In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., n nodes are placed uniformly at random in a square region of area n). They showed that for small path-loss exponents alpha isin (2,3], cooperative communication is order optimal, and for large path-loss exponents alpha > 3, multihop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents alpha isin (2,3], we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for alpha isin (2,3]. The situation is, however, markedly different for large path-loss exponents alpha > 3. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly ldquointerpolaterdquo between multihop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for alpha > 3.
Since @cite_1 , the problem has received a considerable amount of attention. One stream of work @cite_13 @cite_7 @cite_12 @cite_5 @cite_3 @cite_9 @cite_11 has progressively broadened the conditions on the channel model and the communication model, under which multi-hop communication is order optimal. Specifically, with a power loss of @math for signals sent over distance @math , it has been established that under signal attenuation @math and random node placement, the best achievable per-node rate @math for random source-destination pairing scales essentially like @math and that this scaling is achievable with multi-hop communication.
@cite_7 @cite_9 @cite_1 @cite_3 @cite_5 @cite_13 @cite_12 @cite_11
2114106914 2116844604 2020650131 2171882038 2124107362 2013180246 2168582397 2114927595
We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability. In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., n nodes are placed uniformly at random in a square region of area n). They showed that for small path-loss exponents alpha isin (2,3], cooperative communication is order optimal, and for large path-loss exponents alpha > 3, multihop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents alpha isin (2,3], we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for alpha isin (2,3]. The situation is, however, markedly different for large path-loss exponents alpha > 3. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly ldquointerpolaterdquo between multihop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for alpha > 3. The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for power-limited and bandwidth-limited communication regimes. We regard channel state information (CSI) at the receiver and point-to-point capacity-achieving codes for the additive white Gaussian noise (AWGN) channel as practical features, interference cancellation (IC) as possible, but less practical, and synchronous cooperation (CSI at the transmitters) as impractical. We consider a communication network with a single source node, a single destination node, and N-1 intermediate nodes placed equidistantly on a line between them. We analyze the minimum total transmit power needed to achieve a desired end-to-end rate for several schemes and demonstrate that multihop communication with spatial reuse performs very well in the power-limited regime, even without IC. However, within a class of schemes not performing IC, single-hop transmission (directly from source to destination) is more suitable for the bandwidth-limited regime, especially when higher spectral efficiencies are required. At such higher spectral efficiencies, the gap between single-hop and multihop can be closed by employing IC, and we present a scheme based upon backward decoding that can remove all interference from the multihop system with an arbitrarily small rate loss. This new scheme is also used to demonstrate that rates of O(log N) are achievable over linear wireless networks even without synchronous cooperation. The authors obtain the optimum transmission ranges to maximize throughput for a direct-sequence spread-spectrum multihop packet radio network. In the analysis, they model the network self-interference as a random variable which is equal to the sum of the interference power of all other terminals plus background noise. The model is applicable to other spread-spectrum schemes where the interference of one user appears as a noise source with constant power spectral density to the other users. The network terminals are modeled as a random Poisson field of interference power emitters. The statistics of the interference power at a receiving terminal are obtained and shown to be the stable distributions of a parameter that is dependent on the propagation power loss law. The optimum transmission range in such a network is of the form CK sup alpha where C is a constant, K is a function of the processing gain, the background noise power spectral density, and the degree of error-correction coding used, and alpha is related to the power loss law. The results obtained can be used in heuristics to determine optimum routing strategies in multihop networks. > We consider a frequency-flat fading multihop network with a single active source-destination pair terminals communicating over multiple hops through a set of intermediate relay terminals. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) for a simple communication protocol based on time-division decode-and-forward relaying in meaningful asymptotic regimes of signal-to-noise ratio (SNR) under a system-wide power constraint on source and relay transmissions. The impact of multi-hopping and channel fading on the key performance measures of the high and low SNR regimes is investigated to shed new light on the possible enhancements in power bandwidth efficiency and link reliability. In contrast to the common belief that in fading environments communicating over multiple hops suffers significantly in performance due to the worst link limitation, our results indicate that hopping could significantly improve the outage behavior over slow-fading networks and stabilize links against the random channel fluctuations. In particular, we prove that there exists an optimal number of hops that minimizes the end-to-end outage probability and characterize the dependence of this optimal number on the fading statistics and target energy and spectral efficiencies. In multi-hop ad hoc networks, stations may pump more traffic into the networks than can be supported, resulting in high packet-loss rate, re-routing instability and unfairness problems. This paper shows that controlling the offered load at the sources can eliminate these problems. To verify the simulation results, we set up a real 6-node multi-hop network. The experimental measurements confirm the existence of the optimal offered load. In addition, we provide an analysis to estimate the optimal offered load that maximizes the throughput of a multi-hop traffic flow. We believe this is a first paper in the literature to provide a quantitative analysis (as opposed to simulation) for the impact of hidden nodes and signal capture on sustainable throughput. The analysis is based on the observation that a large-scale 802.11 network with hidden nodes is a network in which the carrier-sensing capability breaks down partially. Its performance is therefore somewhere between that of a carrier-sensing network and that of an Aloha network. Indeed, our analytical closed-form solution has the appearance of the throughput equation of the Aloha network. Our approach allows one to identify whether the performance of an 802.11 network is hidden-node limited or spatial-reuse limited. Multichannel communication in a wireless mesh network with routers having multiple radio interfaces significantly enhances the network capacity. Efficient channel assignment and routing is critical for realization of optimal throughput in such networks. In this paper, we investigate the problem of finding the largest number of links that can be activated simultaneously in a wireless mesh network subject to interference, radio and connectivity constraints. Our goal is to activate all such links and we present an interference aware channel assignment algorithm that realizes this goal. We show that the Link Interference Graph created by utilizing a frequently used interference model gives rise to a special class of graphs, known as overlapping double-disk (ODD) graphs. We prove that the Maximum Independent Set computation problem is NP-complete for this special class of graphs. We provide a Polynomial Time Approximation Scheme (PTAS) for computation of the Maximum Independent Set of an ODD graph. We use this PTAS to develop a channel assignment algorithm for a multiradio multichannel Wireless Mesh Network. We evaluate the performance of our channel assignment algorithm by comparing it with the optimal solution obtained by solving an integer linear program. Experimental results demonstrate that our channel assignment algorithm produces near optimal solution in almost all instances of the problem. We consider networks consisting of nodes with radios, and without any wired infrastructure, thus necessitating all communication to take place only over the shared wireless medium. The main focus of this paper is on the effect of fading in such wireless networks. We examine the attenuation regime where either the medium is absorptive, a situation which generally prevails, or the path loss exponent is greater than 3. We study the transport capacity, defined as the supremum over the set of feasible rate vectors of the distance weighted sum of rates. We consider two assumption sets. Under the first assumption set, which essentially requires only a mild time average type of bound on the fading process, we show that the transport capacity can grow no faster than O(n), where n denotes the number of nodes, even when the channel state information (CSI) is available noncausally at both the transmitters and the receivers. This assumption includes common models of stationary ergodic channels; constant, frequency-selective channels; flat, rapidly varying channels; and flat slowly varying channels. In the second assumption set, which essentially features an independence, time average of expectation, and nonzeroness condition on the fading process, we constructively show how to achieve transport capacity of spl Omega (n) even when the CSI is unknown to both the transmitters and the receivers, provided that every node has an appropriately nearby node. This assumption set includes common models of independent and identically distributed (i.i.d.) channels; constant, flat channels; and constant, frequency-selective channels. The transport capacity is achieved by nodes communicating only with neighbors, and using only point-to-point coding. The thrust of these results is that the multihop strategy, toward which much protocol development activity is currently targeted, is appropriate for fading environments. The low attenuation regime is open.