference will arise. This is verified by comparing Figure 21 and Figure 22. Here it can be
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Fig. 18: Weights convergence 1000 bit BMEQ O-BAND
(a) y1(t) (b) y2(t)
Fig. 19: Eye diagram of equalized waveforms, SH in LMS, gear shifting LMS, O-band, 20 km fiber dispersion
(a) y1(t) (b) y2(t)
Fig. 20: Eye diagram of equalized waveforms, no SH in LMS, gear shifting LMS, O-band, 20 km fiber dispersion
(a) y1(t) (b) y2(t)
Fig. 21: Eye diagram of equalized waveforms, SH in LMS, gear shifting LMS, O-band, 30 km fiber dispersion
(a) y1(t) (b) y2(t)
Fig. 22: Eye diagram of equalized waveforms, no SH in LMS, gear shifting LMS, O-band, 30 km fiber dispersion
the two structures arises. In both cases however, equalization is still present and the eye is opened. The obtained vertical eye openings are compared with the fully analog LMS algorithm (Table III). It can be seen that both the SH in LMS and no SH in LMS cases still yield a significant improvement over the analog LMS algorithm for higher levels of dispersion.
TABLE III: Vertical eye opening comparison SH in LMS vs no SH in LMS vs analog LMS SH in LMS (y1(t)| y2(t)) no SH in LMS (y1(t)| y2(t)) analog LMS 20 km 157 mV | 153 mV 160 mV | 157 mV 134 mV 25 km 158 mV | 167 mV 143 mV | 155 mV 90 mV 30 km 126 mV | 133 mV 99 mV | 105 mV 31 mV
C. Other Required Circuits
The sample and hold circuits were designed because their per-formance is essential to the correct functioning of this equalization structure. The other building blocks for such a system on chip have been demonstrated in previous studies. The operations and their respective building blocks that are required are:
• Multiplication. Multiplications of the taps with the weights and
of the taps with the error signal, are required in the structure. This requires a type of variable gain amplifier. A potential implementation of this can be using a Gilbert cell mixer [17]. The addition can be done inherently by connecting several such cells together. Since eight taps are present, this problems is less trivial than a simple connection. This requires further investigation.
• Subtraction. For the comparison of the output with the training
data, a subtraction needs to be done. This can potentially be achieved by using a fully differential difference amplifier (FDDA) [18].
• Integration. It is well known that an integration can be achieved
using an operational amplifier structure.
VI. CONCLUSION ANDFUTUREWORK
This thesis presents a novel sample and hold based equalization structure for fully analog (burst-mode) equalization purposes on chip. The thesis focused greatly on implementation capabilities, and it was proven that such a system can be beneficial and can function satisfactorily. A further study is however required that rigorously compares the performance of such a system with similar traditional equalization systems and that compares aspects such as implementation complexity and power consumption of these blocks, in order to come to a final conclusion on the effectiveness of implementation of such a system. An important aspect here will be the comparison in implementation complexity and power consumption between the designed sample and hold circuits and active delay cell
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[17] N. Nambath, R. Ashok, S. Manikandan, N. B. Thaker, M. Anghan, R. Kamran, S. Anmadwar, and S. Gupta, “All-analog adaptive equalizer for coherent data center interconnects,” Journal of Lightwave Technol-ogy, 2020.
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Contents
Contents i
List of Figures iii
List of Tables vii
List of Abbreviations vii
1 Introduction 1
1.1 Burst-mode . . . 1
1.2 Passive Optical Networks . . . 2
1.3 Goals and Outline . . . 4
2 Electronic Equalization 7 2.1 Dispersion . . . 7
2.2 Feedforward Equalizer . . . 8
2.3 Weight Calculation . . . 9
2.3.1 Zero Forcing Algorithm . . . 9
2.3.2 Least Mean Square Algorithm . . . 10
2.4 Decision Feedback Equalizer . . . 11
2.5 Clock Synchronization . . . 13
2.6 Fractionally Spaced . . . 13
2.7 Gear Shifting . . . 15
3 Modeling of Fiber Link 17 3.1 Reduction of Laser Power . . . 20
4 Modeling of Equalizer 23 4.1 FFE . . . 23
4.2 DFE . . . 25
4.3 Digital LMS Algorithm . . . 27
4.3.1 Influence of Sampling Point . . . 28
4.4 Analog LMS Algorithm . . . 29
4.4.1 Algorithm Description . . . 29
4.4.2 Performance . . . 30
4.5 Sample and Hold Based Equalizer . . . 35
4.6 Parallel LMS Algorithm . . . 40
4.7 Parallelization of FFE . . . 47
4.8 Impact of Limiting Training Duration . . . 53
4.9 Total BMEQ Structure . . . 57
4.10 Impact of Omitting Sample and Hold in LMS . . . 64
5 Circuit Level Implementation 67 5.1 Sample and Hold . . . 69
5.1.1 Track and Hold Amplifier . . . 69
5.1.2 Sample and Hold Amplifier . . . 79
5.2 Clock Buffer . . . 84
5.3 FFE . . . 85
5.4 Multiplication . . . 92
5.5 Fully Differential Difference Amplifier . . . 95
5.6 Integrator . . . 96
6 Conclusion and Future Work 97
List of Figures
1.2.1 General PON structure . . . 2
1.2.2 Evolution PON standards . . . 3
2.1.1 Chromatic dispersion . . . 8
2.2.1 General structure feedforward equalizer . . . 9
2.4.1 General structure decision feedback equalizer . . . 11
2.6.1 Symbol spaced versus fractionally spaced equalizer . . . 14
3.0.1 Model of 25G TDM PON optical communication system . . . 17
3.0.2 Eye diagrams of extracted waveforms, O-band . . . 18
3.0.3 Eye diagrams of extracted waveforms, C-band . . . 19
3.1.1 BER curve for laser input power, O-band . . . 21
4.1.1 7-tap Tb 2 fractionally spaced FFE . . . 23
4.1.2 Eye diagram of equalized waveforms, 7-tap FFE, C-band . . . 24
4.2.1 7-tap FFE, 1-tap DFE . . . 25
4.2.2 Eye diagram of equalized waveforms, 7-tap FFE, 1-tap DFE, C-band . . 26
4.2.3 BER curve comparison 7-tap FFE vs 7-tap FFE, 1-tap DFE . . . 27
4.3.1 Effect of changing sampling point in LMS algorithm . . . 28
4.4.1 Eye diagram of equalized waveforms, 7-tap FFE, analog LMS, C-band . 30 4.4.2 Eye diagram of equalized waveforms, 7-tap FFE, 1-tap DFE, analog LMS, C-band . . . 31
4.4.3 BER comparison analog vs digital LMS . . . 33
4.4.4 Eye diagram of equalized waveforms, 7-tap FFE, O-band . . . 34
4.5.1 Delay implementation using sample and hold cascade . . . 35
4.5.2 50G sample and hold chain for FFE delay line . . . 36
4.5.4 Eye diagram of equalized waveforms, 25G SH equalizer, C-band . . . 38 4.5.5 Dispersion level BER comparison digital equalizer vs SH equalizer . . . 39 4.5.6 Sample point BER comparison digital equalizer vs SH equalizer . . . 39 4.6.1 12.5G sample and hold chain for FFE delay line . . . 45 4.6.2 SH error signal circuit . . . 46 4.7.1 Tap values for different sampling moments . . . 50 4.8.1 Weight comparison for different µ values . . . 53 4.8.2 Weight comparison for different µ values, gear-shifted LMS . . . 54 4.8.3 Final weights comparison 1000 bits vs 100 000 bits . . . 55 4.9.1 Final FFE structure for BMEQ . . . 57 4.9.2 Total BMEQ structure . . . 58 4.9.3 Structure of the LMS algorithm block . . . 59 4.9.4 Weight comparison O-band vs C-band . . . 60 4.9.5 Eye diagram of equalized waveforms, total BMEQ, 20 km fiber dispersion 61 4.9.6 Eye diagram of equalized waveforms, total BMEQ, 25 km fiber dispersion 62 4.9.7 Eye diagram of equalized waveforms, total BMEQ, 30 km fiber dispersion 62 4.9.8 BER curve comparison digital LMS vs SH equalizer . . . 63
4.10.1 BER curve comparison SH in LMS vs no SH in LMS vs analog LMS . . 64
4.10.2 Eye diagram of equalized waveforms, total BMEQ, no SH in LMS, O-band 65 5.1.1 Cascade of track and hold amplifiers . . . 69 5.1.2 Sample and hold functionality based on two track and hold amplifiers . 69 5.1.3 General track and hold structure . . . 70 5.1.4 Track and hold amplifier . . . 70 5.1.5 Input buffer for track and hold amplifier . . . 71 5.1.6 Input buffer characteristic . . . 72 5.1.7 Track and hold core: track phase . . . 73 5.1.8 Track and hold core: hold phase . . . 74 5.1.9 Characteristic track and hold in track phase . . . 75 5.1.10 Transient analysis track and hold in hold phase . . . 76 5.1.11 25G track and hold signal . . . 77 5.1.12 12.5G track and hold signal . . . 78 5.1.13 12.5G sample and hold, CH = 120 f F . . . 79
5.1.14 25G sample and hold signal . . . 80 5.1.15 25G sample and hold signal, longer time snippet . . . 81
5.1.16 Chain of four 25G sample and hold signal . . . 81 5.1.17 Chain of two 12.5G sample and hold signals, CH = 120 f F . . . 82
5.1.18 Chain of two 12.5G sample and hold signals, CH = 210 f F . . . 82
5.1.19 Final FFE delay line structure . . . 83 5.2.1 Clock driver circuit . . . 84 5.3.1 Final FFE delay line sample and hold taps . . . 86 5.3.2 Weights SH equalizer, C-band, 20 km fiber . . . 87 5.3.3 Eye diagram of equalized waveforms, SH in LMS, gear shifting LMS,
C-band, 20 km fiber dispersion . . . 88 5.3.4 Eye diagram of equalized waveforms, SH in LMS, gear shifting LMS,
O-band, 20 km fiber dispersion . . . 88 5.3.5 Weights SH equalizer, gear shifting LMS, no SH in LMS, O-band, 20 km
fiber . . . 89 5.3.6 Eye diagram of equalized waveforms, no SH in LMS, gear shifting LMS,
O-band, 20 km fiber dispersion . . . 89 5.3.7 Eye diagram of equalized waveforms, SH in LMS, gear shifting LMS,
O-band, 30 km fiber dispersion . . . 91 5.3.8 Eye diagram of equalized waveforms, no SH in LMS, gear shifting LMS,
O-band, 30 km fiber dispersion . . . 91 5.4.1 Gilbert cell Mixer . . . 92 5.4.2 Addition using two Gilbert cell mixers . . . 94 5.5.1 Fully differential difference amplifier structure . . . 95 5.5.2 Simple FDDA topology . . . 96 5.6.1 Differential integrator . . . 96
List of Tables
3.0.1 BER for several fiber lengths for preset sampling point . . . 20
4.4.1 BER and RMS comparison Analog LMS vs Digital LMS for 7-tap FFE . 32
4.4.2 Vertical eye opening comparison digital vs analog LMS, O-band . . . 32 4.5.1 BER comparison digital equalizer vs SH equalizer . . . 38 5.3.1 Vertical eye opening comparison SH in LMS vs no SH in LMS vs analog
List of Abbreviations
3G third generation. 1 4G fourth generation. 1 5G fifth generation. 1
ADC analog-to-digital-converter. 40 APD avalanche photodiode. 3
BER bit error rate. 19–21, 24, 25, 27, 30, 32, 33, 38, 39, 61, 63, 64 BMEQ burst-mode equalizer. 4, 57
DC direct current. 84, 85
DFB distributed feedback laser. 4, 17
DFE decision feedback equalizer. 11–13, 25, 27, 31, 33 DML directly modulated laser. 3, 4
DSP digital signal processor. 8, 27, 28, 40, 97 EDC electronic dispersion compensation. 1, 2 EML electroabsorption modulated laser. 3, 4 FDDA fully differential difference amplifier. 95
FFE feedforward equalizer. 9, 11, 12, 23, 25, 27, 31–33, 36–38, 48–52, 57, 67, 68, 80, 83, 85, 87, 95
IC integrated circuit. 35, 84, 85
ISI intersymbol interference. 8–10, 12, 14
LMS least mean square. 4, 10, 24, 27–33, 35–37, 39, 40, 45, 47, 48, 51, 52, 54, 57, 58, 64–68, 80, 87–90, 95, 97
MMSE minimum mean squared error. 10 MSE mean squared error. 10
NRZ non-return-to-zero. 4, 13, 17, 18 OLT optical line terminal. 2, 13 ONU optical network unit. 2, 13 PON passive optical network. 1–4, 33 PRBS pseudorandom binary sequence. 17 RMS root mean square. 31, 32, 64
SEF switched emitter follower. 69, 71
SH sample and hold. 36, 38, 39, 43, 63, 64, 66, 89, 90 SNR signal-to-noise-ratio. 10, 20, 64, 68, 90
TDM PON time-division multiplexed passive optical network. 2–4, 13, 17, 20, 63 TDMA time-division multiple access. 2
THA track and hold amplifier. 69, 72, 73, 75, 76, 78, 79, 82–85, 87 TIA transimpedance amplifier. 3, 18, 94
Chapter 1
Introduction
Over the last two decades, the world has seen an evolution from the third generation (3G) wireless network to the currently employed fourth generation (4G) and the currently under development fifth generation (5G) network. This evolution has brought a dramatic increase in total internet traffic. This increase is set to continue in the foreseeable future as 5G networks will implement massive device connectivity and increased traffic in general [1].
1.1
Burst-mode
To accommodate for these rapid increases, intelligent designs of the access networks have to be done. These high data rates have caused a shift from coaxial and twisted pair copper cables towards optical fibers for very high speed communication, as for high data rates the transmission properties, such as distortion and attenuation, of copper cables are less optimal than optical fibers. Using optical fibers, signals can be transmitted up to higher rates at lower attenuation and distortion. When moving towards data rates of 25 Gb/s or even 50 Gb/s however, optical fibers also exhibit severe distortion, mainly caused by optical dispersion in the fiber [2] [3]. In order to continue increasing data rates, this distortion has to be compensated for. For this purpose, electronic equalization is done for electronic dispersion compensation (EDC).
Because optical fibers and equipment are expensive, special cost-efficient access network structures called passive optical networks (PONs) (Figure 1.2.1) [4] are used, that share the cost of several fibers. In a tree-like structure a shared fiber arrives at a central office
Figure 1.2.1: General PON structure
and is split up for different customers. Although reducing cost, this increases complexity as access schemes are required for multiple access from the customers. This is done in burst mode (time-division multiple access (TDMA)) [5] operation, which puts stringent requirements on the to be designed hardware [6] [7]. The EDC circuit hence also has to operate in burst mode [8], meaning that it needs to be able to switch between channels very quickly. This calls for a EDC circuit that converges very quickly and does not require a lot of training bits.
1.2
Passive Optical Networks
Passive optical networks (PONs) are being used to share the cost for several users over a single fiber. By doing this, the evolution from copper coaxial and twisted pair cables towards optical fibers for fiber-to-the-home for very high speed communication can be continued, while keeping this affordable and implementable.
A PON (Figure 1.2.1) consists of one optical line terminal (OLT) at the service provider’s central office. Here the shared fiber is split up into several fibers in a tree-like structure towards the customers: the optical network units (ONUs). Because this splitting is done using a passive optical splitter, these networks are referred to as passive optical networks. As several ONUs now share a common fiber, an access scheme is required. This is done using TDMA, giving rise to time-division multiplexed passive optical networks (TDM PONs).
TDM PONs [4] were first invented in the late 1980s. The first official PON standard that was published was Asynchronous Transfer Mode (ATM) PON that could provide
Figure 1.2.2: Evolution PON standards
622 Mbits/s of downstream bandwidth and 155 Mbit/s of upstream traffic. This ATM PON or APON evolved into BPON for broadband PON. Mass deployment of this BPON started in 2003. The ongoing increase of required data rates had been started. EPON, which could offer 1 Gb/s symmetrically in upstream and in downstream was employed in 2004, followed by GPON, offering 2.488 Gb/s downstream and 1.248 Gb/s upstream in 2008. At this time, research was being done for extending EPON and GPON towards 10 Gb/s, which was standardized in 2010. After this, it was quiet for a while around possible future improvements in PON data rates. 10G PONs are currently in the process of being employed around the world. The last few years research on this topic has started to surface again with research being done for potential 25G, 50G and even 100G PONs [9] and its challenges. In 2016, standardization process for 25G TDM PON [10] was started by the IEEE P802.3ca task force. This evolution is graphically represented on Figure 1.2.2 [9].
In history, PONs could only be deployed because of the pre-existence of mature optical and electronic components at the required speeds. Components such as: directly modu-lated lasers (DMLs), electroabsorption modumodu-lated lasers (EMLs), avalanche photodiodes (APDs), transimpedance amplifiers (TIAs) and serializer/deserializers. Once such com-ponents existed and became low cost due to sufficient cost erosion, they could be adapted by the PON market. Hence an existing market is required for the deployment for new generation PON networks. In history for EPON, GPON up to 10G PON the metro market drove the development of these components, enabling the deployment of these PONs. One of the reasons why 25G PON and 50G PON are now being researched and are potentially deploy-able in the future is because the data center intra-connect market
is driving 100G Ethernet technologies, using 25 Gb/s lanes [10]. Hence 25G TDM PON could leverage the optical and electronic components used for this.
The success of 25G PON will greatly depend on its ability to supply the improved data rate (2,5 times higher than 10G PON), with a small incremental cost. Keeping the incremental cost low for 25G PON relies on several techniques [4]. Firstly, O-band wave-lengths will be used. In the O-band the standard telecom optical fiber (ITU-T G.652), exhibits its zero-dispersion wavelength (1330 nm), significantly decreasing the effect of chromatic dispersion in this fiber. Secondly non-return-to-zero (NRZ) modulation will be maintained. Despite the potential dispersion performance improvement, possible with higher level modulation schemes, the increased cost and power that these higher level modulation schemes come with make NRZ modulation still the preferred modulation for 25G PON. As was the case for 10G PON, 25G PON will still leverage DMLs (also called distributed feedback laser (DFB)), instead of EMLs. The lowered cost and power con-sumption of DMLs are here chosen, over the improved dispersion characteristic of EMLs [4].
From 25G PON, the question arises whether higher bitrates (50G, 100G) [9] are still achievable in a TDM PON, NRZ modulation, in a cost-effective way. If not, alternative modulation formats have to be researched for this purpose. Also, potential data rate increases greater than 25G can potentially be achieved by employing wavelength-division multiplexed passive optical networks (WDM PONs) [11], expanding capacity via multiple wavelengths. This research was already being done at the beginning of PON research, however, all commercially deployed PONs have been of the TDM PON variety.
Standardization of the 25G TDM PON [10] started in 2016 and is expected to be published in 2020. 50G PON could also be realized by using these 25G PONs by wavelength-stacking two 25G TDM PONs on top of each other. When moving towards higher data rates of 25 Gb/s and beyond optical dispersion in the deployed fibers becomes significant, proving the need for burst mode equalization for these data rates [7].
1.3
Goals and Outline
In this thesis potential burst-mode equalizer (BMEQ) architectures for 25G PONs and 50G PONs are studied. The goal is to research and model several potential equalization architectures and implementations, to study several algorithms such as gear shifting least mean square (LMS) algorithm and to explore whether more advanced equalization
struc-tures can be possible for passive optical networks. A complete chip-level implementation is out of the scope of this thesis. It is however useful to have a circuit level implementation of certain essential building blocks of the designed structure.
Chapter 2
Electronic Equalization
When optical fibers are used for lower data rates, very low distortion of the original signal appears, making it easy to detect the originally transmitted symbols. As data rates increase, the phenomenon of optical dispersion becomes more prevalent and specific dispersion compensation circuits are needed to allow detection of the originally trans-mitted symbols. Such electronic dispersion is here achieved using electronic equalization techniques. A basic understanding of the distortion phenomenon is required to under-stand equalization techniques. Based on this, several equalization architectures can be studied.
An optical fiber will exhibit a frequency dependent transfer function. Equalization tech-niques are used to try to flatten this characteristic, as to provide the same response for each frequency component. The equalizer should also neutralize any group delay or phase delay between different frequency components.
2.1
Dispersion
Optical dispersion is the phenomenon that different frequency components of light un-dergo different phase delays when traveling through a dispersive media, such as an optical fiber. In other words, the phase velocity of transmission through an optical fiber becomes frequency dependent.
If lasers emitted a perfect frequency Dirac pulse of light, dispersion would not be a problem. In reality, however, the frequency of the light emitted by a laser looks more like a narrow normal distribution around the center frequency fc[12]. Hence when emitting a
Figure 2.1.1: Chromatic dispersion
certain pulse, this pulse can be thought of as consisting of an infinite sum of pulses with slightly varying frequencies. Since the phase velocity in the fiber is frequency dependent, this means that all these pulses arrive at the receiver at different times. At the receiver side the total signal is then the sum of all these slightly out of phase pulses, which results in a pulse that is spread out. This is schematically represented in Figure 2.1.1 [2]. The spreading of these pulses is the main reason why chromatic dispersion becomes more problematic for higher data rates. When a sequence of symbols is transmitted, each pulse will get spread out when traveling over a fiber. When the pulses are narrow and close to each other (high data rates), the spreading of the pulses causes the subsequent pulses to interfere with each other, distorting the data and making the final sequence of symbols potentially unfit for detection [3]. This is phenomenon is called intersymbol interference (ISI).
2.2
Feedforward Equalizer
The most common types of equalizers are linear equalizers [13]. These use a simple linear finite impulse response (FIR) filter (Figure 2.2.1) to attempt to equalize the signal. This directly realizes the convolution of the input signal with the equalizer coefficients. In this thesis an analog equalizer is designed. An analog implementation of a FIR filter is realistically possible. This is therefore the chosen technique for this purpose. The majority of equalizers (also when implemented on digital signal processors (DSPs)) are
Figure 2.2.1: General structure feedforward equalizer
implemented using a FIR filter. When w = [w1 w2 w3 .. wK] are the taps, coefficient or
weights of the FIR filter, the output of a FIR filter is:
y(n) =X
k
x(n − kTs)wk (2.1)
The output is hence a linear combination of delayed versions of the input. The combina-tion that is made is imposed by the values of the FIR filter coefficients. For equalizacombina-tion purposes these are often referred to as weights, which is also be the way it is done in this thesis. In equalization terms, this is called a feedforward equalizer (FFE) [14].
2.3
Weight Calculation
It is clear that the functionality of the equalizer is determined by the weights. Based on the values of these weights, the equalizer will perform its functionality accordingly. These weights thus have to be decided. Several algorithms are possible for this purpose.
2.3.1
Zero Forcing Algorithm
The total transfer function of the communication system can be written as:
H(f ) = Htx(f )Hch(f )Hrx(f )Heq(f ) (2.2)
Good design will result in the combination Htx(f )Hrx(f ) to be ISI-free. In order for the
total system to be ISI-free, the equalizer hence has to invert the effect of the channel (up to a delay nT ). The response of the equalizer should thus be:
Heq(f ) =
1 Hch(f )
ej2πf nT (2.3) If this can be achieved, the total system will have a total suppression of ISI. This is the principle of the zero-forcing criterion [13]. An algorithm is used that finds the weights that approach this response as well as possible.
A problem with such a system is the noise behavior. This transfer function will not only act on the data signal but also on the receiver noise.
|Nout|2 = N0|Heq|2 =
N0
|Hc(f )|2
(2.4) Here the problem with the zero-forcing algorithm is apparent. Where the channel response gets small or approaches zero, the receiver noise is amplified, potentially completely deteriorating output signal-to-noise-ratio (SNR).
For this reason, usually another criterion is used for the weight calculation.
2.3.2
Least Mean Square Algorithm
If y(n) is the ideal signal that should be received and ˆy(n) is the output of the equalizer. Then an error signal can be constructed:
e(n) = y(n) − ˆy(n) (2.5)
Based on this error, a cost function is defined:
C(n) = E[(e(n))2] (2.6)
A new set of weights can now be calculated by minimizing this cost function. This allows some ISI, but will not have the noise amplification that zero-forcing has. This cost function C(n) is the mean squared error (MSE) of the system. Using this cost function as a criterion for the weight calculation is hence called the minimum mean squared error (MMSE) criterion [13]. An algorithm thus has to be decided that finds the following weights:
ˆ
W = arg min
W
E[(e)2] (2.7)
When a fixed channel is used, this can be done once and these weights can be used in the equalizer. In several applications however, including the burst mode operation that this thesis describes, the channel is not known beforehand. This requires adaptive equalization. In this case an algorithm is designed that iteratively tries to find the optimal weight coefficients. This is done using the least mean square (LMS) algorithm [15]. This is done in the following manner. When communication starts over a certain channel, a preamble is sent before the actual data is transmitted. This preamble contains training data. These are N symbols that both the transmitter and the receiver know. By sending these signals over the channel and by comparing this distorted sequence with the desired
Figure 2.4.1: General structure decision feedback equalizer
sequence, weights can iteratively be updated. The error signal e(n) can then easily be calculated:
e(n) = y(n) − ˆy(n) (2.8)
The cost function is minimized by method of gradient descent [15]. Using this method, for each iteration, the coefficients are updated with the negative gradient of the cost function with respect to this specific coefficient. This results in:
Wk(n + 1) = Wk(n) + µE[e∗(n)xk(n)] (2.9)
This expectation is often approximated: E[e∗(n)xk(n)] ≈ e∗(n)xk(n). Which results in
the final weight update formulas:
e(n) = y(n) − ˆy(n) (2.10)
Wk(n + 1) = Wk(n) + µe(n)x(n − kT ) (2.11)
The factor µ determines the update rate. When this factor is chosen to be large, the weights update very fast. This increases convergence speed but this comes at the cost of a lower accuracy and generalizability. Choosing this factor low improves the accuracy but reduces the speed of convergence. A speed-accuracy trade-off has to be made here. A third aspect to his trade-off is the stability of the algorithm. An update rate that is too large can result in no convergence being found, and hence an unstable circuit [15]. This has to be taken care of.
2.4
Decision Feedback Equalizer
The general structure of a decision feedback equalizer (DFE) [13] [16] can be seen in Figure 2.4.1. A DFE consists of a first FFE stage, indicated by A(z) on the figure. The
extra functionality lies however in the feedback filter that is present. A slicer makes decision of the output symbols, based on the output of the equalizer. These decided symbols are fed back to the output of the FFE using a second filter: B(z), hence the name: decision feedback equalizer.
This thesis won’t go too deep into the signal processing properties that explain the phe-nomena and improvements related to a DFE. It will however accept certain pre-studied results and look at the hardware implementation of this. However, in order to briefly asses the performance enhancement made possible by a DFE, a simple example is given that immediately makes clear the improvement that a DFE can offer.
The scenario is as follows. The training signal is called: u(t). The input signal x(t) is equal to u(t) + 0.1u(t − Tb). The distortion that arises is thus the spreading of a previous
value, into the current value: a typical intersymbol interference (ISI) scenario. With a N-tap FFE, it is not possible to completely equalize this type of distortion. This can be seen from the following equation (N = 3 in this example):
y(t) =w1(u(t) + 0.1u(t − Tb))+
w2(u(t − Tb) + 0.1u(t − 2Tb))+
w3(u(t − 2Tb) + 0.1u(t − 3Tb))
(2.12)
It is quickly clear that no solution for (w1, w2 and w3) exists that makes y(t) = u(t). The
best solution will be:
w1 = 1 (2.13)
w2 = −0.1 (2.14)
w3 = 0.01 (2.15)
In this case y(t) = u(t) + 0.001u(t − 3Tb). Driving up the amount of taps of this FFE,
leads to a smaller fraction of still present intersymbol interference (ISI) in the output signal. It is however not possible to completely equalize this type of distortion.
If however a single tap DFE is present this type of distortion can easily be equalized. A single tap DFE means that B(z) = wz−1. The decided symbol is fed back with a delay Tb
to the input of the DFE. The input of this DFE is: u(t) + 0.1u(t − Tb). In this case this
distortion is easily equalized by having DFE weight w = −0.1. Because decision is done on the signal y(t), and since it can be assumed that the distortion is limited, such that correct detection is still done, the decided signal ˆy(t) = u(t) This then leads to:
Which proves the correct functioning. Note that this does require the BER to be suffi-ciently small such that in most cases, correct decision is done on y(t). In literature it is found that in general, when the BER approaches 10−2, the incorrect decision errors can
start to propagate and a DFE can start deteriorating performance [13].
2.5
Clock Synchronization
In a communication channel, the transmitter modulates the information symbols on a waveform. It has been discussed that for 25G TDM PONs, this will still be the simple NRZ modulation scheme [4]. At the receiver side, the transmitted symbols are recovered by sampling the obtained incoming waveform. Correct decision will only occur if the receiver clock is synchronized to the transmitter clock. If not, the receiver might sample on bit transition moments, which results in incorrect symbol detection. This could be avoided by providing the transmitter clock directly from the transmitter. This is however not very efficient, as it requires an additional channel for this. Because of this, clock recovery chips are designed, that attempt to recover the transmit clock from the obtained data signal [17] [18] . Any error on such clock recovery results in a misalignment between the receiver and transmitter clock. These errors are referred to as synchronization errors and these have to be taken into account in the design of a receiver chain.
In passive optical networks, the ONUs have clock recovery chips that extract the used clock by the OLT [8]. This same clock is used for upstream data transmission to the OLT. The synchronization error is hence limited to a phase error from burst-to-burst. No frequency errors on this clock will occur.
2.6
Fractionally Spaced
So far the delay used in the FIR filter was said to be equal to the symbol period. When this is the case, the equalizer is called a symbol spaced equalizer. Another option is a fractionally spaced equalizer. Here the delay is equal to a certain fraction of the symbol period. Often a delay of Tb
2 is taken [19], but other options are possible. These generally
have superior performance when compared to symbol spaced equalizers.
The performance benefits of fractionally spaced equalizers are a well-studied phenomenon. A short intuitive explanation is given for the improvement offered by fractionally spaced equalizers [15]. The reader is referred to more specific literature on this topic for more
Figure 2.6.1: Symbol spaced versus fractionally spaced equalizer
concise studies. Let X(f) be the frequency response of the to-be equalized introduced distortion. Generally X(f) consists of the cascade of the transmit pulse G(f), the channel response C(f) and the receive filter H(f). Generally the filters G(f) and H(f) are chosen such that, for a flat channel, ISI-free communication is achieved. G(f) and H(f) are then respectively transmitter and receiver square root raised cosine pulses, for example. The distortion introduced by the non-flat C(f) then has to be equalized. The spectrum is mainly from [−2T1 2T1 ], but it also stretches out beyond that, up to ±T1, for a roll-off factor β = 1. The time that it takes to travel over the fiber is unknown. For this reason the phase of the incoming signal at the receiver is also unknown. Call this time delay τ0. For a symbol spaced equalizer, the incoming signal is sampled at nT . If y(kT) is the
sampled version of x(t), then the spectrum of y(kT) is: YT(f ) = 1 T X n X(f − n T)e j2π(f−n T)τ0 (2.17)
In other words, aliasing effects occur (Figure 2.6.1). The equalizer will not be able to compensate for the actual channel distortion X(f )ej2πf τ0 but only for the aliased version.
Because of this, the timing offset τ0 can not explicitly be compensated for, resulting in
the fact that a symbol spaced equalizer’s performance is very dependent on the timing phase. A T
2 fractionally spaced equalizer samples the incoming signal at twice the rate,
resulting in the following YT(f );
YT(f ) = 1 T X n X(f − 2n T )e j2π(f−2n T)τ0 (2.18)
Because X(f) = 0 for |f | > T1, no aliasing occurs. Because of this, the equalizer can di-rectly compensate for the inherent distortion in X(f )ej2πf τ0. All the phase and amplitude
distortion that is present over the entire channel bandwidth can be captured uniquely. It can then compensate for the arbitrary timing phase τ0.
2.7
Gear Shifting
Previously, the update rate was discussed. A possible improvement to the algorithm is to make this update rate time-varying in a step-wise way. This method is called gear shifting LMS [20]. Starting with a high update rate quickly gets a fast estimate of the weights. Moving towards a lower update rate afterwards then searches for a more precise solution [21]. This generally improves convergence speed.
Chapter 3
Modeling of Fiber Link
The data transmission over a potential 25G TDM PON system is modeled using VPIpho-tonics. This is done in order to better assess the distortion of the to-be designed equalizer, using more realistic data signals. The model of this communication system (Figure 3.0.1) contains the following components.
• DFB laser emitting CW light a 1 mW. It was previously explained that future 25G TDM PONs will continue to work in O-band [4], for lower dispersion properties. The modeling will be verified for O-band and C-band. More significant distortion should arise in the C-band [22].
• A pseudorandom binary sequence (PRBS). For this purpose prbs15 is used.
• The generated bits are coded into a NRZ modulation scheme with rise and fall times of 0.4Tb
(a) Training data (b) 20 km fiber
(c) 25 km fiber (d) 30 km fiber
Figure 3.0.2: Eye diagrams of extracted waveforms, O-band
• The OOK modulator modulates the NRZ data waveform onto the laser. This is done using a Mach-Zehnder modulator.
• Variable length fiber with 16nm.kmps of dispersion. For this purpose, the non-linearity of this fiber is made negligible, since the goal of the equalizer is to minimize this distortion.
• PIN photodiode. This contributes to overall noise performance by adding noise having 10.10−14√A
(Hz) noise spectral density.
• TIA having a cut-off frequency of 34fb = 18.75 GHz, a noise bandwidth of 0.8fb = 20
GHz and an input-referred noise of 2 µA. The transimpedance of this TIA is chosen such that the output is again re-scaled to a -1V to 1V range.
This is just a basic rudimentary model, yet it suffices to test equalization capabili-ties.
These simulated waveforms are shown in Figure 3.0.2 for O-band and in Figure 3.0.3 for C-band. The fiber is given no attenuation, thus the receive power is equal to the transmit power of 1 mW. The dispersion that arises, when compared to the reference signal, is
(a) Training data (b) 20 km fiber
(c) 25 km fiber (d) 30 km fiber
Figure 3.0.3: Eye diagrams of extracted waveforms, C-band
clearly visible. The time axis in these eye diagrams is normalized with respect to the bit duration. Hence the 0, 1 and 2 points indicate the multiples of the bit duration nTb on
the time axis. The 0.5 and 1.5 points indicate the odd multiples of the half bit periods (2n + 1)Tb
2. On this original training data it can be seen that ideal sampling would be
done at times (2n + 1)Tb
2.
The simulation is done for 100 000 training bits. This means that when bit error rate (BER) = 0, it actually means that no error occurs in 100 000 simulation bits and that hence BER < 1000001 = 10−5. This limited amount of bits simulated also does not
neces-sarily give accurate BERs. The trends are however correct and this is what is of main importance in this design now. To keep simulation times of the full equalizer structure within bounds, it is decided to only simulate 105 bits.
The figures also show the optimal sampling points and the corresponding BER. For O-band communication, BER = 0 is still achievable in all three cases. This is however not the case for C-band communication. This is to be expected, as distortion should be more significant in C-band. It however needs to be noted that in real-time communication, no calculation of the optimal sampling point is possible of course. In other words, even the
seemingly error-free cases would likely result in bit errors, since the receiver chain will sample at a specific sampling point, not necessarily the optimal one. If in this study, the receiver chain is set to sample at (2n + 1)Tb
2 (corresponding to the 0.5 points in the eye
diagram) and the decision level is set at 0, the following BERs are obtained: Table 3.0.1: BER for several fiber lengths for preset sampling point
BER O-band BER C-band
20 km 0 7.75e-2
25 km 6.310e-2 1.506e-1
30 km 1.108e-1 2.253e-1
It is clear that now the BERs have deteriorated. This indicates that the need for equal-ization is twofold:
• Reshape the waveform to obtain a new waveform that is as close as possible to the non-distorted waveform. This results in a waveform that creates an open eye, at some sampling point.
• Align the phase of the incoming waveform with the sampling moment of the receiver chain.
It is clear the equalization is required in both cases. Since the distortion is stronger in C-band, this band requires stronger equalization. In order to put more stringent requirements on the equalization capabilities of the to-be designed equalizer, further results are studied for C-band. An equalization structure that can equalize C-band, will be able to equalize O-band as well. This is verified when the total equalization structure is researched.
3.1
Reduction of Laser Power
The previous BERs were given for a laser power of 1 mW, reducing this power will result in lower signal power for approximately the same noise power. The SNR will hence decrease. This effect is also verified (Figure 3.1.1). This plot is here made for O-band communication because that is how it will actually be done in 25G TDM PON. C-band already shows very significant distortion at 1 mW receive power, and hence this curve is
Figure 3.1.1: BER curve for laser input power, O-band not very meaningful for C-band.
This curve also already shows the BER curves for the final equalized signal. The im-provement is clear. The sidenote that BER = 0 is in fact BER < 10−5 is even more
