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Recent Submissions

  • Hybrid FSO/THz-based Backhaul Network for mmWave Terrestrial Communication

    Singya, Praveen Kumar; Makki, Behrooz; D'Errico, Antonio; Alouini, Mohamed-Slim (IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers (IEEE), 2022-12-01) [Article]
    In this work, a hybrid free-space optics (FSO)/ teraHertz (THz) based backhaul network is considered to provide high-data-rate reliable communication to the terrestrial mobile users (MUs) operating at millimeter-wave (mmWave) bands. The FSO link is affected by atmospheric turbulence and pointing error impairments. At the FSO receiver, both intensity-modulated direct detection and heterodyne detection techniques are considered. The multi-antenna THz link suffers from high path-loss, small-scale fading, and misalignment error. To minimize the effect of back-and-forth switching, soft switching method is introduced at the access point (AP) to select the signal coming through the hybrid FSO/THz link, and a comparison with hard switching method is presented. Selective decode-and-forward relaying is considered at the AP. In this context, we derive closed-form expressions of the individual link’s outage probability, end-to-end (E2E) outage probability, asymptotic outage probability, ergodic capacity, and generalized average bit-error-rate. Finally, we study the effect of different parameters such as atmospheric turbulence, pointing/misalignment errors, link distance, atmospheric attenuation/path-loss, fading parameters of the THz and access links, and number of antennas on the network performance. Our results indicate that, with a proper switching method, the joint implementation of FSO/THz links improves the rate/reliability of the backhaul links with limited switching overhead.
  • On Secure CDRT with NOMA and Physical-Layer Network Coding

    Lei, Hongjiang; She, Xusheng; Park, Kihong; Ansari, Imran Shafique; Shi, Zheng; Jiang, Jing; Alouini, Mohamed-Slim (IEEE Transactions on Communications, Institute of Electrical and Electronics Engineers (IEEE), 2022-11-30) [Article]
    This paper proposes a new scheme to enhance the secrecy performance of non-orthogonal multiple access (NOMA)-based coordinated direct relay transmission (CDRT) systems with an untrusted relay. The physical-layer network coding (PNC) and the NOMA schemes are combined to improve spectrum efficiency. Furthermore, inter-user interference and friendly jamming signals are utilized to suppress the eavesdropping ability of the untrusted relay without compromising the acceptance quality of legitimate users. Specifically, the far user in the first slot and the near user in the second slot act as jammers that generate jamming signals to ensure secure transmissions of confidential messages. We investigate the secrecy performance of the NOMA-based CDRT systems with the PNC scheme and derive the closed-form expression for the ergodic secrecy sum rate. The asymptotic analysis at a high signal-to-noise ratio is performed to obtain more insights. Finally, simulation results are presented to demonstrate the proposed scheme’s effectiveness and the theoretical analysis’s correctness.
  • Performance Analysis of Charging Infrastructure Sharing in UAV and EV-involved Networks

    Qin, Yujie; Kishk, Mustafa Abdelsalam; Alouini, Mohamed-Slim (IEEE Transactions on Vehicular Technology, Institute of Electrical and Electronics Engineers (IEEE), 2022-11-04) [Article]
    Electric vehicles (EVs) and unmanned aerial vehicles (UAVs) show great potential in modern transportation and communication networks, respectively. However, with growing demands for such technologies, the limited energy infrastructure becomes the bottleneck for their future growth. It might be of high cost and low energy efficiency for all the operators to each have their own dedicated energy infrastructure, such as charging stations. In this paper, we analyze a wireless charging infrastructure sharing strategy in UAV and EV-involved networks. We consider a scenario where UAVs can charge in EV charging stations and pay for the sharing fee. On the EVs' side, sharing infrastructure can earn extra profit but their service quality, such as waiting time, might slightly reduce. On the UAVs' side, if renting EV charging stations can achieve an acceptable system performance, say high coverage probability, while considering the cost, they may not need to build their dedicated charging stations. In this case, we use tools from stochastic geometry to model the locations and propose an optimization problem that captures the aforementioned trade-offs between cost or profit and quality of service. Our numerical results show that sharing infrastructure slightly increases the waiting time of EVs, say within 5 min, but dramatically decreases the waiting time of drones, say more than 50 min, and deploying more charging stations do achieve better performances, but all these better performances are expected to cost more.
  • Maritime Communications: A Survey on Enabling Technologies, Opportunities, and Challenges

    Alqurashi, Fahad S.; Trichili, Abderrahmen; Saeed, Nasir; Ooi, Boon S.; Alouini, Mohamed-Slim (IEEE Internet of Things Journal, Institute of Electrical and Electronics Engineers (IEEE), 2022-11-04) [Article]
    Water covers 71% of the Earth’s surface, where the steady increase in oceanic activities has promoted the need for reliable maritime communication technologies. The existing maritime communication systems involve terrestrial, aerial, and space networks. This paper presents a holistic overview of the different forms of maritime communications and provides the latest advances in various marine technologies. The paper first introduces the different techniques used for maritime communications over the radio frequency (RF) and optical bands. Then, we present the channel models for RF and optical bands, modulation and coding schemes, coverage and capacity, and radio resource management in maritime communications. After that, the paper presents some emerging use cases of maritime networks, such as the Internet of Ships and the ship-to-underwater Internet of things. Finally, we highlight a few exciting open challenges and identify a set of future research directions for maritime communication, including bringing broadband connectivity to the deep sea, using terahertz and visible light signals for on-board applications, and data-driven modeling for radio and optical marine propagation.
  • Dominance of Smartphone Exposure in 5G Mobile Networks

    Chiaraviglio, Luca; Lodovisi, Chiara; Bartoletti, Stefania; Elzanaty, Ahmed; Alouini, Mohamed-Slim (arXiv, 2022-11-02) [Preprint]
    The deployment of 5G networks is sometimes questioned due to the impact of ElectroMagnetic Field (EMF) generated by Radio Base Station (RBS) on users. The goal of this work is to analyze such issue from a novel perspective, by comparing RBS EMF against exposure generated by 5G smartphones in commercial deployments. The measurement of exposure from 5G is hampered by several implementation aspects, such as dual connectivity between 4G and 5G, spectrum fragmentation, and carrier aggregation. To face such issues, we deploy a novel framework, called 5G-EA, tailored to the assessment of smartphone and RBS exposure through an innovative measurement algorithm, able to remotely control a programmable spectrum analyzer. Results, obtained in both outdoor and indoor locations, reveal that smartphone exposure (upon generation of uplink traffic) dominates over the RBS one. Moreover, Line-of-Sight locations experience a reduction of around one order of magnitude on the overall exposure compared to Non-Line-of-Sight ones. In addition, 5G exposure always represents a small share (up to 28%) compared to 4G EMF.
  • Stochastic Geometry-based Analysis of Multi-Purpose UAVs for Package and Data Delivery

    Qin, Yujie; Kishk, Mustafa A.; Alouini, Mohamed-Slim (IEEE Internet of Things Journal, IEEE, 2022-11-01) [Article]
    Using drones for communications and transportation is drawing great attention in many practical scenarios, such as package delivery and providing additional wireless coverage. However, the increasing demand for UAVs from industry and academia will cause aerial traffic conflicts in the future. This, in turn, motivates the idea of this paper: multi-purpose UAVs, acting as aerial wireless data relays and means of aerial transportation simultaneously, to deliver packages and data at the same time. This paper aims to analyze the feasibility of using drones to collect and deliver data from the Internet of Things (IoT) devices to terrestrial base stations (TBSs) while delivering packages from warehouses to residential areas. We propose an algorithm to optimize the trajectory of UAVs to maximize the size of collected/delivered data while minimizing the total round trip time subject to the limited onboard battery of UAVs. Specifically, we use tools from stochastic geometry to model the locations of the IoT clusters and the TBSs and study the system performance with respect to energy efficiency, average size of collected/delivered data, and package delivery time. Our numerical results reveal that multi-functional UAVs have great potential to enhance the efficiency of both communication and transportation networks.
  • Asymptotic Analysis of RLS-based Digital Precoder with Limited PAPR in Massive MIMO

    Ma, Xiuxiu; Kammoun, Abla; Alrashdi, Ayed M.; Ballal, Tarig; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim (IEEE Transactions on Signal Processing, IEEE, 2022-10-31) [Article]
    This paper focuses on the performance analysis of a class of limited peak-to-average power ratio (PAPR) precoders for downlink multi-user massive multiple-input multiple-output (MIMO) systems. Contrary to conventional precoding approaches based on simple linear precoders such as maximum ratio transmission (MRT) and regularized zero-forcing (RZF), the precoders in this paper are obtained by solving a convex optimization problem. To be specific, these precoders are designed so that the power of each precoded symbol entry is restricted, and the PAPR at each antenna is tunable. By using the Convex Gaussian Min-max Theorem (CGMT), we analytically characterize the empirical distribution of the precoded vector and the joint empirical distribution between the distortion and the intended symbol vector. This allows us to study the performance of these precoders in terms of per-antenna power, per-user distortion power, signal-to-noise and distortion ratio (SINAD), and bit error probability. We show that for this class of precoders, there is an optimal transmit per-antenna power that maximizes the system performance in terms of SINAD and bit error probability.
  • Performance of Integrated Ground-Air-Space FSO Links over Various Turbulent Environments

    Ata, Yalçın; Alouini, Mohamed-Slim (IEEE Photonics Journal, IEEE, 2022-10-31) [Article]
    We analyze the outage probability of integrated ground-air-space free-space optical (FSO) communication links for different atmospheric turbulence channel models. The performance of ground to high altitude platforms (HAPS), HAPS to geostationay Earth orbit (GEO) satellite, HAPS to HAPS and ground to GEO satellite is investigated for various link configurations (downlink, horizontal, and uplink) and parameters such as zenith angle, channel state, horizontal and vertical deviations, altitude, beam waist, receiver aperture diameter, wind speed, and visibility. The atmospheric attenuation (the effects of fog, cloud and volcanic activities), atmospheric turbulence, angle of arrival (AOA) fluctuations and pointing error are included in the considered model. Closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) are obtained for Lognormal, Gamma and exponentiated Weibull distributed channel models. The benefit of using HAPS is shown by comparison of outage probabilities for direct ground to GEO satellite and HAPS assisted ground to GEO satellite links.
  • On Secure Uplink Transmission in Hybrid RF-FSO Cooperative Satellite-Aerial-Terrestrial Networks

    Ma, Yuanyuan; Lv, Tiejun; Pan, Gaofeng; Chen, Yunfei; Alouini, Mohamed-Slim (IEEE Transactions on Communications, IEEE, 2022-10-14) [Article]
    This work investigates the secrecy outage performance of the uplink transmission of a radio-frequency (RF)-free-space optical (FSO) hybrid cooperative satellite-aerial-terrestrial network (SATN). Specifically, in the considered cooperative SATN, a terrestrial source (S) transmits its information to a satellite receiver (D) via the help of a cache-enabled aerial relay (R) terminal with the most popular content caching scheme, while a group of eavesdropping aerial terminals (Eves) trying to overhear the transmitted confidential information. Moreover, RF and FSO transmissions are employed over S-R and R-D links, respectively. Considering the randomness of R, D, and Eves, and employing a stochastic geometry framework, the secrecy outage performance of the cooperative uplink transmission in the considered SATN is investigated and a closed-form analytical expression for the end-to-end secrecy outage probability is derived. Finally, Monte-Carlo simulations are shown to verify the accuracy of our analysis.
  • Dedicating Cellular Infrastructure for Aerial Users: Advantages and Potential Impact on Ground Users

    Chen, Lin; Kishk, Mustafa A.; Alouini, Mohamed-Slim (IEEE Transactions on Wireless Communications, IEEE, 2022-10-12) [Article]
    A new generation of aerial vehicles is hopeful to be the next frontier for the transportation of people and goods, becoming even as important as ground users in the communication systems. To enhance the coverage of aerial users, appropriate adjustments should be made to the existing cellular networks that mainly provide services for ground users by the down-tilted antennas of the terrestrial base stations (BSs). It is promising to up-tilt the antennas of a subset of BSs for serving aerial users through the mainlobe. With this motivation, in this work, we use tools from stochastic geometry to analyze the coverage performance of the adjusted cellular network (consisting of the up-tilted BSs and the down-tilted BSs). Correspondingly, we present exact and approximate expressions of the signal-to-interference ratio (SIR)-based coverage probabilities for users in the sky and on the ground, respectively. Numerical results verify the analysis accuracy and clarify the advantages of up-tilting BS antennas on the communication connectivity of aerial users without the potential adverse impact on the quality of service (QoS) of ground users. Moreover, it is unveiled that there exists an optimal value of the up-tilted/down-tilted BS density ratio for maximizing the coverage probability of the aerial or ground users.
  • A Game-Theoretic Framework for Coexistence of WiFi and Cellular Networks in the 6-GHz Unlicensed Spectrum

    Ur Rahman, Aniq; Kishk, Mustafa Abdelsalam; Alouini, Mohamed-Slim (IEEE Transactions on Cognitive Communications and Networking, Institute of Electrical and Electronics Engineers (IEEE), 2022-10-11) [Article]
    The recently unlocked 6-GHz spectrum is accessible to cellular and WiFi networks for unlicensed use while they conform to the constraints imposed by the incumbent nodes. We allow only a fraction of the cellular base stations (BSs) and a fraction of WiFi access points (APs) to use the 6-GHz band so that sources of interference are spatially segregated and made sparse, thereby decreasing the overall interference to each other. Through our proposed framework, we control this fraction as we group portions of cellular and WiFi network elements into entities competing with the other entities for the spectrum resources. These entities interact to satisfy their Quality of Service demands by playing a non-cooperative game. The action of an entity corresponds to the fraction of its network elements (WiFi APs and cellular BSs) operating in the 6-GHz band. We use tools from stochastic geometry to derive the theoretical performance metrics for users of each radio access technology, which helps us capture the aggregate behaviour of the network in a snapshot. Due to the decentralized nature of the game, we find the solution using distributed Best Response Algorithm (D-BRA), which improves the average datarate by 11.37% and 18.59% for cellular and WiFi networks, respectively, with random strategy as the baseline. The results demonstrate how the system parameters affect the performance of a network at equilibrium and highlight the throughput gains of the networks as a result of using the 6-GHz bands, which offer considerably larger bandwidths. We tested our framework using real-world data, which shows that practical implementation of multi-entity spectrum sharing is feasible even when the spatial distribution of the network elements and population are non-homogeneous.
  • On the Asymptotic Performance Analysis of the k-th Best Link Selection over Non-identical Non-central Chi-square Fading Channels

    Subhash, Athira; Kalyani, Sheetal; Al-Badarneh, Yazan H.; Alouini, Mohamed-Slim (IEEE Transactions on Communications, IEEE, 2022-10-10) [Article]
    This paper derives the asymptotic distribution of the normalized k-th maximum order statistics of a sequence of non-central chi-square random variables with non-identical non-centrality parameters. We demonstrate the utility of these results in characterizing the signal-to-noise ratio in three different applications in wireless communication systems where the statistics of the k-th maximum channel power over Rician fading links are of interest. Furthermore, we derive simple expressions for the asymptotic outage probability, average throughput, achievable throughput, and average bit error probability. The proposed results are validated via extensive Monte Carlo simulations.
  • On the transport of molecular information in sub-diffusion media with reflecting boundary

    Chouhan, Lokendra; Alouini, Mohamed-Slim (ACM, 2022-10-05) [Conference Paper]
    This work exploits a one-dimensional (1-D) molecular communication (MC) between two nodes considering the sub-diffusion phenomenon for the propagation of information-carrying molecules (ICMs). We also assume that the transmitter (Tx) is surrounded on both sides by an absorbing receiver (Rx) and a reflecting boundary. In this context, we emanate the expressions for the probability density function (PDF) for the spatial-temporal distribution of molecules in terms of the Mittag-Leffler function (MLF). Further, we also find closed-form expressions for ICMs' survival probability (SP) and first arrival probability (FAP) for the considered setup. Moreover, we also derive a closed-form expression of the first arrival time density (FATD) function, an essential mathematical tool to analyze any MC system. We also investigate the effects of reflecting boundary presence on the MC setup based on bit-error-rate performance. Above all, particle-based and Monte-Carlo simulations are performed to validate our analytical expressions.
  • Evanescence reaction in subdiffusion molecular communication channel

    Briantceva, Nadezhda; Chouhan, Lokendra; Parsani, Matteo; Alouini, Mohamed-Slim (ACM, 2022-10-05) [Conference Paper]
    This work considers the subdiffusion motion of information carrying molecules inside a molecular communication (MC) channel. Additionally, an evanescence process is taken into account, which leads to the degradation of molecules prior to their hitting to the receiver's boundary. The closed-form expressions of the arrival probability and the first-passage-time-density (FPTD) are obtained. Furthermore, the performance of MC was investigated by using the concentration-based modulation technique. The probability of detection is presented for different parameters of a reaction rate. The performance results were validated by the Monte-Carlo simulation.
  • Joint Communication and Computation in Hybrid Cloud/Mobile Edge Computing Networks

    Reifert, Robert-Jeron; Dahrouj, Hayssam; Shihada, Basem; Sezgin, Aydin; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim (arXiv, 2022-10-05) [Preprint]
    Facing a vast amount of connections, huge performance demands, and the need for reliable connectivity, the sixth generation of communication networks (6G) is envisioned to implement disruptive technologies that jointly spur connectivity, performance, and reliability. In this context, this paper proposes, and evaluates the benefit of, a hybrid central cloud (CC) computing and mobile edge computing (MEC) platform, especially introduced to balance the network resources required for joint computation and communication. Consider a hybrid cloud and MEC system, where several power-hungry multi-antenna unmanned aerial vehicles (UAVs) are deployed at the cell-edge to boost the CC connectivity and relieve part of its computation burden. While the multi-antenna base stations are connected to the cloud via capacity-limited fronthaul links, the UAVs serve the cell-edge users with limited power and computational capabilities. The paper then considers the problem of maximizing the weighted network sum-rate subject to per-user delay, computational capacity, and power constraints, so as to determine the beamforming vectors and computation allocations. Such intricate non-convex optimization problem is tackled using an iterative algorithm that relies on ℓ0-norm relaxation, successive convex approximation, and fractional programming, and has the compelling ability to be implemented in a distributed fashion across the multiple UAVs and the CC. The paper results illustrate the numerical prospects of the proposed algorithm for enabling joint communication and computation, and highlight the appreciable improvements of data processing delays and throughputs as compared to conventional system strategies.
  • Generalized Fully Coherent Closed-form Receiver Design for Joint Radar and Communication System

    Zubair, Muhammad; Ahmed, Sajid; Alouini, Mohamed-Slim (IEEE Transactions on Communications, Institute of Electrical and Electronics Engineers (IEEE), 2022-09-28) [Article]
    Conventional radars repeat the transmission of the same waveform after a predefined interval of time called pulse-repetition-interval (PRI). This technique helps estimate the range and Doppler shift of the targets and suppress clutter. However, in dual-function radar communication (DFRC), a different symbol waveform is transmitted after each PRI. Depending on the number of targets, radar receiver output yields several peaks representing different targets’ ranges. Each peak comes with its side-lobes called range-side-lobes (RSL). In DFRC, due to different symbol waveform transmission, peaks and RSLs do not remain coherent, making Doppler shift estimation and clutter suppression challenging tasks. In most of the available literature, iterative receive filters have been designed for DFRC to minimize RSLs and achieve coherent output for different waveforms. However, the proposed receive filter does not guarantee coherent output for more than two waveforms. In contrast, we proposed two novel closed-form algorithms to design receive filters for DFRC that guarantee coherent output response for several waveforms and suppress RSLs. Simulation results demonstrate that the proposed receivers achieve full coherency, and the RSLs are significantly lower than the conventional method. Furthermore, the advantage of achieving coherent output response is shown in target detection and bit-error-rate improvement.
  • How Much Exposure from 5G Towers is Radiated over Children, Teenagers, Schools and Hospitals?

    Chiaraviglio, Luca; Lodovisi, Chiara; Franci, Daniele; Grillo, Enrico; Pavoncello, Settimio; Aureli, Tommaso; Blefari-Melazzi, Nicola; Alouini, Mohamed-Slim (IEEE Open Journal of the Communications Society, IEEE, 2022-09-23) [Article]
    The rolling-out of 5G antennas over the territory is a fundamental step to provide 5G connectivity. However, little efforts have been done so far on the exposure assessment from 5G cellular towers over young people and “sensitive” buildings, like schools and medical centers. To face such issues, we provide a sound methodology for the numerical evaluation of 5G (and pre-5G) downlink exposure over children, teenagers, schools and medical centers. We then apply the proposed methodology over two real scenarios. Results reveal that the exposure from 5G cellular towers will increase in the forthcoming years, in parallel with the growth of the 5G adoption levels. However, the exposure levels are well below the maximum ones defined by international regulations. Moreover, the exposure over children and teenagers is similar to the one of the whole population, while the exposure over schools and medical centers can be lower than the one of the whole set of buildings. Finally, the exposure from 5G is strongly lower than the pre-5G one when the building attenuation is introduced and a maturity adoption level for 5G is assumed.
  • Optimal phase shift design for fair allocation in RIS aided uplink network using statistical CSI

    Subhash, Athira; Kammoun, Abla; Elzanaty, Ahmed; Kalyani, Sheetal; Al-Badarneh, Yazan H.; Alouini, Mohamed-Slim (arXiv, 2022-09-19) [Preprint]
    Reconfigurable intelligent surface (RIS) can be crucial in next-generation communication systems. However, designing the RIS phases according to the instantaneous channel state information (CSI) can be challenging in practice due to the short coherent time of the channel. In this regard, we propose a novel algorithm based on the channel statistics of massive multiple input multiple output systems rather than the CSI. The beamforming at the base station (BS), power allocation of the users, and phase shifts at the RIS elements are optimized to maximize the minimum signal to interference and noise ratio (SINR), guaranteeing fair operation among various users. In particular, we design the RIS phases by leveraging the asymptotic deterministic equivalent of the minimum SINR that depends only on the channel statistics. This significantly reduces the computational complexity and the amount of controlling data between the BS and RIS for updating the phases. This setup is also useful for electromagnetic fields (EMF)-aware systems with constraints on the maximum user's exposure to EMF. The numerical results show that the proposed algorithms achieve more than 100% gain in terms of minimum SINR, compared to a system with random RIS phase shifts, with 40 RIS elements, 20 antennas at the BS and 10 users, respectively.
  • Energy Consumption Minimization for Data Collection from Wirelessly-powered IoT Sensors: Session-Specific Optimal Design with DRL

    Xu, Fang; Yang, Hong Chuan; Alouini, Mohamed-Slim (IEEE Sensors Journal, IEEE, 2022-09-14) [Article]
    Reliable and energy-efficient data collection from resource-limited sensors is essential to the success of future Internet of Things (IoT). In this article, we study the energy consumption minimization problem during the data collection from a generic wirelessly-powered sensor. Specifically, we determine the optimal data collection parameters, in terms of charging duration and charging power as well as sensor transmission rate, in real time according to the instantaneous channel condition while satisfying a certain latency constraint. For the scenario of ideal rate adaptive transmission with linear energy harvesting, we derive closed-form expressions for optimal transmission parameters. We also establish the condition on channel quality for successful data collection under a latency constraint. For the more practical case of finite block-length transmission with non-linear energy harvesting, we develop a deep reinforcement learning (DRL) solution for efficient online implementation. We also propose an online tuning scheme to cater for model inaccuracy and environment variation. The accuracy and effectiveness of our proposed approaches are verified by comparing with benchmark schemes. Our DRL-based approach has broad applicability and can solve other real-time optimal design problems in wireless communications.
  • Optimal Positioning of Hovering UAV Relays For Mitigation of Pointing Error in Free-Space Optical Communications

    Bashir, Muhammad Salman; Alouini, Mohamed-Slim (IEEE Transactions on Communications, Institute of Electrical and Electronics Engineers (IEEE), 2022-09-06) [Article]
    The relay positions or hop distances in a multi-hop relaying scheme is an important parameter that can be optimized in order to mitigate the angle-of-arrival variance or pointing error in a free-space optical (FSO) backhaul link. In this study, we have optimized the relay positions for amplify-and-forward and decode-and-forward relays in a multi-hop unmanned aerial vehicle-based relaying scheme for FSO. Particularly, we have shown that a significant performance improvement may be achieved by optimizing the outage probability as a function of the hop distance for amplify-and-forward relays when the relays are constrained by a finite power gain. Additionally, we have discovered that for a low signal-to-noise ratio channel, the optimal hop distance of a particular hop for decode-and-forward relays is inversely proportional to angle-of-arrival variance in that hop.

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