161 research outputs found

    ์˜คํ”„์…‹ ์ œ๊ฑฐ๊ธฐ์˜ ์ ์‘ ์ œ์–ด ๋“ฑํ™”๊ธฐ์™€ ๋ณด์šฐ-๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋ฅผ ํ™œ์šฉํ•œ ์ˆ˜์‹ ๊ธฐ ์„ค๊ณ„

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    ํ•™์œ„๋…ผ๋ฌธ(๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์ „๊ธฐยท์ •๋ณด๊ณตํ•™๋ถ€, 2021.8. ์—ผ์ œ์™„.In this thesis, designs of high-speed, low-power wireline receivers (RX) are explained. To be specific, the circuit techniques of DC offset cancellation, merged-summer DFE, stochastic Baud-rate CDR, and the phase detector (PD) for multi-level signal are proposed. At first, an RX with adaptive offset cancellation (AOC) and merged summer decision-feedback equalizer (DFE) is proposed. The proposed AOC engine removes the random DC offset of the data path by examining the random data stream's sampled data and edge outputs. In addition, the proposed RX incorporates a shared-summer DFE in a half-rate structure to reduce power dissipation and hardware complexity of the adaptive equalizer. A prototype chip fabricated in 40 nm CMOS technology occupies an active area of 0.083 mm2. Thanks to the AOC engine, the proposed RX achieves the BER of less than 10-12 in a wide range of data rates: 1.62-10 Gb/s. The proposed RX consumes 18.6 mW at 10 Gb/s over a channel with a 27 dB loss at 5 GHz, exhibiting a figure-of-merit of 0.068 pJ/b/dB. Secondly, a 40 nm CMOS RX with Baud-rate phase-detector (BRPD) is proposed. The RX includes two PDs: the BRPD employing the stochastic technique and the BRPD suitable for multi-level signals. Thanks to the Baud-rate CDRโ€™s advantage, by not using an edge-sampling clock, the proposed CDR can reduce the power consumption by lowering the hardware complexity. Besides, the proposed stochastic phase detector (SPD) tracks an optimal phase-locking point that maximizes the vertical eye opening. Furthermore, despite residual inter-symbol interference, proposed BRPD for multi-level signal secures vertical eye margin, which is especially vulnerable in the multi-level signal. Besides, the proposed BRPD has a unique lock point with an adaptive DFE, unlike conventional Mueller-Muller PD. A prototype chip fabricated in 40 nm CMOS technology occupies an active area of 0.24 mm2. The proposed PAM-4 RX achieves the bit-error-rate less than 10-11 in 48 Gb/s and the power efficiency of 2.42 pJ/b.๋ณธ ๋…ผ๋ฌธ์€ ๊ณ ์†, ์ €์ „๋ ฅ์œผ๋กœ ๋™์ž‘ํ•˜๋Š” ์œ ์„  ์ˆ˜์‹ ๊ธฐ์˜ ์„ค๊ณ„์— ๋Œ€ํ•ด ์„ค๋ช…ํ•˜๊ณ  ์žˆ๋‹ค. ๊ตฌ์ฒด์ ์œผ๋กœ ๋งํ•˜๋ฉด, ์˜คํ”„์…‹ ์ƒ์‡„, ๋ณ‘ํ•ฉ๋œ ์„œ๋จธ๋ฅผ ์‚ฌ์šฉํ•˜๋Š” ๊ฒฐ์ • ํ”ผ๋“œ๋ฐฑ ๋“ฑํ™”๊ธฐ ๊ธฐ์ˆ , ํ™•๋ฅ ์  ๋ณด์šฐ ๋ ˆ์ดํŠธ ํด๋Ÿญ๊ณผ ๋ฐ์ดํ„ฐ ๋ณต์›๊ธฐ, ๊ทธ๋ฆฌ๊ณ  ๋‹ค์ค‘ ๋ ˆ๋ฒจ ์‹ ํ˜ธ์— ์ ํ•ฉํ•œ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ์ฒซ์งธ๋กœ, ์ ์‘ ์˜คํ”„์…‹ ์ œ๊ฑฐ ๋ฐ ๋ณ‘ํ•ฉ๋œ ์„œ๋จธ๋ฅผ ์‚ฌ์šฉํ•˜๋Š” ๊ฒฐ์ • ํ”ผ๋“œ๋ฐฑ ๋“ฑํ™”๊ธฐ๋ฅผ ๊ฐ–์ถ˜ ์ˆ˜์‹ ๊ธฐ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ์ œ์•ˆ๋œ ์ ์‘ ์˜คํ”„์…‹ ์ œ๊ฑฐ ์—”์ง„์€ ์ž„์˜์˜ ๋ฐ์ดํ„ฐ ์ŠคํŠธ๋ฆผ์˜ ์ƒ˜ํ”Œ๋ง ๋ฐ์ดํ„ฐ, ์—์ง€ ์ถœ๋ ฅ์„ ๊ฒ€์‚ฌํ•˜์—ฌ ๋ฐ์ดํ„ฐ ๊ฒฝ๋กœ ์ƒ์˜ ์˜คํ”„์…‹์„ ์ œ๊ฑฐํ•œ๋‹ค. ๋˜ํ•œ ํ•˜ํ”„ ๋ ˆ์ดํŠธ ๊ตฌ์กฐ์˜ ๋ณ‘ํ•ฉ๋œ ์„œ๋จธ๋ฅผ ์‚ฌ์šฉํ•˜๋Š” ๊ฒฐ์ • ํ”ผ๋“œ๋ฐฑ ๋“ฑํ™”๊ธฐ๋Š” ์ „๋ ฅ์˜ ์‚ฌ์šฉ๊ณผ ํ•˜๋“œ์›จ์–ด์˜ ๋ณต์žก์„ฑ์„ ์ค„์ธ๋‹ค. 40 nm CMOS ๊ธฐ์ˆ ๋กœ ์ œ์ž‘๋œ ํ”„๋กœํ† ํƒ€์ž… ์นฉ์€ 0.083 mm2 ์˜ ๋ฉด์ ์„ ๊ฐ€์ง„๋‹ค. ์ ์‘ ์˜คํ”„์…‹ ์ œ๊ฑฐ๊ธฐ ๋•๋ถ„์— ์ œ์•ˆ๋œ ์ˆ˜์‹ ๊ธฐ๋Š” 10-12 ๋ฏธ๋งŒ์˜ BER์„ ๋‹ฌ์„ฑํ•œ๋‹ค. ๋˜ํ•œ ์ œ์•ˆ๋œ ์ˆ˜์‹ ๊ธฐ๋Š” 5GHz์—์„œ 27 dB์˜ ๋กœ์Šค๋ฅผ ๊ฐ–๋Š” ์ฑ„๋„์—์„œ 10 Gb/s์˜ ์†๋„์—์„œ 18.6 mW๋ฅผ ์†Œ๋น„ํ•˜๋ฉฐ 0.068 pJ/b/dB์˜ FoM์„ ๋‹ฌ์„ฑํ•˜์˜€๋‹ค. ๋‘๋ฒˆ์งธ๋กœ, ๋ณด์šฐ ๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๊ฐ€ ์žˆ๋Š” 40 nm CMOS ์ˆ˜์‹ ๊ธฐ๊ฐ€ ์ œ์•ˆ๋˜์—ˆ๋‹ค. ์ˆ˜์‹ ๊ธฐ์—๋Š” ๋‘๊ฐœ์˜ ๋ณด์šฐ ๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋ฅผ ํฌํ•จํ•œ๋‹ค. ํ•˜๋‚˜๋Š” ํ™•๋ฅ ๋ก ์  ๊ธฐ๋ฒ•์„ ์‚ฌ์šฉํ•˜๋Š” ๋ณด์šฐ ๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ์ด๋‹ค. ๋ณด์šฐ ๋ ˆ์ดํŠธ ํด๋Ÿญ ๋ฐ์ดํ„ฐ ๋ณต์›๊ธฐ์˜ ์žฅ์  ๋•๋ถ„์— ์—์ง€ ์ƒ˜ํ”Œ๋ง ํด๋Ÿญ์„ ์‚ฌ์šฉํ•˜์ง€ ์•Š์Œ์œผ๋กœ์„œ ํŒŒ์›Œ์˜ ์†Œ๋ชจ์™€ ํ•˜๋“œ์›จ์–ด์˜ ๋ณต์žก์„ฑ์„ ์ค„์˜€๋‹ค. ๋˜ํ•œ ํ™•๋ฅ ์  ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋Š” ์ˆ˜์ง ์•„์ด ์˜คํ”„๋‹์„ ์ตœ๋Œ€ํ™”ํ•˜๋Š” ์ตœ์ ์˜ ์œ„์ƒ ์ง€์ ์„ ์ฐพ์„ ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋‹ค๋ฅธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋Š” ๋‹ค์ค‘ ๋ ˆ๋ฒจ ์‹ ํ˜ธ์— ์ ํ•ฉํ•œ ๋ฐฉ์‹์ด๋‹ค. ์‹ฌ๋ณผ ๊ฐ„ ๊ฐ„์„ญ์ด ๋‹ค์ค‘ ๋ ˆ๋ฒจ ์‹ ํ˜ธ์— ๋งค์šฐ ์ทจ์•ฝํ•œ ๋ฌธ์ œ๊ฐ€ ์žˆ๋”๋ผ๋„ ์ œ์•ˆ๋œ ๋‹ค์ค‘ ๋ ˆ๋ฒจ ์‹ ํ˜ธ์šฉ ๋ณด์šฐ ๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋Š” ์ˆ˜์ง ์•„์ด ๋งˆ์ง„์„ ํ™•๋ณดํ•œ๋‹ค. ๊ฒŒ๋‹ค๊ฐ€ ์ œ์•ˆ๋œ ๋ณด์šฐ ๋ ˆ์ดํŠธ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ๋Š” ๊ธฐ์กด์˜ ๋ฎฌ๋Ÿฌ-๋ฎ๋Ÿฌ ์œ„์ƒ ๊ฒ€์ถœ๊ธฐ์™€ ๋‹ฌ๋ฆฌ ์ ์‘ํ˜• ๊ฒฐ์ • ํ”ผ๋“œ๋ฐฑ ๋“ฑํ™”๊ธฐ๊ฐ€ ์žˆ๋”๋ผ๋„ ์œ ์ผํ•œ ๋ฝ ์ง€์ ์„ ๊ฐ–๋Š”๋‹ค. ํ”„๋กœํ† ํƒ€์ž… ์นฉ์€ 0.24mm2์˜ ๋ฉด์ ์„ ๊ฐ€์ง„๋‹ค. ์ œ์•ˆ๋œ PAM-4 ์ˆ˜์‹ ๊ธฐ๋Š” 48 Gb/s์˜ ์†๋„์—์„œ 10-11 ๋ฏธ๋งŒ์˜ BER์„ ๊ฐ€์ง€๊ณ , 2.42 pJ/b์˜ FoM์„ ๊ฐ€์ง„๋‹ค.CHAPTER 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 THESIS ORGANIZATION 5 CHAPTER 2 BACKGROUNDS 6 2.1 BASIC ARCHITECTURE IN SERIAL LINK 6 2.1.1 SERIAL COMMUNICATION 6 2.1.2 CLOCK AND DATA RECOVERY 8 2.1.3 MULTI-LEVEL PULSE-AMPLITUDE MODULATION 10 2.2 EQUALIZER 12 2.2.1 EQUALIZER OVERVIEW 12 2.2.2 DECISION-FEEDBACK EQUALIZER 15 2.2.3 ADAPTIVE EQUALIZER 18 2.3 CLOCK RECOVERY 21 2.3.1 2X OVERSAMPLING PD ALEXANDER PD 22 2.3.2 BAUD-RATE PD MUELLER MULLER PD 25 CHAPTER 3 AN ADAPTIVE OFFSET CANCELLATION SCHEME AND SHARED SUMMER ADAPTIVE DFE 28 3.1 OVERVIEW 28 3.2 AN ADAPTIVE OFFSET CANCELLATION SCHEME AND SHARED-SUMMER ADAPTIVE DFE FOR LOW POWER RECEIVER 31 3.3 SHARED SUMMER DFE 37 3.4 RECEIVER IMPLEMENTATION 42 3.5 MEASUREMENT RESULTS 45 CHAPTER 4 PAM-4 BAUD-RATE DIGITAL CDR 51 4.1 OVERVIEW 51 4.2 OVERALL ARCHITECTURE 53 4.2.1 PROPOSED BAUD-RATE CDR ARCHITECTURE 53 4.2.2 PROPOSED ANALOG FRONT-END STRUCTURE 59 4.3 STOCHASTIC PHASE DETECTION PAM-4 CDR 64 4.3.1 PROPOSED STOCHASTIC PHASE DETECTION 64 4.3.2 COMPARISON OF THE STOCHASTIC PD WITH SS-MMPD 70 4.4 PHASE DETECTION FOR MULTI-LEVEL SIGNALING 73 4.4.1 PROPOSED BAUD-RATE PHASE DETECTOR FOR MULTI-LEVEL SIGNAL 73 4.4.2 DATA LEVEL AND DFE COEFFICIENT ADAPTATION 79 4.4.3 PROPOSED PHASE DETECTOR 84 4.5 MEASUREMENT RESULT 88 4.5.1 MEASUREMENT OF THE PROPOSED STOCHASTIC BAUD-RATE PHASE DETECTION 94 4.5.2 MEASUREMENT OF THE PROPOSED BAUD-RATE PHASE DETECTION FOR MULTI-LEVEL SIGNAL 97 CHAPTER 5 CONCLUSION 103 BIBLIOGRAPHY 105 ์ดˆ ๋ก 109๋ฐ•

    Wireless Channel Equalization in Digital Communication Systems

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    Our modern society has transformed to an information-demanding system, seeking voice, video, and data in quantities that could not be imagined even a decade ago. The mobility of communicators has added more challenges. One of the new challenges is to conceive highly reliable and fast communication system unaffected by the problems caused in the multipath fading wireless channels. Our quest is to remove one of the obstacles in the way of achieving ultimately fast and reliable wireless digital communication, namely Inter-Symbol Interference (ISI), the intensity of which makes the channel noise inconsequential. The theoretical background for wireless channels modeling and adaptive signal processing are covered in first two chapters of dissertation. The approach of this thesis is not based on one methodology but several algorithms and configurations that are proposed and examined to fight the ISI problem. There are two main categories of channel equalization techniques, supervised (training) and blind unsupervised (blind) modes. We have studied the application of a new and specially modified neural network requiring very short training period for the proper channel equalization in supervised mode. The promising performance in the graphs for this network is presented in chapter 4. For blind modes two distinctive methodologies are presented and studied. Chapter 3 covers the concept of multiple cooperative algorithms for the cases of two and three cooperative algorithms. The select absolutely larger equalized signal and majority vote methods have been used in 2-and 3-algoirithm systems respectively. Many of the demonstrated results are encouraging for further research. Chapter 5 involves the application of general concept of simulated annealing in blind mode equalization. A limited strategy of constant annealing noise is experimented for testing the simple algorithms used in multiple systems. Convergence to local stationary points of the cost function in parameter space is clearly demonstrated and that justifies the use of additional noise. The capability of the adding the random noise to release the algorithm from the local traps is established in several cases

    Receiver equalization for a 10 gigabit per second high-speed serial link in 65 nm CMOS technology

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    This thesis addresses the receiver equalization techniques for a 10 Gbps USB 3.1 link in 65 nm CMOS technology. Two types of equalizers are implemented: a continuous time linear equalizer (CTLE) and a 1-tap full-rate decision feedback equalizer (DFE). The combined CTLE and DFE architecture is simulated with an rms receiver clock jitter of 5.3 ps and achieves a BER < 10Eโˆ’12 while consuming 3.3 mW at the Nyquist frequency of 5 GHz

    High-Speed Link Modeling: Analog/Digital Equalization and Modulation Techniques

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    High-speed serial input-output (I/O) link has required advanced equalization and modulation techniques to mitigate inter-symbol interference (ISI) caused by multi-Gb/s signaling over band-limited channels. Increasing demands for transceiver power and area complexity has leveraged on-going interest in analog-to-digital converter (ADC) based link, which allows for robust equalization and flexible adaptation to advanced signaling. With diverse options in ISI control techniques, link performance analysis for complicated transceiver architectures is very important. This work presents advanced statistical modeling for ADC-based link, performance comparison of existing modulation and equalization techniques, and proposed hybrid ADC-based receiver that achieves further power saving in digital equalization. Statistical analysis precisely estimates high-speed link margins at given implementation constrains and low target bit-error-rate (BER), typically ranges from 1e-12 to 1e-15, by applying proper statistical bound of noise and distortion. The proposed statistical ADC-based link modeling utilizes bounded probability density function (PDF) of limited quantization distortion (4-6 bits) through digital feed-forward and decision feedback equalizers (FFE-DFE) to improve low target BER estimation. Based on statistical modeling, this work surveys the impact of insufficient equalization, jitter and crosstalk on modulation selection among two and four level pulse amplitude modulation (PAM-2 and PAM-4, respectively) and duobinary, and ADC resolution reduction performance by partial analog equalizer (PAE). While the information of channel loss at effective Nyquist frequency and signaling constellation loss initially guides modulation selection, the statistical analysis results show that PAM-4 best tolerates jitter and crosstalk, and duobinary requires the least equalization complexity. Meanwhile, despite robust digital equalization, high-speed ADC complexity and power consumption is still a critical bottleneck, so that PAE is necessitated to reduce ADC resolution requirement. Statistical analysis presents up to 8-bit resolution is required in 12.5Gb/s data communications at 46dB of channel loss without PAE, while 5-bit ADC is enough with 3-tap FFE PAE. For optimal ADC resolution reduction by PAE, digital equalizer complexity also increases to provide enough margin tolerating significant quantization distortion. The proposed hybrid receiver defines unreliable signal thresholds by statistical analysis and selectively takes additional digital equalization to save potentially increasing dynamic power consumption in digital. Simulation results report that the hybrid receiver saves at least 64% of digital equalization power with 3-tap FFE PAE in 12.5Gb/s data rate and up to 46dB loss channels. Finally, this work shows the use of embedded-DFE ADC in the hybrid receiver is limited by error propagation

    Modeling and Design of High-Speed CMOS Receivers for Short-Reach Photonic Links

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    This dissertation presents several research outcomes towards designing high-speed CMOS optical receivers for energy-efficient short-reach optical links. First, it provides a wide survey of recently published equalizer-based receivers and presents a novel methodology to accurately calculate their noise. The proposed methodology is then used to find the receiver that achieves the best sensitivity. Second, the trade-off between sensitivity and power dissipation of the receiver is optimized to reduce the energy consumption per bit of the overall link. Design trade-offs for the receiver, transmitter, and the overall link are presented, and comparisons are made to study how much receiver sensitivity can be sacrificed to save its power dissipation before this power reduction is outpaced by the transmitterโ€™s increase in power. Unlike conventional wisdom, our results show that energy-efficient links require low-power receivers with input capacitance much smaller than that required for noise-optimum performance. Third, the thesis presents a novel equalization technique for optical receivers. A linear equalizer (LE) is realized by adding a pole in the feedback paths of an active feedback-based wideband amplifier. By embedding the peaking in the main amplifier (MA), the front-end meets the sensitivity and gain of conventional LE-based receivers with better energy efficiency by eliminating the standalone equalizer stage(s). Electrical measurements are presented to demonstrate the capability of the proposed technique in restoring the bandwidth and improving the performance over the conventional design

    Silicon Integrated Arrays: From Microwave to IR

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    Integrated chips have enabled realization and mass production of complex systems in a small form factor. Through process miniaturization many novel applications in silicon photonics and electronic systems have been enabled. In this thesis I have provided several examples of innovations that are only enabled by integration. I have also demonstrated how electronics and photonics circuits can complement each other to achieve a system with superior performance.</p

    40 Gb/s optical transmission systems

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    PMD impairments in optical fiber transmission at 10 Gbps and 40 Gbps

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    The continuous need for greater bandwidth and capacity to support existing and emerging technologies, such as fiber-to-the-home (FTTH) and Internet Protocol Television(IPTV), drive optical-communication systems to higher and higher data rates per wavelength channel, from 10 to 40 Gbps and above. Degrading effects that tended to cause non catastrophic events at lower bit rates have become critical concerns for high-performance networks. Among them, polarization-mode dispersion (PMD) is perhaps the largest concern and, therefore, has garnered a great amount of attention. The PMD arises in an optical fiber from asymmetries in the fiber core that induce a small amount of birefringence that randomly varies along the length of the fiber. This birefringence causes the power in each optical pulse to split between the two polarization modes of the fiber and travel at different speeds, creating a differential group delay (DGD) between the two modes that can result in pulse spreading and intersymbol interference. PMD becomes a unique and challenging hurdle for high-performance systems mainly due to its dynamic and random nature. The polarization state is generally unknown and wanders with time. In general, PMD effects are wavelength (channel) dependent and can vary over a time scale of milliseconds. As a random variable, the DGD follows a Maxwellian distribution for which high-DGD points in the tail of the distribution can lead to network outages. Typically, system designers require the outage probability for high-performance networks to be 10โˆ’5 or less (penalty > 1dB for <30 min/yr). Clearly, the most straightforward approach to overcoming the effects of PMD is to employ newly manufactured low-PMD optical fibers, which have PMD values < 0.1 . However, much of the previously embedded fiber has high PMD values between 0.5 and 1 or even higher. The reality of deploying new systems over the embedded fiber means that the PMD monitoring and compensation are important for PMD mitigation. Unlike other degrading effects such as chromatic dispersion, the PMD is a time-varying random process making compensation difficult.The aim of this work is to study the trend of PMD effects over two different system, at 10 and 40 Gbps with two kind of fiber with high (0.5 ) and low (0.1 ) PMD coefficient. The first one corresponds to an old fiberโ€™s type, that is used in the majority in the current transmission system; while the second one corresponds to a new fiberโ€™s type, designed to have a lower response to the PMD phenomenon, making possible the transmission over long distances at high bit-rates. This work is structured as follows: After a short introduction, the second chapter is a review of PMD theory; where the PMD is faced from a theoretical point of view. Itโ€™s reported how the PMD arises in a fiber, how the DGD has a Maxwellian probability distribution, and the outage limits to design a system under the influences of PMD. In the third chapter there is a literary review over the PMD mitigation. Over the years, research groups from around the globe have proposed and/or demonstrated different strategies for PMD compensation. In this chapter an overview of these strategies shall be given, mentioning their relative merits and demerits. Following that, methods to increase the tolerance of a fiber-optic communication system to PMD, will also be discussed. After this theoretical introduction the central partโ€™s of this study starts. In the fourth chapter the limitations imposed by the PMD are investigated. We starts probing the theoretical distance limits imposed by the only PMD, setting all other fiberโ€™s impairments and attenuation to be negligible. Sequentially two single span optical transmission systems are compared on the basis of fiber PMD coefficient and bit-rates, to find the maximum distance that can be reached with a bit error rate of 10-10, taking in account or not the PMD and setting only the attenuation of the fiber. After this first investigation, the real impact of PMD was reported, performing a simulation of a multi span system, where the fiberโ€™s attenuation of each section is compensated by an amplifier, so to find the maximum reachable distances over long-haul transmission and clearly see how is the PMD impact.In the last chapter a first-order polarization compensator is tested. Firstly in order to show how the compensator could works, the monitor signalโ€™s simulation (based on the analysis of the Power Spectral Densities at selected frequency) is made, to show how the PMD level is related to the PSD. After that, the compensator is tested, performing two simulations at 10 and 40 Gbps with different value of DGD reached at the end of the fiber, to demonstrate the real capability of the compensator. The last study done is over the compensation applied to the previous multi-span system, to study how the performance of a system get increasing with a PMD compensation, and what is the system tolerance to PMD with or without compensation. All the simulation of this work are made with the use of a software package (1) used in the optical laboratory of Universitat Politรจcnica de Catalunya
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