# Mobile Ad Hoc Networking (Cutting Edge Directions) || Resource Optimization in Multiradio Multichannel Wireless Mesh Networks

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PART II

MESH NETWORKING

7RESOURCE OPTIMIZATION INMULTIRADIO MULTICHANNELWIRELESS MESH NETWORKS

Antonio Capone, Ilario Filippini, Stefano Gualandi,and Di Yuan

ABSTRACT

Wireless mesh networks (WMNs) can partially replace the wired backbone oftraditional wireless access networks and, similarly, they require to carefully plan radioresource assignment in order to provide the same quality guarantees to traffic flows.While single radio mesh nodes operating on a single channel suffer from capacityconstraints, equipping mesh routers with multiple radios using multiple nonover-lapping channels can significantly alleviate the capacity problem and increase theaggregate bandwidth available to the network. In this chapter we discuss the radioresource assignment optimization problem in wireless mesh networks assuming atime division multiple access (TDMA) scheme, a dynamic power control able to varyemitted power slot-by-slot, and a rate adaptation mechanism that sets transmissionrates according to the signal-to-interference-and-noise ratio (SINR). The proposed op-timization framework based on column generation includes routing, scheduling, andchannel assignment. Advanced techniques, like directional antennas and cooperativenetworking, are considered as well.

Mobile Ad Hoc Networking: Cutting Edge Directions, Second Edition. Edited by Stefano Basagni,Marco Conti, Silvia Giordano, and Ivan Stojmenovic. 2013 by The Institute of Electrical and Electronics Engineers, Inc. Published 2013 by John Wiley & Sons, Inc.

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242 RESOURCE OPTIMIZATION

7.1 INTRODUCTION

Wireless mesh networking is one of the most promising solutions for the provisionof wireless connectivity in a flexible and cost-effective way [1]. The wireless meshnetworks (WMNs) comprise a mix of fixed and mobile nodes interconnected viawireless links to form a multihop ad hoc network.

The main differences between WMNs and mobile ad hoc networks (MANETs)are in the general network architecture. The classical MANET paradigm endorses aflat architecture with all the mobile nodes cooperating with the same functionalitiesto build up self-sustained and fully distributed wireless networks. On the other hand,the network devices participating in WMNs are hierarchically organized in terms ofinternetworking functionalities and hardware capabilities [2].

Roughly speaking, the network devices composing WMNs are of three types: meshrouters (MRs), mesh access points (MAPs), and mesh clients (MCs). The functionalityof both the MRs and the MAPs is twofold: They act as classical access points towardthe MCs, whereas they have the capability to set up a wireless distribution system(WDS) by connecting each other through point to point wireless links. Both MRsand MAPs are often fixed and electrically powered devices. Furthermore, the MAPsare geared with some kind of broadband wired connectivity (like ADSL or fiber) andact as gateways toward the wired backbone. MCs may be classical MANET ad hocnodes that can extend the connectivity provided by the WDS through ad hoc links.

The recent success of the WMN architecture is mainly due to its flexibility andcost viability. In fact, different from the wireless access network paradigm where allthe wireless access points are directly connected to the wired backbone, in WMNs theMAPs act like gateways with the wired realm; consequently a potentially low numberof MAPs can provide connectivity to a potentially high number of MCs [3].

The aforementioned flexibility in the network architecture makes the WMNs wellsuited to support a wide spectrum of applications ranging from Intelligent Trans-portation Systems services for vehicle traffic management to municipal networksfor security and territory surveillance purposes (fire brigades and police patrols co-ordination). Eventually, the wireless mesh technology can represent a competitivealternative to wired solutions for the provision of cheap and reliable broadband ac-cess to city neighborhoods (references 2 and 4 provide rather exhaustive overviewsof WMN applications).

WMNs are being considered within several wireless technologies. These includeIEEE 802.11 WLAN, which is probably the most popular technology for WMNsthat have been widely adopted for municipal wireless networks, wireless access net-works in rural areas, and even wireless community networks [4]. Mesh architecturesbased on relay base stations have been also considered for IEEE 802.16 WirelessMetropolitan Area Networks (WMAN) where a wireless backbone is crucial for de-signing cost-effective networks [5]. WMNs are also considered a suitable solutionfor the backhauling of next generation cellular systems based on LTE (long-termevolution) [6]. Besides the standard technologies, several companies are proposingproprietary solutions providing off-the-shelves wireless mesh technology to build

INTRODUCTION 243

up general commodity networks [79]. It is worth mentioning that also short-rangeradio technologies like IEEE 802.15.4 use mesh topologies; however, they have a flatarchitecture and do not fit the definition of WMN we use here.

In all cases mentioned, WMNs partially replace the wired backbone network andshould be able to provide similar services and quality guarantees. The backbonenetwork is usually devised to provide an almost static resource assignment to trafficflows between base stations and network gateways. This approach allows to simplifythe radio resource management at the interface between the network and the mobileusers and to provide quality of service guarantees.

Therefore, traffic engineering methodologies to provide bandwidth guarantees totraffic flows and to optimize transmission resource utilization appears to be a keyelement in these scenarios. Advanced multiple access schemes based on time division,power control mechanisms, and adaptive modulation and coding techniques are themost appropriate tools for defining radio resource management algorithms able toreserve the required rate to traffic flows and to achieve high network efficiency. Thesetools are already available for IEEE 802.16 networks and LTE. Also for WMNs basedon IEEE 802.11 standards, several manufacturers provide solutions able to emulatea time division frame on top of the basic medium access mechanism provided by thehardware platform [10].

Moreover, due to spectrum management rules and wireless technologies limi-tations, the use of multiple radio interfaces in each node is considered a commonsolution in WMNs. Wireless technology standards provide a set of nonoverlappingchannels that wireless interfaces can be tuned on. Multiple orthogonal channels per-mit the full utilization of the wireless medium through noninterfering simultaneouscommunications on different channels. Obviously, two interfaces can communicateonly if they are tuned on the same channel; this requires a careful channel assignmentin order to increase the global capacity without disconnecting the network. Wirelessmesh nodes with multiple radio interfaces tend to be used with directive antennasthat can be static or based on adaptive arrays, in order to increase transmission andlimit the effect of interference.

For these reasons, radio resource optimization techniques of mesh scenarios basedon both centralized and distributed algorithms are important elements. These includescheduling of parallel transmissions, power control, rate adaptation, channel assign-ment, and routing.

In this chapter we present the main optimization models that have been consideredfor the efficient management of TDMA-based WMNs. These models have attractedquite some attention from the research community not only for their practical impacton WMNs but also because they have renovated the interest in the analysis of basicproblems of wireless networks that can provide capacity results in arbitrary networktopologies.

In Section 7.2 we review network and interference models commonly adopted.In this chapter we focus on the physical interference model based on the signal-to-interference-and-noise ratio. In Section 7.3 we discuss the link activation problem,which aims at maximizing the number of parallel transmissions under the interferenceconstraints. The problem of optimal link scheduling is discussed in Section 7.4, where

244 RESOURCE OPTIMIZATION

it is also shown how power control and rate adaptation can be taken into account.Section 7.5 introduces routing and discusses how it can be jointly optimized withscheduling. We show how to deal with channel assignment and directional antennasin Section 7.6. Finally, in Section 7.7 we discuss cooperative relaying and showhow resource optimization models can be generalized to include this transmissiontechnique. Some concluding remarks are given in Section 7.8.

7.2 NETWORK AND INTERFERENCE MODELS

In this chapter we represent a wireless network with a directed graph G = (N,A),where the set of nodes represents the devices of the network, and each element inA represents a bidirectional transmission link. The transmission power of each nodei N is denoted by Pi, and the noise power by . The channel gain between pair ofnodes i and j of G is gij = 1d

ij, where dij is the Euclidean distance between the pair

of nodes, and is the path loss coefficient.In link (i, j) A, i is the transmitter and j the receiver. We assume that nodes

operate in half-duplex mode, thus they can be involved in at most one communicationat a time, being either transmitter or receiver. We use this model also for the caseof multiradio devices operating on multiple orthogonal channels, simply assumingthat the radio interfaces can operate independently on different channels acting asreceivers or transmitters.

At every instant, transmitters can send information, provided that interferenceconstraints at receivers are satisfied. There are basically two interference models thathave been considered in the literature: the protocol model and the physical model,exemplified respectively in Figures 7.1 and 7.2.

The simplest model of interference, the protocol model, considers a couple oftransmissions over link (i, j) and (l, h) as interfering each other if and only if eitherthe Euclidian distance from i to h or from l to j is less than a given value, defined asinterference range. The effect of the interference is considered to be boolean: Nodesinterfere only if they are within the reciprocal interference range, that is, a receiver

n

m

h

i

j

l

v

w

Figure 7.1 Protocol interference model.

MAXIMUM LINK ACTIVATION UNDER THE SINR MODEL 245

n

m

h

i

j

l

v

w

Figure 7.2 Physical interference model.

can correctly decode the transmission if no active transmitter is within its interferencerange. However, this model does not account for the sum of several distant signalsthat, once summed up, cause a significant noise.

In the physical model, instead, given (i, j) A, node i transmits correctly to nodej if and only if the interference at the receiver j is below a given threshold. Usingthe physical model of interference, we have that the signal-to-interference-noise ratio(SINR) at the receiver j is

SINRij = Pigij +lI\{i} Plglj

(7.1)

where I is the set of active senders and is the smallest threshold to have a suc-cessful transmission. The sum at the denominator allows to count all the interferenceexperimented by the receiver.

Note that in order to have a link between the pair of nodes i and j, the SINRconstraint must be satisfied when the node i is the only sender in the network, that is,I \ {i} = . Indeed, each arc (i, j) A must satisfy at least the signal-to-noise ratio:

SNRij = Pigij

(7.2)

7.3 MAXIMUM LINK ACTIVATION UNDER THE SINR MODEL

A fundamental problem is to determine the maximum number of interference-freeparallel transmissions, which is correlated to the maximum throughput the networkcan support.

Using the protocol model, it is possible to define a conflict graph H where there isa node for each link in the original network topology G, and there is an edge betweenany pair of interfering links. In this case, the maximum link activation problem isequivalent to finding a Maximum Independent Vertex Set, which is a notoriouslydifficult NP-hard problem [11].

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In the case of the physical model, this problem can be formulated as an IntegerLinear Program as follows. Let xij be a 01 variable equals to 1 whenever node itransmits to node j.

max

ij Axij (7.3a)

s.t.

(i,j) Axij +

(j,i) Axji 1, i N (7.3b)

Pigij

+lN,l /= i Plgljxlj xij, (i, j) A (7.3c)

xij {0, 1}, (i, j) A (7.3d)The objective function (7.3a) maximizes the number of transmissions. Constraints

(7.3b) impose that each node may either transmit or receive to/from another node, butnot both; these are known as half-duplex and unicast constraints. Constraints (7.3c)are the interference constraints that impose the ratio (7.1) on every active link. Thoughthis constraint is nonlinear, it can be linearized with standard techniques, resulting inthe following big-M constraint:

Pigij

lN,l /= iPlgljxlj Mij(1 xij) (7.4)

where Mij is a constant big enough to guarantee that the constraint holds wheneverxij = 0.

So far we have considered that each node i transmits with a fixed constant powerPi. However, if the power were a variable of the problem, it would be possible toincrease the number of parallel transmissions. For instance, close-by nodes couldtransmit using a lower level of power, yielding a lower interference to distant nodes.

Let pi be a continuous variable representing the transmission power of the node i.The transmission power can be at most equal to Pmax. Let yi be a 01 variableindicating whether the node i is transmitting to any other node. The problem of findingthe maximum number of parallel transmission with variable power is formulated asthe following Mixed Integer Linear Program:

max

(i,j)Axij (7.5a)

s.t.

(i,j)Axij +

(j,i)Axji 1, i N (7.5b)

pi Pmax

(i,j)Axij, i N (7.5c)

pigij

+lN,l /= i plglj xij, (i, j) A (7.5d)

xij {0, 1}, (i, j) A (7.5e)pi 0, i N (7.5f)

OPTIMAL LINK SCHEDULING 247

Differently from the case of fixed nonuniform power (7.3a)(7.3d), we have theconstraints (7.5c), which fix an upper bound on the value of transmission powerand set the variable to zero, whenever the node is not transmitting to any other nodes.In addition, the SINR constraint (7.5d) is modified in order to consider the power asa decision variable. A linearization similar to (7.4) can be applied to (7.5d).

By changing the transmission rate, it is possible to increase the number of packetssent by a link. To keep the transmission quality good, SINR threshold is to be increasedwith the increasing of the rate. Therefore the threshold in (7.1) depends on the chosenrate and is replaced by w, w denoting the admissible rate selected from a set W ofavailable rates. Since higher transmission rates require higher SINR thresholds, weintroduce a binary variable xwij for each link (i, j) and for each rate w. By replacingin problem (7.5a)(7.5f) variables xij with xwij , threshold with w, and re...

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