Fault-Tolerant Small Cells Locations Planning in 4G/5G

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Fault-Tolerant Small Cells Locations Planning in4G/5G Heterogeneous Wireless Networks

Tamer Omar1, Zakhia Abichar2, Ahmed E. Kamal3, J. Morris Chang4 and Mohammad Alnuem5

1Department of Technology Systems, East Carolina University, Greenville, NC 27858, U.S.A.2Department of Electrical Engineering and Computer Science, University of Central Florida, FL 32816, USA.

3,4Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, U.S.A.5Information Systems Department, King Saud University, Riyadh, Saudi Arabia.

Email:[email protected], [email protected], 3,4{kamal, morris}@iastate.edu, [email protected].

Abstract—Fourth/Fifth Generation heterogeneous wireless net-works (4G/5G HetNets) use/will use Small Cells (SC) to extendnetworks coverage and increase spectrum efficiency. However,the standard and technical specifications do not specify how toplan the locations of the SCs within the network. Several papersintroduced strategies for planning the locations of SCs in the4G HetNet architecture. However, SCs placement strategies tosupport the self-healing functionality of the 4G/5G self organizingnetworks (SON) framework has not been studied in the literature.The placement of SCs in 4G HetNets such that an SC failure willnot interrupt service, hence making the network fault-tolerant, isan important design and planning problem that will be addressedin this paper. We present an Integer Linear Program (ILP)formulation for planning operators managed SC locations withfault-tolerance. We allow one SC to fail and using self-healing afault tolerance service is provided at designated fail-over levels(defined in terms of users throughput). We consider the problemof SC locations planning using offloading in both out-band andin-band modes and an interference model is presented to considerthe in-band mode and to address the effect of interference onSCs placement planning. A novel approach to provide a linearinterference model by using an expanded state space to get ridof non-linearity is introduced. We present numerical results thatshow how our model can be used to plan the positions of SCs. Wealso incorporate the existence of obstacles in the planning, suchas large structures or natural formations, that might happen inreal life. To the best of our knowledge, this is the first workthat addresses planning the SC locations in 4G/5G HetNets in afault-tolerant manner.

Index Terms—4G HetNets, Small cells, Network architectureand design, Self-Healing, Fault tolerance, Self Organizing Net-works (SON).

I. INTRODUCTION

After the success and wide deployment of Wireless LocalArea Networks (WLAN) [1], the area of wireless networkshas witnessed the standardization process for broadband wire-less access networks. The fourth generation (4G) broadbandwireless network technologies (LTE and WiMAX) technicalspecifications provide last-mile connectivity and they havebeen touted to fill several needs: last-mile end user access,initial deployment of infrastructure in unwired areas andproviding access to mobile users [2].

This work was funded in part by the National Plan for Science, Tech-nology and Innovation (MAARIFAH), King Abdulaziz City for Science andTechnology, Kingdom of Saudi Arabia, Award Number 11-INF1920-02.

The main mobile service providers stations in a 4G HetNetsare the Base Station (BS)/eNodeB (eNB) and the end usersstations are called Mobile Stations (MS)/User Equipment (UE)in WiMAX/LTE respectively. In some areas voice and dataservices are provided to end users via wireless networksinstead of traditional wire-line infrastructure which is time-consuming and costly to deploy. Both standards address theutilization of Small Cells (SCs) in 4G heterogeneous networks(HetNets). The goal of using SCs is to support the connectivitybetween the BS/eNB on one side, and the MSs/UE, on theother side. The SC can extend the range of a BS. For example,there could be users that are out of reach of the BS/eNBand cannot connect to the network. With the placement ofan SC between the user and the BS/eNB, the user would beable to connect; hence, the range of the BS/eNB is extended.The SC can be also used to enhance the capacity of theBS/eNB. For example, even if all the users are in range withthe BS/eNB, placing one or more SCs in the cell allows higherdata rates and enhances the cell’s capacity as a result. 4GHetNet technologies, however, does not specify how the SCsshould be placed in the network.

The model presented in this paper allows for more than2 hops communication, one of the advantages of this modelis that it accommodates other networks, such as the use ofrelays in IEEE 802.16m. There are also advantages in usingmore than 2 hops in LTE networks, that is, operator controlledSCs (e.g. Pico Cells) can piggyback on other SCs, hence canact as both SCs, and also relay stations, and therefore achievesome gains in terms of coverage and rate enhancement. It isthe goal of this paper to devise a technique for planning theSC locations with fault tolerance to avoid failures in a 4G/5GHetNets.

A. Motivation

In this paper, we consider the operators problem of placingseveral managed SCs to support a BS/eNB in order to extendthe coverage, improve the rate, and at the same time providea resilient operation for HetNets. In real life, users expecta reliable service and many businesses rely on the Internetconnection in order to be able to function. If the networkis planned with no fault tolerance, a SC failure might result

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in disconnecting some users. There are different sources forSCs failures, and the different reasons of failures in HetNetscan be classified into three categories: 1) the first category isequipment malfunction which may occur due to hardware orpower outage; 2) the second category is link outage due tothe failure of the SC back-haul that prevents the SC fromrelaying traffic to the core network; 3) finally outage mayoccur due to the limited capacity and coverage capabilitiesof SCs that may get congested by overwhelming traffic fromend users, or channel impairments. Due to its importance, theself-healing functionality has been introduced as one of themain functionalities of the Self Organizing Networks (SON)[3]. Using the SON framework, self-healing procedures canbe triggered to perform the proper remedy actions when faulttolerance planning is implemented in order to restore theservice interrupted by any failure from the above three failurecategories.

In the model of this paper, we consider the self-healingfunctionality in the case in which at most one SC mightfail at a certain time. It could be any SC among the usedSCs. With an adequate level of service, the SC should berepaired before another SC fails. This assumption (allowingonly one SC to fail) also allows keeping the cost of the systemreasonable. The proposed model is flexible to accommodatethe number of assumed failing SCs, albeit with an increasedcapital expenditure (CAPEX).

In order to provide fault tolerance, we define for each usera full bit rate and a backup bit rate. When there is no failureamong the SCs, users receive service at the full bit rate.However, in the case of a failure, we consider that offeringservice to affected users at a reduced rate is better than noservice at all. Thus, in the case of an SC failure, the usersreceive service at the backup rate. This definition also allowsusers who primarily depend on the Internet for business tohave a backup rate that can be made equal to the full rate.Thus, these users will function without service degradationeven in the case of an SC failure.

The input to our problem is the location of the BS/eNB,the potential locations of the SCs, the location of the users(MSs/UE) and their respective demands represented by the bitrate. To reduce the problem complexity, groups of users arerepresented by Traffic Points (TP). For example, if there areseveral offices located close to each other with demands of50, 100 and 150 Mbps, they could be represented by a TP(located in a centric point to the offices) with a demand equalto the total MSs/UE demands of 300 Mbps.

The planning solution we present in this paper aims atplacing the SCs in the network to achieve several goals. Thespecific goals are:

1) All the service area should be covered with connectionto the network. The service area is defined through theTPs; thus by providing connectivity between all the TPsand the BS/eNB, the service area will be covered.

2) The throughput demand of all the TPs should be satis-fied. There should be a connection between the TP andthe BS/eNB with a flow equal to the predefined demandof the corresponding TP. The connection are assumed tobe within the licensed carrier’s spectrum.

3) The number of SCs placed by our solution should beminimized in order to reduce the equipment, installationand operation cost, i.e., both CAPEX and OPEX.

4) In case an SC in the network fails, the network shouldcontinue to operate and provide service to the TPs ata predefined level of service, which we call the backupservice rate. Thus, our planning method provides fault-tolerance and resilience to single SC failures.

B. Contribution

Self-healing is the main functionality of the SON frameworkthat provides fault tolerant operation. Self-healing mechanismthrough cooperative clusters is proposed in [4] to deployand manage the increasing number of small-cell networks.Resource utilization performance in both normal and failuremodes of a small-cell network is evaluated and the authorsshow that their proposed mechanism outperforms other con-ventional mechanisms.

The study in [5] provided a Relay Station (RS) planningsolution in WiMAX that satisfies only the first three goalslisted above. There was no fault-tolerance provision in theapproach used. Thus, if an RS fails, there is no guaranteethat the level of service provided would be adequate to thesubscribers. In addition the authors only studied WiMAX re-laying without considering the applicable down-link channelsinterference as only out-band transmission was concerned.Hence, in this paper, we extend the approach to incorporatethe in-band SCs planning with fault tolerance in a differentnetwork architecture by modeling the problem of in-bandinterference in HetNets. The new approach will ensure thatusers are served adequately in the case of a SC failure in4G/5G HetNets.

There are several papers in the literature that address theproblem of placing relay nodes in 4G networks. These arereviewed in the next section. However, to the best of ourknowledge, there is no work on planning the locations ofSCs in HetNets with fault-tolerance. There have been someapproaches on placing relays in a fault-tolerant manner in othertypes of networks such as wireless sensor networks.

We formulate the SCs planning problem using a MixedInteger Linear Program (MILP). We present numerical resultsby solving our model with CPLEXr. We believe that solv-ing the model directly to obtain results is a valid approachsince planning is not a real-time operation. The problemis solved and the allocation is made using both out-band(no interference) and in-band (interference due to down-linkresources sharing) transmission modes. To address the in-bandmode, an interference model is introduced and the maximumlink rates are calculated while taking the interference intoconsideration. Since the interference model results in a non-linear formulation of the problem, we mapped the formulationto a binary linear formulation by expanding the state space,hence avoiding non-linearities.

We present numerical results that show how our model findsthe number and locations of SCs. Our model also specifies allthe links that are used and gives the rate on each link. Also,for every SC that is used in the main topology (used when no

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SC is in a failure condition), the model gives a correspondingbackup topology in case this SC fails.

The rest of this paper is organized as follows. SectionII presents the related work, and Section III presents thenetwork model. The optimization model with fault-toleranceis provided in Section IV for out-band mode and in SectionV for in-band operational mode. Numerical results are givenin Section VI, and the conclusions are given in Section VII.

II. RELATED WORKThis section presents earlier work in the literature that is

related to the problem of planning the SC locations with faulttolerance.

a) Planning Locations in LTE: The in-band mode isaddressed by authors in [6] as one of the strategies used in5G HetNets to share the network resources between the eNBand the SCs. This study shows the importance of creatingan interference model like the one proposed in this paper toaddress this issue in HetNets using in-band strategy. Authorsin [7] proposed an in-band strategy to multiplex traffic toseveral relay node in LTE. Interference coordination is pro-posed to increase coverage and improve capacity. Howeverfault tolerance and self-healing was not discussed by theauthors. An in-band mode performance evaluation for differentdeployments is investigated by the authors in [8]. Differentscenarios are presented to show the performance of relayingin LTE networks, and results show that relaying is stronglyaffected by the back-haul. However, fault tolerance is notaddressed in the study to show the effect of failure on networkplanning.

A clustering algorithm based on uniform cluster concepts isproposed in [9] to select the BS and RS locations from candi-date positions depending on the traffic demands. The authorsintroduce a scheme that makes adaptive decision for selectingthe deployment sites of the BS and RS. Simulation resultsshow that the scheme achieves good performance in termsof network throughput and coverage. The authors presentanother RS placement solution in [10], where the cooperativetransmission paradigm is used in multi-hop relaying for thepurpose of range extension. Also, the same authors presentin [11] and [12] an RS placement solution that uses thecooperative transmission technique for the purpose of capacityenhancement.

b) Planning Locations in WiMAX: Our previous workin [5] presents a model for planning the RS locations in aWiMAX network. However, in the previous work, there wasno guarantee of service if an RS fails since fault-tolerance wasnot considered. In this paper, we extend our model to provideresilience to relay failures.

A planning model is presented in [13] to find the locationsof BSs and RSs in the network. The model is formulated asan optimization problem using integer programming. In thismodel, there is at most one RS between the SS/MS and theBS and a maximum of two hops is allowed. Since the standarddoes not have a limit on the number of hops going throughthe RSs, this assumption may impose unneeded restrictions.

The same authors of the work above present an extension oftheir work in [14]. In this paper, they consider a large coverage

area which increases the computation time of the model. Toreduce the computation time, they divide the area into clustersand apply the approach above to every cluster. Then, the caseson the boundaries of the clusters are solved to find the overallsolution. This paper similarly limits the number of hops totwo.

In [15], a model is presented to find the locations of RSsthat extend the range of a BS in a WiMAX network. Thiswork defines preset topologies and finds the RS placement forthese topologies; in comparison, our model in this paper and in[5] can work with any topology. This work also considers RSlocation planning for sector-based topology. Each sector usesa frequency that is different from adjacent sectors in order toreduce interference.

In [16], an RS placement model is presented. This work isbased on cooperative transmission between the source nodeand the relay node to provide a better signal to the destinationnode. They consider the decode-and-forward scheme and thecompress-and-forward scheme for cooperative transmission.This model is different from our work since it considers theplacement of a single RS to serve multiple MSs.

In [17], the problem of joint BS and RS deployment isconsidered and an optimization model is presented. Due tothe large size of the problem, the model takes a long timeto solve. Thus, the authors also present an efficient heuristicalgorithm to find the problem sub-optimal solution.

In [18], the problem of RS placement in the WiMAXnetwork is considered. The location of the RSs and thebandwidth allocation to users are found. This work assumesthat users’ demands could change due to fluctuations in trafficdemands and due to mobility. Thus, the optimization of theRS locations is found on a long-term basis and the bandwidthallocation to users is found on a short-term basis.

The authors of [19] consider using relays for the purpose ofcapacity enhancements as follows. There is a BS, an area thatcan be totally covered by the BS and a given number of relays.This work decides where to place the relays to maximize thesystem capacity.

In [20], the following paradigm is considered for the place-ment of RSs in WiMAX networks. The number and locationsof BSs are given. The goal of the problem is to place RSsthat use the transparent mode. In this mode, the RSs do nottransmit control information; the control information are onlytransmitted by the BS. The RSs are thus in range of the BS andthe goal of the RS placement is capacity enhancement. Otherapproaches used in BSs and RSs placement are presented in[21] and [22] with the goal of enhancing the overall networkcapacity.

c) Planning Locations in Wireless Sensor Networks(WSN): There are approaches in the literature that providerelay location planning with fault-tolerance. But these ap-proaches have been designed for wireless sensor networks andnot for WiMAX networks.

In [23], an Integer Linear Program (ILP) model is presentedfor placing relays in sensor networks to provide fault-tolerancein case some nodes fail. The main issue was connectivity,regardless of bandwidth requirements, which implies that allrelay nodes may be operational all the time. The same authors

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present an extension of their work in [24], which takes intoconsideration the routing strategy in order to reduce batteryconsumption. Other approaches on fault-tolerant placement ofrelay nodes are given in [25]–[32].

The approaches presented in this section consider a multi-tude of issues and configurations for traffic relaying used inbroadband and wireless sensor networks. There are multipleapproaches for planning the placement of nodes that is dis-cussed in these networks, some of them, specifically in WSNs,address the planning of relay nodes locations with fault-tolerance. However, none of this work is applicable to broad-band wireless HetNets. To the best of our knowledge, thereis no approach that provides the planning of SCs locationsoperating within the same frequency band (in-band mode) inHetNets with fault-tolerance. Moreover, neither the approachesintroduced for WSNs that discussed fault tolerance nor ourprevious work in [5] considered the interference caused dueto the in-band transmission mode. Using the SON frameworkthe proposed approach can be implemented as a self-healingfunctionality to compensate for HetNet failures. However, theoffered service in case of failures is downgraded to the backuprates. Hence, our paper is the first to propose such solutions,that map from nonlinear to linear interference using state spacetransformation as an approach to perform HetNet SCs recoveryin an in-band transmission mode and to guarantee the businesscontinuity even in case of partial failures by using the proposedfault tolerance planning.

III. NETWORK MODEL

This section presents the network model that we considerin this paper.

A. Small Cells Offloading Modes

The 4G/5G HetNets defines two modes of macro-cells(MCs) to SCs offloading operation modes: a transparent mode,and a non-transparent mode. In the transparent mode, the users(MSs/UE) are unaware of the presence of a SC. The SC doesnot transmit control information (such as down-link map andup-link map). These are transmitted by the BS/eNB. Thus, allthe MSs/UE are within range of the BS. However, the SCsare used in the transparent mode for the purpose of capacityenhancement.

In the non-transparent mode, the SCs perform all functionsneeded for a standalone cell and transmits control informationas well as data to the MSs/UE it serves. Multi-hop routes areallowed in the non-transparent mode. The goal for using non-transparent SCs is to extend the range of the network and toalso enhance the capacity, currently this mode is widely usedfor SCs deployment and is the mode considered in our study.

B. Duplexing Mode

When SCs are used, transmissions from two stations thatare in range should be duplexed either in the frequencydomain (FDD) or in the time domain (TDD) in order toavoid interference. The 4G standards allow using differentfrequencies for SCs serving the same BS. Thus, we make the

Table IOFDMA RATES (IN MBPS) FOR VARIOUS MODULATION

SCHEMES USING 7 MHZ BANDWIDTH

QPSK QPSK 16-QAM 16-QAM 64-QAM 64-QAM1/2 3/4 1/2 3/4 2/3 3/45.82 8.73 11.64 17.45 23.27 26.18

assumption that the SCs duplex their transmission using theFrequency Division Duplex (FDD) mode. For example, on atwo-hop route eNB - SC - UE, we can have a transmission ofrate r on the eNB - SC hop and another transmission of thesame rate on the SC - UE hop. This happens if the two hopsare using different frequencies. With Time Division Duplex(TDD), the two hops will alternate in transmission using thesame frequency channel. However, each hop will have a largerbandwidth since the bandwidth is not divided anymore. Weuse FDD for simplicity, but our model is logically equivalentto TDD. For more generalization of the studied problem, wealso assumed the utilization of non-orthogonal physical layermultiplexing approaches (e.g CDMA, FDMA). The proposedmodel can benefit from adopting frequency partitioning andreuse techniques where the same channels can be reallocatedto different small cells if they are geographically distributedsuch that the inter-cell interference between them does notnegatively impact their transmission rates.

C. Link Capacity

Our model allocates a rate on each link that is used in theproduced topology. The allocated rate on a link is boundedby the maximum capacity of the link. The maximum capacityof a wireless link can be modeled with the Shannon-Hartleyequation as given in [33]. It is given by the equation: C =B.log2(1 + SINR), where C is the capacity in bit/sec, B isthe channel bandwidth in Hz.

The signal to interference plus noise ratio can be calculatedas SINR = S/ [N0 + I], where S is the received signalpower, N0 is the noise power and I is the signal powerreceived from all interferers, j. The capacity changes withthe distance since the SINR degrades when the distanceincreases. The SINR can be expressed as

SINRi =βpi

(d)α[N0 +

∑j 6=i

pj/(d)α] (1)

where pi is the signal transmission power, d is the Euclideandistance between the transmitter and receiver, α > 2 is thepath loss exponent and β is the antenna gain.

Other factors also affect the link capacity such as the codingand modulation schemes. When a high SINR is measured onthe link, coding and modulation schemes with high rates areused. However, when the SINR is low, robust coding andmodulation schemes are preferred to limit the Bit-Error-Rate(BER), although they provide low data rates. Table I shows theachievable bit rates for the OFDMA physical layer as given inthe standard [34]. QPSK is more robust but achieves a smallrate. On the other hand, 64-QAM is less robust but achievesa high rate.

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The factors that affect a link’s capacity can be combinedin an equation. For any link i, the maximum rate is: mi =Γ(SINRi, χ, Cod, Mod), where χ is the upper-boundon the BER, Cod is the coding scheme and Mod is themodulation scheme. Γ is the function that maps all the threeparameters to the maximum rate.

Any definition of the function Γ can work with our model.However, for simplicity, we assume that the maximum ratechanges with distance. In real-life scenarios, there is usuallya field survey which precedes the network deployment [35]–[37]. The link rates are selected based on the links character-istics such as, the SINR, fading, the specifics of the terrainand interference with other wireless systems.

D. Definition of Fault-Tolerance

The planning model we present in this paper allows thefailure of an SC without interrupting service to the users, albeitat a reduced bit rate, hence tolerating equipment failure.

We assume that only one SC will fail at a given time.This is a reasonable assumption since usually in the time ittakes the SC to be repaired, there is a very small probabilitythat another SC will fail. This is true since the number ofoperator supported SCs (e.g Pico Cells) supporting a BS/eNBwill typically be a small number of SCs. This assumption willkeep the cost of SCs small, since tolerating the failure of twoor more SCs at the same time requires installing many extraSCs, which is not a cost effective approach.

For every set of customers, represented by a Traffic Point(TP), a tuple {ri, rbi} defines the requested service rates.When all the SCs are operational, the full rate for a TPi,given by ri is provided. However, when there is an SC failure,a reduced rate which is the backup rate rbi, is provided, withrbi ≤ ri. Users who request the same service rate even in thecase of an SC failure will have rbi = ri.

IV. OPTIMIZATION MODEL: THE OUT-BAND MODE

This section presents the optimization model for the SCplanning problem with fault-tolerance in the out-band mode.The model takes as input (1) the possible sites where an SCcan be installed, (2) the locations of the Traffic Points (TP)that represent the users’ traffic, (3) the rates (full and reduced)in Mbps of each TP, the full rate is provided when all the SCsare operational and the reduced rate is guaranteed when thereis an SC failure. (4) Finally, the model takes as an input themaximum rate on any link: eNB-SC, SC-TP, SC-SC and SC-TP, which depends on the link characteristics such as distance,SINR and bandwidth. Table III help in clarifying the notationsin the paper.

Parameters DescriptionR Set of candidate sites for SCT Set of TPs that represent the user trafficB Base StationLxi Set of links which can interfere with link iFxn Sets n of active interference links to link iri, rbi Rate requirement, backup rate requirementk Backup topology numberS Total number of SCsT Total number of SCs in backup topologyVariables DescriptiondR, dBR, dBTdRT, dRR

Decision variables

fBR, fBT, fRT, fRR Traffic flownBR, nBT, nRT, nRR Number of sub-carriersmBR,mBTmRT,mRR

Maximum link capacity

cBR, cBT, cRT, cRR Actual link capacitydnBR, dnBTdnRT, dnRR, Ixj , Y xFxn

Binary variables

vBR, vBT, vRT, vRRwBR,wBT,wRT,wRR

Variables

Xi, Zij , Xki , Z

kij Auxiliary variable

Table IIABBREVIATIONS

The output of our model is the full-rate (main) topology andthe reduced-rate (backup) topologies. The full-rate topology isdefined by the number of SCs used, their positions, the linksused, the rate on each link and, finally, the connection nodefor each TP (either the eNB or an SC). Each of the backuptopologies corresponds to a failure in one of the SCs usedin the main topology. For example, if the main topology usesSC1, SC3 and SC8, then there will be three backup topologiesthat are used in the case any of these SCs fails.

For any TP (TPi) the full rate is designated by ri andthe reduced backup rate is designated by rbi, which is theminimum acceptable rate in the case of failure.

Let R = {SC0, ..., SCN−1} be the set of candidate sitesfor SC with cardinality |R| = N . Similarly, let T ={TP0, ..., TPM−1} be the set of TPs that represent the usertraffic with cardinality |T | = M .

A. Decision Variables

The following decision variables define the full-rate topol-ogy.

dRi =

{1; a SC is deployed in site SCi0; otherwise (i ∈ R)

dBRi =

{1; a link is used between the eNB and SCi0; otherwise(i ∈ R)

dBTi =

{1; TPi is assigned to the eNB0; otherwise (i ∈ T )

dRRij =

{1; a link is used between the SCiand SCj0; otherwise (i, j ∈ R)

dRTij =

{1; TPj is assigned to the SCi0; otherwise (i ∈ R, j ∈ T )

We also define variables that are similar to the above inorder to specify the backup topologies. These variables are:dRki , dBR

ki , dBT

ki , dRR

kijand dRT kij . The term k indicates

the backup topology number used when SCki has failed. For

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example, when k = 3, these variables define the backuptopology that is used when SC3 fails.

We also define decision variables that designate the assignedflow (in Mbps) on each link. While the previous variableswere binary, the flow variables take continuous values. In thefull-rate topology, the variables fBRi, and fRRij designatethe flow on the links from eNB to SCi, and SCi to SCj ,respectively, where i and j are indexes of SCs (i, j ∈ R).

Similarly, in the backup topology, the variables fBRki andfRRkij designate the flow on the links from eNB to SCkiand SCki to SCkj , respectively, where i, j are indexes of SCs,k is the index of the backup topology when SCk fails and(i, j, k ∈ R).

B. Topology Constraints

The following constraints define the topology of the SCsdomain. They ensure that when a link is used in the solution,the two end nodes of the link exist (i.e., the SCs are selected).They also ensure that a TP is connected either directly to theeNB or to only one SC; we use this condition in order not toadd complexities to the UEs.

First, when there is a link between the eNB and SCi,there should be a SC deployed at site SCi. This is ensuredby the following constraints in the full-rate and the backuptopologies.

dBRi ≤ dRi ∀ i ∈ R (2)dBRki ≤ dRki i 6= k, ∀ i, k ∈ R (3)

When there is a link between SCi and SCj , two SCs shouldbe installed at sites SCi and SCj . This is ensured by thefollowing constraints

dRRij ≤dRi + dRj

2∀ i, j ∈ R (4)

dRRkij ≤dRki + dRkj

2i 6= k, j 6= k, ∀ i, j, k ∈ R (5)

When there is a link between SCi and TPj , a SC shouldbe deployed at site SCi. This is ensured by the followingconstraints.

dRTij ≤ dRi ∀ i ∈ R, ∀ j ∈ T (6)dRT kij ≤ dRki i 6= k, j 6= k, ∀ i, k ∈ R, ∀ j ∈ T(7)

The following constraints send all the traffic of a TP eitherthrough a direct link with the eNB or through a single SC.

dBTi +∑j ∈ R dRTji = 1 ∀ i ∈ T (8)

dBT ki +∑j ∈ R, j 6=k dRT

kji = 1 ∀ i ∈ T (9)

C. Flow Constraints

The flow constraints ensure that the amount of data that istransported is balanced and sufficient for the demands of allthe TPs.

1) Flow Balance at the BS: In the main topology, the totaltraffic going out of the eNB should be equal to the sum of thefull rates, ri, of all the TPs. This condition is ensured by thefollowing equation.

∑i ∈ R

fBRi · dBRi +∑

j ∈ T, mBTj≥rj

rj · dBTj =∑j ∈ T

rj

(10)

where ( mBTj , mRTj) are the upper bounds of the rates onthe links for the main topology which are input parameters tothe problem and are calculated in section V-A

At a backup topology, the rate provided to TPi is greaterthan or equal to rbi. Then, this condition is used.

∑i ∈ R, i 6=k

fBRki · dBRki +∑

j ∈ T, mBTj≥rbj

rbj · dBT kj =∑j ∈ T

rbj

(11)

We are interested in keeping the system linear. Thus, we usethe following transformation and substitute in eq.(10).

Xi = fBRi · dBRi

where Xi is an auxiliary variable.eq.(10) therefore becomes:

∑i ∈ R

Xi +∑

j ∈ T, mBTj≥rj

rj · dBTj =∑j ∈ T

rj (12)

Xi can be evaluated using the following set of linearconstraints, where Q is a large number such that Q >max(fBRi), ∀ i ε R.

Xi ≥ Q · dBRi −Q+ fBRi ∀ i ∈ R (13)Xi ≤ fBRi ∀ i ∈ R (14)Xi ≥ 0 ∀ i ∈ R (15)

Xi ≤ Q · dBRi ∀ i ∈ R (16)

Similarly, we use the following transformation for eq.(11).

Xki = fBRki · dBRki i 6= k, ∀ i, k ∈ R (17)

Hence, eq.(11) becomes:

∑i ∈ R, i 6=k

Xki +

∑j ∈ T, mBTj≥rbj

rbj · dBT kj =∑j ∈ T

rbj (18)

Xki is evaluated like Xi was evaluated in eq.(13) to eq.(16).2) Flow Balance at a SC: At any SC, the amount of traffic

that is coming from the eNB and from upstream SCs is equalto the amount of traffic that is going to downstream SCs andto TPs that are directly connected to the SC. This is ensuredby the following constraint.

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fBRi · dBRi +∑j ∈ R

fRRji · dRRji =∑j ∈ R

fRRij · dRRij +∑

y ∈ T, mRTj≥ry

ry · dRTiy, ∀ i ∈ R

(19)

The equation above is made linear by using the transformZij = fRRij · dRRij and becomes:

Xi +∑j ∈ R

Zji =∑j ∈ R

Zij +∑

y ∈ T, mRTiy≥ry

ry · dRTiy

∀ i ∈ R(20)

For the backup topologies, the flow conservation at the SC isensured by the following equation.

fBRki · dBRki +∑

j ∈ R, j 6=k

fRRkji · dRRkji =∑j ∈ R, j 6=k

fRRkij · dRRkij +∑

y ∈ T, mBTiy≥rby

rby · dRT kiy

i 6= k, ∀ i, k ∈ R(21)

The equation above is made linear by using the transformZkij = fRRkij .dRR

kij and it becomes:

Xki +

∑j ∈ R, j 6=k

Zkji =∑

j ∈ R, j 6=k

Zkij+∑y ∈ T, mBTiy≥rby

rby · dRT biy i 6= k, ∀ i, k ∈ R (22)

Zij and Zkij are evaluated similar to how Xi was evaluated ineq.(13) to eq.(16).

3) Flow Balance at a TP: In the main topology, the amountof traffic between the eNB or the SC and the TP should beequal to the full-rate, ri of the TP. This is ensured by thefollowing constraint.

i∑i=i, mBTi≥ri

ri · dBTi +∑

j ∈ R, mRTji≥ri

ri · dRTji = ri

∀ i ∈ T(23)

For the backup topologies, the amount of traffic at the TPshould be equal to rbi. This is ensured by the followingconstraint.

i∑i=i, mBTi≥rbi

rbi · dBT ki +∑

j ∈R, j 6=k,mRTji≥rbi

rbi · dRTji = rbi

∀ i ∈ T , k ∈ R (24)

SC Traffic flow

a_i

L1

L3

L2

L_i = {L1,L2,L3}

F_1

F_2

Fig. 1. An example for link interference

V. OPTIMIZATION MODEL

A. The In-Band Model

The model that we have so far assumes the out-band mode,and in this case the maximum capacity of link BRi, RRi, BTiand RTi are mBRi, mRRi, mBTi and mRTi respectively.

To accommodate the in-band mode, the capacity on link idepends on the activity of other links j, which may interferewith link i. We will need to set the capacity on link i suchthat it corresponds to the capacity that is subject to interferencewith other active links in the system. Rather than using a non-linear formulation, we use a linear formulation that comes atthe cost of an expanded space state.

The basic idea of the transformation is to precomputethe capacity of the target link, i, for all possible cases ofinterference. This is can be done off-line, and outside theoptimization formulation. Then, for each of the interferencecases we have a binary variable that is equal to 1 if this caseis valid. Multiple interference cases may occur at the sametime, e.g., if two links interfere with the target link, then thereare 3 cases of interference, one for each link, and the third forboth links. Then, the optimization problem by determiningthe interference cases can select the corresponding capacityas the minimum capacity for all valid interference cases. Theexpansion in the state space is the result of the use of thebinary variable corresponding to the interference cases.

It is worth mentioning that the conversion of the interfer-ence nonlinear characteristics to linear is developed withoutchanging the parameters of the original problem (e.g. no. ofsub-carriers allocated for an SC). This is done by using abinary linear formulation in which the capacity of link i isdefined as follows:

• Assume that the maximum number of other links whichcan interfere with link i is ai, and the set of such linksis Lxi = l1, l2, ..., lai where x ∈ {BR, RR, BT, RT}.

• The capacity of link i given that links in the nth subsetFxn ⊆ Lxi are active, including the empty subset, isgiven by cxFxn , and is precomputed.

An example is shown in Fig 1 for the interference sets andsubsets to explain the interference that a link may suffer.

In order to find out which combination of links are active,a binary variable Ixj is defined as being equal to 1 if link j

8

is active. The number of active links in each Fxn is evaluatedas follows:

AxFxn =∑j ∈ Fxn

Ixj , ∀ Fxn ⊆ Lxi (25)

Then, to find the combination that has all of its member linksactive. We define a binary variables Y xFxn , which will beequal 1 only if all links in the subset Fxn are active. Y xFxncan be evaluated using the following constraints

Y xFxn ≥ AxFxn − |Fxn|+ 1 (26)

Y xFxn ≤AxFxn+δ|Fxn|+δ (27)

where δ is a small number. The addition of δ to both thenumerator and denominator is to include the case of emptysubset, in which case both |Fxn| and AxFxn are zeros.

Therefore, the maximum capacity of a link can be evaluatedas the minimum for all cases in which Y xFxn = 1. The upperbounds on the rates on this link (mBRiFBRin , mRRij

FRRijn,

mBT iFBT in, mRT ij

FRT ijn) for main topology and (mBRikFBRikn ,

mRRijkFRRijkn

, mBT ikFBT ikn , mRT ijkFRT ijkn

) for backup topolo-gies are input parameters to the problem and are calculated asfollows:

mBRiFBRin

= cBRiFBRin

· Y BRiFBRin

+ (1− Y BRiFBRin

) ·M

(28)

mRRij

FRRijn

= cRRij

FRRijn· Y RRij

FRRijn

+ (1− Y RRijFRR

ijn) ·M

(29)

mBTiFBTin

= cBTiFBTin

· Y BT iFBTin

+ (1− Y BT iFBTin

) ·M(30)

mRTij

FRTijn

= cRTij

FRTijn· Y RT ij

FRTijn

+ (1− Y RT ijFRT

ijn

) ·M(31)

mBRik

FBRikn= cBR

ik

FBRikn· Y BRik

FBRikn+ (1− Y BRik

FBRikn) ·M

(32)

mRRijk

FRRijkn

= cRRijk

FRRijkn

· Y RRijkFRR

ijkn

+ (1− Y RRijkFRR

ijkn

) ·M

(33)

mBTik

FBTikn= cBT

ik

FBTikn· Y BT ik

FBTikn+ (1− Y BT ik

FBTikn) ·M

(34)

mRTijk

FRTijkn

= cRTijk

FRTijkn

· Y RRijkFRT

ijkn

+ (1− Y RT ijkFRT

ijkn

) ·M

(35)

where M is a very large number. In eq.(28), if subset FBRinis active, hence Y BRiFBRin is 1, then the capacity of link i isequal to cBRiFBRin . Otherwise, the effect of subset FBRin isexcluded by having this capacity equal to a very large number,M . Equations (29) to (35) follow similar reasoning.

The maximum flow that can be transmitted on a link i islimited by the transmission power, the link distance and thecoding and modulation schemes. The maximum rate that canbe assigned on the link from the eNB to SCi, fBRi, is limitedby mBRiFBRin , where mBRiFBRin is the maximum rate onthis link. A similar notation is used for all the other links andthe constraints that ensure the upper bound are the following

C · fBRi ≤ nBRiFBRin ·mBRiFBRin

∀ FBRin ⊆ LBRi (36)

C · fRRij ≤ nRRijFRR

ijn

·mRRijFRR

ijn

∀ FRRijn ⊆ LRRij (37)

C · fBRki ≤ nBRikFBRikn ·mBRikFBRikn

∀ FBRikn ⊆ LBRki (38)

C · fRRkij ≤ nRRijk

FRRijkn

·mRRijkFRR

ijkn

∀ FRRijkn ⊆ LRRkij (39)

C · fBTi ≤ nBT iFBT in ·mBTiFBT in

∀ FBT in ⊆ LBTi (40)

C · fRTij ≤ nRT ijFRT

ijn

·mRT ijFRT

ijn

∀ FRT ijn ⊆ LRTij (41)

C · fBTki ≤ nBT ikFBT ikn ·mBTikFBT ikn

∀ FBT ikn ⊆ LBTki (42)

C · fRTkij ≤ nRTijk

FRTijkn

·mRT ijkFRT

ijkn

∀ FRT ijkn ⊆ LRTkij (43)

i 6= k, j 6= k, i, j, k ∈ R

where the variable nBRiFBRin ∈ {0, 1, ..., C} correspondsto the number of sub-carriers allocated to any SCi out of atotal of C sub-carriers which is an input parameter, and Cis assumed to be an integral power of 2 (e.g.,C = 512)1.To avoid further complexity of the modeled problem, weassumed that the orthogonality among sub-carriers is main-tained and that there is no inter-carrier interference betweentransceivers of different links. The constraint in eq.(36) is anonlinear constraint with nBRiFBRin

a discrete variable andmBRiFBRin

a continuous variable. The following equationsare used to transform it to a linear form. A new variablevBRiFBRin

= nBRiFBRin∗mBRiFBRin is defined and a binary

expansion [38] for nBRiFBRin is performed as

nBRiFBRin =

ρ∑r=0

2r · dnBRirFBRin ∀ FBRin ⊆ LBRi, i ∈ R

(44)ρ = log2(C) (45)

dnBRirFBRin ∈ {0, 1} (46)

Then vBRiFBRn can be rewritten as

vBRiFBRin =

ρ∑r=0

2r · wBRirFBRin ∀ FBRin ⊆ LBRi, i ∈ R

(47)

where

wBRirFBRin = dnBRirFBRin ·mBRiFBRin

(48)

∀ FBRin ⊆ LBRi, i ∈ R

Now the constraint in eq.(36) is converted into nonlinear con-straint but with dnBRiFBRin a binary variable and mBRiFBRina continuous variable which can be linearized using the sameapproach used in eq.(13) to eq.(16).

Similarly the same conversion is used forvariables (vBT iFBT in , vRRij

FRRijn, vRT ij

FRT ijn)

and the backup topologies variables(vBRikFBT ikn , vBT

ikFBT ikn

, vRRijkFRRijkn

, vRT ijkFRT ijkn

). Also,when an SC fails, the rate on all the links incident on it iszero.

1Without loss of generality, and to reduce the model complexity, weconsider C to be a power of 2

9

B. The Out-Band Model

For out-band mode the interference between the links arenot considered and the maximum rate that can be assigned onthe link from the BS to SCi, fBRi, is limited by fBRi ≤mBRi. Similarly for all the other links the constraints thatensure the upper bound are calculated according to

fBRi ≤ mBRi i ∈ R

fRRij ≤ mRRij i, j ∈ R

fBRki ≤ mBRi i 6= k, i, k ∈ R

fRRkij ≤ mRRij i 6= k, j 6= k, i, j, k ∈ R

C. Objective Function

The primary objective of our solution is to minimize thetotal number of SCs used. This will minimize the cost of SCinstallation. We define the variable Si which indicates if anSC is installed at site SCi either in the main topology or inany other topology.

Si ≥ dRi i ∈ R (49)

Si ≥ dRki i 6= k, i, k ∈ R (50)

To minimize the total number of SCs that are installed,∑iεR Si should be minimized.We also aim at reducing the number of SCs used in backup

topologies. Minimizing the number of SCs used in everytopology allows us to remove lengthy paths. For example, if aTP can connect to the eNB by going through one SC only, itis better not to use two SCs for this TP. Thus, minimizing thenumber of SCs in the backup topologies will make a TP usethe minimum necessary number of SCs it needs to connectto the eNB. The variable T k designates the number of SCsused in the backup topology when SC k fails. We have thefollowing constraint.

Tk ≥∑

i ∈ R, i 6=k

dRki , ∀ k ∈ R (51)

For a similar reason to the above, we aim to minimize thenumber of SCs that is used in the main topology, designatedby the term V . We have the constraint:

V ≥∑i ∈ R

dRi (52)

The term Obj combines the terms above. The main term fromthe above is

∑i ε R Si since it gives the number of SCs that

should be installed. It should be given a higher weight than theother terms. The maximum value of

∑k ε R T k is N2 and the

maximum value of V is N . Thus, we give the weight N2 +Nto the term with Si.

Obj = (N2 +N) ·∑i ∈ R

Si +∑k ∈ R

T k + V (53)

Then, the objective function is:

Minimize Obj (54)

Implementing a system with multi-hop relays increasesthe operational complexity, and also solving the problemwith wireless back-hauling and multi-hop topology adds morecomplexity to the problem. However, using more than twohops has advantages in terms of performance, such as rangeof coverage and bit rate. This is why we opted to develop ageneric model that can accommodate any number of hops. Toaccommodate the case of only two hops, we can force all thenRR, fRR, dRR,mRR and wRR to zero.

VI. NUMERICAL RESULTS

This section introduces numerical results based on theplanning models presented above. Firstly, we show examplesof planning without fault-tolerance in a WiMAX network. Inthese examples, when an SC fails, there is no guarantee ofservice to the TPs. Secondly, we show examples with fault-tolerance, where service will be guaranteed even in case offailure of a SC. We consider both the out-band and in-bandoperation in solving the location planning MILP problem ina WiMAX HetNet. By using CPLEXr, which runs on amodern multi-core machine, we obtained solution times interm of hours for realistic scenarios which shows a reasonablecomputation time for practical cases. The solution of theoptimization problem for the proposed model is feasible aslong as proper design parameters are selected to support therequired resources for a certain network design scenario.

A. Planning SC Locations For Out-Band Mode

1) Planning without Fault-Tolerance: This section presentsthe initial results of planning the SC locations without fault-tolerance. In this section, where no fault-tolerance is consid-ered, the variables and constraints in the model that are usedfor fault-tolerance are omitted. These are all the variables thathave an index k, which are: dRki , dBRki , dBT ki , dRRki ,fBRki , fBRki and fRRkij .

Also, the objective function will change. In the case wherewe do not have fault-tolerance, the objective is simply tominimize the total number of SCs used. Then, the objectivefunction is:

min∑i ∈ R

dRi (55)

a) Theoretical Model: The following is a SC planningexample that uses our solution. The problem is shown in Fig.2(a). The planning area is made discrete by the use of a squaregrid. The BS location is on the top line of the grid as shownin the figure. We select this setting since we consider that theBS is at the edge of the connected area. The area below theBS does not have the connection and we plan to connect thisarea through the BS. Without loss of generality, we can useany topology with our model.

10

SC11

SC15

Potential Small-Cell Site

Base StationTraffic Point

+

+ +

++

+

r = 4

r = 6 r = 8

r = 5 r = 2

a) Problem (main rates and backup rates in Mbps)

SC0 SC3

SC4 SC5 SC6

SC8 SC10

SC12 SC13 SC14

SC7

SC1 SC2

SC9

Selected SC Rate on link

+

+ +

++

2

4

b) Solution

Traffic flow Link to TP

8

5

2

6

2

8

2

10

5 4

SC1

SC5 SC7

Fig. 2. Planning SC Locations without Fault-Tolerance for Out-Band Model

Table IIILINK RATES OUT-BAND MODE

Distance (unit) Link Rate (Mbps)if distance <= 1 rate = 10

else if distance <= 2 rate = 5else if distance <= 3 rate = 2else if distance <= 4 rate = 1

else rate = 0

The potential sites for a SC are the corners of a grid square.In the 4-by-4 grid, the SC sites are numbered 0 to 15, as shownin the figure. The possible site of a TP is in the center of asquare. The TPs are numbered 0 to 9. In the figure, the TPnumbers are TP(2,4,5,6,8). The number shown in the figurenext to each TP is its traffic demand in Mbps.

The maximum rate on the links is shown in Table III. Thedistance unit is the side length of a square in the grid. Thetable shows the feasible rate for the corresponding distanceinterval (per the model in Section III). The solution to thisplanning example is shown in Fig. 2(b). The shaded SC sitesare the ones that have been selected. Three SCs are neededfor this problem, which are SC1, SC5 and SC7. The solidline links are the BS-SC and SC-SC links. The dashed linesare the BS-TP and SC-TP links. The underlined numbers are

the link rates allocated by the solution. The rates of the dottedlinks are equal to the corresponding TPs’ rates. The arrows onthe links show the flow of traffic in the down-link to facilitateinterpreting the results. However, the traffic may go in theup-link or down-link direction.

We note the following observations from this example:• The distance from the TP to the BS does not necessarily

indicate a direct or relayed connection. For example, theTP with demand of 2 Mbps is the farthest from theBS. However, its demand is relatively low which can besatisfied by a single link. On the other hand, TPs whichare closer to the BS have higher demands, and requirethe use of a SC.

• Secondly, the SC-to-SC links help in reducing the numberof SCs in the HetNet. In our example, there is more trafficto the right of the BS (4+8+2 = 14) than the left (5) andthe middle (6). Thus, in the solution, the diagonal andhorizontal links, both with rate of 2 Mbps, between SCs(1,7) and (5,7), respectively, relay the traffic from theright side to the less congested left side. If this was notthe case, more SCs would be needed on the right side.

2) Planning with Fault-Tolerance: In this part, we presentplanning results with fault-tolerance. The problem input isshown in Fig. 3(a) and it has the same TP locations and ratesas the example in Fig. 2(a). In this case, there are also backuprates for each TP, which are smaller than or equal to the themain rate.

Fig. 3(b) shows the main topology which supports the mainrates of the TPs. This topology, similar to that in Fig. 2(b),supports the same normal operation rates, and also uses threeSCs. However, unlike the topology in Fig. 2(b), it uses SC2,SC5 and SC7. Moreover, it also requires the installation of anadditional relay at site SC10. Even though SC10 is not usedin the main topology, it is required in case one of the threeused SCs fails.

In Fig. 3(b), the TPs with rates of 4 and 2 Mbps connectdirectly to the BS since their direct link can support therequired rate. This is similar to Fig. 2(b). Each of the otherTPs connects to the SC that is closest to it.

Fig. 3(c) shows the backup topology that is used when SC2

fails. In this topology, the backup rates are supported, whichare smaller than the main rates in this example. Due to thelower rates, now three TPs are able to have a direct connectionto the BS (compared to two in the main topology). The othertwo TPs connect through SCs. In this topology, SC10 is alsonot used since SC5 and SC7 are able to support the TPs’demands, which makes the recovery from SC2 failure faster,since SC10 need not be used.

The topology in Fig. 3(d) is the case when SC5 fails. Inthis case, three SCs are needed to support the TPs. Noticethat in the previous topology, SC5 was strategically locatedbetween the BS and the TP in the low-left corner. Since SC5

has failed, there is no SC that can satisfy this TP. Thus, twoSCs are used to connect this TP.

In Fig. 3(e), the topology that is used when SC7 fails isshown. Now the TP in the low-left corner is able to connect

11

Potential SC SiteBS TP

+

+ +

++

+

r = 4 rb=2

r = 6 rb=4 r = 8 rb=6

r = 5 rb=4 r = 2 rb=1


Selected SC

+

+ +

++

2

c) Solution: Backup Topology when SC2 Fails

6

4

4

1

1

5

5

Failed SC

Selected SC

+

+ +

++

2

e) Solution: Backup Topology when SC7 Fails

6

4

4

2

1

4

6

Failed SC

4

Selected SC

+

+ +

++

2

d) Solution: Backup Topology when SC5 Fails

6

4

42

1

1

3

Failed SC

52

Selected SC Rate on link

+

+ +

++

2

4

b) Solution: The Main Topology

Traffic flow Link to TP

8

5

2

6

2

4

5

5

9

5SC0 SC3

SC4 SC5 SC6

SC8 SC10 SC11

SC12 SC13 SC14 SC15

SC7

SC1 SC2

SC9

SC5

SC10

SC7

SC2

SC5

SC10

SC7

SC2

SC5

SC10

SC7

SC2

SC5

SC10

SC7

SC2

Fig. 3. Planning SC Locations with Fault-Tolerance for Out-Band Model

via SC5. However, the TP with demand 6 Mbps, which was 9previously relying on SC7 cannot connect with only one SC.Then, SC2 and SC10 convey the traffic of this TP in this case.However, the TP connects only to SC10, and SC10 connectsto both the BS and SC2 in order to receive the data. Finally,when SC10 fails, we can continue to use the main topologyas in Fig. 3(b) since this topology does not use SC10.

We compared our proposed solution to provide fault toler-ance to the one without fault tolerance. The results in Fig. 3(e)shows that with one extra SC for achieving fault tolerance, thetransmission rates achieved is about 68% of the rates achievedin the main topology. Fig. 3(b) shows that in case of SC5

failure and without fault tolerance planning only 44% of therate can be provided and 40% of the TPs will have no serviceat all. This transmission performance can definitely guaranteebusiness continuity in case of failures. However, this comeson an increase of 25% of the capital cost for acquiring theadditional SC.

B. Planning SC Locations For In-Band Model

For in-band mode the interference between different linksis taken into consideration and the maximum rate that can beassigned on any link is calculated according to the interferencemodel listed in Section (V-A). In the following planningcase we are trying to present the effect of the interference

consideration on the allocation of SCs using the planning withfault tolerance model and compare it with out-band model.

Planning results for the in-band with fault-tolerance modelare presented to show the interference effect on the planningprocess. Interference is modeled such that the transmissionfrom each BS to another SC or TP is interfered by transmissionfrom other SCs within 1 unit grid, similarly the transmissionfrom each SC to an SC or TB may suffer from interferenceby the SCs within the 1-by-1 grid distance.

Two scenarios using different numbers of TPs are presentedto examine the network load conditions. The rate requirementschange in each scenario to show the effect of the loadconditions on the SCs allocation. The parameters used in thesimulation are shown in Table IV.

Table IVSYSTEM PARAMETERS

Description ValueBand Width 5 MHZTransmitter Power 46 dBm / (39.81 W)path loss exponent (α) 2Receiver Noise -104 dBmCoverage area 12 KM * 12 KMNumber of SC sites 8

1) Scenario 1 (8 TPs):a) Homogeneous rate requirements: Fig. 4(a) shows the

locations of the TPs and SCs. In this in-band case eight

12


++

+

++

+

TP2r = 10 rb=8

TP3

TP4 TP6


+

+TP7

+TP5


e) Solution: Backup Topology whenSC5 Fails


r = 10 rb=8 r = 10 rb=8

r = 10 rb=8

r = 10 rb=8 r = 10 rb=8

r = 10 rb=8

r = 10 rb=8

TP0

TP1

++

+

++

r = 10

+

++

r = 10 r = 10

r = 10

r = 10 r = 10

r = 10 r = 10

20

20

30

++

+

++

rb=8

+

++

rb=8 rb=8

rb=8

rb=8 rb=8

rb=8rb=8

++

+

++

rb=8

+

++

rb=8 rb=8

rb=8

rb=8 rb=8

rb=8rb=8

c) Solution: Backup Topology whenSC0 Fails

++

+

++

rb=8

+

++

rb=8 rb=8

rb=8

rb=8 rb=8

rb=8rb=8

Failed SC

40

40

4016

16

16

++

+

++

rb=8

+

++

rb=8 rb=8

rb=8

rb=8 rb=8

rb=8rb=8

d) Solution: Main Topology forout-band mode (no interference)

Main SC Link BS to SC

Link BS to TPBackup SCLink SC to TP

SC0

SC2 SC3 SC4

SC5 SC6

SC1

SC7

SC0

SC2 SC3

SC5 SC6

SC0

SC2 SC3

SC5 SC6

SC0

SC2

SC3

SC5 SC6

SC0

SC2 SC3

SC5 SC6

Fig. 4. Planning SC Locations with Fault-Tolerance for In-Band Model

SCs and eight TPs are used. For the case of in-band modethe different maximum link rates are calculated according toeq.(28) to eq.(43) and the SINR is calculated according toeq.(1). The main (ri) and backup rate (rbi) requirement foreach TP are shown in Fig. 4(a), where backup rates are smallerthan the the main topology required rates.

Fig. 4(b) shows the main topology which supports themain rates to the TPs. This topology supports the equalhomogeneous rates for all TPs (10 Mbps), and uses three SC(SC0, SC3, SC5) to satisfy all the TPs rate requirements.In Fig. 4(c,d,e) the backup topology for the in-band mode ispresented, in case of any SC failure in the main topology, thenetwork will implement the backup solution using two SCs(SC2, SC6). Both SCs will operate to support the backup rates(8 Mbps) to the TPs. The solution shows that the BS supportsTP2, SC2 supports TP(0,1,3,4,7) and SC6 supports TP(5,6)

in both backup plans for (SC0 and SC3). However in backupplan for SC5, TP(0,1,2) are supported by the BS. SC6 supportsTP(5,6,7) and SC2 supports TP(3,4). The increase in thenumber of SCs and the diversity of their locations and which

TPs they serve are due to the consideration of the interferencecaused by the in-band mode. Results in Fig. 3(f) for the maintopology without interference considerations shows that theTPs rate requirements are all satisfied by direct links from theBS. The reason is that the BS to TPs links maximum rates arecapable of delivering the TPs rate requirements without anyrelaying. This comparison shows that modeling the problemwith interference constraints requires SCs implementation,but in case of ignoring the interference in the model norelaying is required, in order to support the TPs with same raterequirements. The comparison clearly shows the importanceof considering the interference effect in planning the SCsplacement.

b) Heterogeneous rate requirements: Fig. 5(a) shows themain and backup rate requirement for each TP. The rate re-quirements for the TPs in this heterogeneous case are different,and the same number of SCs are needed to satisfy a smallertotal rate requirements (64 Mbps Vs. 80 Mbps) than that ofthe homogeneous case. The results for the main topology inFig. 5(b) show that SC0 supports TP(0,1,2,3,4), SC3 supports

13


++

+

++

+

TP2r = 9 rb=7

TP3

TP4 TP6


+

+TP7

+TP5


e) Solution: Backup Topology whenSC5 Fails


r = 8 rb= 6 r = 10 rb=8

r = 7 rb= 5

r = 6 rb=5 r = 8.5 rb=7

r = 7.5 rb= 6

r = 8 rb=6

TP0

TP1

++

+

++

r = 9

+

++

r = 8 r = 10

r = 7

r = 6 r = 8.5

r = 7.5 r = 8

40

8.5

15.5

++

+

++

rb=7

+

++

rb=6 rb= 8

rb= 5

rb= 5 rb= 7

rb= 6rb= 6

++

+

++

rb= 7

+

++

rb= 6 rb= 8

rb= 5

rb= 5 rb= 7

rb= 6rb= 6

c) Solution: Backup Topology whenSC0 Fails

++

+

++

rb=7

+

++

rb=6 rb= 8

rb=5

rb=5 rb=7

rb=6rb=6

Failed SC

26

43

77

38

17



7

SC0

SC2 SC3 SC4

SC5 SC6

SC1

SC7

SC0

SC2 SC3

SC6 SC6

SC0

SC2 SC3

SC6 SC6

SC0

SC2 SC3

SC6 SC6

SC0

SC2 SC3

SC6 SC6


TP6 and SC5 supports TP(5,7). Fig. 5(c) shows a the backupplan when SC0 fails, only backup SC2 is activated to supportTP(0,1,2,3), SC3 still supports TP6 and SC5 is supportingTP(4,5,7). Results in Fig. 5(d) show the backup plan when SC3

fails, both backup SC(2,6) are activated where SC2 supportsTP(0,1,2,3,4,5,7) and SC6 is supporting TP6. Fig. 5(e) showsthe backup plan when SC5 fails, also both backup SC(2,6) areactivated but SC2 supports TP(0,1,3,4,5,7), BS supports TP2

and SC3 still supports TP6. It is also noticed that not all ofthe SCs either from the main or backup SCs are used in allbackup plans since part of the objective is to use the minimumamount of SCs in any individual plan.

2) Scenario 2 (16 TPs):a) Homogeneous rate requirements: In this scenario the

number of TPs is increased to 16 TPs to show more insightabout the distribution of the network load in the network. Thecase shown in Fig. 6(a) presents the locations and homoge-neous rate requirements for all TPs. Only 2 SCs are neededin this scenario, Fig. 6(b) shows the main topology whereTPs (0 to 7) are supported by the BS and TPs (8 to 15) are

supported by TP4. Once TP4 has failed, the backup topologyactivates SC3 which supports the TPs (8 to 15) and the BSkeeps supporting TPs (0 to 7).

The results show the capability of the BS to support the TPswhen their rate requirements decrease from 10 Mbps in thefirst scenario to 6.4 Mbps in this scenario. The reason is thatthe maximum link capacities are able to support the requiredrates to the upper SCs without any relaying.

b) Heterogeneous rate requirements: Finally the hetero-geneous case of the 16 TPs, in which the TPs have differentrate requirements as shown in Fig. 7(a). The main topologyshown in Fig. 7(b) requires two SCs to satisfy the TPs. SC0

supports TP(0,1,2,3,4,6,8,11,12) and SC0 supports the rest of theTPs. Figs. 7(c,d) shows the backup solution in case of SC0

or SC4 failure respectively. In case of SC4 failure, multi-hoprelaying occurs from SC0 to SC1 for 11.2 Mbps to be relayedto TP(0,2). This result shows that for this scenario, althoughthe TPs total required rate is less than the homogeneous case

14


++

+

++

+




Failed SC

+

++

++

+

++

+

++

++

+

++

+

++

++

+

++

+

++



TP4

r =6.4 rb=5.2

TP7

TP8 TP12

TP15TP11

r =6.4 rb=5.2 r =6.4 rb=5.2

r =6.4 rb=5.2

r =6.4 rb=5.2 r =6.4 rb=5.2

r =6.4 rb=5.2 r =6.4 rb=5.2

TP0

TP3

TP5

r =6.4 rb=5.2

TP6

TP9 TP13

TP14TP10

r =6.4 rb=5.2 r =6.4 rb=5.2

r =6.4 rb=5.2

r =6.4 rb=5.2 r =6.4 rb=5.2

r =6.4 rb=5.2 r =6.4 rb=5.2

TP1

TP2

51.2

r =6.4

r =6.4

r =6.4r =6.4

r =6.4

r =6.4r =6.4

r =6.4 r =6.4

r =6.4

r =6.4

r =6.4

r =6.4

r =6.4

r =6.4r =6.4

++

+

++

+

++

++

+

++

+

++

51.2

r =6.4

r =6.4

r =6.4r =6.4

r =6.4

r =6.4r =6.4

r =6.4 r =6.4

r =6.4

r =6.4

r =6.4

r =6.4 r =6.4

r =6.4r =6.4

SC0

SC2 SC3 SC4

SC5 SC6

SC1

SC7

SC3 SC4

SC3 SC4


(96.4 Mbps Vs. 102.4 Mbps), the planning still needs moreSCs to serve the TPs. This increase in the number of the SCsis clearly due to the heterogeneity in the rate requirements thatcauses more interference and requires more relaying.

VII. CONCLUSIONSIn this paper, we considered the problem of planning the SC

locations in the WiMAX network in a fault-tolerant manner.To the best of our knowledge, this is the first work thatprovides fault-tolerance in planning SC locations in WiMAX.We provided a Mixed-Integer Linear Program (MILP) thatformulates the planning problem. The allocation problem isstudied in both the out-bound and in-bound relaying modes. Inorder to address the non-linearity in the problem formulationa mapping form non linear to linear formulation is performed.The mapping utilized a binary conversion methodology andtraded the non-linearity by an increase in the state space size ofthe problem. We solved the problem with CPLEX and obtainednumerical results that show how our model produces the maintopology and the backup topologies of a network. Finally, weconsidered the existence of obstacles in the planning field,such as a large structure or a natural obstacle. We showedhow our model can deal with these obstacles and plan thenetwork around them effectively.


++

+

++

+



Link SC to SC


Failed SC

+

++

++

+

++

+

++

++

+

++

+

++

++

+

++

+

++




TP4

r =12 rb=6

TP7

TP8 TP12

TP15TP11

r =10.4 rb=5.2 r =8.8 rb=4.4

r =0.8 rb=0.4

r =6.4 rb=3.2 r =0.4 rb=0.4

r =7.2 rb=3.6 r =1.6 rb=0.8

TP0

TP3

TP5

r =11.2 rb=5.6

TP6

TP9 TP13

TP14TP10

r =9.6 rb=4.8 r =4 rb=2

r =3.2 rb=1.6

r =4.8 rb=2.4 r =5.6 rb=2.8

r =8 rb=4 r =2.4 rb=1.2

TP1

TP2

56.4 35.2

r =12

r =11.2

r =10.4

r =9.6

r =0.4

r =5.6

r =0.4

r =7.2 r =8

r =4

r =3.2

r =8.8

r =6.4

r =4.8

r =2.4r =1.6

++

+

++

+

++

++

+

++

+

++

34.8

rb =6

rb =5.6

rb =5.2

rb =4.8

rb =0.4

rb =2.8

rb =0.4

rb =3.6 rb =4

rb =2

rb =1.6

rb =4.4

rb =3.2

rb =2.4

rb =2.4rb =1.6

++

+

++

+

++

++

+

++

+

++

34.8

rb =6

rb =5.6

rb =5.2

rb =4.8

rb =0.4

rb =2.8

rb =0.4

rb =3.6 rb =4

rb =2

rb =1.6

rb =4.4

rb =3.2

rb =2.4

rb =2.4rb =1.6

11.2

SC0

SC2 SC3 SC4

SC5 SC6

SC1

SC7

SC0

SC4

SC0

SC4

SC1 SC0

SC4

SC1


REFERENCES

[1] Z. Abichar and J. Chang, “A medium access control scheme forwireless lans with constant-time contention,” Mobile Computing, IEEETransactions on, vol. 10, no. 2, pp. 191–204, Feb 2011.

[2] IEEE 802.16-2012, IEEE Standard for Air Interface for BroadbandWireless Access Systems, 2012.

[3] 3GPP, 3GPP TS 132541 version 11 Release 11,Digital cellular telecom-munications system (Phase 2+); Universal Mobile TelecommunicationsSystem (UMTS); LTE; Telecommunication management; Self-OrganizingNetworks (SON); Self-healing concepts and requirements, 2012.

[4] E. Chu, I. Bang, S. H. Kim, and D. K. Sung, “Self-organizing and self-healing mechanisms in cooperative small-cell networks,” in PersonalIndoor and Mobile Radio Communications (PIMRC), 2013 IEEE 24thInternational Symposium on, Sept 2013, pp. 1576–1581.

[5] Z. Abichar, A. Kamal, and J. Chang, “Planning of Relay Station Loca-tions in IEEE 802.16 (WiMAX) Networks,” in Wireless Communicationsand Networking Conference (WCNC), 2010 IEEE, April 2010, pp. 1–6.

[6] M. Peng, Y. Li, Z. Zhao, and C. Wang, “System architecture and keytechnologies for 5g heterogeneous cloud radio access networks,” CoRR,vol. abs/1412.6677, 2014.

[7] M. Eguizabal and A. Hernandez, “Resource allocation and interferencemanagement strategies for inband relaying in lte-a,” TelecommunicationSystems, pp. 1–22, 2015. [Online]. Available: http://dx.doi.org/10.1007/s11235-015-0040-7

[8] M. Minelli, M. Ma, M. Coupechoux, and P. Godlewski, “Schedulingimpact on the performance of relay-enhanced lte-a networks,” IEEETransactions on Vehicular Technology, vol. PP, no. 99, pp. 1–1, 2015.

[9] J.-Y. Chang and Y.-S. Lin, “A clustering deployment scheme for basestations and relay stations in multi-hop relay networks,” in JournalComputers and Electrical Engineering, vol. 40, no. 2, 2014, pp. 407– 420.

[10] B. Lin and P.-H. Ho, “Dimensioning and location planning of broadbandwireless networks under multi-level cooperative relaying,” Wireless

http://dx.doi.org/10.1007/s11235-015-0040-7

http://dx.doi.org/10.1007/s11235-015-0040-7

15

Communications, IEEE Transactions on, vol. 8, no. 11, pp. 5682–5691,November 2009.

[11] B. Lin, M. Mehrjoo, P.-H. Ho, L.-L. Xie, and X. Shen, “CapacityEnhancement with Relay Station Placement in Wireless CooperativeNetworks,” in Wireless Communications and Networking Conference,2009. WCNC 2009. IEEE, April 2009, pp. 1–6.

[12] B. Lin, P.-H. Ho, L.-L. Xie, X. Shen, and J. Tapolcai, “Optimal RelayStation Placement in Broadband Wireless Access Networks,” MobileComputing, IEEE Transactions on, vol. 9, no. 2, pp. 259–269, Feb 2010.

[13] Y. Yu, S. Murphy, and L. Murphy, “Planning Base Station and RelayStation Locations in IEEE 802.16j Multi-Hop Relay Networks,” inConsumer Communications and Networking Conference, 2008. CCNC2008. 5th IEEE, Jan 2008, pp. 922–926.

[14] ——, “A Clustering Approach to Planning Base Station and RelayStation Locations in IEEE 802.16j Multi-Hop Relay Networks,” inCommunications, 2008. ICC ’08. IEEE International Conference on,May 2008, pp. 2586–2591.

[15] S.-J. Kim, S.-Y. Kim, H.-W. Lee, S.-W. Ryu, H.-W. Lee, and C.-H.Cho, “Multi-Hop Relay Based Coverage Extension in the IEEE802.16jBased Mobile WiMAX Systems,” in Networked Computing and Ad-vanced Information Management, 2008. NCM ’08. Fourth InternationalConference on, vol. 1, Sept 2008, pp. 516–522.

[16] B. Lin, P.-H. Ho, L.-L. Xie, and X. Shen, “Optimal Relay StationPlacement in IEEE 802.16J Networks,” in Proceedings of the 2007International Conference on Wireless Communications and Mobile Com-puting, ser. IWCMC ’07. New York, NY, USA: ACM, 2007, pp. 25–30.

[17] H.-C. Lu and W. Liao, “Joint Base Station and Relay Station Placementfor IEEE 802.16j Networks,” in Global Telecommunications Conference,2009. GLOBECOM 2009. IEEE, Nov 2009, pp. 1–5.

[18] D. Niyato, E. Hossain, D. I. Kim, and Z. Han, “Relay-centric radioresource management and network planning in IEEE 802.16j mobilemultihop relay networks,” Wireless Communications, IEEE Transactionson, vol. 8, no. 12, pp. 6115–6125, December 2009.

[19] C.-Y. Chang, C.-Y. Chang, M.-H. Li, and C.-H. Chang, “A NovelRelay Placement Mechanism for Capacity Enhancement in IEEE 802.16jWiMAX Networks,” in Communications, 2009. ICC ’09. IEEE Interna-tional Conference on, June 2009, pp. 1–5.

[20] Y. Yu, S. Murphy, and L. Murphy, “Interference Aware Relay StationLocation Planning for IEEE 802.16J Mobile Multi-hop Relay Network,”in Proceedings of the 4th ACM Workshop on Performance Monitoringand Measurement of Heterogeneous Wireless and Wired Networks, ser.PM2HW2N ’09. New York, NY, USA: ACM, 2009, pp. 201–208.

[21] ——, “Planning Base Station and Relay Station Locations for IEEE802.16j Network with Capacity Constraints,” in Consumer Communica-tions and Networking Conference (CCNC), 2010 7th IEEE, Jan 2010,pp. 1–5.

[22] C.-Y. Chang and M.-H. Li, “A placement mechanism for relay stationsin 802.16j WiMAX networks,” Wireless Networks, vol. 20, no. 2, pp.227–243, 2014.

[23] A. Bari, A. Jaekel, and S. Bandyopadhyay, “Optimal Placement of RelayNodes in Two-Tiered, Fault Tolerant Sensor Networks,” in Computersand Communications, 2007. ISCC 2007. 12th IEEE Symposium on, July2007, pp. 159–164.

[24] A. Bari, Y. Xu, and A. Jaekel, “Integrated Placement and Routing ofRelay Nodes for Fault-Tolerant Hierarchical Sensor Networks,” in Com-puter Communications and Networks, 2008. ICCCN ’08. Proceedings of17th International Conference on, Aug 2008, pp. 1–6.

[25] S. Misra, S. D. Hong, G. Xue, and J. Tang, “Constrained Relay NodePlacement in Wireless Sensor Networks: Formulation and Approxima-tions,” Networking, IEEE/ACM Transactions on, vol. 18, no. 2, pp. 434–447, April 2010.

[26] J. Bredin, E. Demaine, M. Hajiaghayi, and D. Rus, “Deploying SensorNetworks With Guaranteed Fault Tolerance,” Networking, IEEE/ACMTransactions on, vol. 18, no. 1, pp. 216–228, Feb 2010.

[27] X. Han, X. Cao, E. Lloyd, and C.-C. Shen, “Fault-Tolerant Relay NodePlacement in Heterogeneous Wireless Sensor Networks,” in INFOCOM2007. 26th IEEE International Conference on Computer Communica-tions. IEEE, May 2007, pp. 1667–1675.

[28] W. Zhang, G. Xue, and S. Misra, “Fault-Tolerant Relay Node Placementin Wireless Sensor Networks: Problems and Algorithms,” in INFOCOM2007. 26th IEEE International Conference on Computer Communica-tions. IEEE, May 2007, pp. 1649–1657.

[29] P. Meena, D. Gurjar, A. Singh, and S. Verma, “Optimal positioningof base station in wireless sensor networks: A survey,” in IntelligentComputing, Networking, and Informatics, ser. Advances in IntelligentSystems and Computing, D. P. Mohapatra and S. Patnaik, Eds. SpringerIndia, 2014, vol. 243, pp. 1135–1143.

[30] A. Samson Arun Raj, K. Ramalakshmi, and C. Priyadharsini, “A Surveyon Classification of Fault Tolerance Techniques Available in WirelessSensor Network,” in International Journal of Engineering Research andTechnology, vol. 3, no. 1, 2014.

[31] M. Nivedita and G. Raja, “Efficient relay station placement strategyfor broadband wireless networks - 4G,” in International Conferenceon Recent Trends In Information Technology (ICRTIT), April 2012, pp.282–286.

[32] H. Wang, X. Yin, C. Chen, and X. Wang, “DPRP: Dual-path relay place-ment in WiMAX mesh networks,” in IEEE Wireless Communicationsand Networking Conference (WCNC), April 2013, pp. 1597–1602.

[33] W. Stallings, Wireless Communications and Networks. Prentice Hall,2001.

[34] IEEE Std 802.16-2004 (Revision of IEEE Std 802.16-2001), IEEEStandard for Local and Metropolitan Area Networks Part 16: AirInterface for Fixed Broadband Wireless Access Systems, 2004.

[35] T. Tsourakis and K. Voudouris, “WiMax network planning and system’sperformance evaluation,” in Wireless Communications and NetworkingConference, 2007.WCNC 2007. IEEE, March 2007, pp. 1948–1953.

[36] M. Molina-Garcia and J. Alonso, “Planning and Sizing Tool for WiMAXNetworks,” in Radio and Wireless Symposium, 2007 IEEE, Jan 2007, pp.403–406.

[37] J. Garcia-Fragoso and G. Galvan-Tejada, “Cell planning based on theWiMax standard for home access: a practical case,” in Electrical andElectronics Engineering, 2005 2nd International Conference on, Sept2005, pp. 89–92.

[38] P. Rubin, “Integer variables and quadratic terms,” July2013. [Online]. Available: http://orinanobworld.blogspot.com/2013/07/integer-variables-and-quadratic-terms.html

http://orinanobworld.blogspot.com/2013/07/integer-variables-and-quadratic-terms.html

http://orinanobworld.blogspot.com/2013/07/integer-variables-and-quadratic-terms.html

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