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Interference-aware Game-based Channel

Assignment Algorithm for MR-MC WMNs

Amira BEZZINA∗, Mouna AYARI†, Rami LANGAR∗, Guy PUJOLLE∗, Leila SAIDANE†

∗LIP6 Laboratory, University of Paris VI, Paris, France

†CRISTAL lab, National School of Computer Sciences, University of Manouba, Tunisia

Emails: {amira.bezzina, rami.langar, guy.pujolle}@lip6.fr, mouna.ayari@cristal.rnu.tn, leila.saidane@ensi.rnu.tn

Abstract—One of the main challenges of multi-radio multi-

channel wireless mesh networks (MR-MC WMNs) is how

to efﬁciently avail from the radio resources available in

the network. The level of interference experienced by the

mesh nodes rises when the network becomes more connected

and the number of radios per node increases. To mitigate

interference experienced by the wireless mesh nodes while

taking advantage from the multi-channel network aspect,

we propose a novel Interference-aware Game based Channel

Assignment algorithm, named IGCA. We prove through simu-

lations that our proposed algorithm contributes in alleviating

the node interference degree, fairly allocates interfaces to net-

work non-overlapping channels and increases simultaneous

transmissions in the network. An improvement up to 50%

of both interference degree and simultaneous connections is

particularly observed in comparison with a prominent existing

approach - the Near-optimal Partially Overlapping Channel

Assignment algorithm.

Keywords: Wireless Mesh Networks, Multi-Radio Multi-

Channel, Channel Assignment, Interference Aware, Game

Theory, Potential Game.

I. INTRODUCTION

Future wireless mobile communications will be driven

by high-converge networks that integrate a wide range

of technologies and services. In this perspective, wireless

mesh networks (WMNs) are considered as a potentially

attractive key-solution to provide broadband wireless ac-

cess services. Due to their promising features including

self-organization, self-conﬁguration, easy network main-

tenance and reliable service coverage, such networks pro-

vide a ﬂexible high-bandwidth wireless backhaul over

large geographical areas, especially when multiple chan-

nels and multiple radio interfaces are deployed.

While single radio mesh nodes operating on a single

channel suffer from capacity constraints, deploying mul-

tiple radios and multiple channels on mesh routers can

improve signiﬁcantly the capacity of the network and

increase the aggregate bandwidth [1] [2]. However, con-

sidering an efﬁcient channel assignment which pursues an

appropriate mapping between the available channels and

nodes’ radios is required. In fact, despite the availability of

multiple frequencies offered by the IEEE 802.11 standards,

the total number of radio interfaces in a WMN is much

higher than the number of available channels. So, many

neighboring nodes radio interfaces could be assigned the

same channel or channels that are partially overlapping

to each other resulting in a network performance degra-

dation due to interference problem.

To design an efﬁcient channel assignment in multi-radio

multi-channel WMNs, many important issues should be

handled carefully such as minimizing interference effect,

maintaining the network connectivity and improving the

aggregate network capacity. To reach this goal, channel

assignment for multi-channel wireless mesh networks has

been widely proposed in the literature, but still very

knotty when it comes to meet all the challenges.

In this paper, we investigate how to design an efﬁ-

cient channel assignment algorithm that reaches these

requirements. Speciﬁcally, we propose a new interference-

aware game-theoretic approach for channel assignment

in a mesh backbone. We ﬁrst formulate the problem as

a potential game, i.e, an identical interest game. Indeed,

mesh routers (or MRs) are modeled as players trying

to maximize a speciﬁc utility in order to alleviate the

"a priori" interference between them. We then describe

our proposed Interference-aware Game-based Channel

Assignment Algorithm (IGCA) with perfect information.

To gauge the effectiveness of our proposal, we compare

the IGCA algorithm with a prominent existing approach:

the Near-optimal Partially Overlapping Channel Assign-

ment algorithm [3]. Results show that IGCA reduces

signiﬁcantly nodes interference degree, ensures a fair

distribution of radios between channels and most im-

portantly permits a considerable number of simultaneous

connections in the mesh backbone, when compared to

NPOCA.

The reminder of the paper is organized as follows.

Section II discusses literature that is relevant to this work.

Section III presents the system model used in our ap-

proach and the problem formulation as a potential game.

The game-based proposed algorithm is then introduced

in section IV. Simulation results are provided in section

V. Finally, section VI concludes this paper.

II. RELATED WORK

Owing to the importance of efﬁciently assigning ra-

dios to channels in order to improve the performance

of MR–MC WMNs, extensive studies have been carried

out to tackle this issue. Several multi-channel allocation

solutions have been proposed in the literature. Each one

of them focuses on a speciﬁc aspect and addresses a

particular need. Comprehensive literature surveys pro-

viding interested classiﬁcations of channel assignment

approaches designed for MR-MC WMNs can be found in

[2] [4] [5]. Here, we mention only studies that are directly

relevant to our work, i.e. those that have applied game

theory to solve the channel assignment (CA) problem [6].

Gao et al. presented in [7] a static cooperative game

with perfect information in which players within a coali-

tion collaborate to achieve high data rates. The focus was

on the performance improvement of the multihop links,

induced by cooperation gains, without sacriﬁcing the

performance of single-hop ones. Authors introduced the

min-max coalition-proof Nash equilibrium (MMCPNE)

channel allocation scheme in the game. However, this

work has mostly a theoretical interest. Some assumptions

made by the authors like the fact that "each node partic-

ipates in only one communication session" and that "the

whole network is a single collision domain" do not reﬂect

usually a real network behavior.

In [8] and [9], the CA problem has been formulated as a

non-cooperative game where each node aims at maximiz-

ing its own proﬁt selﬁshly. Yang et al. proposed in [8] a

CA scheme designed for MR-MC wireless networks with

multiple collision domains. The proposed strategic game

named ChAlloc has been formulated as a strategic game.

To avoid possible oscillation in ChAlloc game, a charging

scheme was designed to induce players to converge to a

Nash Equilibrium. Manikantan Shila et al. [9] proposed an

algorithm achieving a load balancing Nash Equilibrium

solution in a selﬁsh and a topology-blind environment.

The algorithm is based on imperfect information for single

collision clique wireless networks. The solution operates

in three stages, each stage focuses on improving the total

achievable data rate of each node.

The two above proposed schemes are very interesting.

However, they do not match well with our speciﬁc context

of application. They are designed for non cooperative

MC-MR wireless networks, where the network consists

of heterogeneous wireless nodes each owned by an in-

dependent individual. Nevertheless, we consider in our

study wireless mesh backbones where mesh routers tend

to be cooperative since they are managed by the same

administrator. Assuming that mesh backbone nodes may

have a selﬁsh behavior neglecting the system performance

may not hold in practice.

Nezhad et al. proposed SICA [10], a game formulation

of CA taking into account the co-channel interference. The

proposed interference-aware CA scheme is semi-dynamic

and distributed. Besides, it applies an on-line learner

algorithm which assumes that nodes do not have perfect

information. Thus, players (mesh routers) play a mixed

strategy based on their weights to solve it. However,

besides having selﬁsh nodes that try to occupy the best

channels, SICA uses three radios for each node (the ﬁrst

to receive, the second to transmit and the third tuned to a

common channel for all nodes) which cannot be managed

in all WMNs.

In the same context and aiming to especially reduce

physical-layer interference, Yen et al. proposed in [11] a

two-stage radio allocation scheme where wireless inter-

faces are modeled as players participating in a radio re-

source game. On one hand, the ﬁrst stage assigns channels

to radios using a game-theoretic approach. On the other

hand, the second stage assigns the resulting radio-channel

pairs to links using a greedy method.

Availing from partially overlapped Channels, Duarte et

al. presented respectively in [3] and [12] the Near-optimal

Partially Overlapping Channel Assignment (NPOCA)

and Heuristic Partially Overlapped Channel Assignment

(HPOCA) schemes using a cooperative and potential

game. These algorithms have the overall objective of

maximizing the network throughput while reducing co-

channel interference. Unfortunately, the proposed channel

selection mechanisms are not optimal. They broadcast a

lot of coordination messages in the network. Moreover,

they do not take into account the connectivity issue.

Later, we compare our proposal to the NPOCA scheme,

arising the interest in developing strategic approaches

with perfect information to solve the CA problem.

III. CONTEXT AND PROBLEM FORMULATION

We consider a wireless MR-MC backbone mesh con-

sisting of several mesh routers. In our study, we focus on

providing a suitable CA algorithm that aims to reduce

channel interference while keeping a connected network

and avoiding channel congestion. In the following, we

ﬁrst present the necessary notions used in our model.

Then we expose the corresponding problem formulation

based on a game theoretic approach.

A. Notations

•A={a1, a2, ..., an}is the set of nodes, where |A|

is the total number of nodes deployed in the mesh

backbone.

•Idenotes the number of radios per node.

•Cdenotes the number of non-overlapping channels

in the network.

•kij is the number of radios of player iassigned to

channel j.

•nij is the number of interfering neighbors of player

iwhich are using channel jon one of their radios.

•Nidenotes the number of potentially interfering

neighbors of i(i.e. nodes in the interference range

of node i)

•Sirepresents the strategy of player iand is denoted

by Si={ki1, ki2, .., kiC }

•S=×i∈ASi=S1×S2×... ×Snis the game proﬁle

deﬁned as the Cartesian product of the players’

strategy vector.

For our model, we assume the following:

•Pj∈CKij = 1 : All radios must be affected to

channels.

•kij ≤1: Radios of a same player must be affected

to different channels.

• |C|> I : The number of interfaces per node is

smaller than the number of channels available in

the network.

•Iis ﬁxed and is the same for all players.

B. Utility

The main objective of our game is to minimize the

network interference. Thus, we deﬁne an interference-

aware metric Gias the gain of player i:

Gi= 1 −X

j∈C

kij ×nij

Ni×I(1)

Each player is a decision maker which chooses a strat-

egy Si. It maximizes its gain by minimizing the cost of

interference expressed by the second term of the metric

Gi. This cost can be seen as a penalty fee imposed on

player i due to its choice.

The player’s utility is deﬁned as:

Ui(S) = U(S) = Pi∈AGi

|A|(2)

Theorem: The proposed channel allocation game is an

identical interest game.

Proof:

We ﬁrst prove that our game is a potential game.

Then, we prove that it belongs to the speciﬁc subclass

of identical interest game.

A potential game is a normal form game such that

any change in the utility function of any player due to

a unilateral deviation by that player is correspondingly

reﬂected in a global function referred to as the potential

function [13].

Deﬁnition: A game is an exact potential game if there

is a function φ:S→Rsuch that ∀S−i∈S,∀S0

i, S00

i∈S:

φ(S0

i, S−i)−φ(S00

i, S−i) = U(S0

i, S−i)−U(S00

i, S−i)

Or, it is obvious that the utility function deﬁned in

Eq. (2) is a potential function for IGCA. Thus, we deal

here with an exact potential game.

Besides, we have: φ(S) = Ui(S)=(S),∀i∈A.

As a result, our game is an identical interest game

(called also common interest game or team game). In such

game, the players’ utilities are chosen to be the same and

players aim to maximize their common utility. Identical

interest games are a particular case of exact potential

games [14]. Thus, they inherit all of their properties. In

fact, for a potential game, the following holds:

•Every ﬁnite potential game possesses at least one

pure strategy Nash Equilibrium (i.e. deterministic

NE).

•All NE are either local or global maximizers of the

utility function.

C. Algorithm

Given the utility function previously described in sec-

tion III.B, we propose a game-based algorithm with per-

fect information in which each player knows the strategies

of the others. We use in our model an "extensive form"

game where players play one after the other. Players’

choices are based on the "better response", a known

scheme used to reach utility function’s maximizers.

Obviously, the "better response" provides less intensive

computation at the cost of a slower convergence to the

equilibrium than the "best response". The latter provides

a fast convergence but requires intensive processing that

grows exponentially according to the size of the network.

Note that usually a wireless mesh backbone is managed

by an administrator. In order to reduce transmission over-

head, our algorithm uses a partially centralized approach

which can be suitable to a large scale mesh backbone. Be-

sides, it avoids congestion by ﬂooding the network with

redundant information. Hence, we made the following

assumptions:

•A common channel for communication between

players in the negotiation phase is assumed to be

available.

•The real allocation of channels is done after the

execution of the following algorithm.

•T is the stop condition in terms of time or maximum

number of negotiations.

Algorithm 1: IGCA Algorithm

Input: A, I, C

Output: S set of strategies S1, S2, . . . , S|A|

1Initiator ←SelectAnI nitiator(A)

2Order ←SelectRandomOrder(I nitiator, |A|)

3Broadcast(Order, A)

4for ifrom 1to |A|do

5Si(0) ←RandomV alidStrategy(I, C )

6Strat[i]←SendI nitialStrategy(Initiator, Si(0))

7j←1

8i←Order[j]

9sender ←Initiator

10 while T=false do

11 SendU pdatedS trategies(sender, i, Strat)

12 Sirand ←RandomV alidStrategy(I, C)

13 if Sirand > Si(t)then

14 Si(t+ 1) ←Sirand

15 else

16 Si(t+ 1) ←Si(t)

17 Strat[i]←Si(t+ 1)

18 sender ←i

19 Updatej

20 i←Order[j]

21 UpdateT

22 SendStrategies(sender, Initiator, Strat)

23 return S

At the beginning, a game initiator is chosen between

all the mesh routers. The choice can be done randomly or

the most connected node can be elected to avoid multi-

hop transmissions in the network. The initiator picks out

the order by which players will perform the game. Then,

it broadcasts a signal containing the order of the game to

all players informing them to start the game.

Each player picks a random valid strategy and sends

it back to the initiator. After collecting all strategies, the

latter sends them to the ﬁrst player. This player selects

a random valid strategy in the set of all valid strategies

that it can perform according to the assumptions men-

tioned earlier and which maintains the connectivity of

the network (i.e. The backbone is a connected graph). It

compares it with its current strategy and keeps the one

that keeps the network connected and yields a higher

value of the utility function (i.e. it compares the following

utilities : Ui(Sirand, S−i)and Ui(Si(t), S−i)). Then, it

sends its new decision (i.e. the chosen strategy), following

the order of the game, to the next player which will do

the same.

The step of selecting an improving strategy or maintain-

ing the previous one is repeated until the stop condition

T is met. Finally, the last player will send the set of

ﬁnal strategies S to the initiator of the game. This step

is needed in case we want to further improve the CA of

the network. In fact, the CA procedure can be dynamic.

Thus, our algorithm can be repeated when needed. It can

restart at the 7th line of the algorithm with the actual set of

strategies S instead of restarting the strategies to random

ones. In general, this step can be seen as a negotiation

phase on a common channel before actually affecting

channels to the interfaces.

It is worth noting that the IGCA algorithm may some-

times not reach the global-optimum if one player is

trapped in a local-optimal NE value since more than one

NE can exist.

IV. PER FO RM AN CE EVALUATION

In this section, we evaluate the performance of our

game theoretic algorithm. We ﬁrst present the simulation

environment and describe the used scenarios. Then, we

describe the results of our experiments. We used the

interference-aware NPOCA [3] algorithm as baseline to

which IGCA improvements are compared. Note that,

although NPOCA was designed to work with partially

overlapped channels, it is supposed to perform well with

a non-overlapping channels environment.

A. Simulation Environment

We consider in our experiments a random wireless

mesh backbone network consisting of 10 mesh routers

placed in a 100m×100mﬁeld. The network uses the

IEEE.802.11a standard as wireless technology and pos-

sesses 8 non-overlapping channels. We shift the number

of nodes’ radios from 2 to 5. The break parameter T is

ﬁxed to 1000 iterations. All nodes have the same commu-

nication range CR = 30m. The interference range (IR) is

estimated as follows: IR = 1.5×CR. Simulations were

performed using 50 different seeds regarding a speciﬁc

random node distribution. It is worth noting that to test

the scalability of our proposal, we conducted the same

experimentation on a 50 nodes’ backbone. However, due

to space limitation, we only present here the results of 10

nodes simulations.

B. Performance Metrics

In order to evaluate the performance of IGCA, we have

considered the following metrics:

•Connectivity degree: the connectivity degree of a node

iwith reference to the channel allocation is equal

to the number of neighbors that can communicate

directly with node iusing a common channel.

•Interference Degree: the interference degree of a MR

is deﬁned as the number of interfering neighbors

regarding the chosen CA scheme.

•Channel distribution: the channel distribution of a

channel c∈Cis equal to the number of all interfaces

assigned to channel c. In other words, it is the

number of nodes that can use channel cto send data.

•Number of possible simultaneous connections: It is equal

to the number of possible connections that can

be handled simultaneously on non-interfering links

using a speciﬁc channel c∈C.

C. Simulation Results

In what follows, we present our simulation results in

terms of connectivity degree, interference degree, channel

distribution, and number of possible simultaneous con-

nections.

1) Connectivity Degree:

This evaluation metric is fundamental for the good de-

ployment of any wireless network. It is important to note

that connectivity is well addressed by our algorithm since

IGCA returns always a connected graph. Nevertheless,

NPOCA algorithm can provide a non-connected network

graph. Hence, in order to conduct a fair comparison

between the utility functions of both approaches, we

added the connectivity condition to NPOCA.

In the ﬁrst set of experiments, we studied the perfor-

mance of our proposed IGCA algorithm in terms of Cu-

mulative Distributed Function (CDF) of node connectivity

degree.

Figs. 1(a) and 1(b) show the impact of the number

of interfaces per node on the connectivity degree. From

that ﬁgure, we can observe that with 2 and 3 radios per

node, NPOCA gives slightly better results than IGCA.

In fact, unlike our gain metric Gi, the metric used in

the utility function of the NPOCA algorithm is based on

two topology control factors (i.e. the hop count from the

node to the gateway and a connectivity factor set to 1

if the node can reach the gateway) which warrant the

efﬁciency of network links toward the gateway. But still,

our approach gives a good node connectivity degree and

the improvement of NPOCA is merely of 1 node more. In

addition, we notice that starting from 4 interfaces, IGCA

converges to the best connectivity scheme with regards to

the same random 10 nodes distribution in the network.

2) Interference Degree:

Fig. 2 shows the CDF of interference degree for both

IGRA and NPOCA algorithms. Note that this perfor-

mance metric is closely related to the previous one and

(a) I= 2 (b) I= 3 (c) I= 4 (d) I= 5

Figure 1. CDF of connectivity degree in a 10 nodes backbone with CR=30m

(a) I= 2 (b) I= 3 (c) I= 4 (d) I= 5

Figure 2. CDF of interference degree in a 10 nodes backbone with CR=30m

(a) I= 2 (b) I= 3 (c) I= 4 (d) I= 5

Figure 3. Channel distribution in a 10 nodes backbone with CR=30m

IGCA NPOCA

Channel Identiﬁer I= 2 I= 3 I= 4 I= 5 I= 2 I= 3 I= 4 I= 5

1 0.62 1 1.16 1.32 0.34 0.7 0.76 1.08

2 0.44 0.98 1.14 1.5 0.44 0.72 0.92 1.18

3 0.62 0.98 1.12 1.46 0.52 0.84 1.02 1.1

4 0.62 1.02 1.2 1.32 0.44 0.46 1.02 1.4

5 0.46 1.04 1.22 1.62 0.4 0.82 1.02 1.16

6 0.54 1 1.18 1.54 0.48 0.62 0.98 1.3

7 0.54 1.1 1.18 1.44 0.42 0.58 1.1 1.4

8 0.64 1 1.12 1.44 0.48 0.62 0.88 1.22

Average per number of interfaces 0.56 1.015 1.165 1.45 0.44 0.67 0.9625 1.23

Average possible communications in the network 4.64 8.12 9.32 11.6 3.52 5.36 7.7 9.84

Table I

AVERAGE NUMBER OF POSSIBLE SIMULTANEOUS CONNECTIONS PER CHANNEL ON A 10 NODES MESH BACKBONE

a good interpretation must be done with reference to the

both.

From Fig. 2(a), we can notice that, using the IGCA

algorithm, 80% of MRs interfere with 3 nodes or less

while they interfere with the double (i.e. 6 nodes or

less) using NPOCA. Recall that in this same scenario,

80% of nodes are connected to 2 nodes or less with

IGCA and to 3 nodes or less with NPOCA (see Fig.

1(a)). With a same reasoning, we observe that 80% and

60% of the backbone nodes, having respectively 2 and 3

interfaces per node, have at most 1

2of interfering nodes

that can carry transmission data using NPOCA. While,

using IGCA, at most 2

3of them can.

In addition, we observe that the improvement achieved

by IGCA in node interference degree can exceed 50% com-

pared to NPOCA when I63. This can be explained by

the good design of our interference-aware utility function

that strengthens the interference awareness of the nodes.

However, we notice that the performance of IGCA de-

grades and becomes closer to NPOCA for high values of

I (i.e., when the number of radios increases and exceeds 5

in our case). This is simply because, with considering high

number of interfaces per node, the interference becomes

unavoidable whatever the CA scheme used.

3) Channel Distribution:

Fig. 3 further investigates how the assigned channels

are distributed within the network. Note that in our

simulations, 8 channels per radio interface are available.

Recall that this performance metric indicates the average

number of radio interfaces assigned to use the same

channel for transmitting data. From this ﬁgure, we can

clearly observe the unrelenting fairness of IGCA ap-

proach in distributing interfaces between channels. This is

very important to avoid having underused and overused

channels in the network. Whereas, channel distribution

graphs related to NPOCA become more serrated when

the number of radios per node increases.

4) Number of possible simultaneous connections:

To further show the beneﬁt of our approach, we plot

in Table I the average number of possible simultaneous

connections, i.e., the average number of non-interfering

links per channel using the aforementioned scenarios. We

can clearly observe that the average number of possible

communications in the network is improved using IGCA

in comparison with NPOCA and this result is indepen-

dent from the number of interfaces per node. The gain

is up to 51%. In addition, the values given by IGCA for

every speciﬁc value of Iare smoother than those given by

NPOCA. Hence, besides being fair in distributing radios

on channels, IGCA enables equitable number of possible

transmissions over channels.

V. CONCLUSION

In this paper, we have envisioned a new channel as-

signment algorithm for Multi-Radio Multi-Channel Wire-

less Mesh Networks. We proposed an interference-aware

channel assignment algorithm based on a potential game,

called IGCA, which intends to alleviate the interference

experienced by the Mesh routers (MRs) and maintains the

connectivity of the network. To gauge the effectiveness

of our proposal, numerous simulations were performed.

We evaluated the potential performance gains of IGCA

and proved that it achieves signiﬁcant gains. We ap-

preciate how much our proposed CA game theoretic

algorithm contributes in minimizing interference between

neighbors, generates a fair distribution of nodes’ radios

between the available network channels and, above all,

allows a better number of simultaneous connections in

the network in comparison with a prominent game-based

approach: the NPOCA algorithm.

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