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

Deadline for manuscript submissions: 31 July 2026 | Viewed by 7450

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Prof. Dr. Sébastien Roy

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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 V1V 1V7, Canada
Interests: machine learning for wireless communications; wireless optical technology; quantum communications
Special Issues, Collections and Topics in MDPI journals

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;
Modulation and waveform design;
Integrated sensing and communication.

Prof. Dr. Sébastien Roy
Prof. Dr. Julian Cheng
Guest Editors

Manuscript Submission Information

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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.

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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, modulation and waveform design
integrated sensing and communication

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Related Special Issue

Wireless Communications: Signal Processing Perspectives in Entropy (11 articles)

Published Papers (8 papers)

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Research

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29 pages, 1964 KB

Open AccessArticle

Unified Space–Time-Message Interference Alignment: An End-to-End Learning Approach

by Elaheh Sadeghabadi and Steven Blostein

Entropy 2026, 28(2), 249; https://doi.org/10.3390/e28020249 - 21 Feb 2026

Viewed by 340

Abstract

This paper investigates the performance of a multi-user multiple-input single-output (MU-MISO) broadcast channel under the practical constraints of imperfect, delayed, and quantized channel state information at the transmitter (CSIT). Conventional interference alignment (IA) strategies—classified into spatial (SIA), temporal (TIA), and message-domain (MIA) techniques— typically designed for specific, idealized CSI regimes and often rely on successive interference cancellation (SIC) at the receiver. However, the iterative structure of SIC is highly susceptible to error propagation, particularly under CSI uncertainty and high-order modulation. We propose Deep-STMIA, a novel end-to-end deep learning framework that jointly optimizes interference management across the space, time, and message domains. Using a neural network-based autoencoder architecture with structural message-domain regularization, Deep-STMIA learns to mitigate the catastrophic effects of error propagation and adapts to a continuum of CSIT conditions. Simulation results demonstrate that Deep-STMIA matches the performance of degrees-of-freedom (DoF) optimal benchmarks in extreme CSI regimes and significantly outperforms state-of-the-art baselines, such as rate-splitting multiple access (RSMA), in practical imperfect CSIT scenarios. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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24 pages, 23360 KB

Open AccessArticle

Model-Data Hybrid-Driven Wideband Channel Estimation for Beamspace Massive MIMO Systems

by Yang Nie, Zhenghuan Ma and Lili Jing

Entropy 2026, 28(2), 154; https://doi.org/10.3390/e28020154 - 30 Jan 2026

Cited by 1 | Viewed by 397

Abstract

Accurate channel estimation is critical for enabling effective directional beamforming and spectrally efficient transmission in beamspace massive multiple-input multiple-output (MIMO) systems. However, conventional model-driven algorithms are derived from idealized mathematical models and typically suffer severe performance degradation under model mismatches caused by complex and nonideal propagation environments. Although data-driven deep learning (DL) approaches can learn channel characteristics from data, they typically require large-scale training datasets and demonstrate limited generalization capability. To overcome these limitations, we propose a model-data hybrid-driven network (MD-HDN) scheme to address the wideband beamspace channel estimation problem. In the MD-HDN scheme, we unfold the vector approximate message passing (VAMP) algorithm into a trainable network, where a novel shrinkage function is introduced to enhance the estimation accuracy. Extensive numerical results confirm that the proposed MD-HDN scheme can significantly outperform existing schemes under various signal-to-noise ratio (SNR), and achieve substantial improvements in both estimation accuracy and robustness. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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14 pages, 1572 KB

Open AccessArticle

A Transformer–LSTM Hybrid Detector for OFDM-IM Signal Detection

by Leijun Wang, Zian Tong, Kuan Wang, Jinfa Xie, Xidong Peng, Bolong Li, Jiawen Li, Xianxian Zeng, Jin Zhan and Rongjun Chen

Entropy 2026, 28(1), 102; https://doi.org/10.3390/e28010102 - 14 Jan 2026

Viewed by 380

Abstract

This paper addresses the signal detection problem in orthogonal frequency division multiplexing with index modulation (OFDM-IM) systems using deep learning (DL) techniques. In particular, a DL-based detector termed FullTrans-IM is proposed, which integrates the Transformer architecture with long short-term memory (LSTM) networks. Unlike conventional methods that treat signal detection as a classification task, the proposed approach reformulates it as a sequence prediction problem by exploiting the sequence modeling capability of the Transformer’s decoder rather than relying solely on the encoder. This formulation enables the detector to effectively learn channel characteristics and modulation patterns, thereby improving detection accuracy and robustness. Simulation results demonstrate that the proposed FullTrans-IM detector achieves superior bit error rate (BER) performance compared with conventional methods such as zero-forcing (ZF) and existing DL-based detectors under Rayleigh fading channels. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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20 pages, 7914 KB

Open AccessArticle

Channel Estimation for Intelligent Reflecting Surface Empowered Coal Mine Wireless Communication Systems

by Yang Liu, Kaikai Guo, Xiaoyue Li, Bin Wang and Yanhong Xu

Entropy 2025, 27(9), 932; https://doi.org/10.3390/e27090932 - 4 Sep 2025

Viewed by 1080

Abstract

The confined space of coal mines characterized by curved tunnels with rough surfaces and a variety of deployed production equipment induces severe signal attenuation and interruption, which significantly degrades the accuracy of conventional channel estimation algorithms applied in coal mine wireless communication systems. To address these challenges, we propose a modified Bilinear Generalized Approximate Message Passing (mBiGAMP) algorithm enhanced by intelligent reflecting surface (IRS) technology to improve channel estimation accuracy in coal mine scenarios. Due to the presence of abundant coal-carrying belt conveyors, we establish a hybrid channel model integrating both fast-varying and quasi-static components to accurately model the unique propagation environment in coal mines. Specifically, the fast-varying channel captures the varying signal paths affected by moving conveyors, while the quasi-static channel represents stable direct links. Since this hybrid structure necessitates an augmented factor graph, we introduce two additional factor nodes and variable nodes to characterize the distinct message-passing behaviors and then rigorously derive the mBiGAMP algorithm. Simulation results demonstrate that the proposed mBiGAMP algorithm achieves superior channel estimation accuracy in dynamic conveyor-affected coal mine scenarios compared with other state-of-the-art methods, showing significant improvements in both separated and cascaded channel estimation. Specifically, when the NMSE is

10^{- 3}

, the SNR of mBiGAMP is improved by approximately 5 dB, 6 dB, and 14 dB compared with the Dual-Structure Orthogonal Matching Pursuit (DS-OMP), Parallel Factor (PARAFAC), and Least Squares (LS) algorithms, respectively. We also verify the convergence behavior of the proposed mBiGAMP algorithm across the operational signal-to-noise ratios range. Furthermore, we investigate the impact of the number of pilots on the channel estimation performance, which reveals that the proposed mBiGAMP algorithm consumes fewer number of pilots to accurately recover channel state information than other methods while preserving estimation fidelity. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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22 pages, 4895 KB

Open AccessFeature PaperArticle

Machine Learning-Assisted Secure Random Communication System

by Areeb Ahmed and Zoran Bosnić

Entropy 2025, 27(8), 815; https://doi.org/10.3390/e27080815 - 29 Jul 2025

Viewed by 1360

Abstract

Machine learning techniques have revolutionized physical layer security (PLS) and provided opportunities for optimizing the performance and security of modern communication systems. In this study, we propose the first machine learning-assisted random communication system (ML-RCS). It comprises a pretrained decision tree (DT)-based receiver [...] Read more.

α

-stable) noise as a random carrier to encode the incoming binary bits securely. The DT model is pretrained on an extensively developed dataset encompassing all the selected parameter combinations to generate and detect the

α

-stable noise signals. The legitimate receiver leverages the pretrained DT and a predetermined key, specifically the pulse length of a single binary information bit, to securely decode the hidden binary bits. The performance evaluations included the single-bit transmission, confusion matrices, and a bit error rate (BER) analysis via Monte Carlo simulations. The fact that the BER reached 10⁻³ confirms the ability of the proposed system to establish successful secure communication between a transmitter and legitimate receiver. Additionally, the ML-RCS provides an increased data rate compared to previous random communication systems. From the perspective of security, the confusion matrices and computed false negative rate of 50.2% demonstrate the failure of an eavesdropper to decode the binary bits without access to the predetermined key and the private dataset. These findings highlight the potential ability of unconventional ML-RCSs to promote the development of secure next-generation communication devices with built-in PLSs. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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18 pages, 821 KB

Open AccessArticle

Joint Iterative Decoding Design of Cooperative Downlink SCMA Systems

by Hao Cheng, Min Zhang and Ruoyu Su

Entropy 2025, 27(7), 762; https://doi.org/10.3390/e27070762 - 18 Jul 2025

Cited by 1 | Viewed by 809

Abstract

Sparse code multiple access (SCMA) has been a competitive multiple access candidate for future communication networks due to its superiority in spectrum efficiency and providing massive connectivity. However, cell edge users may suffer from great performance degradations due to signal attenuation. Therefore, a cooperative downlink SCMA system is proposed to improve transmission reliability. To the best of our knowledge, multiuser detection is still an open issue for this cooperative downlink SCMA system. To this end, we propose a joint iterative decoding design of the cooperative downlink SCMA system by using the joint factor graph stemming from direct and relay transmission. The closed form bit-error rate (BER) performance of the cooperative downlink SCMA system is also derived. Simulation results verify that the proposed cooperative downlink SCMA system performs better than the non-cooperative one. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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20 pages, 528 KB

Open AccessArticle

Analysis of Outage Probability and Average Bit Error Rate of Parallel-UAV-Based Free-Space Optical Communications

by Sheng-Hong Lin, Jin-Yuan Wang and Xinyi Hua

Entropy 2025, 27(6), 650; https://doi.org/10.3390/e27060650 - 18 Jun 2025

Cited by 1 | Viewed by 1550

Abstract

Recently, free-space optical (FSO) communication systems utilizing unmanned aerial vehicle (UAV) relays have garnered significant attention. Integrating UAV relays into FSO communication and employing cooperative diversity techniques not only fulfill the need for long-distance transmission but also enable flexible adjustments of relay positions based on the actual environment. This paper investigates the performance of a parallel-UAV-relay-based FSO communication system. In the considered system, the channel fadings include atmospheric loss, atmospheric turbulence, pointing errors, and angle-of-arrival fluctuation. Using the established channel model, we derive a tractable expression for the probability density function of the total channel gain. Then, we derive closed-form expressions of the system outage probability (OP) and average bit error rate (ABER). Moreover, we also derive the asymptotic OP and ABER for a high-optical-intensity regime. Our numerical results validate the accuracy of the derived theoretical expressions. Additionally, the effects of the number of relay nodes, the field of view, the direction deviation, the signal-to-noise ratio threshold, the atmospheric turbulence intensity, the transmit power, and the transmission distance on the system’s performance are also discussed. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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Review

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47 pages, 645 KB

Open AccessReview

A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with p-Modular Lattice Constructions

by Hassan Khodaiemehr, Khadijeh Bagheri, Amin Mohajer, Chen Feng, Daniel Panario and Victor C. M. Leung

Entropy 2026, 28(2), 235; https://doi.org/10.3390/e28020235 - 18 Feb 2026

Viewed by 575

Abstract

Physical-layer security (PLS) provides an information-theoretic framework for securing wireless communications by exploiting channel and signal-structure asymmetries, thereby avoiding reliance on computational hardness assumptions. Within this setting, lattice codes and their algebraic constructions play a central role in achieving secrecy over Gaussian and fading wiretap channels. This article offers a comprehensive survey of lattice-based wiretap coding, covering foundational concepts in algebraic number theory, Construction A over number fields, and the structure of modular and unimodular lattice families. We review key secrecy metrics, including secrecy gain, flatness factor, and equivocation, and consolidate classical and recent results to provide a unified perspective that links wireless-channel models with their underlying algebraic lattice structures. In addition, we review a newly proposed family of p-modular lattices in Khodaiemehr, H., 2018 constructed from cyclotomic fields

Q (ζ_{p})

for primes

p \equiv 1 (\mod 4)

via a generalized Construction A framework. We characterize their algebraic and geometric properties and establish a non-existence theorem showing that such constructions cannot be extended to prime-power cyclotomic fields

Q (ζ_{p^{n}})

with

n > 1

. Finally, motivated by the fact that these p-modular lattices naturally yield mixed-signature structures for which classical theta series diverge, we integrate recent advances on indefinite theta series and modular completions. Drawing on Vignéras’ differential framework and generalized error functions, we outline how modularly completed indefinite theta series provide a principled analytic foundation for defining secrecy-relevant quantities in the indefinite setting. Overall, this work serves both as a survey of algebraic lattice techniques for PLS and as a source of new design insights for secure wireless communication systems. Full article

(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)

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