Optimization Channel Assignment Method for MaximumThroughput under Communication and Positioning Requirements

Ming Li 1, Long Han1, Weiqiang Kong2, Shigeaki Tagashira3, Yutaka Arakawa2, and Akira Fukuda 2

1Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan2Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

3Faculty of Informatics, Kansai University, Osaka, Japan

Abstract— In this paper, we first discuss a throughput esti-mate method based on RTS/CTS, and then propose a channelassignment method that could achieve two goals: (a) themaximum throughput of overall network can be guaranteedand (b) terminals can be located in our system. Traditionally,channel assignment is used to mitigate interference forcommunication. In the area of positioning, to meet therequirement of highly-accurate positioning, wireless AccessPoints (APs) are always assigned to a single channel. Inother words, although mutual interference occurs seriously,channel assignment is not discussed in this area. To thebest of our knowledge, we are the first to propose a trade-off method that gives considerations to communication andlocation simultaneously. To confirm its effectiveness, weevaluate our approach by simulation. The results illustratethat the throughput of our channel assignment method ishigher than other methods.

Keywords: channel assignment, communication, positioning,throughput.

1. Introduction802.11-based wireless access is a widely used technology

in public hot spots such as university campus, airports, coffeebars, and hospitals, etc. A typical development of it in recentyears is Wireless LAN (WLAN) of Wi-Fi by which mobileterminals can access wireless networks smoothly through aWLAN Access Point (AP) [1]. However, with the extensiveestablishment of WLAN environment in public facilities,radio wave interference has become a severe problem.

On the other hand, as wireless networks rapidly gainedpopularity, various services that are based on context-awareof ubiquitous have been changing our daily life. As an essen-tial part of context-aware service, positioning technologiesare important for improving convenience of context-awaresoftware. The most well-known positioning system is GPS,which is broadly used in vehicles and mobile phones etc.However, a major problem of conventional GPS is that itcannot achieve a satisfactory accuracy degree for users inindoor environment such as in buildings or underground [2].Therefore, technologies like ultraviolet, RFID and WLANare researched and developed for indoor positioning [2][3].

In our research, wireless APs are utilized as positioningdevices since rapid development of WLAN provides a plat-form for positioning through APs. From our point of view,there are two primary reasons of using WLAN in positioningsystem.

1) WLAN is used initially for communication and Inter-net access. Since existing infrastructures such as APscan be used for positioning purpose in our system, wedo not need to install other special devices or software.

2) WLAN can be used in indoor environment as wellas outdoor environment. It would be very convenientif both indoor and outdoor LBS could be invoked byusing the same mobile devices.

The foremost contribution of our research is that we arethe first, to the best of our knowledge, to propose a channelassignment method that provides simultaneously wirelessbroadband communication service as well as precise posi-tioning service. Based on CSMA/CA with RTS/CTS [11],we propose a throughput estimate method suitable for ourresearch. The objective function of our channel assignmentmethod is to achieve the maximum throughput based onthe proposed estimate method. The necessity (or technicalobstacles that have to be solved) of channel assignment inour research can be explained in detail as follows. To avoidradio wave interference (that impairs network throughput),it is required that an AP within the interference range ofother APs is assigned with a different channel. In addition,to achieve the purpose of positioning, it is required that amobile terminal could be able to receive radio waves from atleast three APs since trilateration or multilateration locationmethod [4] is used in our system for positioning. And thus,adjacent APs must be assigned to the same signal channel.Therefore, channel assignment is one of main work in thisresearch.

We extend the description of our work as follows. Section2 discusses related work. Section 3 introduces backgroundtechnologies related to this paper. Section 4 defines the prob-lem to be addressed, formalizes the problem, and proposesa channel assignment method that could achieve maximumthroughput for overall network. Section 5 evaluates theproposed method and compares with other methods. Section6 concludes the paper and mentions future work.

2. Related WorksAs 802.11-based equipments have been vastly utilized,

their supporting communication devices have correspond-ingly developed and become spatially dense. It leads toa severe mutual interference among devices which resultsin a poor communication throughput. Most related worksthus merely target on how to realize maximum throughputfor high-speed communication through optimized channelassignments. Different from those works, our research dis-cusses channel assignments by taking both communicationperformance and positioning into account at the same time.

Channel assignment problem can be classified from dif-ferent point of views. Based on AP management, it can beclassified intocentrally managedmode anduncoordinatedmode. The former is mainly applied in public places such ascampus or airports where all APs are managed by a centralentity. The latter is often used in residential neighborhoods orprivate hot spots without a central manager. In both modes,an efficient mechanism for addressing interference issue toimprove WLAN performance is needed.

Based on centrally managed mode, the work in [5] dis-cusses the problems of channel assignment and AP place-ment simultaneously, and proposes an approximate solutionwith Integer Linear Programming (ILP). By adjusting thenumber of mobile terminals connected to APs, it evaluatesnetwork performance such as throughput. The main purposeis to find out optimized (minimized) AP locations from APcandidate points while considering a channel assignmentmethod with a maximized throughput. However, a problemof this work is that the proposed algorithm takes an expo-nential computation time due to exhaustive searching. Thus,it is considered to be not suitable for large scale networks.

In [6], to investigate the fairness issue of channel as-signment in resource sharing among mobile terminals, theauthors proposed, based on centrally managed mode, aclose-to-optimal approach calledpatching algorithm, whichis better than exhausting searching w.r.t. time complexity.Furthermore, the work proposes a probability-based through-put estimation method. However, to evaluate throughputperformance, the authors compare the method with otherthroughput evaluation standard. Due to the difference be-tween calculation methods, it is difficult to illustrate that themethod outperforms others.

The work in [7] uses centrally managed mode, in whichAP placement and channel assignment problems are opti-mized by mathematical programing. In particular, the ob-jective is to minimize overlapping coverage areas and tomaximize network throughput. The authors propose esti-mated accumulation of overlapping coverage and through-put, respectively. To balance these two aspects, a trade-off parameterα was introduced into integrated functions.By tuning α, the value of multi-objective functions can beobtained.

The mode used in [8] is uncoordinated, in which a

distributed, self-configure channel assignment scheme is pro-posed for uncoordinated WLANs. Core feature of this workis client-assisted, which means that APs are assisted withfeedback from clients for gathering adjacent devices’ trafficinformation. Since WLAN becomes uncoordinated and in-dependently managed with high AP density, an automaticchannel assignment method like the one in [8] becomesimportant. However, realization of this proposed approachis restricted by hardware development of communicationdevices.

All the above mentioned related works utilizenon-overlapping channels. Another viewpoint for classifyingchannel assignment problem is based onoverlapping chan-nels. The work in [9] uses the 802.11b/g standard forchannel assignment, in which Interference-factor (I-factor) isintroduced to judge whether adjacent nodes are overlappingwith each other. I-factor is the signal-to-noise ratio (SNR),which depends on the extent of frequency overlap betweenadjacent channels. Particularly, in [10], they propose an ideathat partially overlapped channels are not always harmful,and they judge the interface according to threshold of SNR,not simply by the color graph theory.

3. Technology BackgroundWLAN can be worked in infrastructure mode or ad-hoc

mode, where one of the difference between them lies onhow they are connected. In infrastructure mode, APs areconnected to each other with wired link to form backbonenetwork (that can be utilized by terminals). In ad-hoc mode,APs interconnect through single/multiple hop wireless linksto the backbone. And we consider the former mode in ourresearch.

3.1 Channel Assignment and Data RateBased on specifications, 802.11 mainly consist of

802.11b/g and 802.11a.1 Because of the limitation of802.11a in outdoor environment, and thus it is not furtherconsidered in this paper. The ISM (Industrial, Scientific andMedical) band of 802.11b/g contains 11∼14 channels. In-ferred from Fig.1, there are only 3 non-overlapping channelin 802.11b/g (namely, channel 1, channel 6 and channel11) [12].2 We utilize three non-overlapping channels in thispaper.

IEEE 802.11k was established and completed [13] totransfer and measure information of adjacent APs. Ac-cording to 802.11k, AP channel and neighbor informationcan be periodically transmitted along with beacon. By thismechanism, APs can clear the channel assignment infor-mation of neighborhood. Therefore, 802.11k is useful forthe development of channel assignment problem. In our

1Although not considered in this paper, our work is applicable to thenewest specification 802.11n as well.

2Actually, 802.11b has one more channel – channel 14 in japan, but wedo not discuss this case.

Fig. 1: 802.11b/g 2.4GHz Channels.

research, channel information can be gathered according tothis protocol.

According to IEEE802.11b/g standard specification, datarate can be automatically selected by connection quality.IEEE802.11g works in 2.4MHz with a maximum rawdata rate of 54Mbps. And the maximum raw date rate ofIEEE802.11b is 11Mbps. The data rate is changed accordingto signal quality and network environment. In this paper, weassume that change of data rate is only related with distancebetween APs and terminals.

In general, transmission range of APs or terminals can bedivided into communication range and interference range.If packets are sent/received between APs and terminals,they have to be located in a mutual communication range.Medium contentions occur if APs or terminals are in the mu-tual interference range. The received sensitivity thresholds ofthe two ranges are defined by the APs’ hardware.

3.2 Medium Access ControlAt present 802.11b/g is widely used in WLAN environ-

ment. According to communication protocol of Ethernet,802.11 mechanism of MAC layer is called CSMA/CA[11]. However, it cannot avoid collision problem such ashidden terminal problem and multiply simultaneous terminalrequests. Therefore, the RTS/CTS handshake-based MACis proposed. In our research, RTS/CTS is involved whendiscussing Potential Restrainer. As shown in Fig.2, the twoterminals (i.e.,t1 and t2) are in the communication rangeof ap, and they may not know the mutual existence ofeach other. The general access procedure of RTS/CTS isas follows.

1) Terminal t1 wants to send data through accessingapby sending a message RTS (Request To Send).

2) After receiving RTS,ap sends a receipt message CTS(Clear to Send). The CTS can be detected by othercommunication devices (such ast2) that are in theinterference range ofap. And all devices exceptt1 andap must keep silence until the confirmation messageACK (Acknowledgment) is received byap. Of courset1 will wait for a period if ap is busy.

3) t1 then obtains an authorization to send data toap. Onthe contrary,t1 can also receive data fromap.

4) When this data transmission finishes,ap sends ACKto all the other devices in its interference range,informing that they could now send RTS messages.

ap becomes idle again and waits the next RTS fromterminals such ast1 or t2.

We can summary the above access procedure as four-wayhandshakes of RTS-CTS-DATA-ACK. To avoid the situationthat t1 and t2 send RTS messages simultaneously,ap waitsa random time, and the terminal whose RTS is receivedfirst can send data. According to the principle, whenapsends CTS, terminals in the interference range ofap canbe restrained, hence we analysis four types of PotentialRestrainers in subsection 4.2 .

Fig. 2: CSMA/CA with RTS/CTS.

3.3 Location MethodIn this subsection, we describe the mechanism of our po-

sitioning system and the multilateration positioning method[4] used in this paper.

Firstly, in our positioning system, the strength of dataframe is observed and used to estimate the distance betweenAPs and terminals. A terminal can communicate with a APin a period of time. However, the communication (exchangedata frame) strength can be observed by other APs whichwork in the same channel. Considering the principle ofmultilateration used in our system, we require a terminalmust observe three APs at least for positioning.

Next, we explain the multilateration by RSSI (ReceivedSignal Strength Indication) for positioning. RSSI can bedetected by mobile devices. It is an advantage for us that weestimate accuracy by RSSI of APs, while do not depend onspecial hardware. It means that the positioning environmentis established by existed equipment of WLAN.

X

YA（xa,ya）

C（xc,xc）B（xb,yb）0

1 2 3n 4（a） (b)

D（x,y）

Fig. 3: Triangle and Multilateration Method for Positioning.

We can measure the distance between transmitters andreceivers by RSSI and calculate coordinate by pythagorean

theorem. For example, there are three points A(xa, ya),B(xb, yb), and C(xc, yc) which are known, and shown asFig.3(a). The coordinate of intersection point D(x, y) isunknown. We denote the distance form point D to A,B,Cas ra, rb, rc respectively. We can acquire the equations asfollows and solve it.

√(x− xa)2 + (y − ya)2 = ra√(x− xb)2 + (y − yb)2 = rb√(x− xc)2 + (y − yc)2 = rc

However, in real environment, there are not only threetransmitters(APs) emitting signals. Hence we have to con-sider multiple known points such asn which shown asFig.3(b), and the equations can be described as follows.

√(x− x1)2 + (y − y1)2 = r1√(x− x2)2 + (y − y2)2 = r2

...√(x− xn)2 + (y − yn)2 = rn

Obviously, the coordinate of D is clear if the(x, y) aresolved. The equations above cannot be solved directly soeasily because it is a non-linear equations. However, we cansolve it by Maximum-Likelihood Estimation (MLE).

4. The Proposed MethodBased on the technologies mentioned in the previous sec-

tion, we first propose a throughput estimation method, andthen propose an optimized channel assignment method witha maximized overall network (terminals) throughput. Mean-while, since the best solution must satisfy the requirementsof both positioning and communication, we summary someassumptions/preconditions made in this work as follows:

(a) To achieve the goal of positioning, every terminal mustbe able to observe in its interference range three APsof the same channel.

(b) To satisfy the requirement of communication, everyterminal must be able to connect with a AP for com-munication that is in its communication range.

(c) The APs whose coordinates are known can be placedas a uniform deployment or not in a field beforehand.

(d) Every device (AP and terminal) has only one NetworkInterface Card (NIC) in this work, and thus, the channelof communication AP is the same as the channel ofpositioning APs.

4.1 Problem FormulationWe first define some core concepts – the setsAP and

T of APs and Terminals, respectively, that are used in thework.

The set of APs:AP = {api | i = 1, 2, ...,m}, whereeachapi is an AP.

The set of Terminals: T = {tj | j = 1, 2, ..., n}, whereeachtj is a terminal.

Based on the three non-overlapped channels of 802.11b/g,we consider that each AP can be assigned with a channelk(k ∈ {1, 6, 11}), and thus the setAP is divided into threesubsetsAPk, where eachap ∈ APk is assigned with channelk. For∀k, k′ (∈ {1, 6, 11}), APk∩APk′ = Φ and∪APk =AP .

Since each AP is assumed to have one interface only andthus an AP only works with one channel. In addition, allAPs are assigned with a channelk, wherek ∈ {1, 6, 11}.The distance between an APapi and a terminaltj can becalculated by a functionD(api, tj).

As mentioned in subsection 3.1, every AP or terminalhas an interference range and a communication range. WeuseR and r (R ≥ r) to denote the corresponding radiusrespectively. To judge whether a terminaltj is locatedin the interference range ofapi, we define the functionAT (tj , api) as follows.

AT (tj , api) =

{1 if D(api, tj) ≤ R0 otherwise

(1)

wherei ∈ {1, 2, ...,m}, j ∈ {1, 2, ..., n}.To check whether an APapi is assigned with a channel

k, we defined the functionAC(k, api) as follows:

AC(k, api) =

{1 if api ∈ APk

0 otherwise(2)

where i ∈ {1, 2, ...,m}, k ∈ {1, 6, 11}. The meaningof function (2) is that ifapi works with channelk, thenAC(k, api) = 1.

Next, we useSjk to denote the number of APs that areassigned with channelk and are in the interference range ofterminal tj .

Sjk =m∑i=1

AT (tj , api) ·AC(k, api) (3)

wherei ∈ {1, 2, ...,m}, j ∈ {1, 2, ..., n}, k ∈ {1, 6, 11}.We formulate the two assumptions/preconditions (a) and

(b) mentioned in the beginning of this section as follows.Note that we denote them as "Restriction 1" and "Restriction2" respectively, for illustration simplicity in the algorithm insubsection 4.3.

Restriction 1 (on Positioning): The basic condition forpositioning is that in the interference range of any terminaltj , there are at least three APs working in the same channelas this terminal. So we describe the assumption as follows.

∀j, ∃k Sjk ≥ 3. (4)

wherej ∈ {1, 2, ..., n}, k ∈ {1, 6, 11}.Restriction 2 (on Communication): Every terminal must

be able to connect with a AP for communication. To satisfy

this, it is required that at least one AP is in the commu-nication range of the terminal, which can be described asfollows.

∀i, ∃j D(ti, apj) < r (5)

wherei ∈ {1, 2, ...,m}, j ∈ {1, 2, ..., n}.In fact, there may exist multiple APs in the communi-

cation range of a terminal. So we define a setAPTj ={api | D(tj , api) < r}. The element APs of setAPTj

are those that can communicate with terminaltj in theircommunication range. In addition, a setHj , whose elementAPs are those that must be satisfied for both positioning andcommunication for terminaltj , is defined as follows:{

∀j Hj ⊆ APTj ∧ Hj ̸∈ Φ

∀i api ∈ Hj → ∃k ACk(api) ∧ Sik ≥ 3

For providing wireless broadband, terminals are requiredto connect their nearest AP which is selected from the APset that satisfies above formula. The functionO(ti, apj) isused to define this issue.

O(tj , api) =

1 api ∈ Hj ∧ (∃i′ (api′ ∈ Hj ∧ i′ ̸= i)→ D(api, tj) ≤ D(api′ , tj))

0 otherwise(6)

If api is the nearest AP totj , the value of functionO(ti, apj)is 1, otherwise it is 0. In brief, one terminal can only beworked in a channel, and this channel must be taken bothcommunication and positioning into account simultaneously.

4.2 Throughput EstimationIn our research, we estimate terminal throughput accord-

ing to data rate and the number of potential restrainers. Weassume a WLAN environment without interference and ob-stacle, and that AP has no delay in switching communicationfrom one terminal to another.

We imagine that there are one terminal and one AP merelyin an ideal environment. If the terminal is in the area of54Mbps, we consider that the throughput of this terminalis 54Mbps. On the other hand, if the number of terminalsincreases, the phenomenon of Medium Access ContentionConstraints (MACC) [12] happens obviously. In this paper,we estimate throughput of overall network by consideringaccumulation of potential restrainers. Therefore, we analyzefour types of potential restrainers for an arbitrary terminalt1 that communicates with APap1.

Type1:As shown in Fig.4(a), mobile terminals in theinterference range oft1 are considered as restrain-ers of type1. If mobile terminals near tot1 arein its interference area, potential MACC happensdirectly. The number of potential type1 restrainersis denoted byRST1, where in Fig.4(a)r1 and r2are such restrainers.

Fig. 4: Four Types of Potential Restrainers.

Type2:Different from type1, mobile terminals, which arein the interference range ofap1 that connects withterminal t1, are considered as restrainers of type2.potential MACC also happen in this case. Thenumber of potential type2 restrainers is denotedby RST2, where in Fig.4(b)r3 and r4 are suchrestrainers.

Type3:As shown in Fig.4(c), mobile terminals, whichcommunicate with those APs that besidesap1 butalso in the interference range oft1, are consideredas restrainers of type3. According to the princi-ple of CSMA/CA with RTS/CTS, MACC occursbetween those terminals andt1. The number ofpotential type3 restrainers is denoted byRST3,wherer5 andr6 are such restrainers.

Type4:As shown in Fig.4(d), mobile terminals, whichcommunicate with those APs that are in the inter-ference range ofap1, are considered as restrainersof type4. Similar to type3, MACC also occursbetween those terminals andt1. The number ofpotential type4 restrainers is denoted byRST4,wherer7 andr8 are such restrainers.

Based on these types of potential restrainers, the functionof calculating throughput for an arbitrary mobile terminalt ∈ T can be defined as follows, wheretj ̸= t:

TH(t) =DR(t)∑n

j=1 RST (t, tj)(7)

where

RST (t, tj) =

{1 if tj is the potential restrainer of t0 otherwise

(8)DR(t) is the data rate oft which is calculated by the

RSSI (Received Signal Strength Indication) received fromits connecting AP. In this research, we converse it according

to the distance between AP and terminal. For terminalt,the number of all of potential restrainers can be representedby

∑nj=1 RST (t, tj). FunctionRST (t, tj) is used to check

terminal whethertj is the potential restrainer oft.Therefore, the function of calculating throughput for over-

all terminals can be defined as:n∑

j=1

TH(tj) (9)

4.3 Channel Assignment AlgorithmThe objective of the research is to find out the maximum

throughput of overall terminals through channel assignment.Pseudo code of the proposed algorithm is described asfollows.

Channel Assignment AlgorithmInitialization:

All aps are assigned to channel 1;MAXTH =

∑nj=1 TH(tj);

Optimization:Exhaustive search for any possible combinations ofaps’ channels{If (Restriction 1 && Restriction 2)

Calculate throughputTH of this channel combination;If (TH > MAXTH )MAXTH = TH;

}

Output:The channel assignment whenMAXTH ;The valueMAXTH .

Initially, all aps are assigned to the same channel such aschannel 1. The throughput of overall terminals is calculatedaccording to this channel assignment. Thenaps’ channelsare changed by exhaustive enumeration. For every possiblecombination ofaps’ channels, check whether it satisfies bothRestriction 1 and Restriction 2. Finally, find out, from allsatisfied combinations, the channel assignment method bywhich a maximum throughput is obtained.

5. Evaluation and Analysis5.1 Simulation Parameters

We calculate the throughput of our proposed method inthis section. Since we are the first to propose the channelassignment method by considering both communication andpositioning and there are no similar researches, we have tocompare it with single methods and random methods. Bysingle methods we mean the methods in which all APs areassigned with the same channel. By random methods wemean the methods in which APs select three isolated channelrandomly.

As shown in the table 1, we test our simulation in a50×50 (m) area. The radiums of communication and radiusof interference are set as 11m and 16m, respectively. We test

Table 1: The Simulation ParametersSimulation Parameters ValueService area size (m) 50×50Number of APs 6∼15Number of terminals 2∼24Channel Set {channel 1, channel 6, channel 11}The Employed 802.11 Specify 802.11b, 802.11gRadius of Communication (m) 11Radius of Interference (m) 16

every case under two specifies of 802.11b and 802.11g. Andonly three isolated channels can be used in our paper.

5.2 Scenarios and AnalysisWe consider two test scenarios for different numbers of

APs and terminals, respectively. In the first scenario, we fixthe number of APs as 11 such as shown in Fig.5, whereasthe number of terminals is changed from 2 to 24. Accordingto the result of simulation shown in Fig.6, status change ofthroughput are similar for 802.11b and 802.11g. Take thespecify of 802.11g as an example, the throughput of ourproposal is optimal obviously. As a quantitative analysis,the throughput of our proposed method is about three timeshigher than single methods and 1.5 times higher than randommethods. As the the number of terminals grows, the through-put keeps a stable value in every case. However, the averagethroughput is calculated and shown in Fig.7. It is clear that asthe number of terminals growing, the average throughput perterminal decreases for every case. Nevertheless our proposalis always better than other methods in general.

Fig. 5: An Example of AP Deployment.

On the other hand, to present an example of channelassignment, we show an assignment pattern according toour proposal when the number of APs is 11 and the numberof terminals is 14 such as shown in Fig.5. Based on ourassignment, the throughput of overall network is 36.67 Mbps(802.11b) and 180 Mbps (802.11g), respectively, which isbetter than other methods.

In the second scenario shown in Fig.8, we fixed thenumber of terminals, and change the number of APs from 6to 15. As the number of APs increase, the overall throughputof proposed method is higher than others in two specifies re-spectively. Furthermore, we have to point out that the growth

Fig. 6: Overall Throughput of Terminals for Fixed APs.

Fig. 7: Average Throughput of Terminals for Fixed APs.

rate of our proposal is optimal obviously. In this section, weevaluate our simulation by changing some parameters. Theresults are clear that our proposal is better than other twomethods with respect to network throughput.

Fig. 8: Overall Throughput of Terminals for Fixed Terminals.

6. ConclusionIn this paper, a throughput estimate method according

to the number of potential restrainers is proposed basedon CSMA/CA with RTS/CTS. Furthermore, we propose amethod for channel assignment, which, to the best of ourknowledge, are the first channel assignment method thatconsiders communication and positioning simultaneously. To

verify its effectiveness, we compare the method with singlemethods and random methods with respect to throughput byusing our proposed estimate method. The results appear thatour method is better than others in every case that we tested.

In the future, we plan to evaluate the positioning aspectof our proposed method, namely whether positioning couldreach the optimal objectives of communication and position-ing. Moreover, we will improve the performance of channelassignment method and try to avoid extensive search of allpossibilities.

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