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The capacity of wireless networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2000
"... When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally p ..."
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Cited by 2203 (31 self)
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When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission’s range is optimally chosen, the bit–distance product that can be transported by the network per second is 2 @ A bitmeters per second. Thus even under optimal circumstances, the throughput is only 2 bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signaltointerference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.
Joint Scheduling and Power Control for Wireless Adhoc Networks
, 2002
"... In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmi ..."
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Cited by 186 (5 self)
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In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmissions whes node are rej tose information packe  tothe re e e re e sub jej to a constraint on the signaltointealtoinjj ratio.The multiple acce  proble is solve via twoaltej phase name schej and powe r control.The sche algorithm isej tial to coordinate the transmissions ofinde ede t use inorde toejj strong intej (e.g selfinterference) that can not be ove by powe r control. On the othe hand, powe r control isej in adistribute fashion to dej the admissible powe r ve ifone ene that can be use bythe sche use to satisfy thei singlej transmissionrensmissi ts. This isdone for two type s ofne works, namej TDMA and TDMA/CDMA wire/CD adhocne works.
On the complexity of computing minimum energy consumption broadcast subgraphs
 in Symposium on Theoretical Aspects of Computer Science
, 2001
"... Abstract. We consider the problem of computing an optimal range assignment in a wireless network which allows a specified source station to perform a broadcast operation. In particular, we consider this problem as a special case of the following more general combinatorial optimization problem, calle ..."
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Cited by 96 (11 self)
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Abstract. We consider the problem of computing an optimal range assignment in a wireless network which allows a specified source station to perform a broadcast operation. In particular, we consider this problem as a special case of the following more general combinatorial optimization problem, called Minimum Energy Consumption Broadcast Subgraph (in short, MECBS): Given a weighted directed graph and a specified source node, find a minimum cost range assignment to the nodes, whose corresponding transmission graph contains a spanning tree rooted at the source node. We first prove that MECBS is not approximable within a constant factor (unless P=NP). We then consider the restriction of MECBS to wireless networks and we prove several positive and negative results, depending on the geometric space dimension and on the distancepower gradient. The main result is a polynomialtime approximation algorithm for the NPhard case in which both the dimension and the gradient are equal to 2: This algorithm can be generalized to the case in which the gradient is greater than or equal to the dimension. 1
Critical Power for Asymptotic Connectivity
, 1998
"... In wireless data networks the range of each transmitter, and thus its power level, needs to be high enough to reach the intended receivers, while being low enough to avoid generating interference for other receivers on the same channel. If the nodes in the network are assumed to cooperate, perhaps i ..."
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Cited by 95 (0 self)
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In wireless data networks the range of each transmitter, and thus its power level, needs to be high enough to reach the intended receivers, while being low enough to avoid generating interference for other receivers on the same channel. If the nodes in the network are assumed to cooperate, perhaps in a distributed and decentralized fashion, in routing each others' packets, as is the case in ad hoc wireless networks, ([5]), and [7]), then each node should transmit with just enough power to guarantee connectivity of the overall network. Towards this end, we determine the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to innity. Our main result is this: If n nodes are located randomly, uniformly i.i.d., in a disc of unit area in < 2 and each node transmits at a power level so as to cover an area of r 2 = (log n + c(n))=n, then the resulting network is asymptotical...
Power Control and Capacity of Spread Spectrum Wireless Networks
 Automatica
, 1999
"... Transmit power control is a central technique for resource allocation and interference management in spreadspectrum wireless networks. With the increasing popularity of spreadspectrum as a multiple access technique, there has been significant research in the area in recent years. While power contr ..."
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Cited by 55 (5 self)
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Transmit power control is a central technique for resource allocation and interference management in spreadspectrum wireless networks. With the increasing popularity of spreadspectrum as a multiple access technique, there has been significant research in the area in recent years. While power control has been considered traditionally as a means to counteract the harmful effect of channel fading, the more general emerging view is that it is a flexible mechanism to provide QualityofService to individual users. In this paper, we will review the main threads of ideas and results in the recent development of this area, with a bias towards issues that have been the focus of our own research. For different receivers of varying complexity, we study both questions about optimal power control as well as the problem of characterizing the resulting network capacity. Although spreadspectrum communications has been traditionally viewed as a physicallayer subject, we argue that by suitable abstr...
A Framework for Crosslayer Design of EnergyEfficient Communication With . . .
, 2004
"... Efficient use of energy while providing an adequate level of connection to individual sessions is of paramount importance in multihop wireless networks. Energy efficiency and connection quality depend on mechanisms that span several communication layers due to the existing cochannel interference a ..."
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Cited by 54 (0 self)
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Efficient use of energy while providing an adequate level of connection to individual sessions is of paramount importance in multihop wireless networks. Energy efficiency and connection quality depend on mechanisms that span several communication layers due to the existing cochannel interference among competing flows that must reuse the limited radio spectrum. Although independent consideration of these layers simplifies the system design, it is often insufficient for wireless networks when the overall system performance is examined carefully. The multihop wireless extensions and the need for routing users' sessions from source to the destination only intensify this point of view. In this work, we present a framework for crosslayer design towards energyefficient communication. Our approach is characterized by a synergy between the physical and the medium access control (MAC) layers with a view towards inclusion of higher layers as well. More specifically, we address the joint problem of power control and scheduling with the objective of minimizing the total transmit power subject to the endtoend quality of service (QoS) guarantees for sessions in terms of their bandwidth and bit error rate guarantees. Bearing to the NPhardness of this combinatorial optimization problem, we propose our heuristic solutions that follow greedy approaches.
Wireless systems and interference avoidance
 IEEE Trans. Wireless Commun
, 2002
"... Abstract—Motivated by the emergence of programmable radios, we seek to understand a new class of communication system where pairs of transmitters and receivers can adapt their modulation/demodulation method in the presence of interference to achieve better performance. Using signal to interference r ..."
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Cited by 52 (12 self)
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Abstract—Motivated by the emergence of programmable radios, we seek to understand a new class of communication system where pairs of transmitters and receivers can adapt their modulation/demodulation method in the presence of interference to achieve better performance. Using signal to interference ratio as a metric and a general signal space approach, we present a class of iterative distributed algorithms for synchronous systems which results in an ensemble of optimal waveforms for multiple users connected to a common receiver (or colocated independent receivers). That is, the waveform ensemble meets the Welch Bound with equality and, therefore, achieves minimum average interference over the ensemble of signature waveforms. We derive fixed points for a number of scenarios, provide examples, look briefly at ensemble stability under user addition and deletion as well as provide a simplistic comparison to synchronous codedivision multipleaccess. We close with suggestions for future work. Index Terms—Adaptive modulation, codedivision multipleaccess systems, codeword optimization, interference avoidance, multiuser
On the Power Assignment Problem in Radio Networks
 Electronic Colloquium on Computational Complexity (ECCC
, 2000
"... Given a finite set S of points (i.e. the stations of a radio network) on a ddimensional Euclidean space and a positive integer 1 h jSj \Gamma 1, the Min dd hRange Assignment problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided th ..."
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Cited by 50 (3 self)
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Given a finite set S of points (i.e. the stations of a radio network) on a ddimensional Euclidean space and a positive integer 1 h jSj \Gamma 1, the Min dd hRange Assignment problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication beween any pair of stations in at most h hops. Two main issues related to this problem are considered in this paper: the tradeoff between the power consumption and the number of hops; the computational complexity of the Min dd hRange Assignment problem. As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of jSj, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of jSj, h and the maximum distance over all pairs of stations in S (i.e. the d...
Output MAI Distributions of Linear MMSE Multiuser Receivers in DSCDMA Systems
 IEEE TRANS. INFORM. THEORY
, 2001
"... Multipleaccess interference (MAI) in a codedivision multipleaccess (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. In this paper, we study the behavior of the output MAI of the minimum meansquare error (MMSE) receiver employed in t ..."
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Cited by 48 (8 self)
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Multipleaccess interference (MAI) in a codedivision multipleaccess (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. In this paper, we study the behavior of the output MAI of the minimum meansquare error (MMSE) receiver employed in the uplink of a directsequence (DS)CDMA system. We focus on imperfect powercontrolled systems with random spreading, and establish that in a synchronous system 1) the output MAI of the MMSE receiver is asymptotically Gaussian, and 2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of singleuser Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signaltointerference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system.
Efficient Communication Strategies for AdHoc Wireless Networks
, 2000
"... An adhoc wireless network is a collection of wireless mobile hosts forming a temporary network without the aid of any established infrastructure or centralized administration. This type of network is of great importance in situations where it is very difficult to provide the necessary infrastructur ..."
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Cited by 34 (3 self)
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An adhoc wireless network is a collection of wireless mobile hosts forming a temporary network without the aid of any established infrastructure or centralized administration. This type of network is of great importance in situations where it is very difficult to provide the necessary infrastructure, but it is a challenging task to enable fast and reliable communication within such a network. In this paper, we model and analyze the performance of socalled powercontrolled adhoc wireless networks: networks where the mobile hosts are able to change their transmission power. We concentrate on finding schemes for routing arbitrary permutations in these networks. In general, it is NPhard even to find a n 1 approximation for any constant to the fastest possible strategy for routing a given permutation problem on n mobile hosts. However, we here demonstrate that if we allow ourselves to consider slightly less general problems, efficient solutions can be found. We first demonstrate that there is a natural class of distributed schemes for handling nodetonode communication on top of which online route selection and scheduling strategies can be constructed such that the performance of this class of schemes can be exploited in a nearly optimal way for routing permutations in any static powercontrolled adhoc network. We then demonstrate