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Wireless Communications: Signal Processing Perspectives
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Wireless Communications: Signal Processing Perspectives

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (20 January 2025) | Viewed by 9879

Special Issue Editors

Prof. Dr. Sébastien Roy

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, University of Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
Interests: array processing; MIMO systems; massive MIMO; signal processing; wireless communications; radio propagation and channel models
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Julian Cheng

E-Mail Website
Guest Editor
School of Engineering, The University of British Columbia, Kelowna, BC V1Y 8L6, Canada
Interests: wireless digital communications theory; optical wireless communications theory; 5G wireless networks and beyond; quantum information processing and communications; machine learning; deep learning; wireless location technology
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jean-Yves Chouinard

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, Laval University Québec, QC G1V 0A6, Canada
Interests: broadband wireless communication systems; error-correcting codes; information encryption; distributed source coding; high-resolution wide-swath synthetic aperture radar processing

Special Issue Information

Dear Colleagues,

We are in the digital age. Today, humans live and work within an increasingly pervasive digital fabric comprised of multitudes of heterogeneous computing nodes acting as hubs in worldwide interconnected networks of various types. The wireless portion of these networks is of paramount importance, since it enables mobility, connectedness through various portable devices, and machine-to-machine communications in the so-called Internet of Things (IoT). In addition to wireless LANs (WiFi), IoT communications (through LoRa or other radio interfaces), and satellite, there are more than 10 billion active cell phone connections worldwide, which is more than the number of humans.

However, high-bandwidth communication over the air is notoriously difficult, given the fact that the EM spectrum is a limited and congested resource. The relentless evolution of wireless has been made possible through increasingly efficient spectrum usage, thanks to sophisticated spectrum processing, especially by leveraging the spatial dimension. Indeed, staggering gains in spectrum efficiency since 2005 have been achieved through the improved integration of adaptive antenna arrays and the MIMO concept. In fact, massive MIMO is a keystone technology of 5G cellular.

Going forward, data volume will continue to increase rapidly, as will the logistic complexity of wireless networks, which are becoming increasingly heterogeneous and unpredictable. Furthermore, there is a push for ultra-reliable and low-latency communications, which imposes further constraints on the wireless infrastructure. In fact, the need for extremely low-latency responses implies that much of the processing will be pushed towards the network edge, thus radically changing the nature of the wireless domain and its cybersecurity aspects.

Meeting these challenges requires continuous innovation in the signal processing domain to continue leveraging the spatial dimension with increasing efficiency in conjunction with other techniques to yield the desirable traits of ultra-reliability, ultra-low latency, self-organization, scalability, and adaptability to changing environments, operating conditions and network demands. The scope of this Special Issue covers such innovations and the underlying challenges.

We therefore welcome unpublished original papers and comprehensive surveys on the above theme, specifically on the following, non-exhaustive, list of topics:

  • Beamforming, diversity, and MIMO techniques, including for IoT and energy efficiency;
  • Massive MIMO;
  • Cell-free and clustered cell-free MIMO;
  • Antenna selection and antenna subset selection in large arrays;
  • Reconfigurable intelligent surfaces (RISs);
  • The use of unmanned aerial vehicles (UAVs) for wireless networking;
  • Channel estimation and its impact on network performance;
  • Physical-layer security;
  • Relaying and cooperation;
  • Self-organizing networks;
  • Energy efficiency in wireless networks;
  • Machine learning applied to any of the above, especially within some formal mathematical framework;
  • Sound analytical signal processing techniques and/or information theoretic framework applied to any of the above.

Prof. Dr. Sébastien Roy
Prof. Dr. Julian Cheng
Prof. Dr. Jean-Yves Chouinard
Guest Editors

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. Entropy is an international peer-reviewed open access monthly 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 2600 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

  • antenna selection
  • massive MIMO
  • reconfigurable intelligent surfaces (RISs)
  • physical-layer security
  • cell-free MIMO
  • green communications
  • machine learning
  • unmanned aerial vehicles (UAVs)
  • relaying and cooperation
  • self-organization

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

Related Special Issue

Published Papers (8 papers)

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17 pages, 660 KiB  
Article
User-Centric Cell-Free Massive Multiple-Input-Multiple-Output System with Noisy Channel Gain Estimation and Line of Sight: A Beckmann Distribution Approach
by Danilo B. T. Almeida, Marcelo S. Alencar, Wamberto J. L. Queiroz, Rafael M. Duarte and Francisco Madeiro
Entropy 2025, 27(3), 223; https://doi.org/10.3390/e27030223 - 21 Feb 2025
Viewed by 258
Abstract
This paper analyzes for the first time how the Beckmann distribution can be used to characterize the random variable that represents the envelope of the effective channel gain experienced by the k-th user equipment (UE) of a user-centric (UC) cell-free (CF) system [...] Read more.
This paper analyzes for the first time how the Beckmann distribution can be used to characterize the random variable that represents the envelope of the effective channel gain experienced by the k-th user equipment (UE) of a user-centric (UC) cell-free (CF) system in a scenario with noisy channel state information (CSI) estimation and line of sight (LoS). Additionally, it is shown how the Beckmann probability density function (PDF) can be used to derive the PDF and the cumulative density function (CDF) of the instantaneous signal-to-interference-plus-noise ratio (SINR) of the UC CF k-th UE, followed by applications in the ergodic capacity (EC) and outage probability (OP) expression derivations. It is shown that, regardless of the type of distribution considered for the channel gain between each access point (AP) and UE links, the effective gain presents a Beckmann distribution. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>Representation of a UC CF system.</p> Full article ">Figure 2
<p>Curves of OP as a function of <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>th</mi> </msub> </semantics></math> for different values of <span class="html-italic">M</span> and <span class="html-italic">K</span> assuming <math display="inline"><semantics> <mrow> <mo>#</mo> <mi mathvariant="script">M</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> W.</p> Full article ">Figure 3
<p>Curves of the eCDF of the UE EC for different values of <span class="html-italic">M</span> and <span class="html-italic">K</span> assuming <math display="inline"><semantics> <mrow> <mo>#</mo> <mi mathvariant="script">M</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> W.</p> Full article ">Figure 4
<p>Curves of the EC per UE for different values of <span class="html-italic">M</span> and <span class="html-italic">K</span> assuming <math display="inline"><semantics> <mrow> <mo>#</mo> <mi mathvariant="script">M</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Curves of the eCDF of the UE EC for different values of <math display="inline"><semantics> <msub> <mi mathvariant="script">M</mi> <mi>k</mi> </msub> </semantics></math> considering <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> and assuming <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> W.</p> Full article ">
20 pages, 572 KiB  
Article
Channel Estimation for Massive MIMO Systems via Polarized Self-Attention-Aided Channel Estimation Neural Network
by Shuo Yang, Yong Li, Lizhe Liu, Jing Xia, Bin Wang and Xingjian Li
Entropy 2025, 27(3), 220; https://doi.org/10.3390/e27030220 - 21 Feb 2025
Viewed by 247
Abstract
Research on deep learning (DL)-based channel estimation for massive multiple-input multiple-output (MIMO) communication systems has attracted considerable interest in recent years. In this paper, we propose a DL-assisted channel estimation algorithm that transforms the original channel estimation problem into an image denoising problem, [...] Read more.
Research on deep learning (DL)-based channel estimation for massive multiple-input multiple-output (MIMO) communication systems has attracted considerable interest in recent years. In this paper, we propose a DL-assisted channel estimation algorithm that transforms the original channel estimation problem into an image denoising problem, contrasting it with traditional experience-based channel estimation methods. We establish a new polarized self-attention-aided channel estimation neural network (PACE-Net) to achieve efficient channel estimation. This approach addresses the limitations of the conventional methods, particularly their low accuracy and high computational complexity. In addition, we construct a channel dataset to facilitate the training and testing of PACE-Net. The simulation results show that the proposed DL-assisted channel estimation algorithm has better normalization mean square error (NMSE) performance compared with the traditional algorithms and other DL-assisted algorithms. Furthermore, the computational complexity of the proposed DL-assisted algorithm is significantly lower than that of the traditional minimum mean square error (MMSE) channel estimation algorithm. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>Block diagram of massive MIMO communication system structure.</p> Full article ">Figure 2
<p>Flowchart of a channel estimation algorithm utilizing a polarized self-attention-assisted neural network.</p> Full article ">Figure 3
<p>PACE-Net model structure diagram.</p> Full article ">Figure 4
<p>ReLU and LeakyReLU activation function curves.</p> Full article ">Figure 5
<p>The polarized self-attention (PSA) block under the parallel layout.</p> Full article ">Figure 6
<p>The polarized self-attention (PSA) block under the sequential layout.</p> Full article ">Figure 7
<p>Loss function change curve of training set/validation set during model training process.</p> Full article ">Figure 8
<p>Comparison of NMSE performance of different algorithms under independent channel.</p> Full article ">Figure 9
<p>Effect of antenna correlation on the performance of each algorithm, SNR = 0 dB.</p> Full article ">Figure 10
<p>Effect of antenna correlation on the performance of each algorithm, SNR = 5 dB.</p> Full article ">Figure 11
<p>Effect of the number of antennas on the performance of the algorithm, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">a</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 12
<p>PSA module performance validation, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">a</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 13
<p>Performance validation of LeakyReLU activation function, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">a</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 14
<p>Verification of dropout performance, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">
24 pages, 2460 KiB  
Article
An Unequal Clustering and Multi-Hop Routing Protocol Based on Fuzzy Logic and Q-Learning in WSNs
by Zhen Wang and Jin Duan
Entropy 2025, 27(2), 118; https://doi.org/10.3390/e27020118 - 24 Jan 2025
Viewed by 454
Abstract
Clustering-based routing techniques are key to significantly extending the lifetime of wireless sensor networks (WSNs). However, these approaches often do not address the common hotspot issue in multi-hop WSNs. To overcome this challenge and enhance network lifespan, this study presents FQ-UCR, a hybrid [...] Read more.
Clustering-based routing techniques are key to significantly extending the lifetime of wireless sensor networks (WSNs). However, these approaches often do not address the common hotspot issue in multi-hop WSNs. To overcome this challenge and enhance network lifespan, this study presents FQ-UCR, a hybrid approach that merges unequal clustering based on fuzzy logic (FL) with routing optimized through Q-learning. In FQ-UCR, a tentative CH employs a fuzzy inference system (FIS) to compute its probability of being selected as the final CH. By using the Q-learning algorithm, the best forwarding cluster head (CH) is chosen to construct the data transmission route between the CHs and the base station (BS). The approach is extensively evaluated and compared with protocols like EEUC and CHEF. Simulation results demonstrate that FQ-UCR improves energy efficiency across all nodes, significantly extends network lifetime, and effectively alleviates the hotspot issue. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>The network model employed in this study.</p> Full article ">Figure 2
<p>Radio model.</p> Full article ">Figure 3
<p>Flow chart of proposed FQ-UCR protocol.</p> Full article ">Figure 4
<p>Block diagram of FIS.</p> Full article ">Figure 5
<p>FIS developed for selecting CHs in FQ-UCR.</p> Full article ">Figure 6
<p>Membership function for residual energy.</p> Full article ">Figure 7
<p>Membership function for distance to base.</p> Full article ">Figure 8
<p>Membership function for number of neighbors.</p> Full article ">Figure 9
<p>Membership function for node centrality.</p> Full article ">Figure 10
<p>Membership function for output variables for CH selection (probability).</p> Full article ">Figure 11
<p>Membership function for output variables for radius.</p> Full article ">Figure 12
<p>Block diagram of Q-learning.</p> Full article ">Figure 13
<p>(<b>a</b>) Node distribution for Scenario 1. (<b>b</b>) Node distribution for Scenario 2.</p> Full article ">Figure 14
<p>The figure compares the residual energy (in Joules) of 100 nodes, with the BS located at (100, 100), across different protocols.</p> Full article ">Figure 15
<p>The figure compares the residual energy (in Joules) of 200 nodes, with the BS located at (100, 100), across different protocols.</p> Full article ">Figure 16
<p>The figure compares the residual energy (in Joules) of 400 nodes, with the BS located at (100, 100), across different protocols.</p> Full article ">Figure 17
<p>Network lifetime comparison for 100 nodes in Scenario 1.</p> Full article ">Figure 18
<p>Network lifetime comparison for 200 nodes in Scenario 1.</p> Full article ">Figure 19
<p>Network lifetime comparison for 400 nodes in Scenario 1.</p> Full article ">Figure 20
<p>Comparative analysis based on network stability period with BS located at (100, 250).</p> Full article ">Figure 21
<p>Comparative analysis based on throughput in Scenario 1.</p> Full article ">Figure 22
<p>The figure compares the residual energy (in Joules) of 100 nodes, with the BS located at (100, 250), across different protocols.</p> Full article ">Figure 23
<p>The figure compares the residual energy (in Joules) of 200 nodes, with the BS located at (100, 250), across different protocols.</p> Full article ">Figure 24
<p>The figure compares the residual energy (in Joules) of 400 nodes, with the BS located at (100, 250), across different protocols.</p> Full article ">Figure 25
<p>Network lifetime comparison for 100 nodes in Scenario 2.</p> Full article ">Figure 26
<p>Network lifetime comparison for 200 nodes in Scenario 2.</p> Full article ">Figure 27
<p>Network lifetime comparison for 400 nodes in Scenario 2.</p> Full article ">Figure 28
<p>Comparative analysis based on network stability period with BS located at (100, 250).</p> Full article ">Figure 29
<p>Comparative analysis based on throughput in Scenario 2.</p> Full article ">
14 pages, 475 KiB  
Article
Precise Error Performance of BPSK Modulated Coherent Terahertz Wireless LOS Links with Pointing Errors
by Mingbo Niu, Ruihang Ji, Hucheng Wang and Huan Liu
Entropy 2024, 26(8), 706; https://doi.org/10.3390/e26080706 - 20 Aug 2024
Viewed by 974
Abstract
One of the key advantages of terahertz (THz) communication is its potential for energy efficiency, making it an attractive option for green communication systems. Coherent THz transmission technology has recently been explored in the literature. However, there exist few error performance results for [...] Read more.
One of the key advantages of terahertz (THz) communication is its potential for energy efficiency, making it an attractive option for green communication systems. Coherent THz transmission technology has recently been explored in the literature. However, there exist few error performance results for such a wireless link employing coherent THz technology. In this paper, we explore a comprehensive terrestrial channel model designed for wireless line-of-sight communication using THz frequencies. The performance of coherent THz links is analyzed, and it is found to be notably affected by two significant factors, atmospheric turbulence and pointing errors. These could occur between the terahertz transmitter and receiver in terrestrial links. The exact and asymptotic solutions are derived for bit error rate and interrupt probability for binary phase-shift keying coherent THz systems, respectively, over log-normal and Gamma–Gamma turbulent channels. The asymptotic outage probability analysis is also performed. It is shown that the presented results offer a precise estimation of coherent THz transmission performance and its link budget. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>Block diagram of a coherent THz link.</p> Full article ">Figure 2
<p>Detector and beam footprint with misalignment on the detector plane.</p> Full article ">Figure 3
<p>Atmospheric decay due to molecular absorption and FSPL losses in the frequency ranges of 1 GHz to 350 GHz.</p> Full article ">Figure 4
<p>BER performance of coherent THz links for two different turbulent channels with <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> m.</p> Full article ">Figure 5
<p>BER of coherent THz links for different turbulence intensities GG channel with pointing errors for a distance <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> m.</p> Full article ">Figure 6
<p>The outage probability of coherent THz links over the GG fading channel with pointing errors.</p> Full article ">
19 pages, 3471 KiB  
Article
Radio Frequency Fingerprint Identification for 5G Mobile Devices Using DCTF and Deep Learning
by Hua Fu, Hao Dong, Jian Yin and Linning Peng
Entropy 2024, 26(1), 38; https://doi.org/10.3390/e26010038 - 29 Dec 2023
Cited by 3 | Viewed by 3145
Abstract
The fifth-generation (5G) mobile cellular network is vulnerable to various security threats. Radio frequency fingerprint (RFF) identification is an emerging physical layer authentication technique which can be used to detect spoofing and distributed denial of service attacks. In this paper, the performance of [...] Read more.
The fifth-generation (5G) mobile cellular network is vulnerable to various security threats. Radio frequency fingerprint (RFF) identification is an emerging physical layer authentication technique which can be used to detect spoofing and distributed denial of service attacks. In this paper, the performance of RFF identification is studied for 5G mobile phones. The differential constellation trace figure (DCTF) is extracted from the physical random access channel (PRACH) preamble. When the database of all 64 PRACH preambles is available at the gNodeB (gNB), an index-based DCTF identification scheme is proposed, and the classification accuracy reaches 92.78% with a signal-to-noise ratio of 25 dB. Moreover, due to the randomness in the selection of preamble sequences in the random access procedure, when only a portion of the preamble sequences can be trained, a group-based DCTF identification scheme is proposed. The preamble sequences generated from the same root value are grouped together, and the untrained sequences can be identified based on the trained sequences within the same group. The classification accuracy of the group-based scheme is 89.59%. An experimental system has been set up using six 5G mobile phones of three models. The 5G gNB is implemented on the OpenAirInterface platform. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>Structure of PRACH preamble format A2.</p> Full article ">Figure 2
<p>Different PRACH preambles of one cell (in-phase channel): (<b>a</b>) preamble index 1; (<b>b</b>) preamble index 2 and (<b>c</b>) preamble index 11.</p> Full article ">Figure 3
<p>Signal preprocessing flowchart.</p> Full article ">Figure 4
<p>A segment of preamble waveform after preprocessing (in-phase channel).</p> Full article ">Figure 5
<p>The power spectrum of (<b>a</b>) the collected original signal, (<b>b</b>) the standard signal and (<b>c</b>) the preprocessed signal.</p> Full article ">Figure 6
<p>DCTF for (<b>a</b>) standard preamble with index 1, (<b>b</b>) preamble with index 1 of UE1, (<b>c</b>) standard preamble with index 2 and (<b>d</b>) standard preamble with index 11.</p> Full article ">Figure 7
<p>Single-channel DCTF-based CNN structure.</p> Full article ">Figure 8
<p>Multi-channel DCTF-based CNN structure.</p> Full article ">Figure 9
<p>Group-based DCTF identification scheme using a single-channel CNN.</p> Full article ">Figure 10
<p>Experimental set-up and six 5G mobile phones.</p> Full article ">Figure 11
<p>Examples of frequency domain channel fading for one PRACH preamble of one phone.</p> Full article ">Figure 12
<p>Cross-correlation between (<b>a</b>) preamble sequences of the same index, (<b>b</b>) preamble sequences from the same <span class="html-italic">group</span> and (<b>c</b>) preamble sequences from different <span class="html-italic">groups</span>.</p> Full article ">Figure 13
<p>Performance of index-based DCTF identification scheme using a multi-channel CNN.</p> Full article ">Figure 14
<p>Performance of index-based DCTF identification scheme using a single-channel CNN.</p> Full article ">Figure 15
<p>Performance of <span class="html-italic">group</span>-based DCTF identification scheme using a single-channel CNN.</p> Full article ">Figure 16
<p>Classification results of different methods in Scenario 1 and Scenario 2.</p> Full article ">Figure 17
<p>DCTF for PRACH preamble of index 1 with SNR of (<b>a</b>) 25 dB, (<b>b</b>) 20 dB, (<b>c</b>) 15 dB and (<b>d</b>) 10 dB.</p> Full article ">Figure 18
<p>Classification results of different methods in function of SNR for Scenario 1.</p> Full article ">Figure 19
<p>DCTF of UE1 for PRACH preamble of index 1 with an overlap ratio of (<b>a</b>) 1:16, (<b>b</b>) 1:8, (<b>c</b>) 1:4 and (<b>d</b>) 1:2.</p> Full article ">Figure 20
<p>Classification results of UE1 as a function of the overlap ratio.</p> Full article ">
17 pages, 867 KiB  
Article
Performance Analysis of Artificial Noise-Assisted Location-Based Beamforming in Rician Wiretap Channels
by Hua Fu, Xiaoyu Zhang and Linning Peng
Entropy 2023, 25(12), 1626; https://doi.org/10.3390/e25121626 - 6 Dec 2023
Viewed by 1381
Abstract
This paper studies the performance of location-based beamforming with the presence of artificial noise (AN). Secure transmission can be achieved using the location information of the user. However, the shape of the beam depends on the number of antennas used. When the scale [...] Read more.
This paper studies the performance of location-based beamforming with the presence of artificial noise (AN). Secure transmission can be achieved using the location information of the user. However, the shape of the beam depends on the number of antennas used. When the scale of the antenna array is not sufficiently large, it becomes difficult to differentiate the performance between the legitimate user and eavesdroppers nearby. In this paper, we leverage AN to minimize the area near the user with eavesdropping risk. The impact of AN is considered for both the legitimate user and the eavesdropper. Closed-form expressions are derived for the expectations of the signal to interference plus noise ratios (SINRs) and the bit error rates. Then, a secure beamforming scheme is proposed to ensure a minimum SINR requirement for the legitimate user and minimize the SINR of the eavesdropper. Numerical results show that, even with a small number of antennas, the proposed beamforming scheme can effectively degrade the performance of eavesdroppers near the legitimate user. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>The expectation of <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>b</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>e</mi> </msub> </semantics></math> in the function of <math display="inline"><semantics> <msub> <mi>g</mi> <mi>AN</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>∈</mo> <mo>{</mo> <mn>8</mn> <mo>,</mo> <mn>16</mn> <mo>,</mo> <mn>32</mn> <mo>,</mo> <mn>64</mn> <mo>,</mo> <mn>100</mn> <mo>}</mo> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>The simulated and approximate BERs of Eve for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>The expectation of <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>b</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>e</mi> </msub> </semantics></math> with optimal beamforming in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 4
<p>The expectation of the power of the desired signal and AN received by Eve, with different numbers of receive antennas at Eve.</p> Full article ">Figure 5
<p>The simulated BERs of Eve in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 6
<p>The expectation of <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>e</mi> </msub> </semantics></math> without using AN in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 7
<p>The simulated BERs of Eve without using AN in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 8
<p>The expectations of <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>b</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>e</mi> </msub> </semantics></math> when the ergodic secrecy rate is maximized in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 9
<p>The simulated BERs when the ergodic secrecy rate is maximized in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 10
<p>The expectation of <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>b</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>SINR</mi> <mi>e</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>b</mi> </msub> <mo>=</mo> <mrow> <mo>{</mo> <mn>10</mn> <mo>,</mo> <mn>14.8</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> dB in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">Figure 11
<p>The simulated BLERs of Bob and Eve in the function of the location of Eve <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>e</mi> </msub> </semantics></math>.</p> Full article ">
16 pages, 341 KiB  
Article
Nested Variational Chain and Its Application in Massive MIMO Detection for High-Order Constellations
by Qiwei Wang
Entropy 2023, 25(12), 1621; https://doi.org/10.3390/e25121621 - 5 Dec 2023
Cited by 1 | Viewed by 1198
Abstract
Multiple input multiple output (MIMO) technology necessitates detection methods with high performance and low complexity; however, the detection problem becomes severe when high-order constellations are employed. Variational approximation-based algorithms prove to deal with this problem efficiently, especially for high-order MIMO systems. Two typical [...] Read more.
Multiple input multiple output (MIMO) technology necessitates detection methods with high performance and low complexity; however, the detection problem becomes severe when high-order constellations are employed. Variational approximation-based algorithms prove to deal with this problem efficiently, especially for high-order MIMO systems. Two typical algorithms named Gaussian tree approximation (GTA) and expectation consistency (EC) attempt to approximate the true likelihood function under discrete finite-set constraints with a new distribution by minimizing the Kullback–Leibler (KL) divergence. As the KL divergence is not a true distance measure, ’exclusive’ and ’inclusive’ KL divergences are utilized by GTA and EC, respctively, demonstrating different performances. In this paper, we further combine the two asymmetric KL divergences in a nested way by proposing a generic algorithm framework named nested variational chain. Acting as an initial application, a MIMO detection algorithm named Gaussian tree approximation expectation consistency (GTA-EC) can thus be presented along with its alternative version for better understanding. With less computational burden compared to its counterparts, GTA-EC is able to provide better detection performance and diversity gain, especially for large-scale high-order MIMO systems. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1

Figure 1
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> with 16-QAM.</p> Full article ">Figure 2
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> with 64-QAM.</p> Full article ">Figure 3
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math> with 256-QAM.</p> Full article ">Figure 4
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math> with 16-QAM.</p> Full article ">Figure 5
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math> with 64-QAM.</p> Full article ">Figure 6
<p>BER comparison of GTA-EC with existing algorithms when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math> with 256-QAM.</p> Full article ">

Review

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74 pages, 3722 KiB  
Review
Overview of Tensor-Based Cooperative MIMO Communication Systems—Part 2: Semi-Blind Receivers
by Gérard Favier and Danilo Sousa Rocha
Entropy 2024, 26(11), 937; https://doi.org/10.3390/e26110937 - 31 Oct 2024
Viewed by 780
Abstract
Cooperative MIMO communication systems play an important role in the development of future sixth-generation (6G) wireless systems incorporating new technologies such as massive MIMO relay systems, dual-polarized antenna arrays, millimeter-wave communications, and, more recently, communications assisted using intelligent reflecting surfaces (IRSs), and unmanned [...] Read more.
Cooperative MIMO communication systems play an important role in the development of future sixth-generation (6G) wireless systems incorporating new technologies such as massive MIMO relay systems, dual-polarized antenna arrays, millimeter-wave communications, and, more recently, communications assisted using intelligent reflecting surfaces (IRSs), and unmanned aerial vehicles (UAVs). In a companion paper, we provided an overview of cooperative communication systems from a tensor modeling perspective. The objective of the present paper is to provide a comprehensive tutorial on semi-blind receivers for MIMO one-way two-hop relay systems, allowing the joint estimation of transmitted symbols and individual communication channels with only a few pilot symbols. After a reminder of some tensor prerequisites, we present an overview of tensor models, with a detailed, unified, and original description of two classes of tensor decomposition frequently used in the design of relay systems, namely nested CPD/PARAFAC and nested Tucker decomposition (TD). Some new variants of nested models are introduced. Uniqueness and identifiability conditions, depending on the algorithm used to estimate the parameters of these models, are established. Two families of algorithms are presented: iterative algorithms based on alternating least squares (ALS) and closed-form solutions using Khatri–Rao and Kronecker factorization methods, which consist of SVD-based rank-one matrix or tensor approximations. In a second part of the paper, the overview of cooperative communication systems is completed before presenting several two-hop relay systems using different codings and configurations in terms of relaying protocol (AF/DF) and channel modeling. The aim of this presentation is firstly to show how these choices lead to different nested tensor models for the signals received at destination. Then, by capitalizing on these models and their correspondence with the generic models studied in the first part, we derive semi-blind receivers to jointly estimate the transmitted symbols and the individual communication channels for each relay system considered. In a third part, extensive Monte Carlo simulation results are presented to compare the performance of relay systems and associated semi-blind receivers in terms of the symbol error rate (SER) and channel estimate normalized mean-square error (NMSE). Their computation time is also compared. Finally, some perspectives are drawn for future research work. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives)
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Figure 1
<p>Organization of the paper.</p> Full article ">Figure 2
<p>Nested tensor decompositions based on TD and CPD.</p> Full article ">Figure 3
<p>TTD of a <italic>P</italic>th-order tensor, <inline-formula><mml:math id="mm1130"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mi>P</mml:mi></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 4
<p>Graph of the TTD-4 model for a fourth-order tensor <inline-formula><mml:math id="mm1131"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>4</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 5
<p>Graph of the GTTD-(2,4,4,2) model for a sixth-order tensor <inline-formula><mml:math id="mm1132"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>6</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 6
<p>NCPD-4 model as (<bold>a</bold>) a nesting of two CPD-3 models and (<bold>b</bold>) a cascade of two CPD-3 models.</p> Full article ">Figure 7
<p>NTD-4 model as (<bold>a</bold>) a particular TTD and (<bold>b</bold>) a cascade of two TD-(2,3) models.</p> Full article ">Figure 8
<p>Graph of the NTD-4 model for a fourth-order tensor <inline-formula><mml:math id="mm1133"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>4</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 9
<p>Graph of the NTD-6 model for a sixth-order tensor <inline-formula><mml:math id="mm1134"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>6</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 10
<p>Graph of the NGTD-7 model for a seventh-order tensor <inline-formula><mml:math id="mm1135"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>7</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 11
<p>Graph of the NGTD-5 model for a fifth-order tensor <inline-formula><mml:math id="mm1136"><mml:semantics><mml:mrow><mml:mi mathvariant="script">X</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">K</mml:mi><mml:msub><mml:munder><mml:mi>I</mml:mi><mml:mo>̲</mml:mo></mml:munder><mml:mn>5</mml:mn></mml:msub></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 12
<p>Two families of TD- and CPD-based decompositions.</p> Full article ">Figure 13
<p>Classification of relay systems according to the coding scheme and tensor model.</p> Full article ">Figure 14
<p>One-way, two-hop cooperative system.</p> Full article ">Figure 15
<p>Tucker train model of a two-hop relay system using TSTF codings.</p> Full article ">Figure 16
<p>Tucker train model of a two-hop relay system using TST codings.</p> Full article ">Figure 17
<p>NCPD-5 model for the DKRSTF system as a cascade of three CPD-3 models.</p> Full article ">Figure 18
<p>NCPD-4 model for the SKRST system.</p> Full article ">Figure 19
<p>Plan of simulations for performance comparison.</p> Full article ">Figure 20
<p>SER comparison with different receivers for STST and SKRST.</p> Full article ">Figure 21
<p>Comparison of (<bold>a</bold>) computation time for ZF, KronF/KRF, and ALS receivers and (<bold>b</bold>) number of iterations for convergence of ALS receivers for STST and SKRST.</p> Full article ">Figure 22
<p>NMSE of estimated channels with the KronF/KRF and ALS receivers for STST and SKRST: (<bold>a</bold>) <inline-formula><mml:math id="mm1137"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula> and (<bold>b</bold>) <inline-formula><mml:math id="mm1138"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 23
<p>Impact of time-spreading lengths with ZF receivers of STST and SKRST.</p> Full article ">Figure 24
<p>Impact of numbers of antennas with ZF receivers of (<bold>a</bold>) SKRST and (<bold>b</bold>) STST.</p> Full article ">Figure 25
<p>SER comparison for the DKRSTF, STSTF, and TSTF systems with <inline-formula><mml:math id="mm1139"><mml:semantics><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 26
<p>Impact of the number <italic>Q</italic> of symbol matrices in combined codings with ZF receivers.</p> Full article ">Figure 27
<p>Impact of AF/DF protocols on SER performance of STST and SKRST.</p> Full article ">Figure 28
<p>Impact of AF/DF protocols on NMSE of estimated channels for STST and SKRST: (<bold>a</bold>) <inline-formula><mml:math id="mm1140"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula> and (<bold>b</bold>) <inline-formula><mml:math id="mm1141"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 29
<p>SER comparison for all considered relay systems.</p> Full article ">Figure 30
<p>NMSE of estimated channels for all considered relay systems: (<bold>a</bold>) <inline-formula><mml:math id="mm1142"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula> and (<bold>b</bold>) <inline-formula><mml:math id="mm1143"><mml:semantics><mml:msup><mml:mover accent="true"><mml:mi mathvariant="bold">H</mml:mi><mml:mo stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:semantics></mml:math></inline-formula>.</p> Full article ">Figure 31
<p>Comparison of considered relay systems in terms of (<bold>a</bold>) NMSE of reconstructed received signals and (<bold>b</bold>) computation time.</p> Full article ">
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