With the analysis of the hierarchical scheme, the potential influence of the pre-constant in deriving scaling laws is exposed. It is found that a modified hierarchical scheme can achieve a throughput arbitrarily times higher than the original one, although it is still diminishingly small compared to the linear scaling. The study demonstrates the essential importance of the throughput formula itself, rather than the scaling laws consequently derived.
We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like $\mathcal{O}(z^\mathcal C)$ in these parameters, where $\mathcal C$ is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.
We propose a physical layer (PHY) caching scheme for wireless adhoc networks. The PHY caching exploits cache-assisted multihop gain and cache-induced dual-layer CoMP gain, which substantially improves the throughput of wireless adhoc networks. In particular, the PHY caching scheme contains a novel PHY transmission mode called the cache-induced dual-layer CoMP which can support homogeneous opportunistic CoMP in the wireless adhoc network. Compared with traditional per-node throughput scaling results of Θ\left(1/\sqrt{N}\right), we can achieve O(1) per node throughput for a cached wireless adhoc…
We optimize the hierarchical cooperation protocol of Ozgur, Leveque and Tse, which is supposed to yield almost linear scaling of the capacity of a dense wireless network with the number of users $n$. Exploiting recent results on the optimality of "treating interference as noise" in Gaussian interference channels, we are able to optimize the achievable average per-link rate and not just its scaling law. Our optimized hierarchical cooperation protocol significantly outperforms the originally proposed scheme. On the negative side, we show that even for very large $n$, the rate scaling is far from…
A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading (i) the maximum throughput scales like $\log n$ (ii) the maximum throughput is achievable in a distributed f…
Cache-aided wireless device-to-device (D2D) networks have demonstrated promising performance improvement for video distribution compared to conventional distribution methods. Understanding the fundamental scaling behavior of such networks is thus of paramount importance. However, existing scaling laws for multi-hop networks have not been found to be optimal even for the case of Zipf popularity distributions (gaps between upper and lower bounds are not constants); furthermore, there are no scaling law results for such networks for the more practical case of a Mandelbrot-Zipf (MZipf) popularity …
With millimeter wave bands emerging as a strong candidate for 5G cellular networks, next-generation systems may be in a unique position where spectrum is plentiful. To assess the potential value of this spectrum, this paper derives scaling laws on the per mobile downlink feasible rate with large bandwidth and number of nodes, for both Infrastructure Single Hop (ISH) and Infrastructure Multi-Hop (IMH) architectures. It is shown that, for both cases, there exist \emph{critical bandwidth scalings} above which increasing the bandwidth no longer increases the feasible rate per node. These critical …
This paper deals with throughput scaling laws for random ad-hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, $ρ(n)$ of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations pairs operating in isolation. For fixed SNR networks, i.e., where the worst case SNR over the source-destination pairs is fixed independent of $n$, we show that collaborative strategies yield a scaling law of $ρ(n) = {\cal O}(\frac{1}{n^{1/3}})$ in contrast to multi-hop strategies which yield a scaling law of $ρ(n) = {\cal O}(\frac…
We study the scaling laws for the throughputs and delays of two coexisting wireless networks that operate in the same geographic region. The primary network consists of Poisson distributed legacy users of density n, and the secondary network consists of Poisson distributed cognitive users of density m, with m>n. The primary users have a higher priority to access the spectrum without particular considerations for the secondary users, while the secondary users have to act conservatively in order to limit the interference to the primary users. With a practical assumption that the secondary users …
This paper considers large random wireless networks where transmit-and-receive node pairs communicate within a certain range while sharing a common spectrum. By modeling the spatial locations of nodes based on stochastic geometry, analytical expressions for the ergodic spectral efficiency of a typical node pair are derived as a function of the channel state information available at a receiver (CSIR) in terms of relevant system parameters: the density of communication links, the number of receive antennas, the path loss exponent, and the operating signal-to-noise ratio. One key finding is that …
A network of $n$ wireless communication links is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between nodes. The objective is to analyze the achievable throughput of the network when power allocation is allowed. By proposing a decentralized on-off power allocation strategy, a lower bound on the achievable throughput is obtained for a general fading model. In particular, under Rayleigh fading conditions the achieved sum-rate is of order $\log n$, which is, by a constant factor, larger than what is obtained with a centralized scheme in the work o…
We address the optimization of the sum rate performance in multicell interference-limited singlehop networks where access points are allowed to cooperate in terms of joint resource allocation. The resource allocation policies considered here combine power control and user scheduling. Although very promising from a conceptual point of view, the optimization of the sum of per-link rates hinges, in principle, on tough issues such as computational complexity and the requirement for heavy receiver-to-transmitter channel information feedback across all network cells. In this paper, we show that, in …
We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdős-Rényi graph. The former graph is naturally induced by the heterogeneous random key predistribution scheme while the latter graph constitutes a heterogeneous on/off channel model; wherein, the wireless channel between a class-$i$ node and a class-$j$ node is on with probability $α_{ij}$ independently. We presen…
Throughput-Outage scaling laws for single-hop cache-aided device-to-device (D2D) communications have been extensively investigated under the assumption of the protocol model. However, the corresponding performance under physical models has not been explored; in particular it remains unclear whether link-level power control and scheduling can improve the asymptotic performance. This paper thus investigates the throughput-outage scaling laws of cache-aided single-hop D2D networks considering a general physical channel model. By considering the networks with and without the equal-throughput assum…
We study broadcast capacity and minimum delay scaling laws for highly mobile wireless networks, in which each node has to disseminate or broadcast packets to all other nodes in the network. In particular, we consider a cell partitioned network under the simplified independent and identically distributed (IID) mobility model, in which each node chooses a new cell at random every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the cell size. We propose a simple first-come-first-serve (FCFS) flooding scheme that nearly achieves both capacity and minimum…
We investigate optimal channel assignment algorithms that maximize per node throughput in dense multichannel multi-radio (MC-MR) wireless networks. Specifically, we consider an MC-MR network where all nodes are within the transmission range of each other. This situation is encountered in many real-life settings such as students in a lecture hall, delegates attending a conference, or soldiers in a battlefield. In this scenario, we show that intelligent assignment of the available channels results in a significantly higher per node throughput. We first propose a class of channel assignment algor…
Simple and accurate expressions for path gain are derived from electromagnetic fundamentals in a wide variety of common environments, including Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) indoor urban canyons, urban/rural macro, outdoor-indoor and suburban streets with vegetation. Penetration into a scattering region, sometimes aided by guiding, is the "universal" phenomenon shared by the diverse morphologies. Root Mean Square (RMS) errors against extensive measurements are under 5 dB, better than 3GPP models by 1-12 dB RMS, depending on environment. In urban canyons the models have 4.7 d…
In this paper, we examine the benefits of multiple antenna communication in random wireless networks, the topology of which is modeled by stochastic geometry. The setting is that of the Poisson bipolar model introduced in [1], which is a natural model for ad-hoc and device-to-device (D2D) networks. The primary finding is that, with knowledge of channel state information between a receiver and its associated transmitter, by zero-forcing successive interference cancellation, and for appropriate antenna configurations, the ergodic spectral efficiency can be made to scale linearly with both 1) the…
We consider a wireless Device-to-Device (D2D) network where communication is restricted to be single-hop, users make arbitrary requests from a finite library of possible files and user devices cache information in the form of linear combinations of packets from the files in the library (coded caching). We consider the combined effect of coding in the caching and delivery phases, achieving "coded multicast gain", and of spatial reuse due to local short-range D2D communication. Somewhat counterintuitively, we show that the coded multicast gain and the spatial reuse gain do not cumulate, in terms…
Modern medical wireless systems, such as wireless body area networks (WBANs), are applications of wireless networks that can be used as a tool of data transmission between patients and doctors. Accuracy of data transmission is an important requirement for such systems. In this paper, we will propose a WBAN which is robust against erasures and describe its properties using graph theoretic techniques.
In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real-world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present zero-one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws help specify th…
Throughput scaling laws of an ad hoc network equipping directional antennas at each node are analyzed. More specifically, this paper considers a general framework in which the beam width of each node can scale at an arbitrary rate relative to the number of nodes. We introduce an elastic routing protocol, which enables to increase per-hop distance elastically according to the beam width, while maintaining an average signal-to-interference-and-noise ratio at each receiver as a constant. We then identify fundamental operating regimes characterized according to the beam width scaling and analyze t…
Next-generation wireless networks will provide users ubiquitous low-latency computing services using devices at the network edge, called mobile edge computing (MEC). The key operation of MEC, mobile computation offloading (MCO), is to offload computation intensive tasks from users. Since each edge device comprises an access point (AP) and a computer server (CS), a MEC network can be decomposed as a radio access network (RAN) cascaded with a CS network (CSN). Based on the architecture, we investigate network constrained latency performance, namely communication latency (comm-latency) and comput…
Driven by new types of wireless devices and the proliferation of bandwidth-intensive applications, data traffic and the corresponding network load are increasing dramatically. Network densification has been recognized as a promising and efficient way to provide higher network capacity and enhanced coverage. Most prior work on performance analysis of ultra-dense networks (UDNs) has focused on random spatial deployment with idealized singular path loss models and Rayleigh fading. In this paper, we consider a more precise and general model, which incorporates multi-slope path loss and general fad…
We consider a wireless device-to-device (D2D) network where the nodes have pre-cached information from a library of available files. Nodes request files at random. If the requested file is not in the on-board cache, then it is downloaded from some neighboring node via one-hop "local" communication. An outage event occurs when a requested file is not found in the neighborhood of the requesting node, or if the network admission control policy decides not to serve the request. We characterize the optimal throughput-outage tradeoff in terms of tight scaling laws for various regimes of the system p…
An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously considered in the literature. Unicast and multicast messages, topology, hierarchy, and effects of reliability protocols are discussed. We show how two key factors, bottlenecks and erasures, can often domi- nate the network scaling behavior. Scaling of through- put or delay with the number of transmitting nodes, the number of receiving nodes, and the file size is de…
Physical layer security has been recently recognized as a promising new design paradigm to provide security in wireless networks. In addition to the existing conventional cryptographic methods, physical layer security exploits the dynamics of fading channels to enhance secured wireless links. In this approach, jamming plays a key role by generating noise signals to confuse the potential eavesdroppers, and significantly improves quality and reliability of secure communications between legitimate terminals. This article presents theoretical limits and practical designs of jamming approaches for …
We provide a tight approximate characterization of the $n$-dimensional product multicommodity flow (PMF) region for a wireless network of $n$ nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information theoretic sense and for a combinatorial interference model (e.g., Protocol model). These provide an inner approximation to the $n^2$ dimensional capacity region. These results answer the following questions which arise naturally from previous work: (a) What is the significance of $1/\sqrt{n}$ in the scaling laws for the …
In this two-part paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel. We define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for …
We consider an ad hoc network in which each multi-antenna transmitter sends independent streams to multiple receivers in a Poisson field of interferers. We provide the outage probability and transmission capacity scaling laws, aiming at investigating the fundamental limits of Space Division Multiple Access (SDMA). We first show that super linear capacity scaling with the number of receive/transmit antennas can be achieved using dirty paper coding. Nevertheless, the potential benefits of multi-stream, multi-antenna communications fall off quickly if linear precoding is employed, leading to subl…
As location-based applications become ubiquitous in emerging wireless networks, Location Verification Systems (LVS) are of growing importance. In this paper we propose, for the first time, a rigorous information-theoretic framework for an LVS. The theoretical framework we develop illustrates how the threshold used in the detection of a spoofed location can be optimized in terms of the mutual information between the input and output data of the LVS. In order to verify the legitimacy of our analytical framework we have carried out detailed numerical simulations. Our simulations mimic the practic…
We consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studied -- dense random networks and constant density (extended) random networks. In addition, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state infor…
Channel reciprocity greatly facilitates downlink precoding in time-division duplexing (TDD) multiple-input multiple-output (MIMO) communications without the need for channel state information (CSI) feedback. Recently, reconfigurable intelligent surfaces (RISs) emerge as a promising technology to enhance the performance of future wireless networks. However, since the artificial electromagnetic characteristics of RISs do not strictly follow the normal laws of nature, it brings up a question: does the channel reciprocity hold in RIS-assisted TDD wireless networks? After briefly reviewing the reci…
The reconfigurable intelligent surface (RIS) is a promising technology that is anticipated to enable high spectrum and energy efficiencies in future wireless communication networks. This paper investigates optimum location-based RIS selection policies in RIS-aided wireless networks to maximize the end-to-end signal-to-noise ratio for product-scaling and sum-scaling path-loss models where the received power scales with the product and sum of the transmitter-to-RIS and RIS-to-receiver distances, respectively. These scaling laws cover the important cases of end-to-end path-loss models in RIS-aide…
Low-latency communication is currently attracting significant attention due to the emergence of mission-critical Internet of Things (IoT) applications and content-centric services. A deep understanding of the delay performance is essential for efficient wireless system design and end-to-end latency guarantees. In this paper, we investigate the network-layer performance of physical layer multi-antenna multicasting, i.e., when the same data is simultaneously conveyed to multiple users. We provide a statistical characterization of the service process in terms of its Mellin transform and derive pr…
We consider a wireless device-to-device (D2D) network where the nodes have cached information from a library of possible files. Inspired by the current trend in the standardization of the D2D mode for 4th generation wireless networks, we restrict to one-hop communication: each node place a request to a file in the library, and downloads from some other node which has the requested file in its cache through a direct communication link, without going through a base station. We describe the physical layer communication through a simple "protocol-model", based on interference avoidance (independen…
This paper presents a stochastic geometry model for the investigation of fundamental information theoretic limitations in wireless networks. We derive a new unified multi-parameter cut-set bound on the capacity of networks of arbitrary Poisson node density, size, power and bandwidth, under fast fading in a rich scattering environment. In other words, we upper-bound the optimal performance in terms of total communication rate, under any scheme, that can be achieved between a subset of network nodes (defined by the cut) with all the remaining nodes. Additionally, we identify four different opera…
We consider a wireless sensor network in which all the nodes wish to spread their updates over the network using CSMA/CA protocol. We investigate the age of information of the spreading process from a transmitter perspective, which is referred to as the \textit{broadcast age of information (BAoI)}. To be specific, BAoI is the age of the latest update successfully broadcasted to the one-hop neighbors of a node, and thus is suitable to measure the rapidity of the update spreading process. We establish an equivalent transmission model of the network by deriving the transmission probability and th…
This work studies the throughput scaling laws of ad hoc wireless networks in the limit of a large number of nodes. A random connections model is assumed in which the channel connections between the nodes are drawn independently from a common distribution. Transmitting nodes are subject to an on-off strategy, and receiving nodes employ conventional single-user decoding. The following results are proven: 1) For a class of connection models with finite mean and variance, the throughput scaling is upper-bounded by $O(n^{1/3})$ for single-hop schemes, and $O(n^{1/2})$ for two-hop (and multihop) sch…
In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes--bandwidth- and power-limited--have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, bandwidt…
We investigate the fundamental information theoretic limits of cache-aided wireless networks, in which edge nodes (or transmitters) are endowed with caches that can store popular content, such as multimedia files. This architecture aims to localize popular multimedia content by proactively pushing it closer to the edge of the wireless network, thereby alleviating backhaul load. An information theoretic model of such networks is presented, that includes the introduction of a new metric, namely normalized delivery time (NDT), which captures the worst case time to deliver any requested content to…
It is unrealistic to assume that all nodes in an ad hoc wireless network would be willing to participate in cooperative communication, especially if their desired Quality-of- Service (QoS) is achievable via direct transmission. An incentivebased auction mechanism is presented to induce cooperative behavior in wireless networks with emphasis on users with asymmetrical channel fading conditions. A single-object secondprice auction is studied for cooperative partner selection in singlecarrier networks. In addition, a multiple-object bundled auction is analyzed for the selection of multiple simult…
Federated learning (FL) is a type of distributed machine learning at the wireless edge that preserves the privacy of clients' data from adversaries and even the central server. Existing federated learning approaches either use (i) secure multiparty computation (SMC) which is vulnerable to inference or (ii) differential privacy which may decrease the test accuracy given a large number of parties with relatively small amounts of data each. To tackle the problem with the existing methods in the literature, In this paper, we introduce PHY-Fed, a new framework that secures federated algorithms from…
In Part I of this two-part paper on confidential communication over wireless channels, we studied the fundamental security limits of quasi-static fading channels from the point of view of outage secrecy capacity with perfect and imperfect channel state information. In Part II, we develop a practical secret key agreement protocol for Gaussian and quasi-static fading wiretap channels. The protocol uses a four-step procedure to secure communications: establish common randomness via an opportunistic transmission, perform message reconciliation, establish a common key via privacy amplification, and…
The underwater acoustic channel is characterized by a path loss that depends not only on the transmission distance, but also on the signal frequency. Signals transmitted from one user to another over a distance $l$ are subject to a power loss of $l^{-α}{a(f)}^{-l}$. Although a terrestrial radio channel can be modeled similarly, the underwater acoustic channel has different characteristics. The spreading factor $α$, related to the geometry of propagation, has values in the range $1 \leq α\leq 2$. The absorption coefficient $a(f)$ is a rapidly increasing function of frequency: it is three orders…
Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading
Manning College of Information and Computer Sciences, University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校曼宁信息与计算机科学学院）；Department of Electrical and Computer Engineering, University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校电气与计算机工程系）
In this paper, delay-limited transmission of quasi-stationary sources over block fading channels are considered. Considering distortion outage probability as the performance measure, two source and channel coding schemes with power adaptive transmission are presented. The first one is optimized for fixed rate transmission, and hence enjoys simplicity of implementation. The second one is a high performance scheme, which also benefits from optimized rate adaptation with respect to source and channel states. In high SNR regime, the performance scaling laws in terms of outage distortion exponent a…
We investigate the secure connectivity of wireless sensor networks under the pairwise key distribution scheme of Chan et al.. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so that the network i) has no secure node which is isolated and ii) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of zero-one laws…
Artificial Noise Versus Artificial Noise Elimination: Redefining Scaling Laws of Physical Layer Security
Nanyang Technological University（南洋理工大学）；University of Electronic Science and Technology of China（电子科技大学）；Khalifa University（哈利法大学）；Princeton University（普林斯顿大学）
We consider performance enhancement of asymmetrically-clipped optical orthogonal frequency division multiplexing (ACO-OFDM) and related optical OFDM schemes, which are variations of OFDM in intensity-modulated optical wireless communications. Unlike most existing studies on specific designs of improved receivers, this paper investigates information theoretic limits of all possible receivers. For independent and identically distributed complex Gaussian inputs, we obtain an exact characterization of information rate of ACO-OFDM with improved receivers for all SNRs. It is proved that the high-SNR…
This paper studies the performance of partial-Rake (PRake) receivers in impulse-radio ultrawideband wireless networks when an energy-efficient power control scheme is adopted. Due to the large bandwidth of the system, the multipath channel is assumed to be frequency-selective. By using noncooperative game-theoretic models and large system analysis, explicit expressions are derived in terms of network parameters to measure the effects of self- and multiple-access interference at a receiving access point. Performance of the PRake is compared in terms of achieved utilities and loss to that of the…
A key challenge in wireless networking is the management of interference between transmissions. Identifying which transmitters interfere with each other is a crucial first step. In this paper we cast the task of estimating the a wireless interference environment as a graph learning problem. Nodes represent transmitters and edges represent the presence of interference between pairs of transmitters. We passively observe network traffic transmission patterns and collect information on transmission successes and failures. We establish bounds on the number of observations (each a snapshot of a netw…
Two-hop wireless network serves as the basic net-work model for the study of general wireless networks, while cooperative jamming is a promising scheme to achieve the physi-cal layer security. This paper establishes a theoretical framework for the study of eavesdropper-tolerance capability (i.e., the exact maximum number of eavesdroppers that can be tolerated) in a two-hop wireless network, where the cooperative jamming is adopted to ensure security defined by secrecy outage probability (SOP) and opportunistic relaying is adopted to guarantee relia-bility defined by transmission outage probabi…
