site-specific knowledge and interference measurement for

2366 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 5, JUNE 2009

Site-Specific Knowledge and InterferenceMeasurement for Improving Frequency

Allocations in Wireless NetworksJeremy K. Chen, Member, IEEE, Gustavo de Veciana, Fellow, IEEE, and Theodore S. Rappaport, Fellow, IEEE

Abstract—We present new frequency allocation schemes forwireless networks and show that they outperform all other pub-lished work. Two categories of schemes are presented: 1) thosepurely based on measurements and 2) those that use site-specificknowledge, which refers to knowledge of building layouts, the lo-cations and electrical properties of access points (APs), users, andphysical objects. In our site-specific knowledge-based algorithms,a central network controller communicates with all APs and hassite-specific knowledge so that it can a priori predict the receivedpower from any transmitter to any receiver. Optimal frequency as-signments are based on predicted powers to minimize interferenceand maximize throughput. In our measurement-based algorithms,clients periodically report in situ interference measurements totheir associated APs; then, the APs’ frequency allocations are ad-justed based on the reported measurements. Unlike other work, weminimize interference seen by both users and APs, use a physicalmodel rather than a binary model for interference, and mitigatethe impact of rogue interference. Our algorithms consistently yieldhigh throughput gains, irrespective of the network topology, APactivity level, number of APs, rogue interferers, and availablechannels. Our algorithms outperform the best published work by18.5%, 97.6%, and 1180% for median, 25th percentile, and 15thpercentile user throughputs, respectively.

Index Terms—Cellular networks, frequency allocation, radiospectrum management, site-specific knowledge, wireless local areanetwork (WLAN).

I. INTRODUCTION

RADIO propagation characteristics are fundamentally sitespecific, since radio propagation mechanisms (e.g., pen-

etration, reflection, and diffraction) are directly related to thelocations, sizes, and electrical properties of physical objects inthe surroundings. Site-specific channel prediction algorithmsare well understood [3]–[7]. These site-specific prediction tech-niques use a building layout or a satellite map and computepath losses between any two locations in indoor or outdoor

Manuscript received July 26, 2008. First published December 12, 2008; cur-rent version published May 11, 2009. This work was supported by the NationalScience Foundation under Grant ACI-0305644 and Grant CNS-0325788. Thispaper was presented in part at the IEEE Vehicular Technology Conference,Baltimore MD, October 2007 [1] and the IEEE Global CommunicationsConference, Washington, DC, November 2007 [2]. The review of this paperwas coordinated by Dr. K. Zangi.

J. K. Chen was with the Wireless Networking and CommunicationsGroup, The University of Texas at Austin, Austin, TX 78712 USA. He isnow with Google Inc., New York, NY 10011 USA (e-mail: [email protected]).

G. de Veciana and T. S. Rappaport are with the Wireless Networking andCommunications Group, The University of Texas at Austin, Austin, TX 78712USA (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TVT.2008.2010862

environments. The complexity of these prediction tools hasbeen reduced, and computing power has increased, so thatthey can be implemented for real-time network managementapplications. This paper is the first work to analyze how site-specific knowledge can improve ongoing frequency allocationin wireless local area networks (WLANs). In WLANs, a num-ber of orthogonal frequency channels are allocated, and eachAP is allocated one channel. When the number of channels islimited relative to the number of APs, some APs inevitably usethe same channel and induce cochannel interference. The sameproblem exists in cellular networks. Judicious channel reusemechanisms are necessary to reduce interference, particularlyfor the case of mobile users, such as in enterprise voice-over-IP networks or in cellular networks. Today, site-specificknowledge is becoming much more available from blueprints,AutoCAD, and Google Maps and Google Earth, for example.This paper demonstrates vast improvement in overall networkperformance, particularly by greatly raising the throughputsof the users that suffer low throughputs. In other words, ourschemes enable many more users to have acceptable through-puts for file transfer or voice-over-IP applications, as comparedto prior published work.

A number of WLAN frequency allocation schemes have beenproposed thus far. The work in [8] assumes each AP has adifferent fixed traffic load and defines the effective channelutilization of an AP as the fraction of time the channel is usedfor data transmission or is sensed busy due to interference fromother APs; then, the maximum effective channel utilizationamong all APs is minimized. AP placement and frequencyallocation are jointly optimized in [9] with the same objec-tive of minimizing the max channel utilization as in [8]. Thework in [8] and [9] fails to maximize throughput or minimizeinterference seen by clients and, hence, perform poorer thanour proposed work in today’s WLANs, where downlink trafficdominates. The frequency allocation problem is modeled as aminimum-sum-weight vertex-coloring problem in [10], wherevertices are APs, and the weight of each edge between twoAPs denotes the number of clients that are associated witheither one of these two APs and are interfered by the otherAP. The work in [11] minimizes the number of clients whosetransmissions suffer channel conflicts; a client associated withan AP suffers conflicts if other clients or other APs interferewith the client or the AP under consideration. The definitionof channel conflict in [11] is more comprehensive than thosein [8]–[10]. The work in [11] has been shown to outperform

0018-9545/$25.00 © 2009 IEEE

CHEN et al.: SITE-SPECIFIC KNOWLEDGE FOR IMPROVING FREQUENCY ALLOCATIONS IN WIRELESS NETWORKS 2367

[8]–[10] but performs poorer than our proposed schemes in thepresence of rogue interferers, i.e., intentional or unintentionalRF interferers, microwave ovens, or other RF devices that alsooperate on the same unlicensed bands as WLANs.

Only [12] presents mechanisms to detect and reduce thenegative impact from rogue interferers. In [12], each APsenses interference and independently selects a channel whosemeasured interference power is below a predefined threshold,without coordinating with other APs. In networks with highinterference, it may not be feasible to find a channel allocationso that every AP senses interference below the threshold; inthis case, the algorithm in [12] does not converge. One couldin principle set a higher threshold for the algorithm in [12] towork in high-interference regimes, but [12] does not mentionmethods to adapt the threshold. It is not trivial to adapt thisthreshold, since a high threshold will degrade network perfor-mance, but a low threshold will yield no feasible solution. Bycontrast, four of our proposed algorithms converge irrespectiveof the overall interference level. The nonconvergence resultof [12] in the high-interference regime is due to the binarymodel for interference, which is also used in [8]–[11]. Our workconsiders a physical model for interference; that is, we assumethat interference power is a continuous quantity, which properlyrepresents the real world. Therefore, our work performs betterthan [12].

Most traffic in WLANs is downlink [6], [13]; hence, max-imizing downlink throughputs and signal-to-interference-and-noise ratios (SINRs) seen by users are key to proper networkdesign. The work in [8], [9], and [12] focuses on minimizingthe interference at APs rather than that seen by users, as isdone in [10] and [11], and thus often perform poorer than [10]and [11].

A. Main Contribution

The main contribution of this paper is our two categories ofnew algorithms for channel allocations that outperform all otherpublished work, i.e., those in [8]–[12]. In the remainder of thispaper, we mainly present the gains of our proposed algorithmsagainst the works in [11] and [12], since the work in [11] hasbeen shown to outperform [8]–[10]. The proposed algorithmsperform well mainly because of the following reasons: 1) Theyminimize interference seen by users rather than that seen byAPs; 2) they use a physical model rather than a binary modelfor interference; and 3) they have the ability to deal withrogue interferers. The first category is based on interferencemeasurements at APs and users, whereas the second categoryis based on site-specific knowledge. We describe our ideas andcontribution in the following discussion.

1) Measurement-Based Algorithms: We propose that all ora subset of clients periodically measure the in situ interferencepower on all frequency channels when their associated APsare idle, and report the average measured power to their asso-ciated APs. This technique is used in mobile-assisted handoff(MAHO) in the cellular field [14], and results in this paper mayalso be applied to cellular networks. APs also measure in situinterference power. Since the measurements at APs or clientsare performed during their idle time, the overhead is negligible.

Each AP then computes a metric, called weighted interference,which captures the overall interference as seen by itself and itsclients by placing different weights on its and the clients’ insitu measurements according to the clients’ traffic loads, signalstrengths, and uplink and downlink traffic volume. Section Vshows by simulation that our measurement-based algorithmssubstantially outperform [11] and [12]. Since the work in [11]has been shown to outperform [8]–[10], we conclude that ouralgorithms outperform [8]–[12].

2) Site-Specific Knowledge-Based Algorithms: The afore-mentioned measurement-based algorithms can still be im-proved if we assume that a central network controller has anduses site-specific knowledge to optimize frequency allocationof each AP and each user. The advantage of using site-specificknowledge is to a priori predict the path loss between anypair of AP and user when the user’s location is obtained viathe Global Positioning System (GPS) or other known positionlocation technologies.1 The predicted path losses can helpformulate a global optimization problem, thereby maximizingthroughputs and saving power, etc. Although the environmentaffects the path losses, empirical results show that by model-ing large fixed partitions and items in the environment (suchas walls, book shelves, and cubicles), the predicted and themeasured path losses show high agreement (e.g., the mean erroris less than 4 dB) [3]–[6].

Distributed measurement-based algorithms with the knowl-edge of APs’ transmit powers via message exchanges canlearn over time the path loss or received power between everytransmitter and every receiver; examples of such algorithms aredescribed in [17]. Nevertheless, the time needed for learningmay be too long when the number of interfering APs is large.The overall learning time could be shortened if each clientlearns the interference power from only the APs that are inthe range of causing nonnegligible interference at the client.To know which base stations are in the interference range, site-specific knowledge (such as the environments and the locationsof APs and clients) is needed. Saving the learning time formeasurement-based algorithms is a topic for ongoing and futurework. In this paper, we choose to use site-specific knowledge toa priori predict the interference power between any transmitterand any receiver.

Note that the central controller must know the active trans-mitters at any point in time to predict correct interference atall times; this information may be too costly to obtain, buttime sampling may be done. Since downlink volume presentlydominates WLAN traffic, this paper considers a case where allAPs are actively transmitting downlink traffic. It is reasonableto assume that frequency allocation is optimized with respect

1Several indoor position-location approaches, based on signal strength sens-ing, are widely known today and used in some WLANs [15], [16]. Other trian-gulation methods can also be used to locate a client. Modern cellular handsetsare equipped with GPS chips or other position-location technologies. The state-of-the-art GPS can work not only outdoors but also indoors; various vendors,e.g., Metris and SnapTrack, provide indoor GPS solutions. For example, theindoor GPS technology by Metris can be compared with the matrix of satellitesthat create the GPS; instead of satellites, Metris’ indoor GPS uses small infraredlaser transmitters that emit laser pulses to create a measurement universe. Basedon the timing of the light pulses received by photo detectors, angle and positionsmay be computed.


to this most active case, since in this case, frequency alloca-tion is most crucial for interference mitigation. Simulations inSection V show that our algorithms also perform well in scenar-ios with both downlink and uplink traffic and with different lev-els of AP activity. In this paper, we consider perfect site-specificknowledge; in other words, we assume that the actual path lossbetween any transmitter and receiver can be correctly predictedby site-specific knowledge. The work in [3] and [4] shows thatsite-specific models can achieve remarkably good predictions(a zero mean error and a standard deviation of 3–4 dB).The study of the effect of imperfect predictions of channel gainsis also an ongoing and future work.

B. Organization

Section II introduces the system model, notation, and as-sumptions and describes in detail our notion of weighted in-terference. The three proposed measurement-based algorithms,denoted No-Coord, Local-Coord, and Global-Coord, have dif-ferent mechanisms for iteratively switching frequency channelsto reduce the weighted interference seen in a single cell, a groupof nearby cells, and all cells, respectively, where a cell meansan AP (or base station) and its associated users. Section IIIpresents the mechanisms used by the three measurement-basedalgorithms and their convergence. Section IV presents twosite-specific knowledge-based algorithms. Section V showsby simulation that our algorithms substantially outperform[8]–[12].

II. SYSTEM MODEL, NOTATION, AND ASSUMPTIONS

We begin by describing the basic notation; then, the firstsection describes weighted interference, which is a metric usedin the three proposed measurement-based algorithms to capturethe overall interference of each cell. The second section definesthe notation exclusively used for the proposed measurement-based Local-Coord algorithm. The third section describes as-sumptions used in site-specific knowledge-based algorithms.

1) Basic Notation: Suppose M APs, indexed by M ={1, 2, . . . ,M}, operate on K orthogonal frequency channels,indexed by K = {1, 2, . . . ,K}. We index users (or clients) byL = {1, 2, . . . , L}. We denote the identity of an AP and a clientby am (m ∈ M) and cl (l ∈ L), respectively. We assume forthis paper that the locations of the APs and the clients do notvary with time, and we assume that no APs or users are at thesame location, although the algorithms given here also applyfor mobile APs and/or clients. Let Lm (Lm ⊆ L) denote theset of users that are associated with the AP am. We assumeevery user is associated with a single AP and define cell Zm ={am} ∪ {cl : l ∈ Lm}. Let fm (fm ∈ K) denote the channelthat am operates on, and let �f = (f1, f2, . . . , fM ) denote thechannels of all M APs.

A. Weighted Interference for Measurement-Based Algorithms

In brief, the weighted interference of each cell (e.g., Zm) isintended to capture the overall interference seen in the cell andis therefore defined as a weighted sum of the average in situ

measurements at am and at all clients associated with am, i.e.,at every u ∈ Zm. We propose that am or the clients associatedwith am measure their in situ interference power when thereis no traffic within cell Zm, i.e., am is neither transmittingnor receiving data. The average in situ measured interferencepower at u (for every u ∈ Zm) on channel k is denoted Iu

k (�f).The averaging period is a design choice and could be the sameas the period that an AP switches its channel, e.g., 1, 2, or5 min. Iu

k (�f) is lower bounded by the noise floor. The weightedinterference function for Zm on channel k is defined by

Wmk (�f) =

∑u∈Zm

Buk

(Iuk (�f)

), k ∈ K (1)

where Buk (·) is a nonnegative and nondecreasing function that

captures the weight of the in situ measurement at u. We requirethat Wm

k (�f) > 0 to capture the existence of the noise floorin the real world. Bu

k (·) should be designed to reflect thedifference of clients’ traffic demands, signal strengths, anduplink and downlink traffic volume. In practice, clients reportthe measurements to am either periodically or upon requestfrom am; then, Wm

k (�f) can be computed at am.In Section III-E, we will show that two of our proposed

algorithms (namely, Local-Coord and Global-Coord) convergeif the weighted interference function has the general form in(1). We will later introduce two simplified forms of Wm

k (·)representing practical metrics. The first form, denoted userbased, places different weights on the in situ interferencemeasurements at clients based on the traffic volume and thesignal strength at each client. The user-based form capturesthe performance of downlink transmission, which is appropriatefor WLANs since traffic measurements show that downlinktraffic volume accounts for more than 84% of total (uplinkplus downlink) traffic volume [6]. The second form, denotedAP based, includes the interference measurements at APs only.The AP-based form can be viewed as a simplified version ofthe user-based form by considering that all users have the sametraffic volume and signal strength.

1) User Based: The user-based weighted interference func-tion for Zm is defined by

W(U),mk (�f) =

∑l∈Lm

Ycl,am

Scl,am

· Icl

k (�f) (2)

where Scl,amdenotes the average received signal power2 from

am to cl, and Ycl,amdenotes the average traffic volume from

am to cl. We incorporate the inverse of Scl,amin (2) because

a client with a stronger Scl,amhas higher tolerance to interfer-

ence and, thus, should contribute less to the overall weightedinterference. Ycl,am

is included in (2) as a scaling factor, sincea client with higher traffic volume should be more importantfor the weighted interference. In practice, some users may be

2Note that cl cannot directly measure Scl,am but can estimate Scl,am asfollows: The average in situ SINR at cl can be measured at cl when am istransmitting to cl and is denoted γl. We assume that the interference at cl is thesame whether am is transmitting to cl or am is idle, i.e., the interference at cl

is always Iclfm

(�f). Then, we estimate Scl,am = γl · Iclfm

(�f).


sampled to reduce the complexity of computing (2), i.e., thesummation in (2) may be over a subset of Lm.

2) AP Based: The AP-based weighted interference functionfor am is defined by

W(A),mk (�f) = Iam

k (�f). (3)

B. Interfering Cells for the Local-Coord Algorithm

When an AP switches its channel, nearby cells may seesubstantial changes in their weighted interference. The notationof such cells is presented in the following discussion andwill be used in describing the proposed Local-Coord algo-rithm in Section III-B. Cell Zn is said to be interfered bycell Zm (or Zm interferes with Zn) if and only if am ora user associated with am induces nonnegligible interference(e.g., the interference power at the receiver is higher than thenoise floor) at an or a user associated with an. We defineGm as the set of cells interfered by Zm, i.e., Gm = {n :Zm interferes with Zn given that am and an are on the samechannel}. The subset of Gm that is on channel k is denotedGm,k(�f). Suppose am switches from channel k to k′, thecells that see changes in their weighted interference are Zm

and the cells indexed by Gm,k(�f) and Gm,k′(�f). We de-fine Hm,k,k′(�f) ≡ {m} ∪ Gm,k(�f) ∪ Gm,k′(�f); we will see inSection III-B that the weighted interference of the cells indexedby Hm,k,k′(�f) is examined by Local-Coord if am switchesfrom channel k to k′.

We define Vm as the set of the indexes of cells that interferewith Zm or the cells indexed by Gm, i.e., i ∈ Vm if andonly if there exists j ∈ {m} ∪ Gm such that Zi interferes withZj . The notion of Vm will be used for describing a parallelprotocol in Section III-B. Suppose we are given the locations ofall controlled APs and possible locations of clients; then, thesets of Gm and Vm can be precomputed and preconfiguredin the controlled APs or a central network controller thatcommunicates with the controlled APs, using radio propagationprediction models as described in [3]–[6], [14], and [18].

C. Assumptions for Site-SpecificKnowledge-Based Algorithms

We assume that the central network controller periodically(e.g., every 5 min) requires the APs to stop transmitting fora short duration of time (e.g., 1 s). In this duration, APs taketurns in requiring all users associated with them to performmeasurements of background interference, which refers to boththe noise floor and rogue interference from RF devices outsidethe controlled network. Note that each user needs to mea-sure the background interference for all available frequencychannels. The users then feed back to APs these measuredbackground interference. Site-specific knowledge, along withmeasurements of background interference, makes the estima-tions of SINR at users or APs much more accurate.

We assume perfect site-specific knowledge; in other words,we assume that the actual path loss between any transmitter andreceiver can be correctly predicted by site-specific knowledge.

A study of the effect of imperfect predictions of channel gainsis an ongoing and future work.

III. THREE MEASUREMENT-BASED ALGORITHMS

The three proposed algorithms all have an iterative nature.At each point in time (predefined, randomly chosen, or deter-mined at runtime), e.g., every 1, 2, or 5 min, one iteration ofchannel switching takes place where one or more APs switchtheir frequency channels according to mechanisms that arespecific to each algorithm, whereas other APs stay on theircurrent channels. The channel switching time in hardware isseveral milliseconds and is thus negligible as compared to theinterval between two iterations. APs and clients measure andaverage their in situ interference between successive iterations.Iterations keep taking place on different AP(s) until the chan-nel allocations converge; of course, when users move or thepropagation environment changes, the algorithms will switchchannels again until the frequency allocations reach anotherconvergence point. We next describe the different conditionsunder which each of the algorithms may switch a representativeAP am’s channel from k = fm to k′ = f ′

m. Throughout thispaper, �f ′ ∈ K

M denotes a vector of channels selected by APsafter the representative AP am moves from channel fm to f ′

m.Hence, �f ′ differs from �f in only the mth element.

A. No-Coord Algorithm

A representative AP am switches from its current channel fm

to f ′m only if the weighted interference on the new channel f ′

m

is lower, i.e., the following No-Coord condition holds:

Wmfm

(�f) > Wmf ′

m(�f ′). (4)

This algorithm is denoted No-Coord, because am makes agreedy channel selection without coordination with other APs.

B. Local-Coord Algorithm

If am switches from channel k to k′, only Zm and thecells indexed by Gm,k(�f) and Gm,k′(�f) see changes in theirweighted interference. The AP am switches from channel kto k′ if the max weighted interference seen by these cellsdecreases after channel switching, i.e., the following Local-Coord condition holds:

maxi∈Hm,k,k′ (�f)

W ifi

(�f) > maxi∈Hm,k,k′ (�f)

W if ′

i(�f ′) (5)

where Hm,k,k′(�f) has been defined in Section II-B. This al-gorithm is denoted Local-Coord, since am needs to locallycoordinate with the APs indexed by Gm,k(�f) and Gm,k′(�f) viaa wired backbone network for channel switching.

For example, Fig. 1 depicts the cells that see changes inweighted interference before and after AP-1 switches its chan-nel. Since the max weighted interference seen by cells 1–4decreases, AP-1 can switch to the new channel.

Since coordination among APs is confined in a local area,multiple APs that are far apart enough can simultaneously


Fig. 1. Decrease of the max weighted interference seen by cells 1–4 beforeand after AP-1 switches from channel 1 to 2.

Fig. 2. Protocol for the distributed implementation of Local-Coord.

change their channels if a proper inter-AP protocol is employed.In general, the number of APs that can simultaneously changechannels grows with the number of total APs; hence, Local-Coord is scalable. Fig. 2 presents a distributed protocol imple-menting Local-Coord. We say an AP am is locked if am is notallowed to switch its channel per other APs’ requests; if am

is unlocked, am may switch its channel. First, we suppose thateach AP has an independent random timer that triggers the APto initiate the process of switching its channel as described inFig. 2(a). If am is locked, am will ignore this trigger and waitfor the next trigger. The key idea of this protocol is describedin Phases 1 and 2 in Fig. 2(a): am needs to lock all the APsindexed by Vm (as defined in Section II-B) before am switchesto a new channel; then, am unlocks those APs after it possiblyswitches the channels. If any AP indexed by Vm cannot belocked, am cannot switch its channel. The procedure to handlelocking and unlocking requests is described in Fig. 2(b) and (c),respectively. An AP can be locked multiple times by different

TABLE IVARIABLE ψm USED IN THE DISTRIBUTED PROTOCOL IN FIG. 2

APs; Table I describes ψm, which denotes the number of timesthat am was locked. Only when ψm = 0 can am initiate theprocess of channel switching. When am is in the process ofswitching its channel (denoted by ψm = −1), it cannot belocked.

Deadlock is a problem that needs to be avoided in suchdistributed algorithm; in this context, deadlock means that twoor more APs that have initiated the process of switching theirchannels are waiting for one other, and thus, none of theseAPs can ever finish. In the sixth and eighth steps of Fig. 2(a),am immediately unlocks other APs whether am switches itschannel or not; hence, deadlock never arises in the protocolin Fig. 2 (see [17] for a detailed description and a proof ofdeadlock prevention).

C. Global-Coord Algorithm

The AP am will switch to a new channel only if the suminterference on the new channel is lower (after am switchesthere) than the sum interference on its current channel, i.e., thefollowing Global-Coord condition holds:∑

n:fn=k

Wnk (�f) >

∑n:f ′

n=k′

Wnk′(�f ′). (6)

This algorithm requires global coordination among APs using acentral network controller that communicates with all APs andis thus denoted Global-Coord.

D. Implementation Concerns

Note that in the descriptions of the three proposed algo-rithms, some terms in the weighted interference function areunknown before am switches to the new channel. An imple-mentation may require am to switch to a new channel on atrial basis and then require one or more cells to measure andcompute their weighted interference after am commits to theswitch. Only when all the quantities needed for the channeldecisions are known can am decide whether switching to thenew channel complies with the condition described for eachalgorithm. If the condition is satisfied, am stays on the newchannel; otherwise, am switches back to the old channel or triesanother channel. No-Coord requires the weighted interferenceat cell Zm; Local-Coord requires the weighted interference atcells indexed by Hm,k,k′(�f); and Global-Coord requires theweighted interference at all cells.

E. Convergence and Characterization of Convergence Points

Theorem III.1: Consider a particular realization of the loca-tions of APs and users and a weighted interference function of


the form of (1). Given any set of initial AP channel choices, thechannel selection process for Local-Coord and Global-Coordconverges in a finite number of steps.

Before characterizing the convergence points for No-Coord,Local-Coord, and Global-Coord, we need some definitions.A vector of frequency allocations denoted by �f is a Nashequilibrium (a concept widely used in game theory [19]) if nosingle cell can lower its weighted interference by unilaterallychanging its channel.

Let �u = (u1, . . . , uN ) and �u′ = (u′1, . . . , u

′N ) denote the

nonincreasing sorted versions of two arbitrary vectors �v =(v1, v2, . . . , vN ) and �v′ = (v′

1, v′2, . . . , v

′N ), respectively. We

say that �v lexicographically dominates �v′ (or �v � �v′) if thereexists some index j, where N ≥ j ≥ 1 for which uj > u′

j

and ui = u′i for all i < j. Vectors �v and �v′ have the same

lexicographic order if �u and �u′ are elementwise the same. Wesay �v �v′ if �v � �v′ or �v and �v′ have the same lexicographicorder. We say that a vector of frequency allocations denotedby �f is a local lexicographic minimum with respect to a vectorfunction �θ(·), if for any vector of frequency allocations �f ′ ∈K

M that differs from �f in only one element, �θ(�f ′) �θ(�f)holds true.

Theorem III.2: Suppose No-Coord converges to a frequencyallocation �f . Then, �f is a Nash equilibrium.

Note that No-Coord does not always converge, althoughsimulation results show that No-Coord converges in most cases.Theorem III.2 is true only for the case where No-Coord con-verges. To resolve the nonconvergence problem of No-Coord,one may limit the number of iterations or specify a minimumdifference of weighted interference (before and after channelswitching) so that No-Coord can stop. We next state a technicalassumption useful in proving Theorem III.3.

Assumption III.1: Since the weighted interference in (1)takes a continuum of values, it is reasonable to assume that theweighted interference values at different cells or channels aredistinct, i.e., ∀k, j ∈ K, ∀m,n ∈ M such that k �= j or m �= n,we have Wm

k (�f) �= Wnj (�f) with a probability of 1.

Theorem III.3: Suppose Local-Coord or Global-Coord con-verges to a frequency allocation �f . Then, with a probability of 1,�f is a local lexicographic minimum with respect to the vectorfunction �α(·) as defined in (7) for Local-Coord, or with respectto �β(·) as defined in (8) for Global-Coord, where

�α(�f)=(W 1

f1(�f),W 2

f2(�f), . . . ,WM

fM(�f)

)(7)

�β(�f)=

⎛⎝ ∑

n:fn=1

Wn1 (�f),

∑n:fn=2

Wn2 (�f), . . . ,

∑n:fn=K

WnK(�f)

⎞⎠ .

(8)

IV. SITE-SPECIFIC KNOWLEDGE-BASED ALGORITHMS

A. SS-S Formulation

We shall consider optimizing a sum of utility functions forall the users’ SINR, assuming all APs are actively transmitting

downlink traffic (but not uplink traffic). That is, we optimize thefollowing problem over �f ∈ K

M , which is denoted site-specificSINR (SS-S) in the rest of this paper:

max�f∈KM

{∑l∈L

U(γl)| (9)

γl =Scl,am

P icl

+∑

n:fn=fm,n �=m Scl,an

∀l ∈ L

}(10)

where am in (10) denotes the AP with which cl is associated,P i

cldenotes the background interference power that cl measures

(as described in Section II-C), γl denotes the SINR at user cl

[as shown in (10)], and Scl,amdenotes the average received

signal power from am to cl. Note that the objective in (9) isnot optimizing the “sum SINR,” since such an objective mayfavor users that are closer to APs and may cause users that arefurther away to suffer a low SINR. A fair SINR distribution canbe achieved if we optimize the sum of utility functions in (9),where the utility function U(·) in (9) can be any function thatis concave, continuously differentiable, and strictly increasing.For example, Mo and Walrand have proposed a class of utilityfunctions that capture different degrees of fairness parameter-ized by q [20], i.e.,

U(γl) ={

(1 − q)−1γ(1−q)l , if q �= 1

log γl, if q = 1, γl ∈ (0,∞). (11)

This family of utility functions is concave, continuously differ-entiable, and strictly increasing. Intuitively, as q increases, thedegree of fairness increases, but the sum SINR decreases. Atradeoff between the sum SINR and fairness of the individualSINR of users that are further away from a serving AP can beobserved. By increasing the degree of fairness, we imply thatusers that are further from APs have a higher SINR (which isneeded to provide high throughputs to distant users). The workin [20] shows that if q → ∞, the formulation in (9) becomesa special case that achieves max–min fairness. At max–minfairness, the degree of fairness is the highest; however, thesum SINR is the lowest. Simulation results in Section V showthat q = 2 may be a good parameter to capture this tradeoff,but this remains a topic for further research. Note that thegeneral form of the weighted interference function in (1) for ourmeasurement-based algorithms could also incorporate utilityfunctions such as those in (11).

As described in Section II, we assume that the APs and/or theusers in the controlled network periodically measure the back-ground interference; hence, P i

clin (10) is known. We assume

that the central network controller has site-specific knowledgeand the locations of all APs and users, can predict signal powerfor any pair of AP and user, and can compute Scl,an

for allcl, an in the denominator of (10). Thus, all the quantities in theoptimization problem in (9) are known, yet measurement-basedalgorithms (such as those presented in Section III) do not knoweach individual component of Scl,an

in (10) and, thus, are notable to directly solve (9). Because the optimization in (9) is a


combinatorial problem, there is no fast algorithm (polynomialtime) that can solve (9). Therefore, we propose an efficientheuristic in Section IV-C that can find the locally optimal solu-tion of (9); simulations show that the algorithm in Section IV-Coutperforms the measurement-based algorithms in Section III,as well as all other frequency allocation algorithms in [8]–[12].

B. SS-R Formulation

The formulation in (9) in Section IV-A strives to provide afair SINR across users. From the users’ perspective, however,the throughput may be a better metric than the SINR for users’performance. We now formulate another problem that aims atproviding a fair throughput across users, and this formulationmay be denoted site-specific rate (SS-R), i.e.,

max�f∈KM

{∑l∈L

U(χl)|χl =rl(γl)Lm

(12)

γl =Scl,am

P icl

+∑

n:fn=fm,n �=m Scl,an

∀l ∈ L

}

(13)

where Lm denotes the number of clients that are associated witham, χl denotes the throughput of cl from am (cl is associatedwith am), and rl(γl) denotes the long-term average data ratethat cl receives from am if cl is the only user associatedwith am; rl depends on the SINR seen at user cl, i.e., γl, asdefined in (10). rl(γl) may also be viewed as the achievablecapacity between cl and am. We assume that the AP am evenlydistributes its resource (e.g., time) among its Lm users andtherefore has the denominator in (12). There are several waysto model rl(γl); for example, we may use Shannon capacity

rl(γl) = log2(1 + γl) (14)

or an empirical model, e.g., such as introduced in [6] and [18],to relate the throughput to the SINR, i.e.,

rl(γl) = Tmax

(1 − e−Ae(γl−γ0)

)(15)

where the three constants Tmax, Ae, and γ0 denote the peakthroughput, the slope of throughput variation, and the cutoffSINR, respectively, as described in [6]. Note that the modelin (15) captures the downlink throughput of a client cl whenall other clients associated with the same AP are idle, andthe received SINR of this client cl is γl. In our simulation,we use a time-division multiplexing model for medium access.Hence, at any point of time, an AP is sending data to only oneclient, and the SINR at this client can be computed by con-sidering interference from all other APs on the same channel.Hence, the model in (15) is valid, as long as we multiply thethroughput in (15) by the time fraction that the AP allocates toclient cl. It is known that the IEEE WLAN operates under acarrier sense multiple access/collision avoidance (CSMA/CA)

algorithm, and the throughput of a WLAN network is actuallymore complicated than the simple equation in (15); however,the works in [6] and [18] have shown that the empirical modelin (15) can serve as a first-order approximation of WLANthroughputs with high accuracy.

C. Local Optimization Algorithm for SS-S and SS-R

The optimization problems in (9) and (12) are combinatorial;solving them exhaustively requires exponential computationtime (exponential in the number of APs). Hence, we presentan iterative local optimization procedure that yields rapid andnearly optimal solutions of (9); the same procedure can alsosolve (12). At the beginning of each iteration, a frequencyallocation �f is given, and at the end of the iteration, we finda better frequency allocation �g that improves the objective in(9); �f and �g may differ in several elements, which means thatthe channels of several APs may change. During each iteration,we do the following steps: First, we select an AP, e.g., am. Wefind V − 1 other APs that produce the strongest interferenceon am, assuming these V − 1 other APs and am are on thesame channel; for example, V = 7 implies that we find sixother APs that are in the vicinity of am so that they willlikely interfere with am’s clients the most. We try all possibleKV permutations of channels for these V APs while fixingthe channels at the other M − V APs. We can find the bestout of the KV permutations so that (9) is maximized and isstrictly larger than the value before this iteration; then, wechange the corresponding V elements in �f and thus form �g.If these V APs have operated on the best channel allocationbefore this iteration, we have �f = �g; in this case, another AP(instead of am) and its V − 1 neighboring APs will be selectedto restart this iteration. This iterative algorithm runs until everyset of V neighboring APs reaches the best frequency allocation.This iterative algorithm converges in a finite number of steps,since the number of channel permutations is finite, and eachiteration strictly increases the objective in (9). In practice,one may limit the number of iterations or specify a minimumdifference of weighted interference so that the iterations can befinished in a reasonable amount of time (e.g., 1, 5, or 30 s).We expect that the channel allocation found by this local opti-mization algorithm will be close to the optimum if V is largeenough, since the exhaustive search can explore more possibleallocations with a larger V . Nevertheless, the simulations inSection V show that this local optimization algorithm withV = 7 outperforms all other algorithms [8]–[12].

The previously proposed algorithm solves the SS-S formu-lation in (9) and the SS-R formulation in (12). When it isapplied to solve SS-S, we refer to the algorithm as the SS-Salgorithm; similarly, when the algorithm is used to maximizethe throughput (rate), we refer to it as the SS-R algorithm.

V. SIMULATION SETUP AND RESULTS

We shall begin by describing our simulation setup inSection V-A. Then, in Section V-B, we present and discuss oursimulation results.


Fig. 3. User throughput (in megabits per second) comparison in a setting withAPs on a uniform 10-by-10 layout, 400 users, and ten rogue RF interferers. Onlythe 200 users with lower throughputs are shown.

A. Simulation Setup

No-Coord, Local-Coord, and Global-Coord, along with theuser-based weighted interference function in (2) and theAP-based weighted interference function in (3), yield six algo-rithms, namely, No-U, Lo-U, Gl-U, No-A, Lo-A, and Gl-A. Thealgorithm in [11], denoted CF, has been shown to outperform[8]–[10]. Hence, we compare our proposed algorithms (thepreceding six combinations, as well as SS-S and SS-R) againstCF and the algorithm in [12], which is denoted LC. We set thenumber of orthogonal channels K to 3 to represent 802.11b/g;other larger values of K produce very similar trends as to thoseshown in Figs. 3–5, making our approach applicable to cellularnetworks and 802.11a. We assume that each AP can source amaximum of 54 Mb/s per the 802.11g standard. We considerthree network sizes, three levels of rogue interference, and twonetwork topologies, and thus have 18 combinations (3×3×2),as shown in the x-axis of Fig. 4. For each of the 18 combina-tions, we randomly generate ten independent cases and com-pute the average. The three network sizes include a 4-by-4 APlayout with 64 users, a 7-by-7 layout with 196 users, and a10-by-10 layout with 400 users. Each AP may be associatedwith a different number of users; the average number of usersfor each AP is four for all three network sizes. We consider low,medium, and high interference from rogue interferers, wherethe ratios of the number of rogue interferers to the numberof APs are 10%, 40%, and 70%, respectively. We consider auniform topology, where APs are regularly located on cornersof hexagons with less than 5 m of random perturbation, asillustrated in Fig. 6(a), and a nonuniform topology, where APsare perturbed from the uniform layout by a random distance (upto 25% of separation), as shown in Fig. 6(b). The separationbetween adjacent APs is 240 m. The path loss exponent is setto be 3. We set a constant transmit power of 10 mW for everyAP and client. The noise floor is set to be 10 dB above the ther-mal noise to properly represent the RF environment [21]; thethermal noise is modeled as kT0B, where k is the Boltzmann’sconstant (k = 1.38 × 10−23 J/K), T0 is the ambient room tem-

perature (typically taken as 300 K), and B is the equivalentbandwidth of the measuring device (B = 30 MHz for thebandwidth of IEEE 802.11b/g systems). We set the fairnessparameter q as 2.

B. Simulation Results and Discussions for Two Kinds ofTraffic Scenarios

We consider results for two traffic scenarios. In the first sce-nario (Section V-B1), we present results for saturated downlinknetworks, i.e., all APs are transmitting downlink traffic. Then,in the second scenario (Section V-B2), we present results fornetworks with both uplink and downlink traffic.

1) Downlink Only: Fig. 3 shows the users’ throughputs(in ascending order) resulting from different algorithms for100 controlled APs and 400 users with ten rogues. Note thatthe algorithms yield very different throughputs for the first200 users with lower throughputs but less different for the last200 users; hence, we emphasize the first 200 users in Fig. 3;more detailed results can be found in [17]. Other scenarios withdifferent numbers of APs, users, and rogue interferers yieldsimilar throughput trends, as in Fig. 3, and are therefore omittedfor the sake of brevity. Our proposed algorithms outperform thebest algorithms in the literature, i.e., LC and CF; particularly,the site-specific knowledge-based algorithms have the bestperformance. Fig. 3 shows that SS-S and SS-R outperform LCby 16.8% and 13.1% in terms of the mean user throughput,18.5% and 13.6% in terms of median, 97.6% and 87.1% interms of 25th percentile, 204% and 188% in terms of 20thpercentile, and 1180% and 1110% in terms of 15th percentileuser throughputs. Although Lo-U achieves lower throughputsthan SS-S or SS-R, yet Lo-U is the best measurement-basedalgorithm, particularly good at uplifting throughputs for userswith low throughputs. Fig. 3 shows that Lo-U outperformsLC by 12.9%, 14.3%, 81.4%, 168%, and 1010% in terms ofmean, 50th percentile, 25th percentile, 20th percentile, and 15thpercentile user throughputs, respectively.

In Fig. 3, SS-R yields the highest 5th and 3rd percentilethroughputs. Generally, SS-R sacrifices the users with higherthroughputs to improve the users with lower throughputs. Al-though SS-R is worse than SS-S for users with high throughputs,SS-R is still better than Lo-U, which is the best measurement-based algorithm. Our algorithms yield enormous throughputgains, particularly for users with low throughputs. Fig. 4 showsthe percentage of users with throughputs more than 512 kb/sin various scenarios. In Fig. 4, our algorithms enable moreusers to operate above 512 kb/s irrespective of the number ofAPs and rogues; this trend is also true for other throughputthresholds (other than 512 kb/s). Fig. 4 shows that SS-R andSS-S accommodate up to 18.8% more users than LC or CF.

2) Both Downlink and Uplink: As described in the pre-ceding discussion, we assumed all traffic was downlink andoptimized the frequency allocation for the most active case,where all APs are transmitting downlink traffic. It is reasonableto optimize frequency allocation for this most active case,since in this case, frequency allocation is most crucial forinterference mitigation at each user. In this section, we examine


Fig. 4. Percent of users that have throughputs higher than 512 kb/s. The x-axis represents the layout of controlled APs and the percentage of rogue APs comparedwith the controlled APs. Nonuniform and uniform AP layouts are denoted “nu” and “u,” respectively.

Fig. 5. Fiftieth and 25th percentile user throughputs (50P and 25P), respec-tively, including both downlink and uplink traffic, for 400 users on a 10-by-10uniform AP layout with ten rogues. Vertical arrows and numbers beside thearrows depict the gains of SS-S over LC in percent (some arrows are omittedwhen the associated gains are relatively small).

the performance of the optimized frequency allocations in thepresence of both downlink and uplink traffic. It has been shownin [22] that uplink and downlink capacities in multiple cells aremutually coupled due to intercell interference, and no system-level analytic model has been found to model activities ofmultiple APs. In our next simulation, we consider that time isslotted and propose an approximate probabilistic model whereAPs independently choose one of the three possible activitystates at each time slot. An AP can be transmitting downlinktraffic, receiving uplink traffic, or idle, with probabilities pd,pu, and pi = 1 − pd − pu, respectively. For any AP that istransmitting downlink traffic or receiving uplink traffic at acertain time slot, a user is randomly chosen (with a uniformprobability distribution) out of all the users associated with thisAP to be the recipient or the sender of the traffic. We fix the ratioof pd to pu as 5:1 [6] and simulate five cases where pd + pu (theprobability that an AP is active) is 0.2, 0.4, . . ., 1.0, respectively.

We intend to see the effect of pd + pu on the performance of theproposed algorithms. The assumption that the activity of eachAP is independent from the other APs simplifies the simulationsand provides a rule of thumb for the performance comparison.Fig. 5 shows that our algorithms consistently yield throughputgains (including both downlink and uplink) irrespective of theprobability of AP activity; particularly, the gains are high (upto 71% for the 25th percentile throughput and 19% for themedian throughput) when APs are highly active (i.e., when thenetwork traffic load is heavy). In Fig. 5, we still see the sametrend as in Fig. 3 that SS-S and SS-R have the best performancein providing high throughputs for users who suffer the lowestthroughputs.

VI. CONCLUSION

A central network controller with site-specific knowledgecan predict the path loss between any AP and client and there-fore predict the impact of the SINR and throughput on everyAP and user when the channel of any AP is changed. This site-specific knowledge leads to vast network improvements, whichwe have demonstrated by using two site-specific algorithmsthat can incorporate the importance of fairness across users.Our proposed algorithms are particularly useful when the trafficload of the network is high and APs are highly active. Thetwo algorithms, namely, SS-S and SS-R, are better in upliftingthe throughputs of users that suffer low throughputs whenparticular utility functions are chosen. Judicious selection ofutility function is a topic of future research. We believe that site-specific knowledge is also useful for other wireless communi-cation problems in both cellular networks and WLANs, whichwill be validated by ongoing and future work; for example,the work in [23] uses site-specific knowledge to perform loadbalancing in wireless networks.

When site-specific knowledge is not available, the proposedmeasurement-based algorithms are good alternatives. Among


Fig. 6. Frequency allocation examples for 49 APs on a 7-by-7 nonuniformor uniform topology. Three kinds of objects (squares, stars, and circles) signifythree orthogonal frequency channels. Filled back objects denote 49 APs, hollowobjects denote 196 users; and double-layered objects with inner part filled withblack denote 20 rogues. The units of the x- and y-axes are meters.

the three measurement-based algorithms, Local-Coord is thebest in uplifting the throughputs of users that suffer lowthroughputs. For Local-Coord, a scalable distributed proto-col is given, and the convergence is proven; hence, Local-Coord is our best measurement-based algorithm for frequencyallocation in wireless networks. If coordination among APscannot be realized as required in Local-Coord, No-Coord isalso a good option, since it does not require coordinationamong APs. Although No-Coord is not guaranteed to con-verge, simulations show that it converges in most cases andhas a comparable throughput gain as Local-Coord. We presentpractical approaches to implement these measurement-basedalgorithms.

APPENDIX

PROOFS OF THEOREMS III.1–III.3

Lemma A.1

Suppose two vectors �v = (v1, v2, . . . , vN ) and �v′ =(v′

1, v′2, . . . , v

′N ) differ in at least one element. Assume all

elements in �v are distinct and so are those in �v′. Let D denoteindexes where �v and �v′ differ, i.e., D = {i : vi �= v′

i}. Then, wehave �v � �v′ if maxi∈D vi > maxi∈D v′

i.Proof sketch: We sort the elements of �v and �v′, respec-

tively, in descending order and compare their elements oneby one from the largest to the smallest. Then, the first dif-ferent pair of elements between the two sorted vectors ismaxi∈D vi and maxi∈D v′

i, respectively. Since maxi∈D vi >

maxi∈D v′i, we have �v � �v′ according to the definition of lex-

icographic order in Section III-E. A detailed proof is givenin [17]. �

Lemma A.2

Suppose am is a representative AP switching its channelfrom k to k′ according to the Local-Coord condition in (5)or Global-Coord condition in (6), and the channels of all theother APs remain unchanged. Then, we have �α(�f) � �α(�f ′) forLocal-Coord or �β(�f) � �β(�f ′) for Global-Coord [�α(�f) definedin (7) and �β(�f) defined in (8)].

Proof: If am switches from channel k to k′, only thecells indexed by Hm,k,k′(�f) see changes in their weightedinterference. Note that the nth element of �α(�f) signifies theweighted interference of Zn. Hence, the different elementsbetween �α(�f) and �α(�f ′) are those indexed by Hm,k,k′(�f).According to Lemma A.1, it suffices to show that the maxi-mum of these different elements in �α(�f) is greater than themaximum of those in �α(�f ′), i.e., maxi∈Hm,k,k′ (�f) W i

fi(�f) >

maxi∈Hm,k,k′ (�f) W if ′

i(�f ′), which is equal to the Local-Coord

condition in (5). Hence, the proof for Local-Coord is done. Theproof for Global-Coord is similar and is omitted for the sake ofbrevity (see [17] for the proof). �

Proof of Theorem III.1: We will first prove the convergenceof Local-Coord. We form a directed graph G with all possiblechannel vectors �f as nodes (hence the number of nodes isfinite) and all channel adjustments that satisfy the Local-Coordcondition in (5) as edges, assuming only one AP switches itschannel at any point of time. We will show that this graphis acyclic; then, since G is acyclic and finite, any initial nodewill converge to a sink in a finite number of steps of channeladjustments. Note that the lexicographic order possesses thetransitive property, that is, if �v � �v′ and �v′ � �v′′, then �v � �v′′

[24]. Suppose there exists a cycle on G, and �f0, �f1, �f2, . . . arenodes on this cycle. As we travel through this cycle once, wewill see that �α(�f0) � �α(�f1) � �α(�f2) � · · · � �α(�f0) accord-ing to Lemma A.2. This implies �α(�f0) � �α(�f0) according tothe transitive property, which is a contradiction since �α(�f0)does not lexicographically dominate itself. Therefore, G isacyclic, and the proof is done. The proof of Global-Coord isthe same as the preceding proof except that the edges of G are


the channel adjustments satisfying the Global-Coord conditionin (6), and �α(·) is replaced with �β(·). �

Proof of Theorem III.2: Suppose No-Coord converges at afrequency allocation �f , but �f is not a Nash equilibrium. Then,there exists at least one AP, e.g., am, and one channel f ′

m (f ′m �=

fm) so that am can switch from its current channel fm to f ′m

to strictly decrease the weighted interference of Zm. Then, thefrequency allocation has not converged, since am can switch tochannel f ′

m according to the No-Coord condition in (4). Thisproof is done by contradiction. �

Proof of Theorem III.3: Recall from the Proof of Lemma A.2that �α(�f) differs from �α(�f ′) only in the elements indexed byHm,k,k′(�f). To prove that �α(�f ′) �α(�f) holds with a probabil-ity of 1, it suffices to show that

maxi∈Hm,k,k′ (�f)

W if ′

i(�f ′) > max

i∈Hm,k,k′ (�f)W i

fi(�f) (16)

holds with a probability of 1, according to Lemma A.1. SinceLocal-Coord converges at �f , no AP can move to a new channelso that the Local-Coord condition in (5) is satisfied. Hence, forevery AP am (e.g., it is currently on channel k) and every newchannel k′ (k′ �= k), the converse of (5) holds. The inequalityin the converse of (5) holds with a probability of 1 accordingto Assumption III.1 and is the same as (16); thus, the proof isdone. The proof for Global-Coord is similar and is omitted forthe sake of brevity (see [17] for the proof). �

REFERENCES

[1] J. K. Chen, T. S. Rappaport, and G. de Veciana, “Site specific knowl-edge for improving frequency allocations in wireless LAN and cellularnetworks,” in Proc. IEEE Veh. Technol. Conf., Baltimore, MD, Oct. 2007,pp. 1431–1435.

[2] J. K. Chen, G. de Veciana, and T. S. Rappaport, “Improved measurement-based frequency allocation algorithms for wireless networks,” in Proc.IEEE GLOBECOM, Washington, DC, Nov. 2007, pp. 4790–4795.

[3] S. Y. Seidel and T. S. Rappaport, “914 MHz path loss prediction mod-els for indoor wireless communications in multifloored buildings,” IEEETrans. Antennas Propag., vol. 40, no. 2, pp. 207–217, Feb. 1992.

[4] R. R. Skidmore, T. S. Rappaport, and A. L. Abbott, “Interactive coverageregion and system design simulation for wireless communication systemsin multifloored indoor environments: SMT Plus,” in Proc. IEEE Int. Conf.Universal Pers. Commun., Oct. 1996, vol. 2, pp. 646–650.

[5] M. Hassan-Ali and K. Pahlavan, “A new statistical model for site-specificindoor radio propagation prediction based on geometric optics andgeometric probability,” IEEE Trans. Wireless Commun., vol. 1, no. 1,pp. 112–124, Jan. 2002.

[6] C. Na, J. K. Chen, and T. S. Rappaport, “Measured traffic statisticsand throughput of IEEE 802.11b public WLAN hotspots with threedifferent applications,” IEEE Trans. Wireless Commun., vol. 5, no. 11,pp. 3296–3305, Nov. 2006.

[7] R. R. Skidmore, A. Verstak, N. Ramakrishnan, T. S. Rappaport,L. T. Watson, J. He, S. Varadarajan, C. A. Shaffer, J. Chen, K. K. Bae,J. Jiang, and W. H. Tranter, “Towards integrated PSEs for wireless com-munications: Experiences with the S4W and SitePlanner projects,” ACMSIGMOBILE Mobile Comput. Commun. Rev., vol. 8, no. 2, pp. 20–34,Apr. 2004.

[8] K. K. Leung and B.-J. Kim, “Frequency assignment for IEEE 802.11wireless networks,” in Proc. IEEE Veh. Technol. Conf., Oct. 2003, vol. 3,pp. 1422–1426.

[9] Y. Lee, K. Kim, and Y. Choi, “Optimization of AP placement and channelassignment in wireless LANs,” in Proc. IEEE Conf. LCN, Nov. 2002,pp. 831–836.

[10] A. Mishra, S. Banerjee, and W. Arbaugh, “Weighted coloring based chan-nel assignment for WLANs,” ACM Mobile Comput. Commun. Rev., vol. 9,no. 3, pp. 19–31, Jul. 2005.

[11] A. Mishra, V. Brik, S. Banerjee, A. Srinivasan, and W. Arbaugh, “A client-driven approach for channel management in wireless LANs,” in Proc.IEEE INFOCOM, Apr. 2006, pp. 1–12.

[12] D. J. Leith and P. Clifford, “A self-managed distributed channel selectionalgorithm for WLANs,” in Proc. Int. Symp. Model. Optimization Mobile,Ad Hoc Wireless Netw., Apr. 2006, pp. 1–9.

[13] C. Na, J. K. Chen, and T. S. Rappaport, “Hotspot traffic statistics andthroughput models for several applications,” in Proc. IEEE GLOBECOM,Nov. 29–Dec. 3 2004, vol. 5, pp. 3257–3263.

[14] T. S. Rappaport, Wireless Communications: Principles and Practice,2nd ed. Englewood Cliffs, NJ: Prentice–Hall, 2002.

[15] R. R. Skidmore and T. S. Rappaport, “System and method for measur-ing and monitoring wireless network performance in campus and indoorenvironments,” U.S. Patent no. 7 096 160, Aug. 22, 2006.

[16] P. Bahl and V. N. Padmanabhan, “A software system for locating mobileusers: Design, evaluation, and lessons,” Microsoft Res., Redmond, WA,Apr. 2000. Tech. Rep.

[17] J. K. Chen, “Frequency allocation, transmit power control, and loadbalancing with site specific knowledge for optimizing wireless networkperformance,” Ph.D. dissertation, Univ. Texas, Austin, TX, May 2007.

[18] S. Shakkottai, T. S. Rappaport, and P. C. Karlsson, “Cross-layer designfor wireless networks,” IEEE Commun. Mag., vol. 41, no. 10, pp. 74–80,Oct. 2003.

[19] D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press,1991.

[20] J. Mo and J. Walrand, “Fair end-to-end window-based congestion con-trol,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 556–567, Oct. 2000.

[21] E. N. Skomal and A. A. Smith, Jr., Measuring the Radio FrequencyEnvironment. New York: Van Nostrand, 1985.

[22] T. Bonald, S. Borst, N. Hegde, and A. Proutiére, “Wireless data perfor-mance in multi-cell scenarios,” in Proc. ACM SIGMETRICS, Jun. 2004,pp. 378–387.

[23] J. K. Chen, T. S. Rappaport, and G. de Veciana, “Iterative water-fillingfor load-balancing in wireless LAN or microcellular networks,” in Proc.IEEE Veh. Technol. Conf., May 2006, vol. 1, pp. 117–121.

[24] Lexicographical order, Dec. 2008. [Online]. Available: http://en.wikipedia.org/wiki/Lexicographical order

Jeremy K. Chen (S’03–M’07) received the B.S.E.E.degree from the National Taiwan University, Taipei,Taiwan, in 2001 and the M.S. and Ph.D. degreesin electrical and computer engineering from TheUniversity of Texas at Austin (UT Austin) in 2004and 2007, respectively.

He is currently with Google Inc., New York, NY.He was with Qualcomm Flarion Technologies from2007 to 2008. He was a Research Assistant with theWireless Networking and Communications Group(WNCG), UT Austin, during 2003–2007. He held

summer internships with Wireless Valley Communications (now Motorola)in 2004 and Intumit Technology in 2000. During 1998 and 2001, he was anUndergraduate Research Assistant with Academia Sinica, Taipei, where hecodeveloped a cross-platform Chinese-input software package called Chewing.He has extensive experience in networks, wireless communications, algorithms,and software engineering.

Dr. Chen was the recipient of the following awards: the Silver Medal inthe International Olympics in Informatics in 1997; First Place at the AnnualJoint College Entrance Exam in the Republic of China (Taiwan) in 1997; theAsian Championship and World Final’s 10th Place (out of 1400) in the ACMInternational Collegiate Programming Contest in 1999; and the Taiwan FreeSoftware Community Awards in 2003 for the Chinese-input software packageChewing, which is now widely used in the Chinese community.


Gustavo de Veciana (S’88–M’94–SM’01–F’09) re-ceived the B.S., M.S., and Ph.D. degrees from theUniversity of California, Berkeley, in 1987, 1990,and 1993, respectively, all in electrical engineering.

He is currently a Professor with the Departmentof Electrical and Computer Engineering, The Uni-versity of Texas at Austin, where he served as theAssociate Director and then the Director of theWireless Networking and Communications Group(WNCG) during 2004–2008. His research focuseson the design, analysis, and control of telecommu-

nication networks. His current interests include measurement, modeling, andperformance evaluation; wireless and sensor networks; and architectures andalgorithms to design reliable computing and network systems.

Dr. de Veciana has served as the Editor of the IEEE/ACM TRANSACTIONS

ON NETWORKING and as a Cochair of the International Conference on Emerg-ing Networking Experiments and Technologies 2008 (ACM CoNEXT 2008).He was a recipient of the General Motors Foundation Centennial Fellowship inElectrical Engineering and the National Science Foundation CAREER Awardin 1996. He was a corecipient of the IEEE William McCalla Best ICCAD PaperAward in 2000 and the Best Paper Award in the ACM Transactions on DesignAutomation of Electronic Systems in 2002–2004.

Theodore S. Rappaport (S’83–M’84–SM’91–F’98) received the B.S., M.S., and Ph.D. degreesfrom Purdue University, West Lafayette, IN, in1982, 1984, and 1987, respectively, all in electricalengineering.

He is the William and Bettye Nowlin Chair inEngineering with The University of Texas at Austin(UT Austin) and is the Founding Director of theWireless Networking and Communications Group(WNCG), UT Austin (http://www.wncg.org/), whichis a center he founded in 2002. Prior to joining UT

Austin, he was with the Faculty of Electrical and Computer Engineering,Virginia Polytechnic Institute and State University, Blacksburg, where hefounded one of the world’s first university research and teaching centersdedicated to the wireless communications field. He has been a pioneer in thefields of radio wave propagation and wireless communication system design,and his work has influenced many international wireless standard bodies.In 1989, he founded TSR Technologies, Inc., which is a cellular radio/PCSsoftware radio manufacturer that he sold in 1993 to what is now CommScope,Inc. In 1995, he founded Wireless Valley Communications, Inc., which is asite-specific wireless network design and management firm that he sold in 2005to Motorola, Inc. He has testified before the U.S. Congress, has served as aninternational consultant for the ITU, has consulted for more than 30 majortelecommunications firms, and works on many national committees pertainingto communications research and technology policy. He is a highly sought-afterconsultant and technical expert. He is one of the world’s most highly citedauthors in the wireless field, having authored or coauthored more than 200technical papers and several books. He has 100 U.S. and international patentsthat are either issued or pending.

Prof. Rappaport was elected to serve on the Board of Governors of the IEEECommunications Society (ComSoc) in 2006 and the Board of Governors of theIEEE Vehicular Technology Society (VTS) in 2008. He was the recipient of theIEEE Communications Society Stephen O. Rice Prize Paper Award in 1999 forhis pioneering work on site-specific radio-frequency propagation and systemdesign.

site-specific knowledge and interference measurement for

Documents