A deterministic approach to throughput scaling in wireless networks

We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain /spl Omega/(/spl radic/n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the /spl radic/n//spl radic/(logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.     

On the improvement of scaling laws for large-scale MANETs with network coding

This paper investigates the problem of how much benefit network coding can contribute to the network performance in terms of throughput, delay, and storage requirements for mobile ad hoc networks (MANETs), compared to when only replication, storage and forwarding are allowed in relay nodes. We characterize the throughput-delay-storage tradeoffs under different node mobility patterns, i.e., i.i.d. and random walk mobility, with and without network coding. Our results show that when random linear coding instead of replication is used in MANETs, an order improvement on the scaling laws of MANETs can be achieved. Note that previous work showed that network coding could only provide constant improvement on the throughput of static wireless networks. Our work thus differentiates MANETs from static wireless networks by the role network coding plays.     

Product Multicommodity Flow in Wireless Networks

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. Our results hold for general node distributions, traffic models, and channel fading models. We first establish that the random source-destination model assumed in many previous results on capacity scaling laws, is essentially a one-dimensional approximation to the capacity region and a special case of PMF. We then build on the results for a wireline network (graph) that relate PMF to its spectral (or cut) properties. Specifically, for a combinatorial interference model given by a network graph and a conflict graph, we relate the PMF to the spectral properties of the underlying graphs resulting in simple computational upper and lower bounds. These results show that the 1/radicn scaling law obtained by Gupta and Kumar for a geometric random network can be explained in terms of the scaling law of the conductance of a geometric random graph. For the more interesting random fading model with additive white Gaussian noise (AWGN), we show that the scaling laws for PMF can again be tightly characterized by the spectral properties of appropriately defined graphs-such a characterization for general wireless networks has not been available before. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor.     

Variable-Range Transmission Power Control in Wireless Ad Hoc Networks

In this paper, we investigate the impact of variable-range transmission power control on the physical and network connectivity, on network capacity, and on power savings in wireless multihop networks. First, using previous work by Steele (1988), we show that, for a path attenuation factor a = 2, the average range of links in a planar random network of A m² having n nodes is ~aradicA/n1. We show that this average range is approximately half the range obtained when common-range transmission control is used. Combining this result and previous work by Gupta and Kumar (2000), we derive an expression for the average traffic carrying capacity of variable-range-based multihop networks. For a = 2, we show that this capacity remains constant even when more nodes are added to the network. Second, we derive a model that approximates the signaling overhead of a routing protocol as a function of the transmission range and node mobility for both route discovery and route maintenance. We show that there is an optimum setting for the transmission range, not necessarily the minimum, which maximizes the capacity available to nodes in the presence of node mobility. The results presented in this paper highlight the need to design future MAC and routing protocols for wireless ad hoc and sensor networks based, not on common-range which is prevalent today, but on variable-range power control     

Optimal throughput-delay scaling in wireless networks - part I: the fluid model

Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is /spl Theta/(1//spl radic/(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=/spl Theta/(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of /spl Theta/(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be /spl Theta/(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of /spl Oscr/(1//spl radic/(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=/spl Theta/(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be /spl Theta/(nlogn), which is the delay for throughput of /spl Theta/(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.     

Capacity of Multichannel Wireless Networks Under the Protocol Model

This paper studies the capacity of a n node static wireless network with c channels and m radio interfaces per node under the protocol model of interference. In their seminal work, Gupta and Kumar have determined the capacity of a single channel network (c=1, m=1). Their results are also applicable to multichannel networks provided each node has one interface per channel (m=c) . However, in practice, it is often infeasible to equip each node with one interface per channel. Motivated by this observation, we establish the capacity of general multichannel networks (m les c). Equipping each node with fewer interfaces than channels in general reduces network capacity. However, we show that one important exception is a random network with up to O(logn) channels, where there is no capacity degradation even if each node has only one interface. Our initial analysis assumes that the interfaces are capable of switching channels instantaneously, but we later extend our analysis to account for interface switching delays seen in practice. Furthermore, some multichannel protocols proposed so far rarely require interfaces to switch, and therefore, we briefly study the capacity with fixed interfaces as well.     

Performance analysis of slotted ALOHA and network coding for single-relay multi-user wireless networks

Deployment of wireless relay nodes can enhance system capacity, extend wireless service coverage, and reduce energy consumption in wireless networks. Network coding enables us to mix two or more packets into a single coded packet at relay nodes and improve performances in wireless relay networks. In this paper, we succeed in developing analytical models of the throughput and delay on slotted ALOHA (S-ALOHA) and S-ALOHA with network coding (S-ALOHA/NC) for single-relay multi-user wireless networks with bidirectional data flows. The analytical models involve effects of queue saturation and unsaturation at the relay node. The throughput and delay for each user node can be extracted from the total throughput and delay by using the analytical models. One can formulate various optimization problems on traffic control in order to maximize the throughput, minimize the delay, or achieve fairness of the throughput or the delay. In particular, we clarify that the total throughput is enhanced in the S-ALOHA/NC protocol on condition that the transmission probability at the relay node is set at the value on the boundary between queue saturation and unsaturation. Our analysis provides achievable regions in throughput on two directional data flows at the relay node for both the S-ALOHA and S-ALOHA/NC protocols. As a result, we show that the achievable region in throughput can be enhanced by using network coding and traffic control.     

Polarization-based cooperative directional MAC protocol for ad hoc networks

Numerous directional medium access control (DMAC) protocols have been developed to enhance the capacity of ad hoc networks using the underlying advanced physical layer techniques, such as beam-forming, multiuser detection (MUD), and multiple-input–multiple-output (MIMO). In this paper, we propose an innovative fully distributed DMAC protocol that cooperatively makes use of polarization diversity in low-mobility urban/suburban outdoor wireless ad hoc network environment. In the proposed cooperative polarization DMAC protocol (CPDMAC), each node directionally senses on both vertical and horizontal polarizations and dynamically adapts polarization that minimizes overall interference in the ad hoc network. Analysis is performed to establish relationship between vertically and horizontally polarized nodes in the network. Further, a theoretical lower bound is derived for probability of successful transmission to show capacity improvement as a function of cross polarization ratio (CPR). Simulation results confirm from 2% up to 400% improvement in average node throughput at data rate of 1.95 Mbps when compared to the traditional DMAC protocol. Moreover, our study clearly shows that the average throughput difference increases with increasing node density when compared to the traditional DMAC protocol.     

Wireless network coding in slotted aloha with two-hop unbalanced traffic

This paper deals with two representative unbalanced traffic cases for two-hop wireless relay access systems employing network coding and a slotted ALOHA protocol. Network coding is a recent and highly regarded technology for capacity enhancement with multiple unicast and multisource multicast networks. We have analyzed the performance of network coding on a two-hop wireless relay access system employing the slotted ALOHA under a balanced bidirectional traffic. The relay nodes will generally undergo this unbalanced multidirectional traffic but the impact of this unbalanced traffic on network coding has not been analyzed. This paper provides closed-form expressions for the throughput and packet delay for two-hop unbalanced bidirectional traffic cases both with and without network coding even if the buffers on nodes are unsaturated. The analytical results are mainly derived by solving queueing systems for the buffer behavior at the relay node. The results show that the transmission probability of the relay node is a design parameter that is crucial to maximizing the achievable throughput of wireless network coding in slotted ALOHA on two-hop unbalanced traffic cases. Furthermore, we show that the throughput is enhanced even if the traffic at the relay node is unbalanced.     

Performance Analysis of Network Coding Based Two-Way Relay Wireless Networks Deploying IEEE 802.11

In this paper, we investigate the performance analysis of the IEEE 802.11 DCF protocol at the data link layer. We analyze the impact of network coding in saturated and non-saturated traffic conditions. The cross-layer analytical framework is presented in analyzing the performance of the encode-and-forward (EF) relaying wireless networks. This situation is employed at the physical layer under the conditions of non-saturated traffic and finite-length queue at the data link layer. First, a model of a two-hop EF relaying wireless channel is proposed as an equivalent extend multi-dimensional Markovian state transition model in queuing analysis. Then, the performance in terms of queuing delay, throughput and packet loss rate are derived. We provide closed-form expressions for the delay and throughput of two-hop unbalanced bidirectional traffic cases both with and without network coding. We consider the buffers on nodes are unsaturated. The analytical results are mainly derived by solving queuing systems for the buffer behavior at the relay node. To overcome the hidden node problem in multi hop wireless networks, we develop a useful mathematical model. Both models have been evaluated through simulations and simulation results show good agreement with the analytical results.     

Network-coding-based scheduling and routing schemes for service-oriented wireless mesh networks - [Service-oriented broadband wireless network architecture]

Service-oriented wireless mesh networks have recently been receiving intensive attention as a pivotal component to implement the concept of ubiquitous computing due to their easy and cost-effective deployment. To deliver a variety of services to subscriber stations, a large volume of traffic is exchanged via mesh routers in the mesh backbone network. One of the critical problems in service-oriented wireless mesh networks is to improve the network throughput. Wireless network coding is a key technology to improve network throughput in multihop wireless networks since it can exploit not only the broadcast nature of the wireless channel, but also the native physical-layer coding ability by mixing simultaneously arriving radio waves at relay nodes. We first analyze the throughput improvement obtained by wireless network coding schemes in wireless mesh networks. Then we develop a heuristic joint link scheduling, channel assignment, and routing algorithm that can improve the network throughput for service-oriented wireless mesh networks. Our extensive simulations show that wireless network coding schemes can improve network throughput by 34 percent.     

Multicast Capacity of Wireless Ad Hoc Networks

Assume that n wireless nodes are uniformly randomly deployed in a square region with side-length a and all nodes have the uniform transmission range r and uniform interference range R > r. We further assume that each wireless node can transmit (or receive) at W bits/second over a common wireless channel. For each node vi , we randomly and independently pick k-1 points pi,j (1 les j les k-1) from the square, and then multicast data to the nearest node for each pi,j. We derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. Under protocol interference model, when a ²/r ²=O(n/log(n)), we show that the total multicast capacity is Theta(radic{n/log n}middot(W/radick)) when k=O(n/log n); the total multicast capacity is Theta(W) when k=Omega(n/log n). We also study the capacity of group-multicast for wireless networks where for each source node, we randomly select k-1 groups of nodes as receivers and the nodes in each group are within a constant hops from the group leader. The same asymptotic upper bounds and lower bounds still hold. We also extend our capacity bounds to d -dimensional networks.     

Optimized multipath network coding in lossy wireless networks

Network coding has been a prominent approach to a series of problems that used to be considered intractable with traditional transmission paradigms. Recent work on network coding includes a substantial number of optimization based protocols, but mostly for wireline multicast networks. In this paper, we consider maximizing the benefits of network coding for unicast sessions in lossy wireless environments. We propose Optimized Multipath Network Coding (OMNC), a rate control protocol that dramatically improves the throughput of lossy wireless networks. OMNC employs multiple paths to push coded packets to the destination, and uses the broadcast MAC to deliver packets between neighboring nodes. The coding and broadcast rate is allocated to transmitters by a distributed optimization algorithm that maximizes the advantage of network coding while avoiding congestion. With extensive experiments on an emulation testbed, we find that OMNC achieves more than two-fold throughput increase on average compared to traditional best path routing, and significant improvement over existing multipath routing protocols with network coding. The performance improvement is notable not only for one unicast session, but also when multiple concurrent unicast sessions coexist in the network.     

Optimal Unicast Capacity of Random Geometric Graphs: Impact of Multipacket Transmission and Reception

We establish a tight max-flow min-cut theorem for multi-commodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-sparsity scale as θ(n²r³(n)/k), for a random choice of k = ω(n) source-destination pairs, where n and r(n) are the number of nodes and the communication range in the network respectively. The MCF equals the interference-free capacity of an ad-hoc network. We exploit this fact to develop novel graph theoretic techniques that can be used to deduce tight order bounds on the capacity of ad-hoc networks. We generalize all existing capacity results reported to date by showing that the per-commodity capacity of the network scales as θ(1/r(n)k) for the single-packet reception model suggested by Gupta and Kumar, and as θ(nr(n)/k) for the multiple-packet reception model suggested by others. More importantly, we show that, if the nodes in the network are capable of (perfect) multiple-packet transmission (MPT) and reception (MPR), then it is feasible to achieve the optimal scaling of θ(n²r³(n)/k), despite the presence of interference. In comparison to the Gupta-Kumar model, the realization of MPT and MPR may require the deployment of a large number of antennas at each node or bandwidth expansion. Nevertheless, in stark contrast to the existing literature, our analysis presents the possibility of actually increasing the capacity of ad-hoc networks with n even while the communication range tends to zero!     

On Joint MAC and Network Coding in Wireless Ad Hoc Networks

This paper addresses network coding in wireless networks in conjunction with medium access control (MAC). It is known that coding over wired networks enables connections with rates that cannot be achieved by routing. However, the properties of wireless networks (e.g., omnidirectional transmissions, destructive interference, single transceiver per node, finite energy) modify the formulation of time-varying network coding in a way that reflects strong interactions with underlying MAC protocols and deviates from the classical approach used in wired network coding. To perform network coding over conflict-free transmission schedules, predetermined network realizations are separately activated by a time-division mechanism and the content of network flows is derived through network coding to optimize performance measures such as achievable throughput and energy costs. A systematic method is presented to construct linear wireless network codes and interactions with MAC schedules are discussed under wireless assumptions. Network coding is also extended to operate with arbitrary (random or scheduled access based) MAC protocols. Alternatively, conflict-free transmission schedules are jointly constructed with network codes by decomposing wireless networks into subtrees and employing graph coloring on simplified subtree graphs. Finally, network coding and plain routing are compared in terms of throughput, energy and delay performance under different MAC solutions.     

Delay analysis in practical wireless network coding

Network coding provides a powerful mechanism for improving performance of wireless networks. In this paper, we present an analytical approach for end‐to‐end delay analysis in wireless networks that employs inter‐session network coding. Prior work on performance analysis in wireless network coding mainly focuses on the throughput of the overall network. Our approach aims to analyze the delay of each flow in the network. The theoretical basis of our approach is network calculus. In order to use network calculus to analyze the performance of traffic flows in the network, we have to address three specific problems: identifying traffic flows, characterizing broadcast links, and measuring coding opportunities. We propose solutions for these problems and discuss the practical issues when applying the approach in practice. We make three main contributions. First, we obtain theoretical formulations for computing the queueing delay bounds of traffic flows in wireless networks with network coding. Second, with the formulations, we figure out the factors that affect the queueing delay of a flow and find that first‐in first‐out scheduling cannot fully exploit the benefit of network coding. Third, in order to exploit our findings, we introduce a new scheduling scheme that can improve the performance of current practical wireless network coding. Copyright © 2012 John Wiley & Sons, Ltd.     

Broadcast capacity of wireless networks

We present an upper bound on the broadcast capacity of arbitrary ad hoc wireless networks. The throughput obtainable by each node for broadcasting to-all-of the other nodes in a network consisting of n nodes with- fixed transmission ranges and C bits per second channel capacity is bounded by O(C/n), which is equivalent to the upper bound for per node capacity of a fully connected single-hop network.     

On capacity of random wireless networks with physical-layer network coding

Throughput capacity of a random wireless network has been studied extensively in the literature. Most existing studies were based on the assumption that each transmission involves only one transmitter in order to avoid interference. However, recent studies on physical-layer network coding (PLNC) have shown that such an assumption can be relaxed to improve throughput performance of a wireless network. In PLNC, signals from different senders can be transmitted to the same receiver in the same channel simultaneously. In this paper, we investigate the impact of PLNC on throughput capacity of a random wireless network. Our study reveals that, although PLNC scheme does not change the scaling law, it can improve throughput capacity by a fixed factor. Specifically, for a one-dimensional network, we observe that PLNC can eliminate the effect of interference in some scenarios. A tighter capacity bound is derived for a two-dimensional network. In addition, we also show achievable lower bounds for random wireless networks with network coding and PLNC.     

基于流的无线网络编码

针对无线链路的不可靠性和物理层的广播特性,将网络编码与无线网络相结合,提出一种基于流的无线网络编码算法——FNC。该算法在先验参考路径的基础上,充分利用每个节点处的路由表项,探测编码机会,在有编码机会的节点对满足编码条件的数据流进行网络编码,达到提高网络吞吐量的目的。仿真结果表明：FNC有效提高了整个网络的吞吐量,改善了网络性能。     

A two‐way relay framework based on interference cancellation in wireless networks

The two‐way relay (TWR) protocols are efficient in providing appreciable throughput gains in wireless networks through the use of network coding to combine packets from multiple channels. The key determinant factor in driving the throughput improvement is the degree of simultaneity achieved in the relay scheme. In this paper, we propose a new TWR protocol named interference cancellation TWR (IC‐TWR), which combines network coding, spatial diversity, and IC techniques to arrive at high degree of simultaneity and in the meanwhile to relax the requirement on channel state information as compared with TWR schemes based on amplify‐and‐forward. Numerical analysis shows that the proposed IC‐TWR is uniformly advantageous over the traditional decode‐and‐forward scheme in terms of system throughput and end‐to‐end delay. The proposed scheme may be useful for system designers of high‐speed multimedia applications in wireless mobile networks, wireless cellular networks, wireless sensor networks, and so on. Copyright © 2015 John Wiley & Sons, Ltd.