We investigate the relationship between graph parameters, which measure the complexity of the tree decompositions of a given graph. The treewidth tw(G) of a graph G measures the largest number of vertices required in a bag of every tree decomposition of G. Similarly, the tree-independence number tree-α(G) and the tree-chromatic number tree-χ(G) measure the largest independence number, respectively the largest chromatic number, required in a bag of every tree decomposition of G. Recently, Dallard, Milanič, and Štorgel asked (JCTB, 2024) whether for all graphs G it holds that tw(G)+1 ≤ tree-α(G) ⋅ tree-χ(G). We provide a negative answer for this question in a strong form: for every function f: {ℕ} → {ℕ}, there exists a graph G such that tw(G) > tree-α(G) ⋅ f(tree-χ(G)). On the other hand, we complement this result with an upper bound, by showing that tw(G)+1 ≤ tree-α(G)² ⋅ tree-χ(G) for every graph G.

The integration of energy harvesting capabilities into mobile edge computing (MEC) edge servers enables their deployment beyond the reach of electrical grids, expanding MEC services to isolated regions and geographically challenging terrains. However, the fluctuating nature of renewable energy sources, such as solar and wind, necessitates dynamic management of server computing power in response to variable energy harvesting rates. Unlike conventional models that assume predetermined amounts of harvested energy per time period, this study illustrates the complex interdependencies between server power consumption and variable energy harvesting rates due to battery charging characteristics. To address this, we introduce a novel energy harvesting model that comprehensively accounts for the interaction between computing power management and energy harvesting rates. We develop both offline and online offline optimal computing power management strategies aimed at maximizing the average computational capacity of edge servers. An analytical solution to the resulting nonlinear optimization problem is provided to determine the optimal computing power configurations. Simulation results indicate that the proposed strategy effectively balances energy harvesting rates and energy utilization, thereby enhancing computational performance in dynamic energy environments.

In this paper, we propose a backbone-aware user association algorithm for heterogeneous hierarchical federated learning. We consider the scenario in which mobile devices have different computation and communication capabilities, while edge servers have different model uploading delays to the cloud server. To find an optimal user association, we formulate a combinatorial optimization problem that takes into consideration mobile-to-edge delays and edge-to-cloud delays. To reduce the computational complexity, we put forward the backbone-aware greedy algorithm. In addition, we prove that it is not always optimal for a mobile device to connect to the edge server with the minimum mobile-to-edge delay. Furthermore, we propose using dynamic bandwidth allocation after assigning users to edge servers to further reduce the latency. We also use simulation results to show the advantages of the proposed approach.

Abstract. A proper coloring of a graph is conflict-free if, for every nonisolated vertex, some color is used exactly once on its neighborhood. Caro, Petruševski, and Škrekovski [ Discrete Math., 346 (2023), 113221] proved that every graph [Formula: see text] has a proper conflict-free coloring with at most [Formula: see text] colors and conjectured that [Formula: see text] colors suffice for every connected graph [Formula: see text] with [Formula: see text]. Our first main result is that even for list-coloring, [Formula: see text] colors suffice for every graph [Formula: see text] with [Formula: see text]; we also prove slightly weaker bounds for all graphs with [Formula: see text]. These results follow from our more general framework on proper conflict-free list-coloring of a pair consisting of a graph [Formula: see text] and a “conflict” hypergraph [Formula: see text]. As another corollary of our results in this general framework, every graph has a proper [Formula: see text]-list-coloring such that every bichromatic component is a path on at most three vertices, where the number of colors is optimal up to a constant factor. Our proof uses a fairly new type of recursive counting argument called Rosenfeld counting, which is a variant of the Lovász local lemma or entropy compression. We also prove an asymptotically optimal result for a fractional analogue of our general framework for proper conflict-free coloring for pairs of a graph and a conflict hypergraph. A corollary states that every graph [Formula: see text] has a fractional [Formula: see text]-coloring such that every fractionally bichromatic component has at most two vertices. In particular, it implies that the fractional analogue of the conjecture of Caro, Petruševski, and Škrekovski holds asymptotically in a strong sense.

Sustainable edge computing (SEC) is a promising technology that can reduce energy consumption and computing latency for the mobile Internet of Things (IoT). By collecting renewable energy such as solar or wind energy from the environment, a sustainable cloudlet outside the electric grid can provide powerful computing capabilities for resource-constrained mobile IoT devices. In the real world, the density of sustainable energy can vary significantly over time. Therefore, the SEC cloudlet needs to dynamically adjust the clock frequency to balance energy consumption and computing latency. In this paper, we consider the limited energy storage of the cloudlet and the dynamic intensity of renewable energy, and then develop offline optimal CPU frequency scaling policies that (a) maximize the computing power of the cloudlet within a certain period of time, and (b) minimize the execution time given tasks offloaded to the cloudlet. An optimal tightest string policy is proposed to solve the optimization problem. In addition, a dynamic programming (DP) based suboptimal solution is introduced to simplify the practical implementation. How to design an online CPU frequency management strategy is also briefly discussed.

There is a growing research interest in Federated Learning (FL), a promising approach for data privacy preservation and proximity of training to the network edge, where data is generated. Resource consumption for Machine Learning (ML) training and inference is important for edge nodes, but most of the proposed protocols and algorithms for FL are evaluated by simulations. In this demo paper, we present an environment based on distributed mini-PCs to enable experimental study of FL protocols and algorithms. We have installed low-capacity mini-PCs within a wireless city-level mesh network and deployed container-based FL components on these nodes. We show the deployed FL clients and server at different nodes in the city and demonstrate how an FL experiment can be set and run in a real environment.

This paper presents a novel approach to conduct highly efficient federated learning (FL) over a massive wireless edge network, where an edge server and numerous mobile devices (clients) jointly learn a global model without transporting the huge amount of data collected by the mobile devices to the edge server. The proposed FL approach is referred to as spatio-temporal FL (STFL), which jointly exploits the spatial and temporal correlations between the learning updates from different mobile devices scheduled to join STFL in various training epochs. The STFL model not only represents the realistic intermittent learning behavior from the edge server to the mobile devices due to data delivery outage, but also features a mechanism of compensating loss learning updates in order to mitigate the impacts of intermittent learning. An analytical framework of STFL is proposed and employed to study the learning capability of STFL via its convergence performance. In particular, we have assessed the impact of data delivery outage, intermittent learning mitigation, and statistical heterogeneity of datasets on the convergence performance of STFL. The results provide crucial insights into the design and analysis of STFL-based wireless networks.

Terahertz (THz) communication with ultra-wide available spectrum is a promising technique that can achieve the stringent requirement of high data rate in the next-generation wireless networks, yet its severe propagation attenuation significantly hinders its implementation in practice. Finding beam directions for a large-scale antenna array to effectively overcome severe propagation attenuation of THz signals is a pressing need. This paper proposes a novel approach of federated deep reinforcement learning (FDRL) to swiftly perform THz-beam search for multiple base stations (BSs) coordinated by an edge server in a cellular network. All the BSs conduct deep deterministic policy gradient (DDPG)-based DRL to obtain THz beamforming policy with limited channel state information (CSI). They update their DDPG models with hidden information in order to mitigate inter-cell interference. We demonstrate that the cell network can achieve higher throughput as more THz CSI and hidden neurons of DDPG are adopted. We also show that FDRL with partial model update is able to nearly achieve the same performance of FDRL with full model update, which indicates an effective means to reduce communication load between the edge server and the BSs by partial model uploading. Moreover, the proposed FDRL outperforms conventional non-learning-based and existing non-FDRL benchmark optimization methods.

Federated learning (FL) is a promising distributed learning technique particularly suitable for wireless learning scenarios since it can accomplish a learning task without raw data transportation so as to preserve data privacy and lower network resource consumption. However, current works on FL over wireless networks do not profoundly study the fundamental performance of FL over wireless networks that suffers from communication outage due to channel impairment and network interference. To accurately exploit the performance of FL over wireless networks, this paper proposes a novel intermittent FL model over a cellular-connected Unmanned Aerial Vehicle (UAV) network, which characterizes communication outage from UAV (clients) to their server and data heterogeneity among the datasets at UAVs. We propose an analytically tractable framework to derive the uplink outage probability and use it to devise a simulation-based approach so as to evaluate the performance of the proposed intermittent FL model. Our findings reveal how the intermittent FL model is impacted by uplink communication outage and UAV deployment. Extensive numerical simulations are provided to show the consistency between the simulated and analytical performances of the proposed intermittent FL model.

This paper studies how to achieve a high and flexible coverage performance of a large-scale cellular network that enables unmanned aerial vehicles (UAVs) for non-orthogonal multiple access (NOMA) transmission to simultaneously serve multiple users. The considered cellular network consists of a tier of base stations and a tier of UAVs. Each UAV is mounted with an intelligent reflecting surface (IRS) in order to serve as an aerial IRS reflecting signals between a base station and a user in the network. All the UAVs in the network are deployed based on a newly proposed three-dimensional (3D) point process that leads to a tractable and accurate analysis of the association statistics, which is traditionally difficult to analyze due to the mobility of UAVs. In light of this, we are able to analyze the downlink coverage of UAV-IRS-assisted NOMA transmission for two users and derive the corresponding coverage probabilities. Our coverage analyses shed light on the optimal allocations of transmit power between NOMA users and UAVs to accomplish the goal of ubiquitous and flexible NOMA transmission. We also conduct numerical simulations to validate our coverage analytical results while demonstrating the improved coverage performance achieved by aerial IRSs.

This paper aims to propose a three-dimensional (3D) point process that can be employed to generally deploy unmanned aerial vehicles (UAVs) in a large-scale cellular network and tractably analyze the fundamental network-wide performances of the network. This 3D point process is devised based on a 2D marked Poisson point process in which each point and its random mark uniquely correspond to the projection and the altitude of each point in the 3D point process, respectively. We elaborate on some important statistical properties of the proposed 3D point process and use them to tractably analyze the coverage performances of a UAV-enabled cellular network wherein all the UAVs equipped with multiple antennas are served as aerial base stations. The downlink coverage of the UAV-enabled cellular network is found and its closed-form results for some special cases are explicitly derived as well. Furthermore, the fundamental limits achieved by cell-free massive antenna array are characterized when coordinating all the UAVs to jointly perform non-coherent downlink transmission. These findings are validated by numerical simulation.

Traditional means of achieving highly reliable wireless communications are to rely on a closed-loop communication methodology, which needs to implement complicated feedback communication mechanisms. Such closed-loop communication means inevitably incur feedback communication latency and thus lead to a fundamental tradeoff problem of simultaneously achieving high reliability and low latency. To avoid encountering this tradeoff problem, in this paper we adopt an open-loop communication methodology in a mobile network and propose a multi-cell association scheme to enhance the reliability of open-loop communication. The multi-cell association scheme helps users connect to multiple base stations (BSs), which form a virtual cell of the user. We first characterize the distribution of the number of the users associating with a BS for the multi-cell association scheme and then use it to establish the accurate models of signal-to-interference ratios (SIRs) in the downlink and uplink. The downlink and uplink communication reliabilities, which are defined based on the SIRs in the downlink and uplink, are accurately analyzed and their explicit upper bounds are found. Our analytical and simulated results show that jointly adopting open-loop communication and multi-cell association is able to significantly improve the communication reliability of users, thereby creating an ultra-reliable mobile network.

Sustainable edge computing (SEC) is a promising technology that can reduce energy consumption and computing latency for the mobile Internet of things (IoT). By collecting solar or wind energy from the environment, an SEC cloudlet outside the electric grid can provide powerful computing capabilities for resource-constrained mobile IoT devices. Considering significant density variation of sustainable energy over time, the SEC cloudlet needs to dynamically adjust the clock frequency of the central processing unit (CPU) to balance energy consumption and computing power. In this paper, we consider the limited energy storage of the cloudlet and develop an offline optimal CPU frequency scaling policy to maximize the overall computing power of the cloudlet within a certain period of time. The tightest string policy that gives a graphical viewpoint of the optimal CPU frequency scaling is found.

The asymptotic dimension of metric spaces is an important notion in geometric group theory introduced by Gromov. The metric spaces considered in this paper are the ones whose underlying spaces are the vertex-sets of graphs and whose metrics are the distance functions in graphs. A standard compactness argument shows that it suffices to consider the asymptotic dimension of classes of finite graphs. In this paper we prove that the asymptotic dimension of any proper minor-closed family, any class of graphs of bounded tree-width, and any class of graphs of bounded layered tree-width are at most 2, 1, and 2, respectively. The first result solves a question of Fujiwara and Papasoglu; the second and third results solve a number of questions of Bonamy, Bousquet, Esperet, Groenland, Pirot and Scott. These bounds for asymptotic dimension are optimal and improve a number of results in the literature. Our proofs can be transformed into linear or quadratic time algorithms for finding coverings witnessing the asymptotic dimension which is equivalent to finding weak diameter colorings for graphs. The key ingredient of our proof is a unified machinery about the asymptotic dimension of classes of graphs that have tree-decompositions of bounded adhesion over hereditary classes with known asymptotic dimension, which might be of independent interest.

Smart manufacturing based on artificial intelligence and information communication technology will become the main contributor to the digital economy of the upcoming decades. In order to execute flexible production, smart manufacturing must holistically integrate wireless networking, computing, and automatic control technologies. This article discusses the challenges of this complex system engineering from a wireless networking perspective. Starting from enabling flexible reconfiguration of a smart factory, we discuss existing wireless technology and the trends of wireless networking evolution to facilitate multirobot smart factories. Furthermore, the special sequential decision-making of a multirobot manufacturing system is examined. Social learning can be used to extend the resilience of precision operation in a multirobot system by taking network topology into consideration, which also introduces a new vision for the cybersecurity of smart factories. A summary of highlights of technological opportunities for holistic facilitation of wireless networked multirobot smart factories rounds off this article.

Attaining reliable communications traditionally relies on a closed-loop methodology but inevitably incurs a good amount of networking latency thanks to complicated feedback mechanism and signaling storm. Such a closed-loop methodology thus shackles the current cellular network with a tradeoff between high reliability and low latency. To completely avoid the latency induced by closed-loop communication, this article aims to study how to jointly employ open-loop communication and multi-cell association in a heterogeneous network (HetNet) so as to achieve ultra-reliable and low-latency communications. We first introduce how mobile users in a HetNet adopt the proposed proactive multi-cell association (PMCA) scheme to form their virtual cell that consists of multiple access points (APs) and then analyze the communication reliability and latency performances. We show that the communication reliability can be significantly improved by the PMCA scheme and maximized by optimizing the densities of the users and the APs. The analyses of the uplink and downlink delays are also accomplished, which show that extremely low latency can be fulfilled in the virtual cell of a single user if the PMCA scheme is adopted and the radio resources of each AP are appropriately allocated.

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted$\ell _{1} $-minimization, which also generalizes a two-step$\ell _{1} $-minimization algorithm introduced by E. J. Candèset al.in [The Annals of Statistics, vol. 42, no. 2, pp. 669–699, 2014] without incurring extra algorithmic complexity. To fully exploit the prior information offered by the computed sparse representation vector in the first step, our approach places a weight on each component of the regression vector, and solves a weighted LASSO in the second step. We propose a data weighting rule suitable for enhancing neighbor identification accuracy. Then, under the formulation of the dual problem of weighted LASSO, we study in depth the theoretical neighbor recovery rates of the proposed scheme. Specifically, an interesting connection between the locations of nonzeros of the optimal sparse solution to the weighted LASSO and the indexes of the active constraints of the dual problem is established. Afterwards, under the semi-random model, analytic probability lower/upper bounds for various neighbor recovery events are derived. Our analytic results confirm that, with the aid of data weighting and if the prior neighbor information is accurate enough, the proposed scheme with a higher probability can produce many correct neighbors and few incorrect neighbors as compared to the solution without data weighting. Computer simulations are provided to validate our analytic study and evidence the effectiveness of the proposed approach.

This paper aims to propose a three-dimensional (3D) point process that can be employed to generally deploy unmanned aerial vehicles (UAVs) in a large-scale 3D cellular network and to tractably analyze the fundamental network-wide performances of the network. The proposed 3D point process is devised based on a 2D marked Poisson point process in which each point and its random mark uniquely correspond to the projection and the altitude of each point in the 3D point process, respectively. We study some of the important statistical properties of the proposed 3D point process and shed light on some crucial insights into them that facilitate the analyses of a UAV-enabled cellular network wherein all UAVs equipped with multiple antennas are deployed by the proposed 3D point process to serve as aerial base stations. The salient features of the proposed 3D point process lie in its suitability in practical 3D channel modeling and tractability in analysis. The downlink coverages of the UAV-enabled cellular network are found and their closed-form results for some special cases are also derived. Most importantly, their fundamental limits achieved by cell-free massive antenna array are characterized when coordinating all the UAVs to jointly perform non-coherent downlink transmission. These key findings and observations are numerically validated in this paper.

Consider a large-scale cellular network in which base stations (BSs) serve massive Internet of Things (IoT) devices. Since IoT devices are powered by a capacity-limited battery, how to prolong their working lifetime is a paramount problem for the success of cellular IoT systems. This article proposes how to use BSs to manage the active and dormant operating modes of the IoT devices via downlink signaling in an energy-efficient fashion and how the IoT devices perform energy-efficient uplink power control to improve their uplink coverage. We first investigate the fundamental statistical properties of an activation signaling process induced by BSs that would like to activate the devices in their cells, which helps to derive the neat expressions of the true, false, and total activation probabilities that reveal joint downlink power control and BS coordination is an effective means to significantly improve the activation performance. We then propose an energy-efficient uplink power control for IoT devices which is shown to save power and ameliorate the uplink coverage probability at the same time. We also propose an energy-efficient downlink power control and BS coordination scheme, which is shown to remarkably improve the activation and uplink coverage performances at the same time.

Built on the sparse representation framework, sparse subspace clustering (SSC) received considerable attention in the recent years. Conventional SSC employs ℓ1-minimization based sparse regression for neighbor identification on a sample-by-sample basis, and is unaware of the neighbor information revealed by those already computed sparse representation vectors. To rid this drawback, this paper proposes a weighted ℓ1-minimization based sparse regression method, and an associated data ordering rule able to reflect the reliability of neighbor information for further enhancing the clustering accuracy. The selection of weighting coefficients for SSC is also discussed. Computer simulations using both the synthesis and real data are provided to evidence the effectiveness of the proposed method.

In a heterogeneous cellular network (HetNet) consisting of multiple different types (tiers) of base stations (BSs), the void cell event in which a BS does not have any users has been shown to exist due to user-centric BS association and its probability is dominated by the cell load of each tier. Such a void cell phenomenon has not been well characterized in the modeling and analytical framework of simultaneous wireless information and power transmission (SWIPT) in a HetNet. This paper aims to accurately analyze the energy efficiency of the HetNet with SWIPT by modeling the cell-load impact on the downlink and uplink transmissions of each BS. We first characterize the power-splitting receiver architecture of SWIPT at a user and then specify the model of energy harvesting. First, the rates of users in the downlink and uplink are accurately found for the generalized user association scheme and then they are used to define the energy efficiency of users in the downlink and uplink. We formulate an optimization problem to maximize the energy efficiency under the constraints on the outage probability of energy harvesting and the defined self-power sustainability. Finally, we show that the feasible solutions to the optimization problem indeed exist if certain conditions are satisfied.

This paper aims to study how to achieve high transmission security in the physical (PHY) layer of a multi-tier heterogeneous network (HetNet) through a simple device-to- device (D2D) enabling scheme. For the HetNet, we propose a simple D2D-enabling scheme with low complexity for users to opportunistically enable their D2D mode and become either D2D or cellular users by exploiting the diversity of all user association signals from all base stations (BSs). To evaluate whether the proposed D2D enabling scheme improves the PHY-layer security of the HetNet, the secrecy outage probability of the HetNet is defined and analyzed from two different perspectives of BSs and users. We define the BS- centric and user-centric security outage events and derive the explicit lower bound on their probability when the proposed D2D enabling scheme is adopted. Our analytical and numerical results not only show that the proposed D2D-enabling scheme can achieve high PHY-layer security but also reveal how densely the BSs should be deployed in the HetNet in order to achieve the high PHY-layer security from the perspectives of BSs and users.

In a heterogeneous cellular network (HetNet) consisting of multiple different types (tiers) of base stations (BSs), the void cell event in which a BS does not have any users has been shown to exist due to user-centric BS association, and its probability is dominated by the cell load of each tier. Such a void cell phenomenon has not been well characterized in the modeling and analytical framework of simultaneous wireless information and power transmission (SWIPT) in a HetNet. This paper aims to accurately exploit the fundamental performance limits of the SWIPT between the BS and its user by modeling the cell-load impact on the downlink and uplink transmissions of each BS. We first characterize the power-splitting receiver architecture at a user and analyze the statistical properties and limits of its harvested power and energy, which reveals how much of the average energy can be harvested by users and how likely the self-powered sustainability of users can be achieved. We then derive the downlink and uplink rates that characterize the cell-load and user association effects and use them to define the energy efficiency of a user. The optimality of the energy efficiency is investigated, which maximizes the SWIPT performance of the receiver architecture for different user association and network deployment scenarios.

This paper aims to exploit the fundamental limits on the downlink coverage and spatial throughput performances of a cellular network comprised of a tier of unmanned aerial vehicle (UAV) base stations (BSs) using the millimeter wave (mmWave) band and a tier of ground BSs using the ultra high frequency (UHF) band. To reduce handover signaling overhead, the ground BSs take charge of control signaling delivery whereas the UAVs are in charge of payload data transmission so that users need to be simultaneously associated with a ground BS and a UAV in this network with a control-data plane-split architecture. We first propose a three-dimensional (3D) location distribution model of the UAVs using stochastic geometry which is able to generally characterize the positions of the UAVs in the sky. Using this 3D distribution model of UAVs, two performance metrics, i.e., multi-cell coverage probability and volume spectral efficiency, are proposed. Their explicit low-complexity expressions are derived and their upper limits are found when each of the UAVs and ground BSs is equipped with a massive antenna array. We further show that the multi-cell coverage probability and the volume spectral efficiency can be maximized by optimally deploying and positioning the UAVs in the sky and thereby their fundamental maximal limits are found. These important analytical findings are validated by numerical simulations.

In this paper, we first introduce a generalized modeling and analysis framework to explore the fundamental interactions between user association, coverage probability, and link rate in a millimeter-wave (mmWave) heterogeneous cellular network (HetNet), in which there are multiple tiers of the ultra-high-frequency (UHF) macrocell and small-cell base stations (BSs) and a single tier of mmWave small-cell BSs. A generalized user association scheme that can cover many path-loss-based user association schemes is proposed, and its related probabilistic properties that facilitate the derivations of the coverage probability and link rate are derived. The derived general expressions of the coverage and link rate not only shed light on how to design user association functions in order to maximize the coverage and link rate but also show that it is impossible to devise a user association scheme that maximizes the coverage and link rate at the same time. Namely, there exists a fundamental tradeoff between the coverage and link rate in mmWave HetNets with distinct bandwidths in the UHF and mmWave bands while a user is my margin associating with a BS. We characterize the coverage-optimal and rate-optimal user association schemes and numerically validate their performances and show the coverage-rate tradeoff problem.

Full-duplex (FD) transmission in a point-to-point (P2P) link, wherein bidirectional traffic flows simultaneously share the same spectrum, has the capability of doubling the link rate by completely removing self-interferences. However, the rate performance of an FD heterogeneous network (HetNet) is not as clear as that of an FD P2P link due to the co-channel interferences induced by the complex FD and half-duplex (HD) transmission behaviors in the HetNet. To thoroughly investigate the achievable link rate performances of users and base stations (BSs) in a HetNet with decoupled user association, a hybrid-duplex approach is proposed to model a HetNet in which all BSs and users can perform HD or FD transmission depending on their traffic patterns. We first characterize the decoupled rate-optimal user association scheme and use it to define and evaluate the downlink and uplink rates in the HetNet. The tight lower bounds on the link rates of the FD users and BSs are found in a neat form that characterizes general channel fading, imperfect self-interference cancellation, and the intensities of users and BSs. These bounds outline the rate regions of the FD users that inspire us to propose the opportunistic FD scheduling algorithms that maximize the sum rate of each bidirectional traffic and stabilize each of the queues in the HetNet.

Full-duplex (FD) transmission in a point-to-point (P2P) link, wherein bidirectional traffic flows simultaneously share the same spectrum, has the capability of doubling the link throughput by completely removing self-interferences. However, the throughput gain of FD transmission in an interference-limited network is not as clear as a P2P link due to the interferences induced by complex FD and half- duplex (HD) transmission behaviors in the network. To thoroughly investigate the link throughputs of users and base stations (BSs) in a heterogeneous network (HetNet) with decoupled user association, a general approach is proposed to model a HetNet in which all BSs and users can perform HD or FD transmission depending on their traffic patterns. We first characterize the decoupled rate-optimal user association scheme and use it to define the downlink and uplink throughputs in the HetNet. The tight lower bounds on the link throughputs of the FD users and BSs are found in a neat form that characterizes general channel fading, user and BS intensities and imperfect self- interference cancellation. Numerical results validate that our analytical results are fairly accurate and the proposed decoupled rate-optimal user association indeed significantly improves the link throughputs.

This paper investigates the achievable downlink and uplink throughputs of users in a full-duplex (FD) heterogeneous network (HetNet) where users are allowed to associate with different downlink and uplink base stations (BSs) and adopt FD transmission to handle bidirectional traffic between them and their associated BSs. In order to exploit the downlink and uplink throughput limits, we propose the model of decoupled generalized user association and use it to define the full-duplex signal-to-interference ratio. We derive the decoupled rate-optimal user association (DROA) scheme that is able to make user associate with the BSs that provide them with the maximum downlink and uplink throughputs. For the DROA scheme, the explicit tight lower bounds on the link throughputs of an FD user are found in a neat form that characterizes general channel fading, user and BS intensities and imperfect self-interference cancellation. These bounds delineate the throughput regions of the FD user that inspire proposing the opportunistic FD scheduling algorithms able to maximize the sum throughput of each bidirectional traffic in the HetNet.

Consider a decentralized device-to-device (D2D) network consisting of K different types of D2D pairs in which the D2D pairs of each specific type form an independent homogeneous Poisson point process (PPP) and the transmitter (TX) of each D2D pair has a unique intended receiver (RX). For this heterogeneous network model, we develop a model-free tractable framework to analyze the coverage probability without any specific model assumptions for channel fading, stochastic transmit power and distance. First we device a novel approach to finding the Laplace transform of the reciprocal of the SIR which is used to characterize the model-free coverage probability of the D2D pair of each type. Our main analytical findings show that the model-free bounds of the coverage probability can be obtained and they reduce to a closed-form result as long as the received signal power has an Erlang distribution. These findings are applied to expound when the randomness of the received signal power benefits/jeopardizes the coverage probability and how to use the distributed stochastic power control to improve the coverage probability of each D2D pair.

For nonnegative integers $k, d_1, \ldots, d_k$, a graph is $(d_1, \ldots, d_k)$-colorable if its vertex set can be partitioned into $k$ parts so that the $i$th part induces a graph with maximum degree at most $d_i$ for all $i\in\{1, \ldots, k\}$. A class $\mathcal C$ of graphs is balanced $k$-partitionable and unbalanced $k$-partitionable if there exists a nonnegative integer $D$ such that all graphs in $\mathcal C$ are $(D, \ldots, D)$-colorable and $(0, \ldots, 0, D)$-colorable, respectively, where the tuple has length $k$. A set $X$ of cycles is a cycle obstruction set of a class $\mathcal C$ of planar graphs if every planar graph containing none of the cycles in $X$ as a subgraph belongs to $\mathcal C$. This paper characterizes all cycle obstruction sets of planar graphs to be balanced $k$-partitionable and unbalanced $k$-partitionable for all $k$; namely, we identify all inclusionwise minimal cycle obstruction sets for all $k$.

In a heterogeneous cellular network (HetNet), consider that a base station in the HetNet is able to simultaneously schedule and serve K users in the downlink by performing the power-domain non-orthogonal multiple access (NOMA) scheme. This paper aims at the preliminary study on the downlink coverage and throughput performances of the HetNet with the non-coordinated NOMA and the proposed coordinated joint transmission NOMA (JT-NOMA) schemes. First, the coverage probability and link throughput of K users in each cell are studied and their accurate expressions are derived for the noncoordinated NOMA scheme in which no BSs are coordinated to jointly transmit the NOMA signals for a particular user. We show that the coverage and link throughput can be largely reduced if transmit power allocations among the K users do not satisfy the constraint derived. Next, we analyze the coverage and link throughput of K users for the coordinated JT-NOMA scheme in which the void BSs without users are coordinated to enhance the farthest NOMA user in a cell. The derived accurate results show that coordinated JT-NOMA can significantly improve the coverage and link throughput of all users. Finally, we show that there exist optimal power allocation schemes that maximize the average cell coverage and throughput under some derived power allocation constraints and numerical results validate our analytical findings.

In a heterogeneous cellular network (HetNet) consisting of M tiers of densely-deployed base stations (BSs), we consider that each BS in the HetNet associated with multiple users is able to simultaneously schedule and serve at most K users in a downlink time slot by performing the (power-domain) non-orthogonal multiple access (NOMA) scheme. This paper aims to provide accurate analyses for the link throughput of a (NOMA) user for the non-cooperative and the proposed cooperative NOMA schemes. The link throughput of the users is first studied for the non-cooperative NOMA scheme in which no BSs are coordinated to jointly transmit the NOMA signals for a particular BS and its tight and accurate lower bound is derived. We show that the link throughput performance can be largely degraded if allocated transmit powers for the users are not satisfied with certain constraints. To improve the link throughput of the users, we propose a cooperative NOMA scheme in which the void BSs that are not tagged by any users are coordinated to enhance the farthest user in a particular cell. The accurate approximated expression of the link throughput of a user is found for this cooperative NOMA scheme. We show that cooperative NOMA is able to significantly improve the link throughput of all users as long as the transmit powers are appropriately allocated among the users.

In this paper, we propose a (cell) load-aware approach to performing the downlink coordinated multi-point joint transmission (JT-CoMP) scheme in a dense heterogeneous cellular network (HetNet) consisting M tiers of different kinds of base stations (BSs). Inspiring from the fact that there could exist a considerable number of the void BSs in a dense HetNet that are not associated by any users, this load-aware JT-CoMP scheme is able to coordinate the void BSs so as to enhance the downlink transmission of the non-void BSs. Using such a CoMP scheme, the fundamental upper and lower limits on the coverage and ergodic link throughput of a user with downlink MISO channel are accurately found in a low-complexity approximated form and they straightforwardly show that the load-aware JT-CoMP scheme has the capability of significantly increasing the coverage and ergodic link throughput of a user as long as the user intensity is not very much higher than the total intensity of the BSs. Numerical results validate the accuracy and correctness of the analytical results and demonstrate the huge gains of the coverage and the ergodic link throughput exploited by the proposed load-aware JT-CoMP scheme.

In this paper, we introduce a generalized analytical framework to evaluate the coverage probability in an mmWave heterogeneous cellular network (HetNet) consisting of UHF macrocell base stations (BSs) and mmWave small cell BSs deployed in an urban area. A generalized user association scheme that can cover a few user association schemes is formulated and applied in the mmWave HetNet. Two important statistical properties of the associated BS under this scheme are derived for the general line-of-sight and non line-of-sight pathloss channel models and they can be largely simplified if the power-law channel model is applied. Using the two statistical properties, the coverage probability of a downlink multiple-input-single-output channel is found in a compact form, which reveals that the coverage probability in the mmWave HetNet can be significantly improved if compared with the cellular network consisting of a single tier of mmWave small cell BSs. Numerical results not only validate the correctness of the coverage probability derived but also indicate that the mmWave HetNet has the potential to achieve a high coverage probability in an urban area.

In a heterogeneous cellular network (HetNet) consisting of M tiers of densely-deployed base stations (BSs), consider that each of the BSs in the HetNet that are associated with multiple users is able to simultaneously schedule and serve two users in a downlink time slot by performing the (power-domain) non-orthogonal multiple access (NOMA) scheme. This paper aims at the preliminary study on the downlink coverage performance of the HetNet with the non-cooperative and the proposed cooperative NOMA schemes. First, we study the coverage probability of the NOMA users for the non-cooperative NOMA scheme in which no BSs are coordinated to jointly transmit the NOMA signals for a particular cell and the coverage probabilities of the two NOMA users of the BSs in each tier are derived. We show that the coverage probabilities can be largely reduced if allocated transmit powers for the NOMA users are not satisfied with some constraints. Next, we study and derive the coverage probabilities for the proposed cooperative NOMA scheme in which the void BSs that are not tagged by any users are coordinated to enhance the far NOMA user in a particular cell. Our analyses show that cooperative NOMA can significantly improve the coverage of all NOMA users as long as the transmit powers for the NOMA users are properly allocated.

In this paper, we adopt a realistic approach to modeling a full-duplex heterogeneous cellular network (HetNet) consisting of a tier of small cell base stations (BSs) that can perform half-duplex (HD) or full-duplex (FD) transmission depending on which duplex transmission is needed by their associated users and a tier of macro BSs that only can perform HD transmission due to their strong self-interference (SI). Two realistic issues, void cell and imperfect SI cancellation, that could exist in this HetNet are also considered in the interference model of this two-tier HetNet. We first study the Laplace transforms of the reciprocals of the signal-to- interference power ratios of users and small cell BSs and derive their explicit expressions. These Laplace transforms lead to the derivations of the ergodic rates of users and small cell BSs found in a very compact form for general power-law channel models. We show that FD does not always outperform HD in terms of ergodic rates and demonstrate how to make FD#x002F;HD transmission benefits the ergodic rates by deploying macro and small cell BSs with appropriate intensities.

This paper studies how to maximize the per-user-based throughput in an M-tier heterogeneous wireless network (HetNet) by optimally managing traffic flows among the access points (APs) in the HetNet. The APs in the first M - 1 tiers can use the licensed spectrum at the same time whereas they share the unlicensed spectrum with the APs in the Mth tier by the proposed opportunistic CSMA/CA protocol. The APs that access the licensed and unlicensed spectra simultaneously are able to integrate their spectrum resources by the carrier aggregation technique. For an AP in each tier, the tight bounds on its mean spectrum efficiencies in the licensed and unlicensed spectra are derived in a low-complexity form for general random channel gain and AP association weight models, and they can provide some insights into how channel gains, AP association weights and void AP probabilities affect the mean spectrum efficiencies of APs. The per-user throughput based on the mean spectrum efficiencies in the licensed and unlicensed spectra is found and maximized by the proposed decentralized traffic management scheme. Numerical results show that the mean spectrum efficiencies and the per-user throughput can be significantly improved by the proposed decentralized traffic management scheme.

This paper devises a general modeling and analyzing framework for a heterogeneous wireless network (HetNet) in which several wireless subnetworks coexist and use multiple radio access technologies (multi-RATs). The coexisting coverage and network capacity in such a multi-RAT HetNet are hardly investigated in prior works. To characterize the coexisting interactions in a multi-RAT HetNet, in this paper, we consider a HetNet consisting of$K$tiers of access points (APs) and two different RATs, RAT-$ \mathsf {L}$and RAT-$ \mathsf {U}$, are adopted in the HetNet. RAT-$ \mathsf {L}$is adopted by the APs in the first$K-1$tiers and APs in the$K$th tier only use RAT-$ \mathsf {U}$. Both noncrossing-RAT and crossing-RAT user association scenarios are considered. In each scenario, the void probability and the channel access probability of the APs in each tier are first found and then the tight lower bounds and their lowest limits on the proposed coexisting coverage and network capacity are derived. We show that multi-RAT networks in general can achieve higher link coverage and capacity by using opportunistic carrier sense multiple access with collision avoidance that avoids/alleviates severe interfering between all coexisting APs. Also, crossing-RAT user association is shown to achieve much higher coexisting coverage and network capacity than noncrossing-RAT user association. Finally, numerical simulations for the LTE-U and WiFi networks coexisting in the HetNet validate our findings.

This paper studies how to maximize the per-user-based throughput in an M-tier heterogeneous wireless network (HetNet) by optimally managing traffic flows among the access points (APs) in the HetNet. The APs in the first M - 1 tiers can use the licensed spectrum at the same time whereas they share the unlicensed spectrum with the APs in the Mth tier by the proposed opportunistic CSMA/CA protocol. We characterize the statistical property of the cell load and channel access probability of each AP using a general AP association scheme. For an AP in each tier, the tight bounds on its mean spectrum efficiencies in the licensed and unlicensed spectra are derived in a low-complexity form for general random channel gain and AP association weight models and they can give some insights on how channel gains, AP association weights and void AP probabilities affect the mean spectrum efficiencies. We define the per-user link throughput and per-user network throughput based on the derived the mean spectrum efficiencies and maximize them by proposing the decentralized and centralized traffic management schemes for the APs in the first M - 1 tiers under the constraint that the per-user link throughput of the tier-M APs must be above some minimum required value. Finally, a numerical example of coexisting LTE and Wi-Fi networks is provided to validate our derived results and findings.

This paper studies the energy efficiency of a dense heterogeneous cellular network (HetNet) consisting of K independent Poisson point processes (PPPs) of base stations (BSs) and what the maximum limit on the energy efficiency can be achieved by cell association. The cell load statistics is first derived for power-law cell association functions and it can characterize the accurate void cell probability of a BS in each tier of the HetNet. A green cell association (GCA) scheme is proposed based on the downlink spectrum efficiency per unit power consumption of a BS and its GCA function is derived in a very simple and feasible form. The energy efficiency of a BS is defined as the mean downlink spectrum efficiency per unit power consumption and its tight lower bounds and limits for the GCA, maximum received power association (MRPA) and nearest base station association (NBA) schemes are all found. We show that the energy efficiency achieved by the GCA scheme is the maximum energy efficiency limit that is not surmounted by other non-green cell association schemes such as MRPA and NBA and the cell loads between different tiers are also balanced by the GCA scheme very well.

This paper proposes an analytical approach to modeling and analyzing the coexisting transmission performance in a multi-tier heterogeneous network with multiple radio access technologies (Multi-RATs). The coexistence issue is a special phenomenon uniquely existing in a multi-RAT network and it is rarely studied in prior works on heterogeneous wireless network. To simply characterize the coexisting transmission impacts in a multi-RAT network, in this paper we consider a three-tier heterogeneous network using the RATs of L and U, where RAT-L is adopted by the access points (APs) in the first two tiers, APs in the third tier only use RAT-U and the APs in the second tier can opportunistically use RAT-U. The opportunistic CSMA/CA protocol is used by the APs contending the RAT-U channel and the channel access probabilities for the RAT-U AP in two different tiers are derived under the proposed user association scheme with random weights. The coexisting coverages of RAT-L and RAT-U are defined and found, respectively. Numerical results show that the proposed modeling and analyzing approach can be well applied to evaluate the coexistence transmission performance while LTE and WiFi APs both access the unlicensed band.

This paper studies the proposed green (energy-efficient) coverage probability, link and network energy efficiencies in the downlink of a heterogeneous cellular network (HetNet) consisting of K independent Poisson point processes of base stations (BSs). The important statistical properties of the universal (general) cell association functions are first studied, and the cell load statistics for power-law cell association functions, which can characterize the accurate void cell probability of a BS in every tier, are also derived. A simple and feasible green channel-aware cell association (GCA) scheme is proposed and the green coverage probability is also proposed for any particular cell association scheme, such as the maximum received power association (MRPA) and the nearest BS association (NBA) schemes. Then, the link and network energy efficiencies are proposed to characterize the mean spectrum efficiency per unit power consumption for a BS and the mean area spectrum efficiency for the HetNet, respectively. All the tight bounds on the green coverage probability, link, and network energy efficiencies for the GCA, MRPA, and NBA schemes are found. They are theoretically shown to pose the fundamental maximum limits on the link and network energy efficiencies achieved by any other cell association schemes, and such a fact is validated by numerical results as well.

This paper thoroughly explores the fundamental interactions between cell association, cell load, and throughput in a green (energy-efficient) small cell network in which all base stations form a homogeneous Poisson point process (PPP) of intensity λBand all users form another independent PPP of intensity λ∪. Cell voidness, usually disregarded due to rarity in cellular network modeling, is first theoretically analyzed under generalized (channel-aware) cell association (GCA). We show that the void cell probability cannot be neglected any more since it is bounded above by exp(-λ∪/λB) that is typically not small in a small cell network. The accurate expression of the void cell probability for GCA is characterized and it is used to derive the average cell and user throughputs. We learn that cell association and cell load λ∪/λBsignificantly affect these two throughputs. According to the average cell and user throughputs, the green cell and user throughputs are defined respectively to reflect whether the energy of a base station is efficiently used to transmit information or not. In order to achieve satisfactory throughput with certain level of greenness, cell load should be properly determined. We present the theoretical solutions of the optimal cell loads that maximize the green cell and user throughputs, respectively, and verify their correctness by simulation.

The fundamental interactions between cell association, cell throughput and load in a green (energy-efficient) small cell network are exploited in this paper. Due to user-centric cell association, a small cell network severely suffers the void cell problem. We propose a weighted channel-aware cell association (WCCA) scheme and derive the average cell throughput under this scheme that characterizes the per-cell throughput with the void cell impact. We show that the average throughput is significantly affected by WCCA and cell load. In order to reflect whether the energy of a base station is efficiently used to transmit information or not, the green cell throughput, which is defined based on the average cell throughput, is derived and it indicates that cell load should be properly determined in order to achieve the satisfactory green cell throughput. The theoretical solution of the optimal cell load that maximizes the green cell throughput is found and verified its correctness by simulation.

In this paper we investigate single-hop multicast transmission in which randomly located multiple transmitters multicast packets to a cluster of receivers. Packet retransmission is known as a promising mechanism for improving the transmission reliability. Our focus is on evaluating (i) the minimum required delay (retransmission attempts), τ*, for establishing an outage-free multicast, where a transmitted packet is successfully decoded by entire nodes in the cluster, and (ii) Multicast Progress Radius (MPR) for a given delay constraint. MPR indicates how far, on average, a packet can successfully progress in a cluster without outage while the retransmission delay is restricted. Assuming general fading distribution, we derive closed-form expressions for the cumulative distribution function of τ*, and MPR. By simulations we confirmed our analysis and studied the impact of several system parameters on the MPR. Based on results of this paper we conclude that outage-free multicast requires a very large number of retransmission attempts, thus not practically achievable only based on retransmission.

This paper studied the fundamental modeling defect existing in Poisson-distributed cellular networks in which all base stations form a homogeneous Poisson point process (PPP) of intensity λBand all users form another independent PPP of intensity λU. The modeling defect, hardly discovered in prior works, is the void cell issue that stems from the independence between the distributions of users and BSs and “user-centric” cell association, and it could give rise to very inaccurate analytical results. We showed that the void probability of a cell under generalized random cell association is always bounded above zero and its theoretical lower bound is exp (-λU/λB) that can be achieved by large association weighting. An accurate expression of the void probability of a cell was derived and simulation results validated its correctness. We also showed that the associated BSs are essentially no longer a PPP such that modeling them as a PPP to facilitate the analysis of interference-related performance metrics may detach from reality if the BS intensity is not significantly large if compared with the user intensity.

In this paper, how to optimally deploy base station density in a small cell network with energy-efficient power control was investigated. Base stations (BSs) and users form two independent Poisson point processes (PPPs) in the network. Since user-centric cell association may lead to void cells that do not have any users, the power of each BS is controlled in either all-on or on-off mode depending on whether its cell is void or not. The average cell rates for each power control mode are first found and their corresponding energy efficiency is also characterized. The optimal BS density that maximizes the energy efficiency under a given user density is theoretically proved to exist and its value can be found numerically. Both analytical and simulated results indicate that on-off power control is significantly superior to all-on power control in terms of energy efficiency if BSs are deployed based on their optimal energy-efficient density.

Power control in a digital handset is practically implemented in a discrete fashion, and usually, such a discrete power control (DPC) scheme is suboptimal. In this paper, we first show that in a Poison-distributed ad hoc network, if DPC is properly designed with a certain condition satisfied, it can strictly work better than no power control (i.e., users use the same constant power) in terms of average signal-to-interference ratio, outage probability, and spatial reuse. This motivates us to propose an N-layer DPC scheme in a wireless clustered ad hoc network, where transmitters and their intended receivers in circular clusters are characterized by a Poisson cluster process on the plane ℝ2. The cluster of each transmitter is tessellated into N-layer annuli with transmit power Piadopted if the intended receiver is located at the ith layer. Two performance metrics of transmission capacity (TC) and outage-free spatial reuse factor are redefined based on the N-layer DPC. The outage probability of each layer in a cluster is characterized and used to derive the optimal power scaling law Pi∈ Θ(ηi-(α/2)), with ηias the probability of selecting power Pi and α as the path loss exponent. Moreover, the specific design approaches to optimize Pi and N based on ηiare also discussed. Simulation results indicate that the proposed optimal N-layer DPC significantly outperforms other existing power control schemes in terms of TC and spatial reuse.

Coverage analysis of a small cell network is very crucial since small cell deployment will dominates the topology of a cellular in the future. The majority of prior work on the coverage probability is studied based on a simple and consistent Rayleigh fading models in a Poisson-distributed cellular network in order to avoid analytical intractability. In this paper, we study the coverage probability problem in a Poisson small cell network with much more general channel impairments. First a neat expression of the coverage probability with compose Rayleigh fading and log-normal shadowing is derived and it discloses two important facts - the coverage performance is not improved by deploying more base stations and it is significantly weakened by shadowing. Then we find the coverage probability with low complexity for the case that a dual-slop path loss is used, the desired signal experiences Nakagami-m fading and interference signals undergo Rayleigh fading. It is able to more practically reflect the coverage performance of a user.

An $(a:b)$-coloring of a graph $G$ is a function $f$ which maps the vertices of $G$ into $b$-element subsets of some set of size $a$ in such a way that $f(u)$ is disjoint from $f(v)$ for every two adjacent vertices $u$ and $v$ in $G$. The fractional chromatic number $\chi_f(G)$ is the infimum of $a/b$ over all pairs of positive integers $a,b$ such that $G$ has an $(a:b)$-coloring. Heckman and Thomas conjectured that the fractional chromatic number of every triangle-free graph $G$ of maximum degree at most three is at most 2.8. Hatami and Zhu proved that $\chi_f(G) \leq 3-3/64 \approx 2.953$. Lu and Peng improved the bound to $\chi_f(G) \leq 3-3/43 \approx 2.930$. Recently, Ferguson, Kaiser, and Král' proved that $\chi_f(G) \leq 32/11 \approx 2.909$. In this paper, we prove that $\chi_f(G) \leq 43/15 \approx 2.867$.

Opportunistic scheduling and routing can in principle greatly increase the throughput of decentralized wireless networks, but to be practical such algorithms must do so with small amounts of timely side information. In this paper, we propose a low-overhead distributed opportunistic scheduling (DOS) scheme, termed distributed interferer-channel aware scheduling (DICAS), and precisely determine its affect on the overall network outage probability and transmission capacity (TC). The main contribution is determining the appropriate channel and interference thresholds that a given isolated transmitter should estimate and apply when scheduling its own transmissions. Using the thresholds, the precise network-wide gain of DICAS is quantified and compared. We conclude by considering the geometric interpretation of DICAS that provides an intuitive concept of how DICAS improves TC.

It is well known that opportunistic scheduling and routing can be significantly leveraged in wireless ad hoc networks to improve the reliability of communication. However, complex opportunistic schemes incur a large overhead in terms of required channel state information leading to an overall degradation of the effective throughput. In this paper, we propose a distributed dynamic scheduling (DDS) scheme that has very little overhead and is easy to implement. DDS schedules a transmission by comparing the quality of the channel between a transmitter and its associated receiver to a dynamic threshold. We show that it is critical to choose the threshold as a function of the intensity of network transmissions and we quantify the gain using the transmission capacity (TC) framework. Our main results show that DDS can significantly increase the TC. In addition, we also show that the outage probability of DDS can be further reduced by using a geometry-based interference cancellation approach, which provides a fundamental view of how much outage probability can be improved by receivers.

A discrete power control scheme based on the locations of receivers is proposed in a wireless clustered ad hoc network. Transmitters in the network form a homogeneous Poisson point process (PPP) on the plane ℝ2, and each of them has a random number of receivers that are distributed in a cluster with N tessellated layers. There are N discrete transmit powers used by each transmitter and which power is used depends on which layer the desired receiver is located in a cluster. The outage probabilities for receivers at different layers are derived. The optimal power control scheme of maximizing the redefined transmission capacity (TC) in our setting is found and it has the effect of balancing the spatial throughput achieved by receivers at all layers such that throughput fairness among receivers is achieved. Simulation results show that the proposed discrete power control significantly improves TC and outperforms other previous power control schemes in a Poisson-distributed wireless ad hoc network.

Coordinated multi-point (CoMP) communication is attractive for heterogeneous cellular networks (HCNs) for interference reduction. However, previous approaches to CoMP face two major hurdles in HCNs. First, they usually ignore the inter-cell overhead messaging delay, although it results in an irreducible performance bound. Second, they consider the grid or Wyner model for base station locations, which is not appropriate for HCN BS locations which are numerous and haphazard. Even for conventional macrocell networks without overlaid small cells, SINR results are not tractable in the grid model nor accurate in the Wyner model. To overcome these hurdles, we develop a novel analytical framework which includes the impact of overhead delay for CoMP evaluation in HCNs. This framework can be used for a class of CoMP schemes without user data sharing. As an example, we apply it to downlink CoMP zero-forcing beamforming (ZFBF), and see significant divergence from previous work. For example, we show that CoMP ZFBF does not increase throughput when the overhead channel delay is larger than 60% of the channel coherence time. We also find that, in most cases, coordinating with only one other cell is nearly optimum for downlink CoMP ZFBF.

A Roman dominating function of a graph G is a function f$: V(G) \to \{0, 1, 2\}$ such that whenever $f(v)=0$, there exists a vertex u adjacent to v such that $f(u) = 2$. The weight of f is $w(f) = \sum_{v \in V(G)} f(v)$. The Roman domination number $\gamma_R(G)$ of G is the minimum weight of a Roman dominating function of G. Chambers, Kinnersley, Prince, and West [SIAM J. Discrete Math., 23 (2009), pp. 1575–1586] conjectured that $\gamma_R(G) \le \lceil 2n/3 \rceil$ for any 2-connected graph G of n vertices. This paper gives counterexamples to the conjecture and proves that $\gamma_R(G) \le \max\{\lceil 2n/3 \rceil, 23n/34\}$ for any 2-connected graph G of n vertices. We also characterize 2-connected graphs G for which $\gamma_R(G) = 23n/34$ when $23n/34 > \lceil 2n/3 \rceil$.

Most work on wireless network throughput ignores the temporal correlation inherent to wireless channels because it degrades tractability. To better model and quantify the temporal variations of wireless network throughput, this paper introduces a metric termed ergodic transmission capacity (ETC), which includes spatial and temporal ergodicity. All transmitters in the network form a homogeneous Poisson point process and all channels are modeled by a finite state Markov chain. The bounds on outage probability and ETC are characterized, and their scaling behaviors for a sparse and dense network are discussed. From these results, we show that the ETC can be characterized by the inner product of the channel-state related vector and the invariant probability vector of the Markov chain. This indicates that distributed channel-aware scheduling (DCAS) does not always increase ETC. Finally, we look at outage probability with interference management from a stochastic geometry point of view. The improved bounds on outage probability and ETC due to interference management are characterized and they provide some useful insights on how to effectively manage interference in sparse and dense networks.

Most work on wireless network throughput ignore the temporal correlation inherent to wireless channels, due to trouble with tractability. In order to better capture the temporal variations of wireless network throughput, this paper introduces the metric of ergodic spatial throughput (EST), which includes spatial and temporal ergodicity. All transmitters in the network form a stationary Poisson point process and all channels are modeled by a finite state Markov chain. The bounds on EST are characterized, and their scaling behaviors for a sparse and dense network are discussed. From these results, we show that the EST can be characterized by the inner product of the channel state vector and the invariant probability vector of the Markov chain. This indicates that channel-aware opportunistic transmission (CAOT) may not always increase the EST.

Multicast transmission, wherein the same packet must be delivered to multiple receivers, is an important aspect of sensor and tactical networks and has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include 1) identical packets must be delivered successfully to several nodes, 2) outage at any receiver requires the packet to be retransmitted at least to that receiver, and 3) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. A first contribution of this paper is the development of a tractable multicast model and throughput metric that captures each of these key traits in a multicast wireless network. We utilize a Poisson cluster process (PCP) consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate per transmission attempt times the maximum intensity of multicast clusters under decoding delay and multicast outage constraints. A multicast cluster is a contiguous area over which a packet is multicasted, and to reduce outage it can be tessellated intovsmaller regions of multicast. The second contribution of the paper is the analysis of several key aspects of this model, for which we develop the following main result. Assuming τ/vtransmission attempts are allowed for each tessellated region in a multicast cluster, we show that the MTC is Θ(ρkxlog(k)vy) where ρ,xandyare functions of τ andvdepending on the network size and intensity, andkis the average number of the intended receivers in a cluster. We derive {ρ,x,y} for a number of regimes of interest, and also show that an appropriate number of retransmissions can significantly enhance the MTC.

In this paper, we propose a two-step tone-mapping algorithm to convert a high dynamic range (HDR) image to a low dynamic range (LDR) image. The first step S1 constructs a global tone mapping which optimizes between uniform quantization and histogram equalization. The second step S2 improves the visual quality by optimizing between global operation and local contrast maintenance. Both S1 and S2 can operate independent of each other. Simulation results suggest that proposed tone mapping algorithm can give good visual quality, with S1+S2 better than S1 alone. Simulation results also suggest that proposed S2 can be combined with other existing tone mapping methods to achieve improved local contrast.

Multicast transmission has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include (i) identical packets must be delivered successfully to several nodes, (ii) outage could simultaneously happen at different receivers, and (iii) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. To capture these key traits, we utilize a Poisson cluster process consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate times the number of multicast clusters per unit volume, accounting for outages and retransmissions. Our main result shows that if τ transmission attempts are allowed in a multicast cluster, the MTC is Θ(ρkxlog(k)) where ρ and x are functions of τ depending on the network size and density, and k is the average number of the intended receivers in a cluster. We also show that an appropriate number of retransmissions can significantly enhance the MTC.

Color bit-depth is an important attribute to image quality. However, the precision in various image capture devices limits the color bit-depth and introduces loss in visual quality. Expanding the color bit-depth is an important image enhancement issue. A good bit-depth expansion system manipulates low color bit-depth image for best visual quality as displayed on high color bit-depth monitors. However, in most color bit-depth expansion algorithms, severe contouring effect is observed in smooth gradient area which degrades the visual quality. In this paper, a novel approach is proposed. By considering the distance from contour edges, fine gradient value are applied to fill the contour gaps to achieve gradual transaction.

Rate-distortion (RD)-based mode selections are important techniques in video coding. In these methods, an encoder may compute the RD costs for all the possible coding modes, and select the one which achieves the best trade-off between encoding rate and compression distortion. Previous papers have demonstrated that RD-based mode selections can lead to significant improvements in coding efficiency. RD-based mode selections, however, would incur considerable increases in encoding complexity, since these methods require computing the RD costs for numerous candidate coding modes. In this paper, we consider the scenario where software-based video encoding is performed on personal computers or game consoles, and investigate how multicore graphics processing units (GPUs) may be efficiently utilized to undertake the task of RD optimized intra-prediction mode selections in audio and video coding standards and H.264 video encoding. Achieving efficient GPU-based intra-mode decisions, however, could be nontrivial for two reasons. First, intra-mode decision tends to be sequential. Specifically, the mode decision of the current block would depend on thereconstructed dataof the neighboring blocks. Therefore, the coding modes of neighboring blocks would need to be computed first before that of the current block can be determined. This dependency poses challenges to GPU-based computation, which relies heavily on parallel data processing to achieve superior speedups. Second, RD-based intra-mode decision may require conditional branchings to determine the encoding bit-rate, and these branching operations may incur substantial performance penalties when being executed on GPUs due to pipeline architectural designs. To address these issues, we analyze the data dependency in intra-mode decision, and propose novel greedy-based encoding orders to achieve highly parallel processing of data blocks. We also prove that the proposed greedy-based orders are optimal in our problem, i.e., they require the minimum number of iterations to process a video frame given the dependency constraints. In addition, we propose a method to estimate the coding rate suitable for GPU implementation. Experimental results suggest our proposed solution can be more than 50 times faster than the previously proposed parallel intra-prediction, since our work can efficiently exploit the massive parallel opportunity in GPUs.

In this paper, we investigate and analyze the expected per-node throughput in a wireless sensor network under a randomized sleep scheduling framework with a connectivity constraint. The unique optimal sleep probability maximizing the per-node throughput in the network is found. A sleep probability range in which the throughput monotonically increases along the sleep probability does exist, and it becomes a large portion of the total range when a network is heavy-traffic. This finding contradicts the common belief that throughput decreases along with the frequency of sleep of nodes. In addition, the connectivity confidence level for the optimal sleep probability is derived and proved to be bounded, and a distributed algorithm that makes each node achieve the maximum throughput is provided. Simulation results verify the aforementioned findings as well. For sensors allowed to choose their own sleep probability, an advisable policy is to choose as high probability as the connectivity constraint allows.

A joint network coding and superposition coding (JNSC) scheme is proposed for information exchange between more than two users in a wireless relaying network. In this paper we consider two scenarios in a relaying network with four nodes: single and multiple information exchange loops between three source nodes, and two alternative transmission schemes, i.e. pure time division (PTD) and pure network coding (PNC), are also considered in order to compare with JNSC. The achievable rate regions of the PTD, PNC and JNSC schemes are all characterized, indicating the JNSC scheme is not always superior to the other two schemes. The sum rate optimization problem with a certain traffic pattern is also solved. We showed that the maximum coding gains of the JNSC and PNC schemes compared with the PTD scheme is achieved as the transmission rate of each node is one third of the sum rate in the network. Simulation results also reveal this phenomenon.

Network coding for two-way relaying in a three-node network is considered. The achievable rate regions under both traditional four-slot multi-hopping (FSMH) and network coding (MAC-XOR) are characterized, showing a combination between the two is needed for a larger region. This is accomplished by an opportunistic network coding scheduling which requires minimal information. Queuing analysis shows that for any pair of random Poisson arrivals with rates within the convex hull of FSMH and MAC-XOR regions is stabilizable. Next we consider how traffic pattern, described by the rate ratio between uplink and downlink, influences the sum rate. It is analyzed and compared with that of FSMH. It is shown that network coding achieves the maximum gain when traffic is symmetric, while it could be worse than FSMH when the traffic is very asymmetric. How multiple antennas influence the performance of network coding is also discussed. Finally, simulations based on Erceg fading model under a WiMAX setting are presented, which shows that the network coding gain (vs FSMH) improves further under MIMO.

This paper presents a novel and efficient tone mapping algorithm for converting high dynamic range (HDR) images back to low dynamic range (LDR) images for displaying purpose because of the limited contrast ratio of common displays and printers. As the ratio between the maximum and minimum values of common HDR images is always very large and also the population usually deflects to one side, for convenient processing, most researchers first take the logarithm on the luminance layer or use another adaptive mapping to shorter the range of the distribution in their tone mapping methods. However, these mappings have already distorted the original imagespsila characteristics. In this paper, there is no such adverse mapping applied on the luminance layer in the proposed tone mapping algorithm. The paper does produce a tone reproduction curve to convert HDR images to LDR images. Adaptive techniques are also manipulated to provide better visual quality. The whole process is automatic and no parameter is required for manual input. The result will be a superior visual quality tone mapped LDR image with original HDR imagepsilas characteristics.

Bit-depth expansion is important for displaying a low bit-depth image in a high bit-depth monitor. Existing methods tend to give disturbing contouring or blurring artifacts. In this paper, we propose a novel, simple and efficient adaptive method to increase bit-depth taking advantage of the existing techniques to give superior image quality.

In this paper, we propose a low-complexity scheme for minimizing energy consumption in a clustered multirate CDMA sensor network with multiple receive antennas by jointly controlling the powers and rates of all transmitting sensor nodes. The non-convex bit-energy optimization model is formulated by the sum product of transmit-plus-hardware powers and processing gains. The reason of taking the hardware consumed power into account is because the consumed energy in hardware is significant in a dense sensor network. We first optimized transmit powers by fixing the processing gains. As a consequence, we acquired the optimal transmit power expressed as a function of the processing gains. Next we reformulated a new simplified optimization problem with convexity. Then we can derive two low-complexity and closed-form algorithms for the transmit power and rate, respectively. A numerical example verifies our proposed algorithms have a nice performance in saving energy.

The collection of physiological signals such as electrocardiogram, electroencephalogram, respiration, blood pressure, body accelerations etc. in a body area network is beneficial for revealing vital signs and investigating spontaneous physiological responses. However, the wire connection between the recording sites and the processing unit may disturb subject's daily activities. Up to now, several multi-users communication protocols such as IEEE 802.11, Bluetooth, etc. have been proposed for this purpose. In this paper we employed the slotted ALOHA for multi-users wireless data transmissions. The slotted ALOHA is so simple that it can be implemented by a 2.4-GHz RF transceiver (nRF2401, Nordic) incorporated on a 16-bit microcontroller (MSP430, Texas Instruments) for the consideration of low-power consumption. In this paper we proposed a modified slotted ALOHA for multi-biosignals transmission and built its simulation model using SIMULINK 2.0 to simulate and evaluate the performance of the proposed algorithm.

In this paper, we propose a distributed stochastic algorithm for power and rate allocation in ad hoc wireless sensor networks. The problem we deal with is formulated as a transmission-plus-circuit energy optimization problem. We showed that the optimal solution can be obtained by solving two power and rate subproblems while either one parameter is fixed. Based on this result we developed two recursive algorithms for power and rate adaptation, respectively. It has been proved that these two recursive algorithms of updating power and rate will converge to a solution pair minimizing the total energy consumption of all the active sensor nodes in a mean square sense. The rate of convergence of these two algorithms is exponential so that the optimal power and rate values can be achieved in a few bit durations. The simulation results reveal that the energy consumption can be largely reduced if powers and rates are updated via the proposed algorithms.

A low-complexity approach is proposed for optimizing the performance of a multiple input multiple-output (MIMO) direct sequence code division multiple-access (DS-CDMA) system in the uplink for frequency selective fading channels. Each user transmits a weighted form of its symbols through its multiple antennas, and a receive antenna array at the base station is equipped with minimum mean square error (MMSE) receivers. We arrive at our system by attempting to find a suboptimal solution based on maximizing the multiuser signal-to-noise interference plus noise ratio (SINR) and minimizing the MMSE of the received signal simultaneously. This provides a noniterative solution for joint transmit beamformer weights of each user and coefficients of the corresponding receiver. In addition, a power control algorithm for suppressing interference is also derived. Numerical results reveal that significant system performance and capacity improvement over conventional approaches are possible.

A servomotor design that is powered and controlled through only one wire is presented. A traditional servomotor needs both a power cable and a control cable connecting the motor to a control amplifier. Cables are bulky, heavy, and expensive and, more importantly, difficult to install and maintain in many applications. Particularly for multi-axis applications, like robots and machine tools, cable harnesses become thick and long, and are difficult to run through a stack of many axes, this is a major burden and bottleneck in electromechanical drives. The objective of this research is to eliminate such bulky cables by integrating and consolidating power cables and signal cables into a single wire, and transmitting control signals through the signal wire. Signals are coded by using a CDMA protocol and are superimposed on the single wire that supplies a DC voltage to each motor. In the paper first the principle of reduced-cable smart motors is described, followed by the architecture of the signal transmission system using direct sequence spread spectrum. A prototype system is designed, and the signal transmission line is simulated to verify the principle.