Temporal fading in wireless channels is governed by the angular distribution of arriving Multipath Components (MPCs), which determines the Doppler spectrum and, consequently, the rate of envelope variation. The Multipath Shape Factor (MSF) framework exploits this relationship to derive second-order fading statistics such as the widely used Level Crossing Rate (LCR) and Average Fade Duration (AFD), from channel angular statistics. However, both the LCR and AFD metrics are defined with respect to a single amplitude threshold, whereas applications such as envelope quantization may require characterization over multiple thresholds. The Average Contiguous Duration (ACD) metric quantifies the average time for which the envelope remains continuously within a bounded amplitude interval, yet its relationship to channel angular statistics has not been established previously. In this paper, we derive an analytical relationship between the ACD and channel angular statistics within the MSF framework, applicable to both two- and three-dimensional propagation. Next, we derive a closed-form expression for the ACD of the generalized α-k-μ fading model, which encompasses Rayleigh, Rice, Nakagami-m, Weibull, k-μ, and α-μ as its special cases. Analytical results are validated through simulations, and the AFD and the Average Non-Fade Duration (ANFD) are shown to be special cases of the proposed analytical framework. The effects of angular spectrum truncation, amplitude interval selection, and the fading shape parameters (α, k, μ) are examined: a narrower angular spectrum and a stronger dominant component both lengthen the ACD. Furthermore, an ACD-based physical-layer Secret Key Generation (SKG) scheme is proposed, in which ACD values set quantization-level-specific thresholds for sample selection. The scheme improves the key generation rate over a widely used fixed-threshold baseline without degrading key agreement, demonstrating the practical utility of the proposed analytical framework for secure wireless communications.

This work investigates the performance of a full-duplex amplify-and-forward (FD-AF) relaying taking into account the residual self-interference at the relay node. We consider the a- mu distribution as fading channel model at the two links which well describes the small scale fading in terahertz (THz) communications. Full- duplex relaying can potentially double the spectral efficiency achievable by half-duplex operation considering the detrimental effects of inevitable self-interference. We derive the closed-form expressions of rate outage probability and ergodic capacity whereas an exact expression of average symbol error probability of coherently detected M-ary phase shift keying (M-PSK) is derived using the univariate and bivariate Fox's H-functions. The derived expressions are valid for arbitrary values of the a- mu fading parameters. Through simulations, it has been revealed that the performance of the system improves when the relay is closer to the source node as compared to destination node. Moreover, it has been observed that the fading parameters of the source- relay link dominates the system's performance as compared to the parameters of relay-destination link. The analytical expressions are ascertained by simulations which are found to be in excellent agreement.

Ensuring reliable and secure communications in the increasingly pervasive beyond 5 th generation (B5G) wireless networks is one of the key research challenges. Within the physical layer security (PLS) paradigm, the secret key generation (SKG) technique exploits the wireless channel's randomness to generate symmetric secret keys for message encryption/decryption by legitimate communication nodes. The SKG procedure involves various steps such as wireless channel probing, quantization, information reconciliation, and privacy amplification to render effective symmetric secret key bits. This work proposes a novel multi-level channel quantization scheme, which for the given distribution of the channel envelopes' gain, ensures an identical likelihood of the envelope samples falling into each quantization interval. Inspired by the classical companding transform (CT), the proposed probability integral transform (PIT)-based quantization scheme works in three sequential steps. First, average contiguous duration (ACD), a second- order fading statistics metric, is considered to select and bias the channel samples that are more likely to fall in the same quantization interval. Subsequently, by using an invertible transform the envelope values are transformed into samples drawn from a uniform distribution, which are then processed through a uniform quantizer. The proposed PIT-based transformation and quantization scheme aims to enhance the trade-offs between the SKG performance metrics namely the key generation rate (KGR), key disagreement rate (KDR), and the key randomness properties. A comprehensive performance analysis of the proposed PIT-based quantization scheme for generalized gamma (GG) fading channels is conducted and its performance is evaluated in relation to several channel and system parameters. Moreover, a comparative analysis of the proposed scheme with its counterparts in the literature is also provided to demonstrate its relative performance gains, where our proposed scheme is observed to outperform the existing schemes. Notably, when the correlation of the reciprocal channel is set to rho = 0.8, the samples excursion qualification threshold is set to L = 3, and GG fading conditions set as defined by alpha = 2, epsilon = 1, and v = 1, the proposed algorithm, which employs sample biasing and transformation, offers an average improvement of 0.02% in KGR and 0.15% in KDR performance compared to the conventional UQ scheme. Additionally, the algorithm demonstrates superior performance in all considered eight the National Institute of Standards and Technology (NIST) randomness tests, exemplified by an average P-value of 0.78 in the frequency monobit test. Furthermore, for the considered system and channel parameters the proposed algorithm provides an average improvement of 0.06% in KDR compared to cumulative distribution function (CDF)-based nonuniform quantization (CDF-NUQ).

As Beyond 5th Generation (B5G) networks expand, securing communication links remains a challenge. Physical Layer Security (PLS) is a promising paradigm, and this work explores wireless channel-based Secret Key Generation (SKG) by proposing an Extended Huffman Coding (EHC) framework to enhance quantization stage. While non-uniform coding is common in Analog-to-Digital (A2D) conversion, it remains largely unexplored in SKG due to key mismatch risks. To address this, we propose a Huffman Coding (HC)-inspired framework that generates binary codes using reversed HC principles and extends them by sequentially altering the Least Significant Bit (LSB), ensuring equal-length unique codes for quantization levels while enhancing generation rate, agreement, and randomness. Additionally, histogram/ Probability Density Function (PDF) matching aligns quantization level probabilities at legitimate nodes to minimize mismatches while exchanging minimal statistical information without compromising secrecy. Unlike conventional quantization, which relies on predetermined codes vulnerable to eavesdropping, our scheme dynamically computes quantization codes at runtime, adding an extra layer of security. Moreover, while conventional HC avoids codes of a level to be a subcode of another level, SKG benefits when one code is a subcode of another, making detection harder. Instead of compression, as desired in conventional A2D conversion, SKG requires longer and random keys that reliably match at legitimate nodes, which our scheme ensures. Simulations are conducted under Rice-fading conditions that evaluate the impact of variations in the Rician K-factor on SKG performance. The proposed method is assessed using key SKG metrics named: Key Agreement Rate (KAR), Key Generation Rate (KGR), and Key Randomness Rate (KRR) (employing the NIST test suite). The obtained results demonstrate the potential of our proposed scheme for secure and scalable SKG solutions in future networks.

With the advent of innovative wireless technologies and the rapid growth of diverse connected devices, ensuring communication security has become a critical challenge for the future massively connected beyond 5 th generation (B5G) wireless networks. The physical layer security (PLS) approach leverages the inherent physical medium characteristics of communication networks to provide secure communications. In particular, the wireless channel-based secret key generation (SKG) is a PLS approach that creates symmetric keys for message encryption/decryption by exploiting the randomness inherent in wireless channels while relying on the channel to be reciprocal between the nodes. This work proposes a novel SKG algorithm that emphasizes the pre-processing and quantization stages with the aim to increase the key generation rate (KGR) and the key agreement rate (KAR) between the legitimate nodes. The algorithm employs biasing of selective samples and sliding-window weighted averaging of the Generalized Gamma fading channel samples based on the channel’s average contiguous duration (ACD) metric, a second-order fading statistic, to enhance the channel reciprocity. The proposed scheme may also be used to improve the key randomness rate (KRR) by using a non-contiguous multi-level quantization strategy that evenly sets the quantization intervals to accommodate a similar number of channel samples across these intervals. Thus, a desired trade-off between the KGR, KAR, and KRR to meet operational requirements can be achieved with the proposed scheme. Finally, a comprehensive analysis of the performance gains of the proposed scheme in relation to other notable works is conducted by investigating the impact of several channel and algorithmic parameters on the KGR, KAR, and KRR of these schemes.

The direction-of-arrival (DoA) estimation algorithms have a fundamental role in target bearing estimation by sensor array systems. Recently, compressive sensing (CS)-based sparse reconstruction techniques have been investigated for DoA estimation due to their superior performance relative to the conventional DoA estimation methods, for a limited number of measurement snapshots. In many underwater deployment scenarios, the acoustic sensor arrays must perform DoA estimation in the presence of several practical problems such as unknown source number, faulty sensors, low values of the received signal-to-noise ratio (SNR), and access to a limited number of measurement snapshots. In the literature, CS-based DoA estimation has been investigated for the individual occurrence of some of these errors but the estimation under joint occurrence of these errors has not been studied. This work investigates the CS-based robust DoA estimation to account for the joint impact of faulty sensors and low SNR conditions experienced by a uniform linear array of underwater acoustic sensors. Most importantly, the proposed CS-based DoA estimation technique does not require a priori knowledge of the source order, which is replaced in the modified stopping criterion of the reconstruction algorithm by taking into account the faulty sensors and the received SNR. Using Monte Carlo techniques, the DoA estimation performance of the proposed method is comprehensively evaluated in relation to other techniques.

The rapid technological advancements in wireless networks have resulted in tremendous increase in the number of connected user and machine-type wireless devices. Physical Layer Security (PLS) has a strong potential for providing security to wireless links in massively connected future wireless networks. The key-based PLS methods aim at generating secret key bits for data encryption/decryption at the legitimate communication nodes by exploiting the randomness inherent in wireless channels. This work proposes a novel secret key-bits extraction algorithm named Moving-Window Wrapped-Envelope Secret Key Generation (MWWE-SKG). The proposed algorithm uses first-order statistics from a sliding temporal window of channel samples to select the channel quantization interval for each window from circularly wrapped channel envelope samples. The differences in hardware noise conditions at the legitimate nodes lead to differences in the measurement of ideally reciprocal channels, which further leads to a mismatch in the generated secret key bits, whereas the channel statistics of the same links are more likely to remain unchanged for a reasonably large length of time window over the channel samples. An extensive analysis on the performance of the proposed algorithm is conducted, where the proposed algorithm is observed to provide a promising trade-off between the critical SKG performance metrics namely the Key Generation Rate (KGR), Bit Mismatch Probability (BMP), and the Key Randomness Property (KRP). Furthermore, a comparative performance analysis of the proposed algorithm with other notable techniques is also conducted to demonstrate the superior performance of the proposed algorithm.

The wireless channel-based Secret Key Generation (SKG) algorithms aim at securing the wireless link against unauthorized eavesdropping by exploiting the channel’s randomness for generating matching secret keys at the legitimate nodes for message encryption/decryption. To counter differences in hardware and noise conditions at the legitimate nodes, which can lead to key mismatch, the SKG algorithms typically include the intermediate steps of sampling, quantization, information reconciliation, and privacy amplification. These steps collectively aim to improve the performance trade-offs between Key Generation Rate (KGR), Key Agreement Probability (KAP), and Secret Key Randomness (SKR) properties. This paper derives a closed-form expression for the Average Contiguous Duration (ACD) of Generalized Gamma (GG) fading wireless channels. The ACD is a recently introduced novel quantifier for characterizing the second-order statistics of fading channels, which includes Average Fade Duration (AFD) as its special case. The proposed GG fading ACD expression is shown to include, as its special cases, the ACD for commonly observed fading distributions such as Gamma, Nakagami- $m$ , and Rayleigh. By exploiting the derived GG ACD expression, a multi-level quantization scheme for SKG is proposed that determines suitable quantization intervals for identical likelihood of an equal number of consecutive channel samples falling in each quantization interval. A comprehensive comparative analysis of the proposed ACD-based quantization for SKG is conducted in relation to conventional Uniform Quantization (UQ) and Cumulative Distribution Function (CDF)-based Non-Uniform Quantization (NUQ) schemes. The presented numerical results confirm the superior performance trade-off between KGR and KAP offered by the proposed ACD-based quantization in relation to that offered by UQ and CDF-based NUQ.

Non-orthogonal multiple access (NOMA) scheme, potentially enabling high spectral efficiency, is one of the key technological innovations in the 5th generation (5G) cellular networks. The massive machine type communications (mMTC) service category of 5G supports ultra-dense deployment of connected devices with low-power and low data-rate requirements, and so it naturally supports internet-of-things (IoT) communications. Also, the ambient backscatter communications (BsC) holds potential for enabling energy-constrained IoT communications due to its extremely low power requirements. This work analyzes the downlink of a NOMA-enabled cellular system bundled with symbiotic radio-based mMTC. Closed-form expressions of the outage probability for the signal-to-interference and noise ratio (SINR) and the ergodic rate are derived for the symbiotic radio backscatter device as well as the primary cellular user. Several interesting use-cases of the proposed system model are discussed for future massive IoT and cell-free networks. The theoretical results presented are validated through numerical evaluations.

Physical layer security (PLS) techniques hold promise for augmenting secure communications in the 5 th generation of mobile wireless networks. Secret key generation (SKG) is a PLS technique which exploits the wireless propagation channel's randomness to generate symmetric key bits for information encryption and decryption. This work proposes symmetric key generation based on non-uniform quantization of the received signal strength (RSS) samples of a Nakagami-$m$ fading channel. The proposed strategy for non-uniform quantization for SKG aims to set quantization thresholds for maximal key randomness and high values of key generation rate (KGR) and key agreement probability (KAP). Finally, a framework is proposed to use single node RSS measurements, readily available in the literature, to generate RSS samples at the other link end. This framework facilitates the testing of new SKG algorithms that require simultaneous RSS measurements by the legitimate nodes, which are not readily available in the open literature. The effectiveness of the proposed SKG scheme is validated through Monte Carlo methods and the National Institute of Standards and Technology (NIST) test suite for assessing the randomness of the generated key sequence.

We define the average contiguous duration (ACD) of the received fading signal as the average time duration during which the signal envelope contiguously remains within a bounded amplitude interval. Also, the multi-interval ACD or L-ACD function is defined as the set of ACD values for L non-overlapping amplitude-intervals whose union spans the received envelope's amplitude range. We derive closed-form expressions of the ACD for Rayleigh, Rice, and Nakagami- m fading signals, which are widely analyzed in the literature. The derived expressions hold practical significance for several signal processing applications such as non-uniform quantization of channel samples for secret key generation (SKG) in physical layer security (PLS) techniques. The well-known channel fading metric of average fade duration (AFD) is shown as a special case of the proposed ACD metric and the proposed theoretical analysis is validated by simulations.

This paper presents a high angular resolution processing approach for improved detection of multiple targets in passive underwater sensor array systems. These array processing systems are used for surveillance and detection of both surface and subsurface targets. Two beamforming techniques namely FFT based beamformer and MVDR beamformer along with two types of energy detection techniques namely CED and PED have been discussed. MATLAB simulations of these techniques have been developed and applied to data acquired through a passive uniform circular array. The simulation results showed that MVDR beamformer with PED for energy detection is the most suitable processing approach for high angular resolution in terms of detecting close space targets in the 3600 angular spectrum.

The Heterogeneous Cellular Network (HCN) paradigm holds promise for increasing the coverage probabilities and date rates of its users. The concept of downlink and uplink decoupling (DUDe) has been extensively investigated to alleviate the load imbalance problem in HCNs. Furthermore, the dual connectivity (DC) access scheme, which allows user equipment (UE) to simultaneously connect with multiple base stations (BSs), has also been investigated for its bandwidth aggregation feature that can provide increased UE data rates. This work uses stochastic geometry to analyze the uplink spectral- and energy-efficiency gains provided in a K-tier HCN with clustered users by introducing DC jointly with DUDe access. The BSs in each tier are modeled by an independent, homogeneous Poisson point process, whereas the spatially clustered UEs are modeled by a Matern cluster process. The exact analytical expressions and the upper-bound on coverage probability, spectral and energy efficiencies of the typical user are derived. The main results demonstrate the relative advantage of using DC with DUDe relative to the cases of single connectivity (SC) with DUDe and SC with the conventional downlink reference received power-based association. Further, the results also show that clustering should be modeled with an MCP to analyze the performance of clustered-HCNs.

To enable reliable connectivity in highly dynamic and dense communication environments, aerial-terrestrial heterogeneous cellular networks (AT-HCNs) have been proposed as a plausible enhancement to the conventional terrestrial HCNs (T-HCNs). In dense urban scenarios, users are often located in clusters and demand high bandwidth in both downlink (DL) and uplink (UL). We investigate this scenario and model the spatial distribution of clustered users using a Matern cluster process (MCP). Based on our analysis we then argue that decoupling of DL and UL in such a setting can significantly improve coverage performance and spectral efficiency. We further obtain closed-form expressions for the system coverage probability, spectral efficiency, and energy efficiency by using the Fox H-function. The obtained results confirm the validity of the proposed analytical model. Our simulations further indicate a significant performance improvement using decoupled access and provide quantitative insights on AT-HCN system design.

The tremendous increase in wireless connectivity demand will result in the degradation of the service quality and the scarcity of network capacity and coverage in the beyond 5 $^{\mathrm{ th}}$ generation era. To ensure reliable connectivity and enhance the network’s performance, the evolution of heterogeneous networks (HetNets) must incorporate aerial platforms in addition to traditional terrestrial base stations. The performance of Aerial-HetNets (A-HetNets) is largely dependent on the users’ association. The conventional user-association scheme based on downlink received power provides sub-optimal performance for the edge users. For this reason, decoupled user-association along with the reverse frequency allocation (RFA) strategy has been employed in A-HetNets. The performance of A-HetNets is also affected if wide-band jammers (WBJs) are present in the vicinity and impose jamming interference. In this paper, a two-tier A-HetNet with RFA and decoupled access is analyzed in the presence of jamming interference. The obtained results show that for a signal-to-interference ratio threshold of −20 dBm, the percentage decrease in the coverage probability of the decoupled access due to WBJ activity is up to 7.4%, 13.5%, and 19.7%, for the average number of WBJs equal to 2, 4, and 6, respectively. The performance of the decoupled access in A-HetNets is further decreased by increasing the transmit power of the WBJs while it is increased by increasing the radius of the WBJ’s cluster.

The extensive increase in the number of mobile devices and their data-rate requirements will lead to the scarcity of network resources. One of the promising solutions to keep up with the capacity and coverage demands of the 5th generation and beyond of cellular networks is to exploit the dual connectivity (DC) feature in heterogeneous networks (HetNets). In this work, a two-tier aerial HetNet with decoupled access and reverse frequency allocation strategy is considered and the DC feature for the network edge users is investigated. The analytical expressions of the coverage probability for the first and second uplink (UL) connections in DC are derived. Our proposed setup improves the coverage performance of the DC with decoupled access in relation to single connectivity (SC) with and without decoupled access. The results show a relative increase in the DC-based coverage performance of 10.6% and 82.6%, for a signal-to-interference-ratio (SIR) threshold of −20 dB, with respect to SC with and without decoupled access, respectively. Moreover, DC-based coverage in aerial HetNets is resilient to jamming interference. The results also show that if the wide-band jammers (WBJs) are present around a target-user equipment, the legitimate UL transmission is severely disrupted by the jamming interference. For instance, the percentage-decrease in the coverage performance of DC with decoupled access for the SIR threshold set to −20 dB is 4.9% and 10.6%, when the WBJs is set to 2 and 4, respectively. The coverage performance further decreases with an increase in the transmit powers of the WBJs and their number, whereas increases with an increase in the radius of the WBJs cluster.

Unmanned aerial vehicle (UAV) assisted cell-free communications hold promise for enhancing the coverage and capacity of heterogeneous cellular networks. However, the network interference in such scenarios must be accurately modeled for efficient system design. The spatial characteristics of the desired and interfering signals can be jointly modeled by considering the characteristics of the signal-to-interference ratio (SIR). This work proposes a generalized framework for modeling the spatial statistics of the SIR encountered in 3-D volumetric inter-vehicular communication channels. Though the novel paradigm of UAV-assisted cell-free vehicular communications is analyzed in particular, the proposed framework is more general in that it incorporates 3-D mobility at both link ends. Also, this framework is shown to include as its special cases, several notable 2-D propagation models of network interference including those for terrestrial vehicle-to-vehicle and fixed-to-vehicle scenarios. Analytical expressions are derived for the SIR level-crossing-rate (LCR), average-fade-duration (AFD), spatial auto-covariance (SAC), and coherence distance (CD). Both single- and multi-cluster scattering environments are analyzed and the impact of channel parameters such as the direction and velocity of mobile nodes as well as the altitudes of the UAV and scattering cluster(s) on the SIR fading statistics is investigated. Finally, some future extensions of this work are also discussed such as the integration of intelligent reflective surfaces in the propagation scenario to generate favorable channel conditions.

This letter investigates the error performance of dual-hop amplify-and-forward (AF) relaying over α-μ fading channels. Specifically, making use of the Fox’s H-function, closed-form exact expressions for the n-th moment of the received signal-to-noise ratio (SNR) and average bit error probability (ABEP) are derived for arbitrary parameter values of the α-μ distribution. To gain insights into the error performance, a closed-form ABEP expression for the case of asymptotically high SNR at the second hop is also derived. The analytical expressions are validated through simulations.

Device to device (D2D) communication that underlay conventional cellular networks can increase their spectrum utilization.However, since D2D pairs share the frequency band with cellular users, interference between these two network tiers can become a major performance bottleneck.In this scenario, use of a spread spectrum technique can be a good choice for D2D communication, due to its inherent interference mitigation capability.In this work, we analyze the achievable ergodic capacity for a D2D user pair that uses multi-carrier code division multiple access (MC-CDMA).Interference from both cellular users and other D2D pairs is considered under Rayleigh faded links and carrier frequency offset.Our derived expression requires a single integration and gives a tight lower bound to achievable ergodic capacity.

Physical layer security (PLS) has been extensively explored as an alternative to conventional cryptographic schemes for securing wireless links. Many studies have shown that the cooperation between the legitimate nodes of a network can significantly enhance their secret communications performance, relative to the noncooperative case. Motivated by the importance of this class of PLS systems, this paper provides a comprehensive survey of the recent works on cooperative relaying and jamming techniques for securing wireless transmissions against eavesdropping nodes, which attempt to intercept the transmissions. First, it provides a in-depth overview of various secure relaying strategies and schemes. Next, a review of recently proposed solutions for cooperative jamming techniques is provided with an emphasis on power allocation and beamforming techniques. Then, the latest developments in hybrid techniques, which use both cooperative relaying and jamming, are elaborated. Finally, several key challenges in the domain of cooperative security are presented along with an extensive discussion on the applications of cooperative security in key enablers for 5G communications, such as nonorthogonal multiple access, device-to-device communications, and massive multiple-input multiple-output systems.