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20 pages, 1627 KiB  
Article
Dynamic Spectrum Co-Access in Multicarrier-Based Cognitive Radio Using Graph Theory Through Practical Channel
by Ehab F. Badran, Amr A. Bashir, Hassan Nadir Kheirallah and Hania H. Farag
Appl. Sci. 2024, 14(23), 10868; https://doi.org/10.3390/app142310868 - 23 Nov 2024
Viewed by 725
Abstract
In this paper, we propose an underlay cognitive radio (CR) system that includes subscribers, termed secondary users (SUs), which are designed to coexist with the spectrum owners, termed primary users (PUs). The suggested network includes the PUs system and the SUs system. The [...] Read more.
In this paper, we propose an underlay cognitive radio (CR) system that includes subscribers, termed secondary users (SUs), which are designed to coexist with the spectrum owners, termed primary users (PUs). The suggested network includes the PUs system and the SUs system. The coexistence between them is achieved by using a novel dynamic spectrum co-access multicarrier-based cognitive radio (DSCA-MC-CR) technique. The proposal uses a quadrature phase shift keying (QPSK) modulation technique within the orthogonal frequency-division multiplexing (OFDM) scheme that maximizes the system data rate and prevents data inter-symbol interference (ISI). The proposed CR transmitter station (TX) and the CR receiver node (RX) can use an advanced smart antenna system, i.e., a multiple-input and multiple-output (MIMO) system that provides high immunity against channel impairments and provides a high data rate through its different combining techniques. The proposed CR system is applicable to coexist within different existing communication applications like fifth-generation (5G) applications, emergence applications like the Internet of Things (IoT), narrow-band (NB) applications, and wide-band (WB) applications. The coexistence between the PUs system and the SUs system is based on using power donation from the SUs system to improve the quality of the PU signal-to-interference-and-noise ratios (SINRs). The green communication concept achieved in this proposal is compared with similar DSCA proposals from the literature. The simulations of the proposed technique show enhancement in the PUs system throughput and data rate along with the better performance of the SUs system. Full article
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Figure 1

Figure 1
<p>Cognitive radio capability characteristics.</p>
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<p>The classification of the DSA management models. (<b>a</b>) Interweave model (<b>b</b>) Underlay Model (<b>c</b>) Overlay Model.</p>
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<p>Topology and spectrum representation of model 1. (<b>a</b>) Model 1 topology of the proposed DSCA-MC-CR using OMNeT. (<b>b</b>) Spectrum representation of model 1.</p>
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<p>Topology and spectrum representation of model 2. (<b>a</b>) Model 2 topology of the proposed DSCA-MC-CR using OMNeT. (<b>b</b>) Spectrum representation of model 2.</p>
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<p>The block diagram design of the proposed DSCA-MC-CR SU-TX tower.</p>
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<p>The proposed correlator receiver design of the SU-RX.</p>
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<p>Simple <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>×</mo> <mi>N</mi> </mrow> </semantics></math> MIMO system diagram.</p>
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<p>The proposed topology classification using conventional DSP and GSP. (<b>a</b>) The proposed topology using conventional DSP. (<b>b</b>) The proposed topology classification using GSP.</p>
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<p>BER of the PU and SU in model 1 over AWGN with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>3</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>a</b>) BER of the PU in model 1. (<b>b</b>) BER of the SU in model 1.</p>
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<p>BER of the PU and SU in model 1 under fading channel with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>3</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>a</b>) BER of the PU in model 1. (<b>b</b>) BER of the SU in model 1.</p>
Full article ">Figure 11
<p>OMNeT proposed network for model 1 with practical medium parameters. (<b>a</b>) OMNeT network of model 1. (<b>b</b>) PU system and SU system in OSA mode.</p>
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<p><math display="inline"><semantics> <msub> <mrow> <mi>P</mi> <mi>U</mi> </mrow> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mrow> <mi>S</mi> <mi>U</mi> </mrow> <mn>1</mn> </msub> </semantics></math> BER vs. SINR with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <msub> <mrow> <mi>P</mi> <mi>U</mi> </mrow> <mn>1</mn> </msub> </semantics></math> BER vs. SINR with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mrow> <mi>S</mi> <mi>U</mi> </mrow> <mn>1</mn> </msub> </semantics></math> BER vs. SINR with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math>.</p>
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<p>PU and SU capacities using different techniques versus SNR. (<b>a</b>) PU capacity versus SNR. (<b>b</b>) SU capacity versus SNR.</p>
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<p>PU and SU BERs of model 2 using Gaussian channel with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>3</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>a</b>) PU BER of model 2. (<b>b</b>) SU BER of model 2.</p>
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<p>PU and SU BERs of model 2 using fading channel with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>3</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>a</b>) PU BER of model 2. (<b>b</b>) SU BER of model 2.</p>
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<p>Systems packet interarrival analysis of LTE using the OSA, DSCA, OC-DSA, and DSCA-MC-CR techniques. (<b>a</b>) PU systems packet interarrival analysis of LTE. (<b>b</b>) SU systems packet interarrival analysis of LTE.</p>
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<p>System packet interarrival analysis for 5G using the OSA, DSCA, OC-DSA, and DSCA-MC-CR techniques. (<b>a</b>) PU system packet interarrival analysis of 5G. (<b>b</b>) SU system packet interarrival analysis of 5G.</p>
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11 pages, 480 KiB  
Article
High-Data-Rate Modulators Based on Graphene Transistors: Device Circuit Co-Design Proposals
by Anibal Pacheco-Sanchez, J. Noé Ramos-Silva, Nikolaos Mavredakis, Eloy Ramírez-García and David Jiménez
Electronics 2024, 13(20), 4022; https://doi.org/10.3390/electronics13204022 - 12 Oct 2024
Viewed by 932
Abstract
The multifunctionality feature of graphene field-effect transistors (GFETs) is exploited here to design circuit building blocks of high-data-rate modulators by using a physics-based compact model. Educated device performance projections are obtained with the experimentally calibrated model and used to choose an appropriate improved [...] Read more.
The multifunctionality feature of graphene field-effect transistors (GFETs) is exploited here to design circuit building blocks of high-data-rate modulators by using a physics-based compact model. Educated device performance projections are obtained with the experimentally calibrated model and used to choose an appropriate improved feasible GFET for these applications. Phase-shift and frequency-shift keying (PSK and FSK) modulation schemes are obtained with 0.6 GHz GFET-based multifunctional circuits used alternatively in different operation modes: inverting and in-phase amplification and frequency multiplication. An adequate baseband signal applied to the transistors’ input also serves to enhance the device and circuit performance reproducibility since the impact of traps is diminished. Quadrature PSK is also achieved by combining two GFET-based multifunctional circuits. This device circuit co-design proposal intends to boost the heterogeneous implementation of graphene devices with incumbent technologies into a single chip: the baseband pulses can be generated with CMOS technology as a front end of line and the multifunctional GFET-based circuits as a back end of line. Full article
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Figure 1

Figure 1
<p><b>Top left</b>: ambipolar transfer characteristic of a GFET showing approximate definitions for the drain current in the different operation regimes. <b>Bottom left</b>: input AC signals. <b>Top right</b>: output AC signal. <b>Bottom right</b>: equations of the analog AC+DC signals for the general case (in black) and specific cases. <span class="html-italic">A</span>, <span class="html-italic">B</span>, <span class="html-italic">C</span>, <span class="html-italic">D</span> and <span class="html-italic">E</span> are arbitrary constants and <math display="inline"><semantics> <mrow> <mo>Γ</mo> <mo>=</mo> <mn>0.5</mn> <msub> <mi>R</mi> <mi mathvariant="normal">d</mi> </msub> <mi>C</mi> <msup> <mi>A</mi> <mn>2</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>Φ</mo> <mo>=</mo> <msub> <mi>V</mi> <mi>DS</mi> </msub> <mo>−</mo> <mi>B</mi> <msub> <mi>R</mi> <mi mathvariant="normal">d</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>R</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> is the output resistance seen from the drain terminal. <math display="inline"><semantics> <msub> <mi>I</mi> <mi>d</mi> </msub> </semantics></math> is obtained by replacing <math display="inline"><semantics> <msub> <mi>V</mi> <mi>GS</mi> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>GS</mi> </msub> <mo>+</mo> <msub> <mi>v</mi> <mi>in</mi> </msub> </mrow> </semantics></math> in the corresponding <math display="inline"><semantics> <msub> <mi>I</mi> <mi mathvariant="normal">D</mi> </msub> </semantics></math>.</p>
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<p>Transfer characteristics of a 300 <math display="inline"><semantics> <mi mathvariant="normal">n</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math> long GFET. <b>Left</b>: Trap-reduced data obtained with opposing pulses. Markers are experimental data and lines are modeling results. Inset shows the applied opposing <math display="inline"><semantics> <msub> <mi>V</mi> <mi>GS</mi> </msub> </semantics></math> pulses and constant <math display="inline"><semantics> <msub> <mi>V</mi> <mi>DS</mi> </msub> </semantics></math>. <b>Right panel</b>: optimized device modeling results. <math display="inline"><semantics> <msub> <mi>V</mi> <mi>DS</mi> </msub> </semantics></math> is 0.1 <span class="html-italic">V</span>, 0.2 <span class="html-italic">V</span> and 0.3 <math display="inline"><semantics> <mi mathvariant="normal">V</mi> </semantics></math> for all cases.</p>
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<p><b>Top</b>: Schematic of the multifunctional GFET circuit used for data modulation at <math display="inline"><semantics> <mrow> <mn>0.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi>GHz</mi> </semantics></math>. In-phase and inverting amplification obtained with <math display="inline"><semantics> <msub> <mi>V</mi> <mi>GS</mi> </msub> </semantics></math> equal to −0.1 V and 0.5 <math display="inline"><semantics> <mi mathvariant="normal">V</mi> </semantics></math>, respectively, whereas the circuit works as a frequency doubler at <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>GS</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>Dirac</mi> </msub> </mrow> </semantics></math>. Matching (stability) networks are indicated by the dashed (dotted) boxes and are the same regardless of the operation mode. DC and AC filtering between signal sources and circuit elements are not shown. Input AC power is of <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>30</mn> </mrow> </semantics></math> dBm at <math display="inline"><semantics> <mrow> <mn>0.6</mn> <mo> </mo> <mrow> <mi>GHz</mi> </mrow> </mrow> </semantics></math>. Values of circuit elements are <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>155</mn> <mo> </mo> <mrow> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">H</mi> </mrow> <mo>,</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>375</mn> <mo> </mo> <mrow> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">F</mi> </mrow> <mo>,</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>41</mn> <mo> </mo> <mrow> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">H</mi> </mrow> <mo>,</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>1.6</mn> <mo> </mo> <mrow> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">F</mi> </mrow> <mo>,</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>10.9</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mo>Ω</mo> </mrow> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>DD</mi> </msub> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>. <b>Bottom</b>: S-parameters of the amplifiers for the PCA design: continuous lines represent results of the in-phase amplifier (<math display="inline"><semantics> <mrow> <mo>@</mo> <msub> <mi>V</mi> <mrow> <mi>GS</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>) and dashed–dotted lines show results of the inverting amplifier (<math display="inline"><semantics> <mrow> <mo>@</mo> <msub> <mi>V</mi> <mrow> <mi>GS</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>).</p>
Full article ">Figure 4
<p><math display="inline"><semantics> <msub> <mi>v</mi> <mi>in</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>v</mi> <mi>out</mi> </msub> </semantics></math> signals for the PCA design in both operation modes: In-phase amplifier (<b>left</b>) and inverting amplifier (<b>right</b>). Only a 10 <math display="inline"><semantics> <mi mathvariant="normal">n</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> fram is shown for a better visualization of the signals.</p>
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<p>Frequency doubler results: <math display="inline"><semantics> <msub> <mi>v</mi> <mi>in</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>v</mi> <mi>out</mi> </msub> </semantics></math> signals over a 10 <math display="inline"><semantics> <mi mathvariant="normal">n</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> frame (<b>left</b>) and output power spectrum over frequency (<b>right</b>).</p>
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<p>Baseband, carrier and modulated signals achieved with the GFET-based multifunctional circuits. <b>Left</b>: PSK signals. Phase of output signal is included in the bottom plot. <b>Right</b>: FSK signals.</p>
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<p>Schematic representation of <math display="inline"><semantics> <mrow> <mn>0.6</mn> <mo> </mo> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">M</mi> </semantics></math><math display="inline"><semantics> <mi>Hz</mi> </semantics></math>-QPSK modulator obtained with two GFET-based PSK circuits. Each PSK block corresponds to the circuit shown in <a href="#electronics-13-04022-f003" class="html-fig">Figure 3</a>. <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>GS</mi> <mn>1</mn> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>GS</mi> <mn>2</mn> </mrow> </msub> </semantics></math> correspond to the baseband signal of the PCA design (with values of −<math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="normal">V</mi> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="normal">V</mi> </semantics></math>).</p>
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<p>Signals involved in the GFET-based quadrature PSK modulation.</p>
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15 pages, 3438 KiB  
Communication
Galileo and BeiDou AltBOC Signals and Their Perspectives for Ionospheric TEC Studies
by Chuanfu Chen, Ilya Pavlov, Artem Padokhin, Yury Yasyukevich, Vladislav Demyanov, Ekaterina Danilchuk and Artem Vesnin
Sensors 2024, 24(19), 6472; https://doi.org/10.3390/s24196472 - 8 Oct 2024
Viewed by 915
Abstract
For decades, GNSS code measurements were much noisier than phase ones, limiting their applicability to ionospheric total electron content (TEC) studies. Ultra-wideband AltBOC signals changed the situation. This study revisits the Galileo E5 and BeiDou B2 AltBOC signals and their potential applications in [...] Read more.
For decades, GNSS code measurements were much noisier than phase ones, limiting their applicability to ionospheric total electron content (TEC) studies. Ultra-wideband AltBOC signals changed the situation. This study revisits the Galileo E5 and BeiDou B2 AltBOC signals and their potential applications in TEC estimation. We found that TEC noises are comparable for the single-frequency AltBOC phase-code combination and those of the dual-frequency legacy BPSK/QPSK phase combination, while single-frequency BPSK/QPSK TEC noises are much higher. A two-week high-rate measurement campaign at the ACRG receiver revealed a mean 100 sec TEC RMS (used as the noise proxy) of 0.26 TECU, 0.15 TECU, and 0.09 TECU for the BeiDou B2(a+b) AltBOC signal and satellite elevations 0–30°, 30–60°, and 60–90°, correspondingly, and 0.22 TECU, 0.14 TECU, and 0.09 TECU for the legacy B1/B3 dual-frequency phase combination. The Galileo E5(a+b) AltBOC signal corresponding values were 0.25 TECU, 0.14 TECU, and 0.09 TECU; for the legacy signals’ phase combination, the values were 0.19 TECU, 0.13 TECU, and 0.08 TECU. The AltBOC (for both BeiDou and Galileo) SNR exceeds those of BPSK/QPSK by 7.5 dB-Hz in undisturbed conditions. Radio frequency interference (the 28 August 2022 and 9 May 2024 Solar Radio Burst events in our study) decreased the AltBOC SNR 5 dB-Hz more against QPSK SNR, but, due to the higher initial SNR, the threshold for the loss of the lock was never broken. Today, we have enough BeiDou and Galileo satellites that transmit AltBOC signals for a reliable single-frequency vTEC estimation. This study provides new insights and evidence for using Galileo and BeiDou AltBOC signals in high-precision ionospheric monitoring. Full article
(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation)
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Figure 1

Figure 1
<p>Autocorrelation functions for BPSK, QPSK, and AltBOC signals.</p>
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<p>Pseudorange noises for BPSK, QPSK, and AltBOC signals.</p>
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<p>Slant TEC (<b>a</b>), SNR (<b>b</b>), and TEC RMS (<b>c</b>) for the ACRG-BeiDou C24 pass on 28 February 2024. In panels (<b>a</b>,<b>c</b>), the green, orange, blue, and red lines correspond to L2L5, L8C8, L2C2, and C2C5 combinations, correspondingly. In panel (<b>b</b>), the orange, green, and blue solid lines correspond to S8, S5, and S2 observables, correspondingly. The purple line in panel (<b>b</b>) shows the satellite’s elevation angle.</p>
Full article ">Figure 4
<p>Slant TEC (<b>a</b>), SNR (<b>b</b>), and TEC RMS (<b>c</b>) for the ACRG-Galileo E05 pass on 28 February 2024. In panels (<b>a</b>,<b>c</b>), the green, orange, blue, and red lines correspond to L1L5, L8C8, L1C1, and C1C5 combinations, correspondingly. In panel (<b>b</b>), the orange, green, and blue solid lines correspond to S8, S5, and S1 observables, correspondingly. The purple line in panel (<b>b</b>) shows the satellite’s elevation angle.</p>
Full article ">Figure 5
<p>Absolute vertical TEC estimates at SGPO station with single-frequency combination of AltBOC signals from Galileo and BeiDou satellites (orange line) and from dual-frequency phase combination of non-AltBOC signals from GPS, GLONASS, Galileo, and BeiDou satellites (blue line).</p>
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<p>Signal-to-noise ratio (SNR) from the Galileo E34 (<b>a</b>) and BeiDou C44 (<b>b</b>) satellites observed at the SGPO station on 28 August 2022, alongside the corresponding solar radio flux at 610 MHz (black curves). In panel (<b>a</b>), the red line shows the SNR S8X of E5(a+b) signal, the green line represents the SNR S7X of E5b sideband, the orange line—SNR S5X of E5a sideband, and the blue line—the SNR S1X of E1 signal; and, in panel (<b>b</b>), the red line shows the SNR S8X of B2(a+b) signal, the green line—the SNR S7Z of B2b sideband, the orange line—SNR S5X of B2a sideband, and the blue line—the SNR S2I of B1I signal.</p>
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<p>Signal-to-noise ratio (SNR) from the Galileo E10 (<b>a</b>) and BeiDou C23 (<b>b</b>) satellites observed at the ACRG station on 9 May 2024, alongside the corresponding solar radio flux at 1415 MHz (black curves). In panel (<b>a</b>), the red line shows the SNR S8X of E5(a+b) signal, the green line—the SNR S7X of E5b sideband, the orange line—SNR S5X of E5a sideband, and the blue line—the SNR S1X of E1 signal; and, in panel (<b>b</b>), the red line shows the SNR S8X of B2(a+b) signal, the green line—the SNR S7Z of B2b sideband, the orange line—SNR S5X of B2a sideband, and the blue line—the SNR S2I of B1I signal.</p>
Full article ">Figure 7 Cont.
<p>Signal-to-noise ratio (SNR) from the Galileo E10 (<b>a</b>) and BeiDou C23 (<b>b</b>) satellites observed at the ACRG station on 9 May 2024, alongside the corresponding solar radio flux at 1415 MHz (black curves). In panel (<b>a</b>), the red line shows the SNR S8X of E5(a+b) signal, the green line—the SNR S7X of E5b sideband, the orange line—SNR S5X of E5a sideband, and the blue line—the SNR S1X of E1 signal; and, in panel (<b>b</b>), the red line shows the SNR S8X of B2(a+b) signal, the green line—the SNR S7Z of B2b sideband, the orange line—SNR S5X of B2a sideband, and the blue line—the SNR S2I of B1I signal.</p>
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11 pages, 4060 KiB  
Communication
Study of a Crosstalk Suppression Scheme Based on Double-Stage Semiconductor Optical Amplifiers
by Xintong Lu, Xinyu Ma and Baojian Wu
Sensors 2024, 24(19), 6403; https://doi.org/10.3390/s24196403 - 2 Oct 2024
Viewed by 695
Abstract
An all-optical crosstalk suppression scheme is desirable for wavelength and space division multiplexing optical networks by improving the performance of the corresponding nodes. We put forward a scheme comprising double-stage semiconductor optical amplifiers (SOAs) for wavelength-preserving crosstalk suppression. The wavelength position of the [...] Read more.
An all-optical crosstalk suppression scheme is desirable for wavelength and space division multiplexing optical networks by improving the performance of the corresponding nodes. We put forward a scheme comprising double-stage semiconductor optical amplifiers (SOAs) for wavelength-preserving crosstalk suppression. The wavelength position of the degenerate pump in the optical phase conjugation (OPC) is optimized for signal-to-crosstalk ratio (SXR) improvement. The crosstalk suppression performance of the double-stage SOA scheme for 20 Gb/s quadrature phase shift keying (QPSK) signals is investigated by means of simulations, including the input SXR range and the crosstalk wavelength deviation. For the case with identical-frequency crosstalk, the double-stage SOA scheme can achieve equivalent SXR improvement of 1.5 dB for an input SXR of 10 dB. Thus, the double-stage SOA scheme proposed here is more suitable for few-mode fiber systems and networks. Full article
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Figure 1

Figure 1
<p>The schematic diagram of the DFWM process in SOAs.</p>
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<p>Four input combinations of the pump, signal and crosstalk wavelengths. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>P</mi> <mi>S</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>S</mi> <mi>C</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>P</mi> <mi>C</mi> <mi>S</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>C</mi> <mi>S</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>The dependences of <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>S</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>C</mi> </msub> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>P</mi> </msub> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>C</mi> </msub> </mrow> </semantics></math> = 0.08 nm and (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>C</mi> </msub> </mrow> </semantics></math> = −0.08 nm.</p>
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<p>The dependences of ∆<span class="html-italic">SXR</span> on <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>P</mi> </msub> </mrow> </semantics></math> along with their fitting curves for (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>C</mi> </msub> </mrow> </semantics></math> = 0.08 nm and (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>C</mi> </msub> </mrow> </semantics></math> = −0.08 nm.</p>
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<p>The double-stage SOA-based crosstalk suppression scheme for QPSK signals.</p>
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<p>The EVM change dependent on PSPR<sub>1</sub> for (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>P</mi> <mi>S</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>C</mi> <mi>S</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>, and the constellation for (<b>c</b>) the degraded signal and (<b>d</b>) the regenerated signal.</p>
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<p>The EVM curves dependent on (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>X</mi> <msub> <mi>R</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mfenced close="|" open="|"> <mrow> <mo>Δ</mo> <msub> <mi>λ</mi> <mi>C</mi> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>Feedback crosstalk suppression scheme for optical switching nodes based on MDM.</p>
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<p>Double-stage SOAs for crosstalk suppression based on MDM.</p>
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<p>The output EVM dependent on PSPR<sub>2</sub> for different driving currents of SOA<sub>2</sub>.</p>
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15 pages, 6740 KiB  
Article
Modulation Format Recognition Scheme Based on Discriminant Network in Coherent Optical Communication System
by Fangxu Yang, Qinghua Tian, Xiangjun Xin, Yiqun Pan, Fu Wang, José Antonio Lázaro, Josep M. Fàbrega, Sitong Zhou, Yongjun Wang and Qi Zhang
Electronics 2024, 13(19), 3833; https://doi.org/10.3390/electronics13193833 - 28 Sep 2024
Viewed by 644
Abstract
In this paper, we skillfully utilize the discriminative ability of the discriminator to construct a conditional generative adversarial network, and propose a scheme that uses few symbols to achieve high accuracy recognition of modulation formats under low signal-to-noise ratio conditions in coherent optical [...] Read more.
In this paper, we skillfully utilize the discriminative ability of the discriminator to construct a conditional generative adversarial network, and propose a scheme that uses few symbols to achieve high accuracy recognition of modulation formats under low signal-to-noise ratio conditions in coherent optical communication. In the one thousand kilometres G.654E optical fiber transmission system, transmission experiments are conducted on the PDM-QPSK/-8PSK/-16QAM/-32QAM/-64QAM modulation format at 8G/16G/32G baud rates, and the signal-to-noise ratio parameters are traversed under experimental conditions. As a key technology in the next-generation elastic optical networks, the modulation format recognition scheme proposed in this paper achieves 100% recognition of the above five modulation formats without distinguishing signal transmission rates. The optical signal-to-noise ratio thresholds required to achieve 100% recognition accuracy are 12.4 dB, 14.3 dB, 15.4 dB, 16.2 dB, and 17.3 dB, respectively. Full article
(This article belongs to the Special Issue Advances in Optical Communication and Optical Computing)
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<p>The general process for implementing ML-assisted MFI, where CDF: cumulative distribution function; AH: amplitude histogram; CD: constellation diagram; ED: eye diagram. A solid line represents the training process and a dotted line represents the recognition process.</p>
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<p>The discriminator of conditional generative adversarial nets algorithm block diagram. Among them, the three colors of red, yellow, and blue represent the three primary color data obtained through three channels of the neural network. And 128 × 128 represents the pixel value of the data.</p>
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<p>Discriminator workflow, in which the input signal is scaled from the original size of <math display="inline"><semantics> <mrow> <mn>891</mn> <mo>×</mo> <mn>656</mn> </mrow> </semantics></math> to a <math display="inline"><semantics> <mrow> <mn>128</mn> <mo>×</mo> <mn>128</mn> </mrow> </semantics></math> square at the image center.</p>
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<p>The 1000-km coherent optical fiber transmission system, where AWG: arbitrary waveform generator; ECL: external cavity laser; DVOA: digitally variable optical attenuator; PBS: polarization beam splitter; PBC: polarization beam combiner; EDFA: erbium-doped fiber amplifier; ICR: integrated coherent receiver; DPO: digital phosphor oscilloscope. Blue represents electrical signals and green represents light signals.</p>
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<p>The 1000 km fiber transmission experimental platform.</p>
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<p>The constellation diagram is processed by general DSP. QPSK, 8PSK, 16QAM, 32QAM and 64QAM are randomly selected from the training dataset from top to bottom. From left to right, the processing processes are orthogonal imbalance compensation, dispersion compensation, timing recovery, polarization demultiplexing, frequency offset estimation, and phase recovery.</p>
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<p>The variation curve of recognition accuracy of each modulation format as the training level deepens.</p>
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<p>Performance comparison between this scheme and traditional machine learning schemes, where DT: decision tree; SVM: support vector machine; CGAN: conditional generative adversarial network.</p>
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<p>Recognition accuracy of various modulation formats under different OSNR indicators.</p>
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14 pages, 3284 KiB  
Article
Low Complexity Parallel Carrier Frequency Offset Estimation Based on Time-Tagged QPSK Partitioning for Coherent Free-Space Optical Communication
by Siqi Zhang, Liqian Wang, Kunfeng Liu and Shuang Ding
Photonics 2024, 11(9), 885; https://doi.org/10.3390/photonics11090885 - 20 Sep 2024
Viewed by 719
Abstract
To effectively mitigate the effects of atmospheric turbulence in free space optical (FSO) communication, we propose a parallel carrier frequency offset estimation (FOE) scheme based on time-tagged QPSK partitioning (TTQP). This scheme can be applied to spatial diversity polarization multiplexing (PM) coherent FSO [...] Read more.
To effectively mitigate the effects of atmospheric turbulence in free space optical (FSO) communication, we propose a parallel carrier frequency offset estimation (FOE) scheme based on time-tagged QPSK partitioning (TTQP). This scheme can be applied to spatial diversity polarization multiplexing (PM) coherent FSO communication systems. Specifically, the TTQP scheme performs QPSK partitioning by time-tagging signal points, accurately recording the time intervals between signals, and significantly reducing implementation complexity through a modified Mth power algorithm. The simulation results for the PM 16-quadrature amplitude modulation (QAM) validate the effectiveness of the proposed scheme. Compared to traditional QPSK partitioning algorithms, the TTQP algorithm achieves high accuracy, low complexity, and multi-format versatility in high-speed coherent FSO communication. Full article
(This article belongs to the Special Issue Challenges and Opportunities in Free Space Optical Communication)
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<p>Block diagram of digital signal processing (DSP).</p>
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<p>Principle block diagram of the Time-Tagged QPSK partitioning (TTQP) FOE algorithm.</p>
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<p>Ideal constellation diagram and actual received signal sequence description for 16QAM. (<b>a</b>) Ideal constellation diagram; (<b>b</b>) Actual received signal Sequence description.</p>
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<p>The QPSK-TMS signal obtained after the time-tagging QPSK partitioning.</p>
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<p>The comparison between the results of squaring the sine and cosine functions and those obtained through absolute value operations demonstrates their similarity. (<b>a</b>) Differences between the squared values of the sine function and their absolute values; (<b>b</b>) Differences between the squared values of the cosine function and their absolute values.</p>
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<p>Calculation and compensation of accumulated frequency offset.</p>
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<p>Simulation platform for a spatial diversity coherent FSO communication system. Insets: Light field distributions (<b>a</b>) before and (<b>b</b>) and (<b>c</b>) after passing through the phase screen.</p>
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<p>The relationship between the Normalized Mean Square Error (NMSE) and received optical power at different symbol block lengths under B2B conditions.</p>
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<p>Performance comparison between the proposed algorithm and traditional QPSK partitioning under B2B conditions: (<b>a</b>) NMSE curve under different average received optical power, (<b>b</b>) BER curve under different average received optical power.</p>
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<p>Performance comparison between the proposed algorithm and traditional QPSK partitioning under weak turbulence conditions: (<b>a</b>) NMSE curve under different average received optical power, (<b>b</b>) BER curve under different average received optical power.</p>
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<p>Performance comparison between the proposed algorithm and traditional QPSK Partitioning under strong turbulence conditions: (<b>a</b>) NMSE curve under different average received optical power, (<b>b</b>) BER curve under different average received optical power.</p>
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<p>Performance comparison between the proposed algorithm and the QPSK algorithm in terms of NMSE under both weak and strong turbulence conditions across different frequency offset ranges: (<b>a</b>): NMSE comparison curve under weak turbulence conditions, (<b>b</b>): NMSE comparison curve under strong turbulence conditions.</p>
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35 pages, 28009 KiB  
Article
Optoelectronics Interfaces for a VLC System for UHD Audio-Visual Content Transmission in a Passenger Van: HW Design
by Carlos Iván del Valle Morales, Juan Sebastián Betancourt Perlaza, Juan Carlos Torres Zafra, Iñaki Martinez-Sarriegui and José Manuel Sánchez-Pena
Sensors 2024, 24(17), 5829; https://doi.org/10.3390/s24175829 - 8 Sep 2024
Viewed by 1292
Abstract
This work aims to provide the hardware (HW) design of the optoelectronics interfaces for a visible-light communication (VLC) system that can be employed for several use cases. Potential applications include the transmission of ultra-high-definition (UHD) streaming video through existing reading lamps installed in [...] Read more.
This work aims to provide the hardware (HW) design of the optoelectronics interfaces for a visible-light communication (VLC) system that can be employed for several use cases. Potential applications include the transmission of ultra-high-definition (UHD) streaming video through existing reading lamps installed in passenger vans. In this use case, visible light is employed for the downlink, while infrared light is used for the uplink channel, acting as a remote controller. Two primary components -a Light Fidelity (LiFi) router and a USB dongle—were designed and implemented. The ‘LiFi Router’, handling the downlink channel, comprises components such as a visible Light-Emitting Diode (LED) and an infrared receiver. Operating at a supply voltage of 12 V and consuming current at 920 mA, it is compatible with standard voltage buses found in transport vehicles. The ‘USB dongle’, responsible for the uplink, incorporates an infrared LED and a receiver optimized for visible light. The USB dongle works at a supply voltage of 5 V and shows a current consumption of 1.12 A, making it well suited for direct connection to a universal serial bus (USB) port. The bandwidth achieved for the downlink is 11.66 MHz, while the uplink’s bandwidth is 12.27 MHz. A system competent at streaming UHD video with the feature of being single-input multiple-output (SIMO) was successfully implemented via the custom hardware design of the optical transceivers and optoelectronics interfaces. To ensure the system’s correct performance at a distance of 110 cm, the minimum signal-to-noise ratio (SNRmin) for both optical links was maintained at 10.74 dB. We conducted a proof-of-concept test of the VLC system in a passenger van and verified its optimal operation, effectively illustrating its performance in a real operating environment. Exemplifying potential implementations possible with the hardware system designed in this work, a bit rate of 15.2 Mbps was reached with On–Off Keying (OOK), and 11.25 Mbps was obtained with Quadrature Phase Shift Keying (QPSK) using Orthogonal Frequency-Division Multiplexing (OFDM) obtaining a bit-error rate (BER) of 3.3259 × 10−5 in a passenger van at a distance of 72.5 cm between the LiFi router and the USB dongle. As a final addition, a solar panel was installed on the passenger van’s roof to power the user’s laptop and the USB dongle via a power bank battery. It took 13.4 h to charge the battery, yielding a battery life of 22.3 h. This characteristic renders the user’s side of the system entirely self-powered. Full article
(This article belongs to the Special Issue Sensing Technologies and Optical Communication)
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<p>The LiFi router, located on the vehicle’s interior roof, connects to the content server via a wireless Internet connection. The USB dongle, connected to the user’s portable device, receives and plays the audio-visual content as described.</p>
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<p>Block diagram of the VLC proposed system.</p>
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<p>Equivalent simplified circuit of the LUW-CN7N-KYLX-EMKM OSRAM LED for AC.</p>
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<p>LED driver based on a division voltage for n-type MOSFET.</p>
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<p>Phase-advance equalizer.</p>
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<p>Phase-advance equalizer implemented for (<b>a</b>) the first stage for a pole located at 1.8 MHz, and (<b>b</b>) the second stage for a pole located at 9 MHz.</p>
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<p>LED driver implemented with 2 equalization and 2 amplification stages.</p>
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<p>Simulated frequency response of the proposed LED driver based on two amplification and two equalization stages.</p>
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<p>(<b>a</b>) Set-up implemented to take the frequency response measurement of the LUW-CN7N-KYLX-EMKM OSRAM LED and its LED driver based on 2 equalization and 2 amplification stages; (<b>b</b>) frequency response measurement of the LUW-CN7N-KYLX-EMKM OSRAM LED and its LED driver based on 2 equalization and 2 amplification stages.</p>
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<p>Frequency response measurement of the IR HSDL-4250 LED and its LED driver based on 2 equalization and 2 amplification stages.</p>
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<p>PD driver implemented with three amplifier stages.</p>
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<p>Simulated frequency response of the PD driver implemented with three amplifier stages.</p>
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<p>(<b>a</b>) Set-up of the frequency response of the PD driver implemented with three amplifier stages using the LUW-CN7N-KYLX-EMKM OSRAM LED; (<b>b</b>) frequency response of the PD driver implemented with three amplifier stages using the LUW-CN7N-KYLX-EMKM OSRAM LED.</p>
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<p>Frequency response of the PD driver implemented with three amplifier stages using the IR HSDL-4250 LED.</p>
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<p>Block diagram of the FPGA/LED driver interface.</p>
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<p>Block diagram of the PD driver/FPGA interface.</p>
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<p>Schematic design of the FPGA/LED driver connection.</p>
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<p>Schematic design of the PD driver/FPGA connection.</p>
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<p>TE0720 SoC includes the FPGA Xilinx XA7z020-1CLG484Q.</p>
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<p>Diagram of the interaction between external interface, TE0720 SoC, and internal interface.</p>
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<p>Internal interface PCB: (<b>a</b>) top view; (<b>b</b>) bottom view.</p>
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<p>(<b>a</b>) LiFi router external interface PCB; (<b>b</b>) USB dongle external interface PCB.</p>
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<p>Block diagram of all PCBs that are part of the system.</p>
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<p>Schematic connection of the components of the system for LiFi router and USB dongle.</p>
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<p>(<b>a</b>) PCBs stack of TE0720 SoC, internal and external interfaces; (<b>b</b>) LiFi router.</p>
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<p>(<b>a</b>) PCBs stack of TE0720 SoC, internal and external interfaces; (<b>b</b>) USB dongle.</p>
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<p>Set-up carried out to test every module of the system.</p>
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<p>Scheme of the testing procedure for the transmitter block.</p>
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<p>Tests carried out in the transmitter block utilizing a (<b>a</b>) visible LED and (<b>b</b>) IR LED.</p>
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<p>Implemented test to validate the receiver block.</p>
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<p>ILA captured at the ADC’s outputs.</p>
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<p>Test carried out to validate the Tx block and Rx block working in closed loop.</p>
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<p>LiFi router and USB dongle packed in boxes.</p>
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<p>The VLC system developed was deployed using a Ford Transit model van.</p>
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<p>The user’s laptop playing a UHD video streaming due to the implemented USB dongle.</p>
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19 pages, 4234 KiB  
Article
Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
by Ke Sun and Jiwei Xu
Electronics 2024, 13(17), 3522; https://doi.org/10.3390/electronics13173522 - 5 Sep 2024
Viewed by 994
Abstract
Accurate and efficient channel estimation (CE) is critical in the context of autonomous driving. This paper addresses the issue of orthogonal frequency-division multiplexing (OFDM) channel estimation in 5G communication systems by proposing a channel estimation model based on the Parrot Optimizer (PO). The [...] Read more.
Accurate and efficient channel estimation (CE) is critical in the context of autonomous driving. This paper addresses the issue of orthogonal frequency-division multiplexing (OFDM) channel estimation in 5G communication systems by proposing a channel estimation model based on the Parrot Optimizer (PO). The model optimizes for the minimum bit error rate (BER) and the minimum mean square error (MMSE) using the Parrot Optimizer to estimate the optimal channel characteristics. Simulation experiments compared the performance of PO-CE with the Least Squares (LS) method and the MMSE method under various signal-to-noise ratios (SNR) and modulation schemes. The results demonstrate that PO-CE’s performance approximates that of MMSE under high SNR conditions and significantly outperforms LS in the absence of prior information. The experiments specifically included scenarios with different modulation schemes (QPSK, 16QAM, 64QAM, and 256QAM) and pilot densities (1/3, 1/6, 1/9, and 1/12). The findings indicate that PO-CE has substantial potential for application in 5G channel estimation, offering an effective method for optimizing wireless communication systems. Full article
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<p>Comb Pilot Pattern with 1/4 Pilot Density.</p>
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<p>16QAM constellation diagram with different dispersions (left is better). <a href="#electronics-13-03522-f002" class="html-fig">Figure 2</a> illustrates the constellation diagrams of a 16QAM signal under different Signal-to-Noise Ratios (SNR). In (<b>a</b>), where the SNR is 15, the constellation points are distinctly concentrated around their ideal positions, indicating minimal noise. This results in higher signal quality and a lower bit error rate (BER). Conversely, in (<b>b</b>), with an SNR of 5, the constellation points are more dispersed, with a greater deviation from their ideal positions. This increased dispersion is due to the higher noise level associated with the lower SNR, leading to poorer signal quality and a higher bit error rate.</p>
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<p>BER performance of LS, MMSE, and PO-CE under 256QAM constellation diagram and 1/12 pilot density. <span class="html-italic">X</span>-axis: SNR [Db]. The curves are the results of simulations.</p>
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<p>MSE performance of LS, MMSE, and PO-CE under 256QAM constellation diagram and 1/12 pilot density (step size is 1 Db). <span class="html-italic">X</span>-axis: SNR [Db]. The curves are the results of simulations.</p>
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<p>BER performance of LS, PO, and MMSE channel estimation algorithms under different modulation schemes. <span class="html-italic">X</span>-axis: SNR [Db]. The curves are the results of simulations.</p>
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<p>MSE performance of LS, PO, and MMSE channel estimation algorithms under different modulation schemes. <span class="html-italic">X</span>-axis: SNR [Db]. The curves are the results of simulations.</p>
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<p>MSE performance comparison of LS, PO, and MMSE under different pilot densities. <span class="html-italic">X</span>-axis: SNR [dB]. The curves are the results of simulations.</p>
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<p>BER performance comparison of LS, PO, and MMSE under different pilot densities. <span class="html-italic">X</span>-axis: SNR [dB]. The curves are the results of simulations.</p>
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<p>BER performance comparison of LS, PO, and MMSE under different pilot densities. <span class="html-italic">X</span>-axis: SNR [dB]. The curves are the results of simulations.</p>
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22 pages, 15279 KiB  
Article
Reconstruction of OFDM Signals Using a Dual Discriminator CGAN with BiLSTM and Transformer
by Yuhai Li, Youchen Fan, Shunhu Hou, Yufei Niu, You Fu and Hanzhe Li
Sensors 2024, 24(14), 4562; https://doi.org/10.3390/s24144562 - 14 Jul 2024
Viewed by 1164
Abstract
Communication signal reconstruction technology represents a critical area of research within communication countermeasures and signal processing. Considering traditional OFDM signal reconstruction methods’ intricacy and suboptimal reconstruction performance, a dual discriminator CGAN model incorporating LSTM and Transformer is proposed. When reconstructing OFDM signals using [...] Read more.
Communication signal reconstruction technology represents a critical area of research within communication countermeasures and signal processing. Considering traditional OFDM signal reconstruction methods’ intricacy and suboptimal reconstruction performance, a dual discriminator CGAN model incorporating LSTM and Transformer is proposed. When reconstructing OFDM signals using the traditional CNN network, it becomes challenging to extract intricate temporal information. Therefore, the BiLSTM network is incorporated into the first discriminator to capture timing details of the IQ (In-phase and Quadrature-phase) sequence and constellation map information of the AP (Amplitude and Phase) sequence. Subsequently, following the addition of fixed position coding, these data are fed into the core network constructed based on the Transformer Encoder for further learning. Simultaneously, to capture the correlation between the two IQ signals, the VIT (Vision in Transformer) concept is incorporated into the second discriminator. The IQ sequence is treated as a single-channel two-dimensional image and segmented into pixel blocks containing IQ sequence through Conv2d. Fixed position coding is added and sent to the Transformer core network for learning. The generator network transforms input noise data into a dimensional space aligned with the IQ signal and embedding vector dimensions. It appends identical position encoding information to the IQ sequence before sending it to the Transformer network. The experimental results demonstrate that, under commonly utilized OFDM modulation formats such as BPSK, QPSK, and 16QAM, the time series waveform, constellation diagram, and spectral diagram exhibit high-quality reconstruction. Our algorithm achieves improved signal quality while managing complexity compared to other reconstruction methods. Full article
(This article belongs to the Special Issue Computer Vision Recognition and Communication Sensing System)
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<p>CGAN model architecture.</p>
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<p>Flowchart of the OFDM baseband communication system.</p>
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<p>Signal reconstruction model.</p>
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<p>Improved CGAN model architecture.</p>
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<p>Discriminator network model.</p>
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<p>Generator network model.</p>
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<p>Reconstruction results of the time-domain waveform map and constellation diagram when SNR was 20 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Original signal time-domain waveform; (<b>b</b>) Reconstruction of signal time-domain waveform; (<b>c</b>) Original signal constellation diagram; (<b>d</b>) Reconstruction of signal constellation diagram.</p>
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<p>Reconstruction results of time-domain waveform map and constellation diagram when SNR was 15 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Original signal time-domain waveform; (<b>b</b>) Reconstruction of signal time-domain waveform; (<b>c</b>) Original signal constellation diagram; (<b>d</b>) Reconstruction of signal constellation diagram.</p>
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<p>Reconstruction results of time-domain waveform map and constellation diagram when SNR was 10 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Original signal time-domain waveform; (<b>b</b>) Reconstruction of signal time-domain waveform; (<b>c</b>) Original signal constellation diagram; (<b>d</b>) Reconstruction of signal constellation diagram.</p>
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<p>Visual comparison of time-domain waveform of OFDM symbol sequence when the SNR was 20 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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<p>Visual comparison of OFDM signal spectrogram when the SNR was 20 dB. (Left to right modulation style is BPSK, QPSK, 16QAM).</p>
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<p>Visual comparison of time-domain waveform of OFDM symbol sequence when the SNR was 15 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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<p>Visual comparison of OFDM signal spectrogram when the SNR was 15 dB. (Left to right modulation style is BPSK, QPSK, 16QAM).</p>
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<p>Visual comparison of time-domain waveform of OFDM symbol sequence when the SNR was 10 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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<p>Visual comparison of OFDM signal spectrogram when the SNR was 10 dB. (Left to right modulation style is BPSK, QPSK, 16QAM).</p>
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<p>Probability density distribution when the SNR was 20 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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<p>Probability density distribution when the SNR was 15 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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<p>Probability density distribution when the SNR was 10 dB. (Left to right modulation style is BPSK, QPSK, 16QAM). (<b>a</b>) Real part; (<b>b</b>) Imaginary part.</p>
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10 pages, 1117 KiB  
Communication
Efficient Direct Detection of Twin Single-Sideband Quadrature-Phase Shift Keying Using a Single Detector with Hierarchical Blind-Phase Search
by Hongbo Zhang, Jiao Liu, Guo-Wei Lu, Min Zhang, Feng Wan, Ju Cai, Weiwei Ling and Liming Hu
Photonics 2024, 11(7), 624; https://doi.org/10.3390/photonics11070624 - 29 Jun 2024
Viewed by 937
Abstract
We propose a novel reception scheme for twin single-sideband (twin-SSB) signals using just a single photodetector (PD), significantly reducing the system complexity and cost. To detect a twin-SSB with power-unbalanced quadrature-phase shift keying (QPSK) sidebands upon detection via a single PD at the [...] Read more.
We propose a novel reception scheme for twin single-sideband (twin-SSB) signals using just a single photodetector (PD), significantly reducing the system complexity and cost. To detect a twin-SSB with power-unbalanced quadrature-phase shift keying (QPSK) sidebands upon detection via a single PD at the receiver side, two QPSKs carried in two sidebands are coherently superposed and detected in a 16-ary quadrature amplitude modulation (16-QAM) format. This technique notably diminishes the linearity and effective number of bits required for the transmitter components in high-speed optical transmission systems. Moreover, a hierarchical blind-phase search (HBPS) algorithm is proposed to compensate for the imperfect phase rotation of QPSK signals during transmission. To demonstrate the effectiveness of our proposed method, we successfully conducted simulations of 112 Gb/s 16-QAM signal transmission over a 10 km standard single-mode fiber (SSMF), achieving bit error ratios (BERs) of 7.84×104, well below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×103. In addition, the synthetic transmission scheme proposed in this paper is compared with the traditional 16-QAM signal transmission scheme, and the results show that the proposed scheme does not introduce a performance cost with the same received optical power (ROP) and transmission distance. Full article
(This article belongs to the Special Issue Photonics for Emerging Applications in Communication and Sensing II)
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<p>Schematic of the twin-SSB-QPSK transmitter with (<b>a</b>) DSP at the transmitter side; (<b>b</b>) transmitter setup; electrical spectra of (<b>i</b>) lower sideband, <math display="inline"><semantics> <msub> <mi>QPSK</mi> <mi>S</mi> </msub> </semantics></math>, and (<b>ii</b>) upper sideband, <math display="inline"><semantics> <msub> <mi>QPSK</mi> <mi>L</mi> </msub> </semantics></math>; (<b>iii</b>) the electric spectrum of twin-SSB-QPSK; and (<b>iv</b>) the optical spectrum of twin-SSB-SSB.</p>
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<p>Receiver side DSP: (<b>i</b>) the twin-SSB-QPSK signal spectrum before the PD and (<b>ii</b>) the received signal spectrum after the PD and filtering.</p>
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<p>A synthesis diagram for the 16-QAM signal.</p>
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<p>Architecture of the proposed HBPS algorithm for correcting the possible imperfect phase rotation in the synthesized 16-QAM: (<b>a</b>) illustration of the 1st stage processing, (<b>b</b>) experiment data processing in the 1st stage, and (<b>c</b>) illustration of the 2nd stage processing. abs: absolute value; slc: selector.</p>
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<p>Constellation diagram for compensating phase rotation using the HBPS algorithm. (<b>a</b>) Constellation diagram before HBPS algorithm. (<b>b</b>) Constellation diagram after the first HBPS stage. (<b>c</b>) Constellation diagram after the second HBPS stage.</p>
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<p>Experimental setup. (<b>a</b>) The LSB signal spectrum. (<b>b</b>) The USB signal spectrum. (<b>c</b>) The twin-SSB-QPSK signal spectrum. (<b>d</b>) The received signal spectrum after the PD and filter.</p>
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<p>The measured constellations of the corresponding signals after the PD. (<b>a</b>) The constellation of the received and linearly equalized signals. (<b>b</b>) The constellation after the processing using the conventional BPS: Q = 14.54 dB and BER = <math display="inline"><semantics> <mrow> <mn>1.54</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. (<b>c</b>) The constellation after the processing using the proposed HBPS: Q = 17.90 dB and BER = <math display="inline"><semantics> <mrow> <mn>7.33</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>BER versus ROP when the bit rate is 112Gb/s.</p>
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<p>BER versus bit rate when the ROP is −13 dBm.</p>
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<p>Q factor comparison of the synthesized 16-QAM using the proposed and conventional (Conv.) approaches under different ROPs. Sub-figures (<b>a</b>) and (<b>b</b>) show the electrical spectra of the synthesized 16-QAM after the PD reception using the proposed and conventional approaches, respectively.</p>
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14 pages, 1448 KiB  
Article
Global Receptive Field Designed Complex-Valued Convolutional Neural Network Equalizer for Optical Fiber Communications
by Lu Han, Yongjun Wang, Haifeng Yang, Yang Zhao and Chao Li
Photonics 2024, 11(5), 431; https://doi.org/10.3390/photonics11050431 - 5 May 2024
Viewed by 968
Abstract
In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms [...] Read more.
In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms of Q-factor performance and complexity compared to seven other related nonlinear equalizers based on both the 64 QAM experimental platform and the QPSK numerical platform. The global convolution operation of the proposed CvGNN is more suitable for the calculation process of perturbation coefficients, and the global receptive field can also be more effective at extracting effective information from perturbation feature maps. The introduction of CvCNN can directly focus on the complex-valued perturbation feature maps themselves without separately processing the real and imaginary parts, which is more in line with the waveform-dependent physical characteristics of optical signals. Based on the experimental platform, compared with the real-valued neural network with small convolutional kernel (RvCNNC), the proposed CvGNNC improves the Q-factor by ∼2.95 dB at the optimal transmission power, while reducing the time complexity by ∼44.7%. Full article
(This article belongs to the Section Optical Communication and Network)
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<p>The construction method for input features.</p>
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<p>The nonlinear equalizer structure for CvCNN.</p>
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<p>Diagram of the different size of ERF and the different structure of CNN.</p>
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<p>Experimental setup.</p>
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<p>Q-factor trace of CvGNNC with different activation functions.</p>
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<p>Structural design of different nonlinear equalizers.</p>
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<p>Nonlinear equalization performance of different neural networks with the same time complexity.</p>
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<p>Simulation setup.</p>
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<p>Nonlinear equalization performance.</p>
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<p>The computational complexity of different NNs, including time and space complexity.</p>
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13 pages, 486 KiB  
Article
Novel Approach towards a Fully Deep Learning-Based IoT Receiver Architecture: From Estimation to Decoding
by Matthew Boeding, Michael Hempel and Hamid Sharif
Future Internet 2024, 16(5), 155; https://doi.org/10.3390/fi16050155 - 30 Apr 2024
Cited by 2 | Viewed by 1554
Abstract
As the Internet of Things (IoT) continues to expand, wireless communication is increasingly widespread across diverse industries and remote devices. This includes domains such as Operational Technology in the Smart Grid. Notably, there is a surge in resource-constrained devices leveraging wireless communication, especially [...] Read more.
As the Internet of Things (IoT) continues to expand, wireless communication is increasingly widespread across diverse industries and remote devices. This includes domains such as Operational Technology in the Smart Grid. Notably, there is a surge in resource-constrained devices leveraging wireless communication, especially with the advances of 5G/6G technology. Nevertheless, the transmission of wireless communications demands substantial power and computational resources, presenting a significant challenge to these devices and their operations. In this work, we propose the use of deep learning to improve the Bit Error Rate (BER) performance of Orthogonal Frequency Division Multiplexing (OFDM) wireless receivers. By improving the BER performance of these receivers, devices can transmit with less power, thereby improving IoT devices’ battery life. The architecture presented in this paper utilizes a depthwise Convolutional Neural Network (CNN) for channel estimation and demodulation, whereas a Graph Neural Network (GNN) is utilized for Low-Density Parity Check (LDPC) decoding, tested against a proposed (1998, 1512) LDPC code. Our results show higher performance than traditional receivers in both isolated tests for the CNN and GNN, and a combined end-to-end test with lower computational complexity than other proposed deep learning models. For BER improvement, our proposed approach showed a 1 dB improvement for eliminating BER in QPSK models. Additionally, it improved 16-QAM Rician BER by five decades, 16-QAM LOS model BER by four decades, 64-QAM Rician BER by 2.5 decades, and 64-QAM LOS model BER by three decades. Full article
(This article belongs to the Special Issue State-of-the-Art Future Internet Technology in USA 2024–2025)
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<p>Overall architecture of the combined deep learning approach.</p>
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<p>CNN-based joint OFDM receiver signal operations.</p>
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<p>GNN architecture for LDPC decoding.</p>
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<p>CNN models−combined Rician results.</p>
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<p>CNN models−combined 3GPP LOS results.</p>
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<p>A 16−QAM Rician LDPC comparison.</p>
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<p>Rician end−to−end comparison.</p>
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<p>3GPP LOS end−to−end comparison.</p>
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13 pages, 935 KiB  
Article
A Temporal Methodology for Assessing the Performance of Concatenated Codes in OFDM Systems for 4K-UHD Video Transmission
by Thiago de A. Costa, Alex S. Macedo, Edemir M. C. Matos, Bruno S. L. Castro, Fabricio de S. Farias, Caio M. M. Cardoso, Gervásio P. dos S. Cavalcante and Fabricio J. B. Barros
Appl. Sci. 2024, 14(9), 3581; https://doi.org/10.3390/app14093581 - 24 Apr 2024
Cited by 1 | Viewed by 867
Abstract
The communication channel is a critical part of the process of information degradation. In the 4K ultra-resolution video transmission domain, the communication channel is a crucial part where information degradation occurs, inevitably leading to errors during reception. To enhance the transmission process in [...] Read more.
The communication channel is a critical part of the process of information degradation. In the 4K ultra-resolution video transmission domain, the communication channel is a crucial part where information degradation occurs, inevitably leading to errors during reception. To enhance the transmission process in terms of fidelity, advanced technologies such as digital video broadcasting terrestrial (DVB-T) and its evolutionary successor, digital video broadcasting terrestrial second generation (DVB-T2), are utilized to mitigate the effects of data transmission errors. Within this scenario, this research presents an innovative methodology for the temporal analysis of 4K ultra-resolution video quality under the influence of additive white Gaussian noise (AWGN) and Rayleigh channels. This analytical endeavor is facilitated through the application of concatenated coding schemes, specifically, the Bose–Chaudhuri–Hocquenghem concatenated low-density parity check (BCH-LDPC) and Reed–Solomon concatenated convolutional (RS-CONV) coders. A more comprehensive understanding of video quality can be attained by considering its temporal variations, a crucial aspect of the ongoing evolution of technological paradigms. In this study, the Structural Similarity Index (SSIM) serves as the main metric for quality assessment during simulations. Furthermore, the simulated Peak Signal-to-Noise Ratio (PSNR) values validate these findings, exhibiting consistent alignment with the SSIM-based evaluations. Additionally, the performance of the BCH-LDPC significantly outperforms that of RS-CONV under the 64-QAM modulation scheme, yielding superior video quality levels that approximate or surpass those achieved by RS-CONV under QPSK (Quadrature Phase Shift Keying) modulation, leading to an increase in spectral efficiency. This enhancement is evidenced by SSIM gains exceeding 78% on average. The computation of average gains between distinct technologies in video quality analysis furnishes a robust and comprehensive evaluation framework, empowering stakeholders to make informed decisions within this domain. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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<p>Simulation of video transmission.</p>
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<p>Noise variation in four selected frames.</p>
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<p>Concatenated BCH-LDPC coding scheme.</p>
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<p>OFDM symbol generation.</p>
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<p>BERxEbN0/RS-CONV over AWGN channel.</p>
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<p>SSIM x frames for Park over AWGN.</p>
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<p>SSIM x frames for Park over Rayleigh.</p>
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16 pages, 4280 KiB  
Article
Modulation Format Identification Based on Multi-Dimensional Amplitude Features for Elastic Optical Networks
by Ming Hao, Wei He, Xuedong Jiang, Shuai Liang, Wei Jin, Lin Chen and Jianming Tang
Photonics 2024, 11(5), 390; https://doi.org/10.3390/photonics11050390 - 23 Apr 2024
Cited by 1 | Viewed by 958
Abstract
A modulation format identification (MFI) scheme based on multi-dimensional amplitude features is proposed for elastic optical networks. According to the multi-dimensional amplitude features, incoming polarization division multiplexed (PDM) signals can be identified as QPSK, 8QAM, 16QAM, 32QAM, 64QAM and 128QAM signals using the [...] Read more.
A modulation format identification (MFI) scheme based on multi-dimensional amplitude features is proposed for elastic optical networks. According to the multi-dimensional amplitude features, incoming polarization division multiplexed (PDM) signals can be identified as QPSK, 8QAM, 16QAM, 32QAM, 64QAM and 128QAM signals using the k-nearest neighbors (KNNs) algorithm in the digital coherent receivers. The proposed scheme does not require any prior training or optical signal-to-noise ratio (OSNR) information. The performance of the proposed MFI scheme is verified based on numerical simulations with 28GBaud PDM-QPSK/-8QAM/-16QAM/-32QAM/-64QAM/-128QAM signals. The results show that the proposed scheme can achieve 100% of the correct MFI rate for all six modulation formats when the OSNR values are greater than their thresholds corresponding to the 20% forward error correction (FEC) related to a BER of 2.4 × 10−2. Meanwhile, the effects of residual chromatic dispersion, polarization mode dispersion and fiber nonlinearities on the proposed scheme are also explored. Finally, the computational complexity of the proposed scheme is analyzed, which is compared with relevant MFI schemes. The work indicates that the proposed technique could be regarded as a good candidate for identifying modulation formats up to 128QAM. Full article
(This article belongs to the Special Issue Optical Performance Monitoring)
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<p>The DSP architecture with the proposed MFI scheme for digital coherent receivers.</p>
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<p>The amplitude histograms of (<b>a</b>) QPSK, (<b>b</b>) 8QAM, (<b>c</b>) 16QAM, (<b>d</b>) 32QAM, (<b>e</b>) 64QAM, (<b>f</b>) 128QAM and the corresponding partition operation.</p>
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<p>The three-dimensional space composed of features (<b>a</b>–<b>c</b>) <span class="html-italic">N</span><sub>1</sub>, <span class="html-italic">N</span><sub>2</sub> and <span class="html-italic">N</span><sub>4</sub>, (<b>d</b>) <span class="html-italic">N</span><sub>1</sub>, <span class="html-italic">N</span><sub>5</sub> and <span class="html-italic">N</span><sub>6</sub> and (<b>e</b>,<b>f</b>) <span class="html-italic">N</span><sub>1</sub>, <span class="html-italic">N</span><sub>3</sub> and <span class="html-italic">N</span><sub>4</sub> for different modulation formats.</p>
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<p>Schematic diagram of identification by KNN.</p>
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<p>The simulation setup of the PDM coherent optical transmission system. PBS: polarization beam splitter; PBC: polarization beam combiner; LPF: low-pass filter.</p>
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<p>Minimum required OSNR values with different numbers of symbols for six modulation formats. The symbol number range for (<b>a</b>) is 5000~9000 with a 1000 step size and (<b>b</b>) is 7000~9000 with a 250 step size.</p>
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<p>The minimum required OSNR values with different <span class="html-italic">k</span> values for six modulation formats.</p>
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<p>The correct MFI rate for the six modulation formats under different OSNR values.</p>
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<p>The tolerance with respect to the residual CD for the six modulation formats.</p>
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<p>The tolerance with respect to the DGD for (<b>a</b>) QPSK, 8QAM, 16QAM, 32QAM, 64QAM and (<b>b</b>) 128QAM.</p>
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<p>Correct MFI rates of the six modulation formats in the long-distance transmission. (<b>a</b>) QPSK, (<b>b</b>) 8QAM, (<b>c</b>) 16QAM, (<b>d</b>) 32QAM, (<b>e</b>) 64QAM, (<b>f</b>) 128QAM.</p>
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<p>Minimum required OSNR for identifying different modulation formats for the three MFI schemes. The green and red star indicate that the modulation format is not identified by these two schemes.</p>
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<p>The execution times used for the (<b>a</b>) training process and (<b>b</b>) prediction process in the three MFI schemes. The blue star indicates that no training process is required for the proposed scheme.</p>
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12 pages, 7946 KiB  
Article
All-in-One BPSK/QPSK Switchable Transmission and Reception for Adaptive Free-Space Optical Communication Links
by Yaling Chen, Chengze Ming, Ke Xie, Shiming Gao, Qingfang Jiang, Zhi Liu, Haifeng Yao and Keyan Dong
Photonics 2024, 11(4), 326; https://doi.org/10.3390/photonics11040326 - 30 Mar 2024
Cited by 1 | Viewed by 1501
Abstract
Adaptive free-space optical (FSO) communication links have been extensively studied in order to adapt to variable atmospheric channel environments due to factors such as atmospheric turbulence. As a supporting technology, an all-in-one BPSK/QPSK switchable transmission and reception method is proposed and experimentally demonstrated [...] Read more.
Adaptive free-space optical (FSO) communication links have been extensively studied in order to adapt to variable atmospheric channel environments due to factors such as atmospheric turbulence. As a supporting technology, an all-in-one BPSK/QPSK switchable transmission and reception method is proposed and experimentally demonstrated for adaptive modulation format switching in FSO links. The transmission and reception of both modulation formats are realized based on the same IQ modulator and single-photodetector coherent receiver. Simulation and experimental results show that the QPSK signal has a power penalty of about 3–4 dB compared to the BPSK signal with a BER of about 1 × 10−3. The basis for format switching is given according to the various atmospheric channel conditions. The proposed method provides a flexible and efficient solution for variable FSO communication environments to improve their performance. Full article
(This article belongs to the Special Issue Free-Space Optical Communication and Networking Technology)
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<p>Experimental setup of FSO transmission and reception with BPSK/QPSK switching. PRBS: pseudorandom binary sequence, PC: Polarization Controller, EDFA: Erbium-doped fiber amplifier, BPF: Bandpass filter, LO: Local Oscillator, PD: photodetector.</p>
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<p>(<b>a</b>) Photo of the rotating phase plate; (<b>b</b>) measured probability density function (PDF) of the normalized received power.</p>
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<p>Measured eye diagrams and BTB constellation diagrams of the generated QPSK and BPSK signals. (<b>a</b>,<b>c</b>) Measured eye diagrams of generated QPSK and BPSK; (<b>b</b>,<b>d</b>) BTB constellation diagrams of the generated QPSK and BPSK.</p>
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<p>Measured and simulated BER results of the QPSK and BPSK signals and measured constellation diagrams of the QPSK and BPSK signals.</p>
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<p>Simulated BER results of the QPSK and BPSK signals under different turbulence conditions of (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.0199, (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.0995, (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.3982, (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.9955, (<b>e</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 3.9819, and (<b>f</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 9.9548.</p>
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<p>Simulated BER results of the QPSK and BPSK signals under different turbulence conditions of (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.0199, (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.0995, (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.3982, (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 0.9955, (<b>e</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 3.9819, and (<b>f</b>) <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </semantics></math> = 9.9548.</p>
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<p>Measurement of the transmitted power for reaching the BER threshold of QPSK and BPSK signals under different turbulence conditions.</p>
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