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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 3243 (42 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 283 (6 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.
Critical power for asymptotic connectivity. In
 Proc. of 37th IEEE Conf. on Decision and Control”,
, 1998
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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 110 (13 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
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 77 (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...
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 77 (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
Power Control in TwoTier Femtocell Networks
, 2008
"... Two tier cellular networks, comprising of a central macrocell underlaid with short range femtocell hotspots offer an economical way to improve cellular capacity. With shared spectrum and lack of coordination between tiers, crosstier interference limits overall capacity. To quantify nearfar effects ..."
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Cited by 74 (6 self)
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Two tier cellular networks, comprising of a central macrocell underlaid with short range femtocell hotspots offer an economical way to improve cellular capacity. With shared spectrum and lack of coordination between tiers, crosstier interference limits overall capacity. To quantify nearfar effects with universal frequency reuse, this paper derives a fundamental relation providing the largest feasible macrocell SignaltoInterferencePlusNoise Ratio (SINR), given any set of feasible femtocell SINRs. A distributed utilitybased SINR adaptation at femtocells is proposed in order to alleviate crosstier interference at the macrocell from overlaid femtocell infrastructure. The FoschiniMiljanic (FM) algorithm is a special case of the adaptation. Each femtocell maximizes its individual utility consisting of a SINR based reward less an incurred cost (interference to the macrocell). Numerical results show greater than 30 % improvement in mean femtocell SINRs relative to FM. In the event that crosstier interference prevents a macrouser from obtaining its SINR target, an algorithm is proposed that adaptively curtails transmission powers of the strongest femtocell interferers. The algorithm ensures that a macrouser achieves its SINR target even with 100 femtocells/cellsite, and requires a worst case SINR reduction of only 16 % at femtocells. These results motivate design of power control schemes requiring minimal network overhead in twotier networks with shared spectrum.
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 72 (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.
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 66 (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.
On the Power Assignment Problem in Radio Networks
, 2004
"... A 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 � S−1, the MIN d D hRANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided t ..."
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Cited by 63 (4 self)
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A 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 � S−1, the MIN d D 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 between 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 d D 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 S, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of S, h and the maximum distance over all pairs of stations in S (i.e. the diameter of S). It turns out that when the minimum distance between any two stations is “not too small ” (i.e. well spread instances) the upper bound matches the lower bound. Previous results for this problem were known only for very special 1dimensional configurations (i.e., when points are arranged on a line at unitary distance) [Kirousis, Kranakis, Krizanc and Pelc, 1997]. As for the second question, we observe that the tightness of our upper bound implies that MIN 2D hRANGE ASSIGNMENT restricted to well spread instances admits a polynomial time approximation algorithm. Then, we also show that the same approximation result can be obtained for random instances. On the other hand, we prove that for h =S−1 (i.e. the unbounded case) MIN 2D hRANGE ASSIGNMENT