Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the ...statistical power of the persistent homology rank functions. For a point pattern X we construct a filtration of spaces by taking the union of balls of radius a centred on points in X, Xa=∪x∈XB(x,a). The rank function βk(X):{(a,b)∈R2:a≤b}→R is then defined by βk(X)(a,b)=rank(ι∗:Hk(Xa)→Hk(Xb)) where ι∗ is the induced map on homology from the inclusion map on spaces. We consider the rank functions as lying in a Hilbert space and show that under reasonable conditions the rank functions from multiple simulations or experiments will lie in an affine subspace. This enables us to perform functional principal component analysis which we apply to experimental data from colloids at different effective temperatures and to sphere packings with different volume fractions. We also investigate the potential of rank functions in providing a test of complete spatial randomness of 2D point patterns using the distances to an empirically computed mean rank function of binomial point patterns in the unit square.
•We use the persistent homology rank function to study spatial point patterns.•The rank function is shown to be amenable to standard statistical techniques.•We demonstrate null hypothesis testing on simulated point patterns.•We develop a principal component analysis method for experimental data.•PCA of rank functions is successfully applied to colloidal and sphere-packing data.
This paper investigates the physical layer security of non-orthogonal multiple access (NOMA) in large-scale networks with invoking stochastic geometry. Both single-antenna and multiple-antenna aided ...transmission scenarios are considered, where the base station (BS) communicates with randomly distributed NOMA users. In the single-antenna scenario, we adopt a protected zone around the BS to establish an eavesdropper-exclusion area with the aid of careful channel ordering of the NOMA users. In the multiple-antenna scenario, artificial noise is generated at the BS for further improving the security of a beamforming-aided system. In order to characterize the secrecy performance, we derive new exact expressions of the security outage probability for both single-antenna and multiple-antenna aided scenarios. For the single-antenna scenario, we perform secrecy diversity order analysis of the selected user pair. The analytical results derived demonstrate that the secrecy diversity order is determined by the specific user having the worse channel condition among the selected user pair. For the multiple-antenna scenario, we derive the asymptotic secrecy outage probability, when the number of transmit antennas tends to infinity. Monte Carlo simulations are provided for verifying the analytical results derived and to show that: 1) the security performance of the NOMA networks can be improved by invoking the protected zone and by generating artificial noise at the BS and 2) the asymptotic secrecy outage probability is close to the exact secrecy outage probability.
Millimeter wave (mmWave) holds promise as a carrier frequency for fifth generation cellular networks. Because mmWave signals are sensitive to blockage, prior models for cellular networks operated in ...the ultra high frequency (UHF) band do not apply to analyze mmWave cellular networks directly. Leveraging concepts from stochastic geometry, this paper proposes a general framework to evaluate the coverage and rate performance in mmWave cellular networks. Using a distance-dependent line-of-site (LOS) probability function, the locations of the LOS and non-LOS base stations are modeled as two independent non-homogeneous Poisson point processes, to which different path loss laws are applied. Based on the proposed framework, expressions for the signal-to-noise-and-interference ratio (SINR) and rate coverage probability are derived. The mmWave coverage and rate performance are examined as a function of the antenna geometry and base station density. The case of dense networks is further analyzed by applying a simplified system model, in which the LOS region of a user is approximated as a fixed LOS ball. The results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages. The results suggest that the cell size to achieve the optimal SINR scales with the average size of the area that is LOS to a user.
UAV-to-UAV Communications in Cellular Networks Azari, M. Mahdi; Geraci, Giovanni; Garcia-Rodriguez, Adrian ...
IEEE transactions on wireless communications,
2020-Sept., 2020-9-00, 20200901, Letnik:
19, Številka:
9
Journal Article
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We consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs share the same spectrum with the uplink (UL) of cellular ground users (GUEs). For this setup, we focus on ...analyzing and comparing the performance of two spectrum sharing mechanisms: (i) underlay, where the same time-frequency resources may be accessed by both UAVs and GUEs, resulting in mutual interference, and (ii) overlay, where the available resources are divided into orthogonal portions for U2U and GUE communications. We evaluate the coverage probability and rate of both link types and their interplay to identify the best spectrum sharing strategy. We do so through an analytical framework that embraces realistic height-dependent channel models, antenna patterns, and practical power control mechanisms. For the underlay, we find that although the presence of U2U direct communications may worsen the uplink performance of GUEs, such effect is limited as base stations receive the power-constrained UAV signals through their antenna sidelobes. In spite of this, our results lead us to conclude that in urban scenarios with a large number of UAV pairs, adopting an overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance.
Motivated by the increasing computational capacity of wireless user equipments (UEs), e.g., smart phones, tablets, or vehicles, as well as the increasing concerns about sharing private data, a new ...machine learning model has emerged, namely federated learning (FL), that allows a decoupling of data acquisition and computation at the central unit. Unlike centralized learning taking place in a data center, FL usually operates in a wireless edge network where the communication medium is resource-constrained and unreliable. Due to limited bandwidth, only a portion of UEs can be scheduled for updates at each iteration. Due to the shared nature of the wireless medium, transmissions are subjected to interference and are not guaranteed. The performance of FL system in such a setting is not well understood. In this paper, an analytical model is developed to characterize the performance of FL in wireless networks. Particularly, tractable expressions are derived for the convergence rate of FL in a wireless setting, accounting for effects from both scheduling schemes and inter-cell interference. Using the developed analysis, the effectiveness of three different scheduling policies, i.e., random scheduling (RS), round robin (RR), and proportional fair (PF), are compared in terms of FL convergence rate. It is shown that running FL with PF outperforms RS and RR if the network is operating under a high signal-to-interference-plus-noise ratio (SINR) threshold, while RR is more preferable when the SINR threshold is low. Moreover, the FL convergence rate decreases rapidly as the SINR threshold increases, thus confirming the importance of compression and quantization of the update parameters. The analysis also reveals a trade-off between the number of scheduled UEs and subchannel bandwidth under a fixed amount of available spectrum.
Millimeter wave (mmWave) links will offer high capacity but are poor at penetrating into or diffracting around solid objects. Thus, we consider a hybrid cellular network with traditional sub-6 GHz ...macrocells coexisting with denser mmWave small cells, where a mobile user can connect to either opportunistically. We develop a general analytical model to characterize and derive the uplink and downlink cell association in the view of the signal-to-interference-and-noise-ratio and rate coverage probabilities in such a mixed deployment. We offer extensive validation of these analytical results (which rely on several simplifying assumptions) with simulation results. Using the analytical results, different decoupled uplink and downlink cell association strategies are investigated and their superiority is shown compared with the traditional coupled approach. Finally, small cell biasing in mmWave is studied, and we show that unprecedented biasing values are desirable due to the wide bandwidth.
Millimeter wave (mmWave) cellular systems will require high-gain directional antennas and dense base station (BS) deployments to overcome a high near-field path loss and poor diffraction. As a ...desirable side effect, high-gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling, i.e., BSs backhauling among themselves in a mesh architecture without significant loss in the throughput, to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that significantly differ from conventional UHF cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis are validated using actual building locations from dense urban settings and empirically derived path loss models. The analysis shows that, in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides the total rate) also increases with the BS density, particularly at the cell edge. Increasing the system bandwidth does not significantly influence the cell edge rate, although it boosts the median and peak rates. With self-backhauling, different combinations of the wired backhaul fraction (i.e., the fraction of BSs with a wired connection) and the BS density are shown to guarantee the same median rate (QoS).
Departing from the conventional cache hit optimization in cache-enabled wireless networks, we consider an alternative optimization approach for the probabilistic caching placement in stochastic ...wireless D2D caching networks taking into account the reliability of D2D transmissions. Using tools from stochastic geometry, we provide a closed-form approximation of cache-aided throughput, which measures the density of successfully served requests by local device caches, and we obtain the optimal caching probabilities via numerical optimization. Compared with the cache-hit-optimal case, the optimal caching probabilities obtained by cache-aided throughput optimization show notable gain in terms of the density of successfully served user requests, particularly in dense user environments.
Future Internet-of-Things (IoT) will connect billions of small computing devices embedded in the environment and support their device-to-device (D2D) communication. Powering the massive number of ...embedded devices is a key challenge of designing IoT, since batteries increase the devices' form factors and battery recharging/replacement is difficult. To tackle this challenge, we propose a novel network architecture that enables D2D communication between passive nodes by integrating wireless power transfer and backscatter communication, which is called a wirelessly powered backscatter communication (WP-BackCom) network. In this network, standalone power beacons (PBs) are deployed for wirelessly powering nodes by beaming unmodulated carrier signals to targeted nodes. Provisioned with a backscatter antenna, a node transmits data to an intended receiver by modulating and reflecting a fraction of a carrier signal. Such transmission by backscatter consumes orders-of-magnitude less power than a traditional radio. Thereby, the dense deployment of low-complexity PBs with high transmission power can power a large-scale IoT. In this paper, a WP-BackCom network is modeled as a random Poisson cluster process in the horizontal plane where PBs are Poisson distributed and active ad hoc pairs of backscatter communication nodes with fixed separation distances form random clusters centered at PBs. The backscatter nodes can harvest energy from and backscatter carrier signals transmitted by PBs. Furthermore, the transmission power of each node depends on the distance from the associated PB. Applying stochastic geometry, the network coverage probability and transmission capacity are derived and optimized as functions of backscatter parameters, including backscatter duty cycle, reflection coefficient, and the PB density. The effects of the parameters on network performance are quantified.
To address the ever increasing high data rate and connectivity requirements in the next generation 5G wireless network, novel radio access technologies (RATs) are actively explored to enhance the ...system spectral efficiency and connectivity. As a promising RAT for 5G cellular networks, non-orthogonal multiple access (NOMA) has attracted extensive research attentions. Compared with the orthogonal multiple access (OMA) that has been widely applied in existing wireless communication systems, NOMA possesses the potential to further improve the system spectral efficiency and connectivity capability. This paper develops analytical frameworks for NOMA downlink and uplink multi-cell wireless systems to evaluate the system outage probability and average achievable rate. In the downlink NOMA system, two different NOMA group pairing schemes are considered, based on which theoretical results on outage and achievable data rates are derived. In the uplink NOMA, revised back-off power control scheme is applied, and outage probability and per UE average achievable rate are derived. As wireless networks turn into more and more densely deployed, inter-cell interference has become a dominant capacity limiting factor but has not been addressed in most of the existing NOMA studies. In this paper, a stochastic geometry approach is used to model a dense wireless system, that supports NOMA on both uplink and downlink, based on which analytical results are derived either in pseudo-closed forms or succinct closed forms and are further validated by simulations. Numerical results demonstrate that NOMA can bring considerable system-wide performance gain compared with OMA on both uplink and downlink when properly designed.
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