Power-conserving centralized organization of ad hoc wireless networks

sThis work was presented in part at the IEEE International Performance, Computing and Communications Conference,Scottsdale, AZ, U.S.A., 10}12 February 1999.

*Correspondence to: Paul G. Flikkema, Department of Electrical Engineering, Northern Arizona University, P.O. Box15600, Flagsta!, AZ 86011-5600, U.S.A. E-mail: paul.#[email protected]

CCC 1074}5351/99/060439}13$17.50 Received 19 February 1999Copyright ( 1999 John Wiley & Sons, Ltd. Accepted 30 May 1999

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS

Int. J. Commun. Syst. 12, 439}451 (1999)

Power-conserving centralized organization of ad hocwireless networkss

Mehul Shah1 and Paul G. Flikkema2*1Department of Electrical Engineering, University of South Florida, Tampa, FL 33620-5350, U.S.A.

2Department of Electrical Engineering, Northern Arizona University, Flagstaw, AZ 86011-5600, U.S.A.

SUMMARY

This paper presents a physical layer-based framework for the organization of ad hoc wireless networks. Thefocus is quasi-static environments, such as multimedia classrooms, and situations characterized by real-timeservices and high tra$c loads. In these cases, centralized control and a star-connected topology may bepreferable due to its simplicity and high e$ciency. Using a link loss matrix, an approach is developed forselection of a network leader that takes into consideration link losses and transmitter powers. Both minimaxand minisum criteria are established, and a number of conditions are established for determining uplink,downlink, Bayesian and universal leaders. A QoS-based iterative algorithm for determination of linktransmit powers is also proposed, a special case of which provides the link loss matrix for leader selection.The algorithm also provides the information required to determine a set of candidate leaders, whosemembers can assume leadership without interruption or degradation of network operation. Copyright( 1999 John Wiley & Sons, Ltd.

KEYWORDS: wireless networks; ad hoc; network organization; power-conserving

1. Introduction

Much research in wireless networks has focused on cases where an infrastructure of base stationssupports a set of mobile users, as in cellular systems. However there are numerous applications inwhich such infrastructure is either infeasible or undesirable. For example, emergency reliefoperations often must be carried out where a "xed station does not exist. Also, a group of peoplemight autonomously form an &instant' and temporary multimedia network using notebookcomputers or personal digital assistants. In these cases, the nodes organize themselves into anad hoc network without resort to any existing infrastructure.

It is often necessary that the organization process be initiated by a particular node, often calleda starter or leader node, which may then assume control of network operation. Thus selection ofsuch a node assumes paramount importance. Many leader selection algorithms assume that thenodes have a unique ID number, and the node with the highest ID number is elected as the leader.However, when a leader is selected in such an arbitrary fashion, its capability to coordinate

network operation is not considered. For example, due to highly variable link losses, the nodewith the highest ID number may not be capable of serving the other nodes in the network withhigh e$ciency. In this paper we propose a selection procedure that is related to the nodes'capabilities to serve others in the network. The goal is to determine which node is in some sensean optimum choice for the network leader, who can then assume management of the network.

Another approach is to use distributed algorithms where the nodes compute the routinginformation for themselves. These methods feature robustness to failures, but distributed topolo-gies can su!er from ine$ciencies due to lack of global information. The centralized approach hascertain advantages over distributed techniques. First, is simplicity: the leader has all the connec-tivity information and can easily implement routing and #ow control algorithms. Second, itadmits reservation-based media access schemes which are more e$cient than random accessmethods when tra$c loads are high. This is especially important in multimedia and real-timenetworks, where guaranteed QoS levels are required. Finally, this work is oriented towardsquasi-static applications such as multimedia classrooms or meetings. In such scenarios, frequentre-organization is not required. Note that all tra$c need not go through the leader node; itcontrols the network, but can set up routing to include densely-connected as well as star-connected topologies. On the other hand, careful selection of the hub in star-connected (two-hop)networks can maximize the range extension advantage over peer-to-peer connectivity. Tradition-ally, centralized topologies are subject to single point failures. In this paper, the leader selectionalgorithm is generalized to include a set of candidate nodes which can take over control in theevent of failure of the leader.

This paper is organized as follows. Section 2 discusses related work in the areas of selforganizing networks, leader selection and power sensitive network architectures. Followingintroduction of some preliminaries in Section 3, leader selection using the minimax and minisumcriteria is presented in Section 4. Conditions for Bayesian and universal optimum leadership forboth minisum and minimax measures are explored in Section 5. Section 6 describes a QoS-basediterative algorithm which leads to power-based leader selection as a special case. In Section 7simulation results for the iterative algorithm are presented, and the paper concludes withSection 8.

2. Related work

One of the "rst approaches to organization of non-infrastructured wireless networks was thelinked cluster algorithm (LCA),1 where the network is organized into a set of node clusters, witheach node belonging to at least one cluster. Every cluster has its own clusterhead which isa controller for the cluster. The clusterheads are linked via gateways if necessary. The algorithmhas two stages: "rst, the formation of the clusters and second, the linking of the clusters. Toaccount for changes in connectivity, the LCA periodically re-executes the clustering algorithm.

The distributed evolutionary algorithm (DEA)2 manages the network topology using the LCA.The DEA schedules TDMA transmissions by organizing the network in layers from a starternode and using a common algorithm to schedule links once the topology is known. In the DEA,the LCA is used to allow each node to determine its neighbors. Once the connectivity informationhas been exchanged, a starter node directs all of its nodes to begin communicating. This starternode and its 1-hop neighbors form the "rst subnetwork to begin communicating.

The layer net algorithm3 commences operation in an asynchronous mode of operation andgradually switches over to a synchronous mode. A starter node initiates the formation of

440 M. SHAH AND P. G. FLIKKEMA

Copyright ( 1999 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 12, 439}451 (1999)

a connectivity tree and coordinates other network organization tasks until the network startsfunctioning in a scheduled manner.

All these algorithms depend on the selection of a starter node to initiate the algorithm.A serious drawback for centralized organizations is that the choice of the starter node is arbitraryfrom the point of network performance. Given that link performance in wireless networks canvary dramatically, poor selection of the starter node can potentially compromise networkcapacity. In addition, there is no provision for the network to continue its operation in the eventthat the starter node fails due to some reason.

Our goal is to develop schemes for selection of the network leader. The nature of the problem isvery similar to the facilities location problem in operations research.4,5 Distance is often used asthe criterion, and thus variations on the centroid or center of mass are employed. However, in ourcase, the nodes are already located and the objective is to choose one to be the leader.

A leader selection algorithm based on the communication delay between nodes was proposedby Singh and Kurose.6 The system performance of a node j is de"ned to be the sum of shortestpaths between nodes i and j for all i. Then the optimal leader is de"ned as the node with thesmallest performance. Though not identi"ed as such, Singh and Kurose's de"nition of optimalityimplicitly employs a vector 1-norm of the columns of a matrix. In this paper, we consider both theone norm (i.e. minisum criterion) and the in"nity norm (i.e. minimax criterion) and apply these tolink losses, rather than delays. Another approach is the preference-based method,6 where thenodes exchange votes representing their preference, and the node with the most votes is declaredthe leader.

For the case of indoor wireless networks, optimization of base station placement and downlinkpower levels is addressed in Reference 7. Sherali et al.8 seek an optimal set of transmitters to servea speci"ed distribution of receivers via an objective function of the path losses. A weightedcombination of minisum and minimax criteria are considered for the optimization of thedownlinks from the base stations. The present work is distinguished from Reference 8 in that weare constrained by the fact that the leader must be selected from the existing set of nodes. Inaddition, we address both uplinks and downlinks, and "nd the overall optimum leader.

Bambos and others (Reference 9 and the references therein) have explored adaptive distributedpower control and minimum power routing. The central theme is to minimize transmitted powerat the various mobile nodes while maintaining a required signal-to-interference ratio (SIR)threshold for each link. Use is made of a gain matrix G, with element g

ijthe power gain from the

transmitter of the ith link to the receiver of the jth link. Our approach uses a similar matrix tocharacterize the link performances. We also consider the minimization of the transmitted powerat each node as a performance measure in order to select the most power-e$cient node as theleader.

3. Preliminaries

A wireless network can be represented as a graph G"MN, EN consisting of a set of nodesN"M1, 2, 2, NN (i.e., with cardinality N) and a set of links or edges E"M(i, j) : i, j3NN. We saythat node i is connected with node j if there exists a link between the two nodes. To account for thegenerally non-reciprocal nature of wireless channels, we model an ad hoc network as a directedgraph, where edges represent direction of #ow, i.e. one-way connectivity.

To characterize the channels between nodes based on link losses, we associate the graph G withmatrix L whose element l

ijis the link loss between nodes i and j, with l

ii"0. A simple model for

AD HOC WIRELESS NETWORKS 441


the link loss uses an exponential path loss with Rayleigh fading

lij"10n log

10Adij

d0B#10 log

10(c) dB, (1)

where dij

is the distance between nodes i and j, d0

is a reference distance, n is the path lossexponent, and c is a Rayleigh fading factor. The ith row of L is the set of downlink (transmit)losses for node i and the jth column is the set of uplink (receive) losses for node j. An equivalentrepresentation is the gain matrix G with elements g

ij"1/l

ij.

4. Leader selection

In the ad hoc networking scenario, a cost is incurred by the network in terms of path loss, BER,data rate constraints, or other parameters that are inherent to the wireless channel. The objectiveis to select the optimum leader from the set of nodes according to some combination of criteria. Inthis paper we focus on link loss as the cost, which in turn can be related to power consumption.

We make the following assumptions in our framework:

1. All the nodes are distinguishable, e.g. each has a unique ID number known to the others.2. The multiple access protocol between the nodes can be TDMA, FDMA or CDMA. All that

is required is orthogonality between dimensions. In practice, this can be perfectly achievedfor TDMA, and is a reasonable approximation for FDMA and CDMA.

3. All the nodes are assumed to be identical, that is, certain nodes do not have additionalcapabilities.

4. The network is completely connected in that a link of at least housekeeping capability canbe established between any pair of nodes.

4.1. Minisum criterion

One possible objective is to "nd the leader so that the power loss averaged over all links isminimized over all (N) potential star topologies. The smallest row sum of the loss matrix L willyield the node which has the smallest total link loss to all the other nodes in the network, while thesmallest column sum will give us the node which has the smallest total link loss from the othernodes in the network.

Speci"cally, let li:, l: j

, respectively, signify row i and column j of the loss matrix L. Thenthe downlink leader is determined by "nding the row in the loss matrix that has the smallestrow sum. Similarly, the uplink leader is determined by "nding the column with smallest columnsum. Thus denote the 1-norm of the vector x as ExE

1. Then node h

Dis the minisum downlink

leader if

hD"arg min

i

Eli:E1

and node hU

is the minisum uplink leader if

hU"arg min

j

El : jE1.



A su$cient condition for agreement, i.e. hD"h

U, is that L"LT. However, the loss matrix is

symmetric with probability zero since wireless channels are generally not reciprocal.The above optimizations can be combined to obtain the overall a-minisum leader

hMS

(a)"arg mini

MaEli :E1#(1!a)El : i

E1N.

Hence a is a mixture parameter placing relative weights on the downlink and uplink losses, andthe minisum downlink and uplink leaders are h

MS(1) and h

MS(0), respectively.

There are several other options. The choice can be based on whether prior knowledge isavailable indicating whether uplink or downlink tra$c is more prevalent (e.g. when a multimediabroadcast will occur). On the other hand, equal tra$c demands may be expected a priori. In thiscase, it may be preferable to choose the overall leader for which the average of the total uplinkand downlink losses is smallest, i.e., h

MS(0.5). Or it may be desirable to choose as overall leader the

node for which the loss disparity

KN+i/1

lhi!

N+j/1

ljh K, h3Mh

D, h

UN

or magnitude of the di!erence between the uplink and downlink losses, is smaller.The minisum criterion takes into consideration all the nodes in the network and o!ers

a reasonable overall choice. However, it may result in the selection of a leader that will not o!ersu$cient quality of service to remotely placed nodes.

4.2. Minimax criterion

As indicated above, if there exists a link which has a high link loss, it will tend to be excluded bythe minisum criterion,8 causing a large variance in required power levels. In contrast to theminisum approach, here we are concerned with "nding the leader whose worst-case link has theleast loss.

Let the concatenation of two row vectors x and y be denoted [x y]. Then the vector[al

i:(1!a)lT:i

] has as its elements all uplink and downlink losses for node i, with weighting factorsa and 1!a, respectively. Also, let ExE

=be the in"nity norm of x. Then the overall a-minimax

leader is

hMM

(a)"argmini

ME[ali :

(1!a) lT: i]E

=N.

The corresponding minimax downlink leader is

hMM

(1)"argmini

Eli :E=,

and the minimax uplink minimax leader is

hMM

(0)"arg minj

El : jE=

.



Figure 1. Example of weighted losses for links to/from node i, i"(1,2, 5) as a function of a for the minisum criterion

Consider the following example: Let the loss matrix L of an ad hoc network consisting of5 nodes be given by

L"

0 5)4 7)0 16)6 12)55)3 0 10)4 20)6 14)56)0 9)7 0 15)6 7)3

15)6 17)3 15)5 0 11)112)3 15)2 7)4 12)6 0

(2)

From Figures 1 and 2, we observe that hMS

(0)5)"3 and hMM

(0)5)"5.

5. Optimum leadership

In general, the mixture parameter a may be considered to be unknown and random, withprobability density having support on [0, 1]. The average downlink/uplink weighted average costfor node i can be represented as

C(i)k"P p

i(a)L(i)

k(a) da, (3)



Figure 2. Example of weighted losses for links to/from node i, i"(1,2, 5) as a function of a for the minimax criterion

where pi()) is the probability density function of a for node i, and where

L(i)1(a)"aEl

i :E1#(1!a)El:i

E1, (4)

L(i)=(a)"E[al

i:(1!a) lT: i

]E=

. (5)

The case where a is a known constant a0, so that p

i(a)"d (a!a

0), leads to C(i)

k"L(i)

k(a

0). It may

be be di$cult or undesirable to estimate a priori the value or distribution of a; in this case we cantake a Bayesian approach and assume that a is uniform on [0, 1]. Then from the de"nition of (3)for the minisum criterion we have

C(i)1"P

1

0

pi(a)[aEl

i:E1#(1!a)El: i

E1] da

"L(i)1 A

1

2B . (6)

Hence, the Bayesian minisum leader is

ıL"argmini

L(i)1 A

1

2 B. (7)

The Bayesian minimax leader can be found using the two easily computed loss measures L(i)=(0)

and L(i)=(1) as follows. First, notice that

L(i)=(a)"maxGa max

j

lij, (1!a) max

j

ljiH"maxMal

im3, (1!a)l

m#iN, (8)



where lim3

and lm#i

are the largest elements of row i and column i of L, respectively. Thus, L(i)=

(a) isthe maximum of two linear functions of a, as illustrated by the example in Figure 2. Thus theminimax loss averaged over all tra$c mixtures for node i can be found via calculus as

C(i)="

[L(i)=(0)]2#L(i)

=(0)L(i)

=(1)#[L(i)

=(1)]2

L(i)=

(0)#L(i)=(1)

(9)

The Bayesian minimax leader is therefore

ıL"arg mini

C(i)=. (10)

Of great interest is "nding the node that is universally the most e$cient leader, i.e. for allpossible uplink and downlink tra$c mixtures.

De,nition. Node ıL is the universally most e.cient (UME) minisum leader if

ıL"hMS

(a) ∀a, 0)a)1 (11)

By the linearity of the cost as a function of a, we have the following result: Node ıL is the UMEminisum leader i! h

MS(0)"h

MS(1)"ıL . Recalling the example loss matrix of (2), we observe from

Figure 1 that hMS

(0)"1 and hMS

(1)"3. Thus in this case there is no UME minisum leader.For the minimax case, we can establish the following:

De,nition. Node ıL is the UME minimaxleader if

ıL"hMM

(a) ∀a, 0)a)1. (12)

As for the Bayesian case, the UME minimax leader can be found using L(i)=(0) and L(i)

=(1).

Recalling (8), and letting

ıL3"arg min

i

lim 3

(13)

ıL#"arg min

i

lm# i

(14)

it follows that if ıL3"ıL

c$%&"ıL , then for all a3[0, 1],

L(ıL )

=(a))L(i)

=(a), i3N, (15)

which proves that node ıL is the UME minimaxleader. However, ıL3"h

MM(0) and ıL

#"h

MM(1) so

ıL"hMM

(0)"hMM

(1). (16)

It is also clear that if hMM

(0)OhMM

(1), then the UME minimax leader does not exist. Thus node ıL isthe UME minimax leader i! it is both the minimax downlink leader and the minimax uplinkleader. This is illustrated in the example, where node 5 is clearly the downlink, uplink, and UMEminimax leader (see Figure 2).



6. Iterative QoS-based selection

In this section we describe an iterative algorithm that allows QoS-based determination of thetransmitted link powers. The algorithm does not require knowledge of absolute transmittedpower levels, and is therefore useful for many situations where the application is not aware ofphysical-layer conditions. In addition, it will be demonstrated that an iterative algorithm todetermine the minisum and minimax leaders is a special case of the general algorithm.

The objective of the algorithm is to determine each node's required transmitted power for eachof a maximum of N!1 links to support the QoS required. Thus the algorithm arms each nodek with the ability to generate a power vector P<

k"(P

k1, P

k2,2P

kN) describing the transmit power

for each link at the required QoS.It is assumed that nodes can estimate to some degree of accuracy the SNR values on their

receive links. The algorithm proceeds with all nodes broadcasting a probe packet within aninterval. The broadcasts can be coordinated (as when TDMA is in use), or a random accessprotocol may be used. The latter case is needed for the case of leader selection. A QoS vectoris sent as part of the probe packet's payload to indicate to the receiving nodes the link qualityrequired for each link from the transmitting node. The elements of the N]1 QoS vector areindices to target link SNR levels. Each index indicates to the receiving node the required linkquality.

Notice that if the receivers can accurately estimate the link SNRs, these can be reported back inan acknowledgement to the transmitters which can then compute the required power levels. Thusonly three transmissions from each node to complete a leader selection algorithm: the initialprobe, the acknowledgment, and a "nal packet for broadcast of the power vector. With thisinformation, all nodes can agree on a leader.

However, due to lack of knowledge on the part of the receiver, it may be that only a binary&su$cient' or &insu$cient' acknowledgment can be sent, leading to an iterative search algorithm.In this case, all probe packets except the "rst contain an acknowledgment "eld indicating whetherthe link (at the requested QoS) can be supported at the previous iterations' power level. Thus, theacknowledgement (positive or negative) for iteration n!1 is piggybacked onto the probe packetfor iteration n.

All nodes start the algorithm at iteration n"1 by broadcasting at their maximum power levelsPk(1)"P(.!9)

k, k"1, 2,2, N. At each iteration n, all nodes send probe packets at a given power

level Pk(n)"P

k(n!1)!*

P. When the probes are received, all nodes check if any acknowledg-

ments are negative. If so, then power levels for the corresponding transmit links are "xed to a levelequal to the previous (successful) level plus a pre-speci"ed margin P

M, margin is designed to

compensate for both measurement errors and fading. If not, the next iteration is performed. Theiteration continues until all nodes have a complete transmit power vector.

A precise description of the algorithm is shown in Figure 3. Each node maintains a #agFkindicating whether its power vector is determined. The count of iterations is n, and thus the

number of probe packets transmitted by each node is n#1 (including the "nal acknowledge-ment).

At completion, each node has constructed a power vector based on the QoS required foreach of N!1 possible links to the other nodes. If the network begins with the same QoS vectorfor all nodes, with each entry of the vector set to the (same) index for housekeeping and net-work co-ordination, then the node selected as leader will be the one with the least costly (interms of transmitted power) set of links (by either the minisum or minimax criteria). Hence, for



Figure 3. Iterative QoS-based algorithm for determination of link transmit powers

leader selection, the general QoS-based algorithm simpli"es to a power-based algorithm. More-over, once all the power vectors are known, it is straightforward to order the nodes according totheir average or minimax power e$ciency so that a group of nodes, each quali"ed to be theleader, can be identi"ed. A member of this group can then assume the role of leader in case offailure.

Both the minimax and minisum criteria use the link loss matrix L for computation of theleader. In the iterative QoS-based algorithm each transmitting node sends a QoS vector in theprobe packet that indicates to the receiving node the required link quality. The higher the loss, thegreater will be the minimum transmit power level at which the transmitting node receivesa positive acknowledgement from the receiving node. This means that the iterative algorithmyields a power vector for each node whose elements are directly proportional to the link losses.Using either the minisum or the minimax criterion on the power vectors thus speci"es the mostpower-e$cient node as the leader. Therefore, for the two conditions of static (i.e., nonfading)channels and vanishingly small step size *

P, this iterative method will give the theoretical

minisum or minimax leader.

7. Numerical results

To explore the e!ect of the step size on performance, a simulation was written. The simulationde"nes an environment consisting of a planar 10]10 unit region in which node locations areuniformly distributed over each dimension. In addition, to investigate the performance of the



Figure 4. Example of leader selection; non-uniformly distributed nodes

algorithm for speci"c network scenarios, a capability to manually place nodes was also imple-mented.

It was assumed that the link loss between the nodes depends on the distance between thetransmitting and receiving nodes and Rayleigh fading as given in (1). The path loss exponent wasset to n"2 and the reference distance was set at d

0"1 unit. The fading was modeled by

a Rayleigh distributed random variable with mean 0)62 and variance of 0)1. All nodes wereassumed stationary with the link loss between them remaining constant for all iterations. Themaximum power level at which all nodes began broadcasting was "xed at 30 dB, and thethreshold received power level to determine success or failure was set to 5 dB. On the assumptionthat the margin should decrease with the step size, we also set P

M"*

P#0)1 dB.

A speci"c scenario is shown in Figure 4. Here, nodes were placed non-uniformly using themanual input mechanism. The per-link random Rayleigh fading caused asymmetry of the lossmatrix, which lead to di!erent nodes being selected as downlink and uplink leaders. In this case,the selections using the iterative algorithm agreed with the theoretical results based on exactknowledge of the loss matrix.

Simulations were carried out for a number of step sizes and the results are shown in Table I.For each trial the resulting leaders (using both minisum and minimax criteria) were comparedwith the results obtained using exact knowledge of the link loss matrix. The probability of successis de"ned as the number of times the leader selected by the iterative algorithm agrees with thetheoretical minisum or minimax leader over 500 trials.

The results con"rm that success of the power-based algorithm depends on *P, with perfor-

mance improving as *P

decreases. However, the tradeo! is that the number of iterationsprogressively becomes larger, which results in loss of throughput. On the other hand, if a highervalue of *

Pis selected, then the ability of the iterative algorithm to accurately determine the link



Table I. Performance over 500 scenarios of iterative algorithm asa function of step size; uniformly distributed nodes

Step size Average no. Prob(Success) for*P

(dB) of iterationsDownlink Uplink

MS MM MS MM

4 4)6 0)59 0)42 0)56 0)453 5)6 0)75 0)54 0)74 0)582 7)7 0)81 0)65 0)79 0)671 14)0 0)91 0)79 0)90 0)810)5 26)5 0)94 0)91 0)95 0)91

MS*Minisum, MM*Minimax.

loss matrix decreases, which results in less power e$ciency. In general, the step size will bedependent on the application domain and physical environment of the network.

8. Conclusion

In this paper we have investigated leader selection algorithms and link power assignment forad hoc wireless networks using performance criteria driven by the link losses between nodes.Expressions for selection of minisum and minimax leaders were presented, and uplink anddownlink leaders were shown to be special cases based on values of a mixture parameter. Inaddition, conditions were found for identi"cation of Bayesian and universally most e$cientleaders assuming a probabilistic model for uplink and downlink tra$c distributions. We alsoproposed a QoS-based iterative search algorithm that uses progressively decreasing transmitpowers to "nd a power vector for each node that speci"es transmit powers for support of speci"cQoS requests on a link-by-link basis. Further, it was shown that a special case of this procedureprovides an estimate of the link loss matrix for leader selection. Finally, simulation results wereemployed to explore the e!ect of step size in the iterative algorithm. Future work includes studyof environments that feature fast fading and network dynamics.

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Computing, pp. 464}471 (1991).7. D. Stamatelos and A. Ephremides, &Spectral e$ciency and optimal base placement for indoor wireless networks', IEEE

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8. H. Sherali and C. Pendyala and T. S. Rappaport, &Optimal location of transmitters for micro-cellular radio commu-nication system design', IEEE J. Selected Areas Commun., 14, 662}673 (1996).

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Authors: biographies:

Mehul J. Shah received the MS degree in Electrical Engineering from the University of SouthFlorida, Tampa and the BE (honors) degree in Electronics Engineering from the University ofBombay in 1998 and 1996 respectively. Since July 1997, he has been a research assistant workingon NASA's Advanced Communications Technology Satellite propagation experiments programat the University of South Florida. He is a member of of Eta Kappa Nu. His areas of interestinclude digital signal processing, communication networks and satellite communications.

Paul G. Flikkema received the BS in Computer Engineering from Iowa State University, and theMS and PhD in Electrical Engineering from the University of Maryland, College Park. DrFlikkema is currently Associate Professor in Electrical Engineering at Northern Arizona Univer-sity. From 1994 to 1998, he was an Assistant Professor at the University of South Florida. Hepreviously worked in industry, most recently with Techno-Sciences, Inc., Greenbelt, MD, wherehe worked on problems in signal processing for spread spectrum and satellite communications.In summer 1998 he was a visiting research scholar at Yokohama National University inYokohama, Japan, supported by a fellowship from the Japan Society for the Promotion ofScience. His current research interests include diversity and equalization for broadband com-munication over wireless channels, and resource allocation in wireless networks.



Power-conserving centralized organization of ad hoc wireless networks

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