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Advances in Signals and Systems Research
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Advances in Signals and Systems Research

A special issue of Electronics (ISSN 2079-9292). This special issue belongs to the section "Computer Science & Engineering".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 2445

Special Issue Editors

Dr. Kok Yew Ng

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Guest Editor
School of Engineering, Ulster University, Belfast BT15 1AP, UK
Interests: control engineering; fault diagnosis; digital twin
Special Issues, Collections and Topics in MDPI journals
Dr. Adrian Moore

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Guest Editor
School of Computing, Ulster University, Belfast BT15 1AP, UK
Interests: intelligent systems; assistive technologies; next generation networks; semantic analytics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Huiru Zheng

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Guest Editor
School of Computing, Ulster University, Belfast BT15 1AP, UK
Interests: machine learning; bioinformatics; healthcare informatics; healthcare technology; intelligent data analysis; integrative data analytics; assistive technologies
Special Issues, Collections and Topics in MDPI journals
Ruth G. Lennon

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Guest Editor Assistant
Computing Department, Atlantic Technological University, F92 FC93 Donegal, Ireland
Interests: DevOps; web services; cloud computing

Special Issue Information

Dear Colleagues,

The 35th Irish Signals and Systems Conference (ISSC 2024), hosted by Ulster University and held in Belfast, Northern Ireland on 13–14 June 2024, has been a longstanding platform for the exchange of groundbreaking research in the fields of signals and systems. To commemorate this event and foster further knowledge dissemination, we are delighted to announce a special issue in Electronics dedicated to the advancements presented at ISSC 2024.

Over the past 34 years, ISSC has established itself as the foremost conference in Ireland, encompassing all aspects of signals and systems. The conference brings together experts and researchers from diverse backgrounds, focusing on Digital Signal Processing, Control Systems, Communications, and related fields of Information and Communication Technology. ISSC 2024 will explore topics such as algorithms, system modelling, and artificial intelligence, as well as design and implementation for a wide range of applications.

In addition to papers selected from ISSC 2024, we invite authors from around the world to contribute their research papers to our special issue. This open call for papers aims to create a broader platform for sharing the latest advancements in signals and systems research.

Aims and scopes: Prospective authors are encouraged to submit previously unpublished contributions within, but not limited to, the following areas:

  1. Signal Processing: This track welcomes research related to signal processing techniques, algorithms, and applications in various domains.
  2. Control Systems: Contributions on control systems theory, design, and applications, including robotics and automation.
  3. Cyberphysical Systems: Manuscripts exploring the integration of physical systems with computational elements and network connectivity.
  4. Communications and Future Networking: Research on communication technologies, protocols, and the future of networking.
  5. Cybersecurity: Papers addressing security challenges in signals and systems, including encryption, privacy, and threat detection.
  6. Machine Learning and AI: Contributions in the areas of machine learning and artificial intelligence applied to signals and systems research.
  7. Signals and Systems for Sustainability: Research on how signals and systems contribute to sustainable practices and environmental conservation

We look forward to receiving your contributions, whether they were presented at ISSC 2024 or are part of our open call. Your participation in this special issue will help continue the tradition of excellence established by ISSC and contribute to the growth of knowledge in these critical fields.

You may choose our Joint Special Issue in Applied Sciences.

Dr. Kok Yew Ng
Dr. Adrian Moore
Prof. Dr. Huiru Zheng
Guest Editors

Ruth G. Lennon
Guest Editor Assistant

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Electronics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • signal processing
  • cybersecurity
  • control systems
  • communications and future networking
  • machine learning

Benefits of Publishing in a Special Issue

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  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

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Research

Jump to: Review

20 pages, 4822 KiB  
Article
Networking 3 K Two-Qubit Logic Gate Quantum Processors to Approach 1 Billion Logic Gate Performance
by Daniel Guidotti, Xiaoli Ma and Gee-Kung Chang
Electronics 2024, 13(23), 4604; https://doi.org/10.3390/electronics13234604 - 22 Nov 2024
Viewed by 295
Abstract
Outlined is a proposal designed to culminate in the foundry fabrication of arrays of singly addressable quantum dot sources deterministically emitting single pairs of energy-time entangled photons at C-band wavelengths, each pair having negligible spin-orbit fine structure splitting, each pair being channeled into [...] Read more.
Outlined is a proposal designed to culminate in the foundry fabrication of arrays of singly addressable quantum dot sources deterministically emitting single pairs of energy-time entangled photons at C-band wavelengths, each pair having negligible spin-orbit fine structure splitting, each pair being channeled into single mode pig-tail optical fibers. Entangled photons carry quantum state information among distributed quantum servers via I/O ports having two functions: the unconditionally secure distribution of decryption keys to decrypt publicly distributed, encrypted classical bit streams as input to generate corresponding qubit excitations and to convert a stream of quantum nondemolition measurements of qubit states into a classical bit stream. Outlined are key steps necessary to fabricate arrays of on-demand quantum dot sources of entangled photon pairs; the principles are (1) foundry fabrication of arrays of isolated quantum dots, (2) generation of localized sub-surface shear strain in a semiconductor stack, (3) a cryogenic anvil cell, (4) channeling entangled photons into single-mode optical fibers, (5) unconditionally secure decryption key distribution over the fiber network, (6) resonant excitation of a Josephson tunnel junction qubits from classical bits, and (7) conversion of quantum nondemolition measurements of qubit states into a classical bit. Full article
(This article belongs to the Special Issue Advances in Signals and Systems Research)
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Figure 1

Figure 1
<p>A semiconductor optical resonator typically comprises two opposing semiconductor Bragg reflectors enclosing a source of light, in this case, one or more semiconductor quantum dots. When the source is electrically biased the structure functions as a semiconductor diode generating currents through the quantum dot that initiate a relaxation process to the ground state with the emission of light out of the upper port. Entangled photon pairs emanate from the top optical port. A bottom optical port may be used as an alternative means to optically pump the quantum dot. Optically transparent and electrically conducting Indium tin oxide (ITO) films may be used to aid in forming more uniform electric fields initiated at the optical contacts.</p> Full article ">Figure 2
<p>The anvil cell comprises (1) a cell wall having a tapered top access port to channel entangled photons into a lensed optical fiber, (2) a bottom optical access port, (3) an electrical I/O port, and means to translate the lensed optical fiber in a horizontal plane provided by an x-y actuator block mounted externally to the upper cell wall. Compressive stress is provided by the action of a piezoelectric actuator and the elastic response to the anvil cell. The lens is used to provide localized subsurface shear strain and to channel entangled photons into the lensed optical fiber.</p> Full article ">Figure 3
<p>Lensed optical fiber fine alignment. The optical fiber is represented by the core and cladding. x- and y-mounting blocks, fixed to the upper wall exterior, enable piezoelectric actuation of push rods to translate the optical fiber so as to maximize photon collection efficiency.</p> Full article ">Figure 4
<p>Simplified side view of the optical system designed to optimize the channeling of entangled photon pairs emanating from a quantum dot in a quantum well layer formed between a p-type and an n-type compound semiconductor stack that comprises an optical field resonator shown in detail in <a href="#electronics-13-04604-f001" class="html-fig">Figure 1</a> and <a href="#electronics-13-04604-f002" class="html-fig">Figure 2</a>. The tip of the lensed optical fiber is represented by the tapered cladding and core fitting in a beveled access port in the top wall of the anvil cell.</p> Full article ">Figure 5
<p>Perspective view of a quantum well (QW) layer fabricated between n-type and p-type semiconductor top Bragg reflectors (BR) and bottom Bragg reflector (BR) that form the optical resonator cavity as shown in <a href="#electronics-13-04604-f001" class="html-fig">Figure 1</a>. In the interest of clarity, the quantum dot distribution in the quantum well (QW) layer is not shown here.</p> Full article ">Figure 6
<p>Hertzian theory of contacting surfaces. Depicted is a side view of the drawing in <a href="#electronics-13-04604-f005" class="html-fig">Figure 5</a> emphasizing a rendition of subsurface shear strain contours resulting when a spherical surface is in compressive contact with a planar surface [<a href="#B21-electronics-13-04604" class="html-bibr">21</a>,<a href="#B22-electronics-13-04604" class="html-bibr">22</a>,<a href="#B23-electronics-13-04604" class="html-bibr">23</a>].</p> Full article ">Figure 7
<p>Shown is a gas flow cryogenic cell containing three anvil cells, some features of which are also depicted in <a href="#electronics-13-04604-f002" class="html-fig">Figure 2</a>, <a href="#electronics-13-04604-f003" class="html-fig">Figure 3</a> and <a href="#electronics-13-04604-f004" class="html-fig">Figure 4</a>. Gas ports allow for continuous gas flow, feed-thru ports allow for current flow while holes and seals enable sealed lensed optical fiber access. Quick-release connectors couple to outgoing optical fibers.</p> Full article ">Figure 8
<p>Concept diagram for a secure external optical network enabling the exchange of classical bits between two quantum servers. QP-A, QP-B quantum processors; TQ R\O Transmon qubit read\out; CBM classical DRAM buffer; QD (A), QD (B) quantum dot transmitter; Rx (B) SNSPD BSM, Rx (A) SNSPD BSM are photon receivers and Bell state measurement stations; Sender (A) BSM and Sender (B) BSM are Bell state measurement (BSM) stations; TESG A and TESG B are Transmon excitation signal generators that generate Transmon qubit of generic frequency 5 GHz from a classical bit waveform. <b>qc1</b>, <b>qc2</b> are quantum channels and <b>pc1</b>, <b>pc2</b> are public channels.</p> Full article ">Figure 9
<p>Concept drawing of networked quantum servers linked to a classical buffer memory via unconditionally secure quantum channels. The direction of the arrowhead indicates the direction of flow of classical bits, B. Q denotes a qubit, B/Q denotes a classical bit-to-qubit interface, and Q/B denotes a qubit-to-classical bit interface.</p> Full article ">Figure 10
<p>The Bit/Qubit Interface. A quantum server receiving a classical bit stream with return-to-zero (RZ) coding is shown in the figure. The frequency spectrum of the classical bit (circled) is mixed with the frequency output of a local oscillator to generate a microwave frequency that is in resonance with the target Transmon qubit microwave energy. Adapted from <a href="#electronics-13-04604-f001" class="html-fig">Figure 1</a> in reference [<a href="#B24-electronics-13-04604" class="html-bibr">24</a>].</p> Full article ">Figure 11
<p>Simplified schematic of a qubit readout through a nonlinear Purcell filter [<a href="#B31-electronics-13-04604" class="html-bibr">31</a>].</p> Full article ">Figure 12
<p>Representation of a quantum server QS_<span class="html-italic">i</span> with an input bus providing streams of classical bits and an output bus delivering streams of readout bits “averaged” over a number of runs to achieve the required fidelity.</p> Full article ">Figure 13
<p>A more detailed view of a quantum server network comprising the number of quantum servers denoted as QS_<span class="html-italic">i</span>, QS_<span class="html-italic">j</span>, QS_m, QS_n, classical DARM memory buffer that provides classical bits as inputs to quantum servers whose primary tasks are to process classical bits and to provide readouts that can be converted to classical bits after classical data post-processing by a “Post-QS Data Processor”.</p> Full article ">
13 pages, 913 KiB  
Article
Application of Genetic Algorithms for Strejc Model Parameter Tuning
by Dawid Ostaszewicz and Krzysztof Rogowski
Electronics 2024, 13(18), 3652; https://doi.org/10.3390/electronics13183652 - 13 Sep 2024
Viewed by 467
Abstract
In this paper, genetic algorithms are applied to fine-tune the parameters of a system model characterized by unknown transfer functions utilizing the Strejc method. In this method, the high-order plant dynamic is approximated by the reduced-order multiple inertial transfer function. The primary objective [...] Read more.
In this paper, genetic algorithms are applied to fine-tune the parameters of a system model characterized by unknown transfer functions utilizing the Strejc method. In this method, the high-order plant dynamic is approximated by the reduced-order multiple inertial transfer function. The primary objective of this research is to optimize the parameter values of the Strejc model using genetic algorithms to obtain the optimal value of the integral quality indicator for the model and step responses which fit the plant response. In the analysis, various structures of transfer functions will be considered. For fifth-order plants, different structures of a transfer function will be employed: second-order inertia and multiple-inertial models of different orders. The genotype structure is composed in such a way as to ensure the convergence of the method. A numerical example demonstrating the utility of the method of high-order plants is presented. Full article
(This article belongs to the Special Issue Advances in Signals and Systems Research)
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Figure 1

Figure 1
<p>Chromosome and genotype structure.</p> Full article ">Figure 2
<p>Chromosome crossing procedure diagram.</p> Full article ">Figure 3
<p>Step responses of object and double inertia model before and after correction.</p> Full article ">Figure 4
<p>Error signal of double-inertia model before and after correction.</p> Full article ">Figure 5
<p>Adaptation process.</p> Full article ">Figure 6
<p>Step responses of object and second-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model.</p> Full article ">Figure 7
<p>Error signal of second-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model before and after correction.</p> Full article ">Figure 8
<p>Step responses of object and third-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model.</p> Full article ">Figure 9
<p>Error signal of third-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model before and after correction.</p> Full article ">Figure 10
<p>Step responses of object and fourth-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model.</p> Full article ">Figure 11
<p>Error signal of fourth-order multi-<math display="inline"><semantics> <msub> <mi>T</mi> <mi>n</mi> </msub> </semantics></math> model before and after correction.</p> Full article ">
22 pages, 15166 KiB  
Article
Continuous Recording of Resonator Characteristics Using Single-Sideband Modulation
by Martin Lippmann, Moritz Hitzemann, Leonardo Hermeling, Kirsten J. Dehning, Jonas Winkelholz, Rene Wantosch and Stefan Zimmermann
Electronics 2024, 13(12), 2247; https://doi.org/10.3390/electronics13122247 - 7 Jun 2024
Viewed by 753
Abstract
Electrical resonators are usually characterized by their resonance frequency, attenuation and quality factor. External quantities can affect these parameters, resulting in a characteristic change in the resonator, which can be used as a sensor effect. This work presents a new concept and electronic [...] Read more.
Electrical resonators are usually characterized by their resonance frequency, attenuation and quality factor. External quantities can affect these parameters, resulting in a characteristic change in the resonator, which can be used as a sensor effect. This work presents a new concept and electronic device for the continuous recording of resonator characteristics using single-sideband modulation. A test signal consisting of a center frequency and two sidebands is generated and the center frequency is set close to the resonator’s resonance frequency while the two sidebands are adjusted symmetrically around the center frequency. By exiting the resonator with the test signal and demodulating the resulting output into individual frequency components, a continuous measurement of the attenuation is possible. The center frequency is adjusted so that both sidebands have equal attenuation, resulting in a center frequency that corresponds to the resonance frequency of the resonator. If the resonator does not show a symmetrical frequency response, the sideband attenuation ratio can be adjusted accordingly. Continuous recording of the resonator characteristics at a sampling rate of 100 Sps was verified using a digitally tunable RLC series resonator with resonance frequencies between 250 MHz and 450 MHz, resulting in a maximum error below 1.5%. Full article
(This article belongs to the Special Issue Advances in Signals and Systems Research)
►▼ Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Basic concept of the new tracking method based on a variable center frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>CN</mi> </mrow> </msub> </mrow> </semantics></math> and the two sidebands <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>LSB</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>USB</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Simplified equivalent circuit of a split-ring resonator (SRR).</p> Full article ">Figure 2
<p>Attenuation at the center frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>CN</mi> </mrow> </msub> </mrow> </semantics></math>, the lower sideband frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>LSB</mi> </mrow> </msub> </mrow> </semantics></math> and the upper sideband frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>USB</mi> </mrow> </msub> </mrow> </semantics></math> for a given center frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>CN</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>Influence of <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>BW</mi> </mrow> </msub> </mrow> </semantics></math> (<b>a</b>), <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> </mrow> </semantics></math> (<b>b</b>), <math display="inline"><semantics> <mi>D</mi> </semantics></math> (<b>c</b>) and <math display="inline"><semantics> <mi>α</mi> </semantics></math> (<b>d</b>) on the error function.</p> Full article ">Figure 4
<p>The figure illustrates the generation of the test signal, its transmission through the SRR and the downstream downconversion. Figure (<b>a</b>) depicts the individual frequency spectrum in each phase of the concept, commencing with the test signal before upconversion, the test signal frequency spectrum, the frequency spectrum after the SRR and finally, the downconversion. Figure (<b>b</b>) shows the frequency spectrum prior to the SSB modulation (I), after the SSB modulation (II), following the damping of the SRR (III), and after the downconversion (IV).</p> Full article ">Figure 5
<p>Schematic representation of the generation of the test signal <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mrow> <mi mathvariant="normal">T</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> </mrow> </semantics></math> by an IQ modulation of the IF signals <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>IF</mi> <mo>,</mo> <mi mathvariant="normal">I</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>IF</mi> <mo>,</mo> <mi mathvariant="normal">Q</mi> </mrow> </msub> </mrow> </semantics></math> generated by using a modified Weaver method from the signals <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>BB</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>CN</mi> <mo>,</mo> <mi mathvariant="normal">I</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>CN</mi> <mo>,</mo> <mi mathvariant="normal">Q</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Block diagram of the downconversion electronics, including filtering and detection of each individual frequency component <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>LSB</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>USB</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mrow> <mi>CN</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>(<b>a</b>) Schematic of the RLC test resonator using a digitally tunable capacitor (DTC) for setting defined resonance frequencies, (<b>b</b>) photo of the assembled resonator with 32 adjustable resonance frequencies.</p> Full article ">Figure 8
<p>The amplitude responses of the adjustable resonator dummy at different DTC settings were measured with a TOSM-calibrated VNA ZNL6 (Rohde &amp; Schwarz).</p> Full article ">Figure 9
<p>Amplitude responses of the adjustable resonator dummy at different DTC settings were measured with the tracking electronics connected with two 25 cm SMA cables.</p> Full article ">Figure 10
<p>(<b>a</b>) Amplitude responses of the adjustable resonator dummy for the lower sideband (LSB), the center frequency (CN) and the upper sideband (USB) measured at 0.6 pF capacitance of the DTC settings; (<b>b</b>) the error signal derived from the lower and the upper sideband.</p> Full article ">Figure 11
<p>Tracking of resonance frequency over time using all 32 settings of the adjustable resonator dummy’s DTC for 4 s each.</p> Full article ">Figure 12
<p>(<b>a</b>) Damping coefficient D derived from the measurements shown in <a href="#electronics-13-02247-f011" class="html-fig">Figure 11</a> compared to the true damping coefficient D; (<b>b</b>) damping coefficient <math display="inline"><semantics> <mi>α</mi> </semantics></math> derived from the measurement shown in <a href="#electronics-13-02247-f011" class="html-fig">Figure 11</a> compared to the true damping coefficient <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> Full article ">Figure A1
<p>Picture of the tracking electronic.</p> Full article ">Figure A2
<p>Picture of the developed measurement setup for investigating the resonance frequency and attenuation of a resonator dummy.</p> Full article ">Figure A3
<p>Output power of the center frequency of the tracking electronics.</p> Full article ">Figure A4
<p>Measured attenuation of a constant −15 dB damping element.</p> Full article ">Figure A5
<p>Amplitude responses of the resonator dummy at different DTC settings measured with the tracking electronics connected with two 50 cm SMA cables.</p> Full article ">Figure A6
<p>Impedance <math display="inline"><semantics> <mrow> <msub> <mi>Z</mi> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> of the resonator dummy terminated with 50 ohms.</p> Full article ">Figure A7
<p>Impedance <math display="inline"><semantics> <mrow> <msub> <mi>Z</mi> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> of the resonator dummy terminated with the demodulation stage of the tracking electronics.</p> Full article ">Figure A8
<p>Input impedance of the demodulation stage of the tracking electronics.</p> Full article ">Figure A9
<p>Difference between the expected resonance frequency and the resonance frequency determined by the tracking electronics in resonance frequency tracking mode. The red lines represent the maximum deviation of the resonance frequency from the expected resonance frequency with the frequency tracking settled.</p> Full article ">

Review

Jump to: Research

15 pages, 2348 KiB  
Review
System-Level Statistical Eye Diagram for Signal Integrity
by Junyong Park and Hyunwook Park
Electronics 2024, 13(22), 4387; https://doi.org/10.3390/electronics13224387 - 8 Nov 2024
Viewed by 385
Abstract
This paper reviews a statistical signal integrity (SI) analysis at the system level for a high-speed system design. An eye diagram graphically shows a system’s performance. However, an eye diagram requires a long acquisition time for accurate results. The time-consuming nature of this [...] Read more.
This paper reviews a statistical signal integrity (SI) analysis at the system level for a high-speed system design. An eye diagram graphically shows a system’s performance. However, an eye diagram requires a long acquisition time for accurate results. The time-consuming nature of this process makes an eye-diagram-based SI analysis inefficient. Thus, a statistical eye diagram was introduced for an efficient SI analysis. The statistical eye diagram provides not only SI metrics such as eye height (EH) and eye width (EW), but also the bit-error rate (BER) profile for each channel. The data transmitted over the high-speed channels are determined by an upper hierarchy such as a system. In other words, the data are a function of the system parameters. In conclusion, a statistical eye diagram is determined by the high-speed channels and the system parameters. Therefore, the previous works on statistical eye diagrams at the channel and system levels have been introduced, respectively. This paper reviews the previous works for a system-level statistical SI analysis with a statistical eye diagram. Full article
(This article belongs to the Special Issue Advances in Signals and Systems Research)
►▼ Show Figures

Figure 1

Figure 1
<p>The eye diagram is a critical SI metric to show electrical degradation such as crosstalk between channels and insertion loss by parasitic resistance and capacitance. The eye diagram is obtained by overlapping the received waveforms; thus, it requires a significant amount of acquisition time.</p> Full article ">Figure 2
<p>(<b>a</b>) The worst contour by the PDA method; (<b>b</b>) statistical eye diagram by the statistical approach. The PDA provides the inner-most contour of the eye diagram. Thus, limited information is provided. In contrast, the statistical eye diagram provides the probability distribution function (PDF) depending on the sampling time. The color represents the probability depending on the sampling time.</p> Full article ">Figure 3
<p>Bit PDF in the statistical eye diagram. The PDF for the main cursors is from the channel response for bit ONE. The amplitude PDF is defined at the sampling time <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>τ</mi> </mrow> <mrow> <mi>s</mi> <mi>a</mi> <mi>m</mi> <mi>p</mi> <mi>l</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>The above figures show the results of (<b>a</b>) 8B/10B and (<b>b</b>) TMDS encoding, respectively. Their purposes are opposite. Thus, the number of bit transitions is increased by 8B/10B encoding and decreased by TMDS encoding [<a href="#B21-electronics-13-04387" class="html-bibr">21</a>].</p> Full article ">Figure 5
<p>The statistical eye diagrams have different probability distributions depending on the 8B/10B and TMDS encoders [<a href="#B21-electronics-13-04387" class="html-bibr">21</a>]: (<b>a</b>) eye diagram without the encoding, (<b>b</b>) eye diagram with 8B/10B encoding, and (<b>c</b>) the eye diagram with TMDS encoding. As a result of the encoding, the probabilities of the bit transitions are different for both cases. In the case of 8B/10B encoding, the non-transition area has a lower probability. The change in the probability can be identified from the darker area in the statistical eye diagram and the same is true for, the case of TMDS encoding.</p> Full article ">Figure 6
<p>Equalized SBRs depend on the equalizer. (<b>a</b>) The SBR is the channel response for the input bits of 01000⋯. (<b>b</b>) The DFE mitigates the inter-symbol interference (ISI) based on the previous bits. Thus, the voltage level with a length of UI is attenuated after the single-bit pulse. (<b>c</b>,<b>d</b>) The pre-/de-emphasis also equalizes the ISI noise in the time domain. The pre-emphasis boosts the high frequencies; thus, the peak of the single-bit pulse is amplified. Likewise, the de-emphasis attenuates the high frequencies after the single-bit pulse. Therefore, the dip after the single-bit pulse is amplified by the de-emphasis. In other words, the emphasis amplifies the high-frequency signals locally in the time domain. (<b>e</b>) The CTLE mitigates the low frequencies or amplifies the high-frequency components in the frequency domain. The high-frequency signals over the whole pulse response are amplified by the CTLE [<a href="#B32-electronics-13-04387" class="html-bibr">32</a>].</p> Full article ">Figure 7
<p>Statistical eye diagrams depending on equalizers: (<b>a</b>) non-equalized channel, (<b>b</b>) DFE, (<b>c</b>) pre-emphasis, (<b>d</b>) de-emphasis, and (<b>e</b>) CTLE [<a href="#B32-electronics-13-04387" class="html-bibr">32</a>].</p> Full article ">Figure 8
<p>Single bit responses (SBRs) in multi-level signaling [<a href="#B34-electronics-13-04387" class="html-bibr">34</a>].</p> Full article ">Figure 9
<p>Statistical eye diagram for the multi-level signaling [<a href="#B36-electronics-13-04387" class="html-bibr">36</a>]. The statistical eye diagrams have different PDFs on the logic level and the pulse levels. (<b>a</b>) When all of the logic levels have the same probability and the scaling factor, the statistical eye diagram is symmetric in terms of the probability and the distribution. (<b>b</b>) The asymmetry on the probability causes the asymmetric statistical eye diagram. (<b>c</b>) The different scaling on the pulse response also leads to the asymmetric PDF.</p> Full article ">Figure 10
<p>Statistical eye diagram depending on the scrambling. (<b>a</b>) When the biased data are given, it has a higher probability for either ONE or ZERO. The biased probability distribution is identified from the asymmetry of the probability. (<b>b</b>) After the scrambling, the corresponding eye diagram become symmetric which means the ONE and ZERO have the same probability [<a href="#B39-electronics-13-04387" class="html-bibr">39</a>].</p> Full article ">Figure 11
<p>Statistical eye diagram depending on the ECC. (<b>a</b>) The BCH code encodes the data bits in a bit-wise fashion, thus the effect of the BCH code on the eye diagram is not significant. (<b>b</b>) In contrast, the RS code encodes the data bits in a symbol-wise fashion, thus the RS code make the bit probability of ZERO higher [<a href="#B15-electronics-13-04387" class="html-bibr">15</a>].</p> Full article ">
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