IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE Fault-Tolerat Small Cells Locatios Plaig i 4G/5G Heterogeeous Wireless Networks Tamer Omar, Zakhia Abichar, Ahmed E. Kamal, J. Morris Chag, ad Mohammad Abdullah Aluem Abstract Fourth/Fifth Geeratio heterogeeous wireless etworks (4G/5G HetNets) use or will use small cells (SCs) to exted etwork coverage ad icrease spectrum efficiecy. However, the stadard ad techical specificatios do ot specify how to pla the locatios of the SCs withi the etwork. Several papers itroduced strategies for plaig the locatios of SCs i the 4G HetNet architecture. However, SCs placemet strategies to support the self-healig fuctioality of the 4G/5G self orgaizig etworks framework has ot bee studied i the literature. The placemet of SCs i 4G HetNets such that a SC failure will ot iterrupt service, hece makig the etwork fault tolerat, is a importat desig ad plaig problem that is addressed i this paper. We preset a iteger liear program formulatio for plaig operators of maaged SC locatios with fault tolerace. We allow oe SC to fail ad by usig self-healig, a fault-tolerace service is provided at desigated fail-over levels (defied i terms of users throughput). We cosider the problem of SC locatio plaig by usig offloadig i both out-bad ad i-bad modes, ad a iterferece model is preseted to cosider the i-bad mode ad to address the effect of iterferece o SCs placemet plaig. A ovel approach to provide a liear iterferece model by usig a expaded state space to get rid of oliearity is itroduced. We preset umerical results that show how our model ca be used to pla the positios of SCs. We also icorporate the existece of obstacles i the plaig, such as large structures or atural formatios, that might happe i real life. To the best of our kowledge, this is the first work that addresses the plaig of SC locatios i 4G/5G HetNets i a fault-tolerat maer. Idex Terms Fault tolerace, 4G HetNets, etwork architecture ad desig, self-healig, self orgaizig etworks (SON), small cells. I. INTRODUCTION AFTER the success ad wide deploymet of Wireless Local Area Networks (WLAN) [1], the area of wireless et- Mauscript received September 27, 2015; revised February 3, 2016, Jue 10, 2016, ad September 8, 2016; accepted September 24, Date of publicatio October 5, 2016; date of curret versio Jue 16, This work was supported i part by the Natioal Pla for Sciece, Techology ad Iovatio (MAARIFAH) ad i part by Kig Abdulaziz City for Sciece ad Techology, Kigdom of Saudi Arabia uder Award 11-INF The review of this paper was coordiated by Prof. C. Assi. T. Omar is with the Departmet of Techology Systems, East Carolia Uiversity, Greeville, NC USA ( omart15@ecu.edu). Z. Abichar is with the Departmet of Electrical ad Computer Egieerig, Uiversity of Cetral Florida, FL USA ( zakhia17@ece.ucf.edu). A. E. Kamal is with the Departmet of Electrical ad Computer Egieerig, Iowa State Uiversity, Ames, IA USA ( kamal@iastate.edu). J. M. Chag is with the Departmet of Electrical Egieerig, Uiversity of South Florida, Tampa, FL USA ( chag5@usf.edu). M. A. Aluem is with the Departmet of Iformatio Systems, Kig Saud Uiversity, Riyadh 11451, Saudi Arabia ( maluem@ksu.edu.sa). Color versios of oe or more of the figures i this paper are available olie at Digital Object Idetifier /TVT works has witessed the stadardizatio process for broadbad wireless access etworks. The fourth geeratio (4G) broadbad wireless etwork techologies (LTE ad WiMAX) techical specificatios provide last-mile coectivity, ad they have bee touted to fill several eeds: last-mile ed user access, iitial deploymet of ifrastructure i uwired areas, ad providig access to mobile users [2]. The mai mobile service providers statios i a 4G HetNets are the base statio (BS)/eNodeB (enb) ad the ed users statios are called mobile statios (MS)/user equipmet (UE) i WiMAX/LTE, respectively. I some areas, voice ad data services are provided to ed users via wireless etworks istead of traditioal wire-lie ifrastructure, which is time-cosumig ad costly to deploy. Both stadards address the utilizatio of small cells (SCs) i 4G heterogeeous etworks (HetNets). The goal of usig SCs is to support the coectivity betwee the BS/eNB o oe side ad the MSs/UE o the other side. The SC ca exted the rage of a BS. For example, there could be users that are out of reach of the BS/eNB ad caot coect to the etwork. With the placemet of a SC betwee the user ad the BS/eNB, the user would be able to coect; hece, the rage of the BS/eNB is exteded. The SC ca also be used to ehace the capacity of the BS/eNB. For example, eve if all the users are i rage withi the BS/eNB, placig oe or more SCs i the cell allows higher data rates ad ehaces the cell s capacity as a result. 4G HetNet techologies, however, does ot specify how the SCs should be placed i the etwork. The model preseted i this paper allows for more tha two hops commuicatio. Oe of the advatages of this model is that it accommodates other etworks, such as the use of relays i IEEE m. There are also advatages i usig more tha two hops i LTE etworks; that is, operator cotrolled SCs (e.g., Pico Cells) ca piggyback o other SCs, hece actig as both SCs, ad also relay statios, ad therefore achieve some gais i terms of coverage ad rate ehacemet. It is the goal of this paper to devise a techique for plaig the SC locatios with fault tolerace to avoid failures i a 4G/5G HetNets. A. Motivatio I this paper, we cosider the operators problem of placig several maaged SCs to support a BS/eNB to exted the coverage, improve the rate, ad at the same time provide a resiliet operatio for HetNets. I real life, users expect a reliable service ad may busiesses rely o the Iteret coectio to be able to fuctio. If the etwork is plaed with o fault tolerace, a SC failure might result i discoectig some users. There U.S. Govermet work ot protected by U.S. copyright.

2 5270 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 are differet sources for SCs failures, ad the differet reasos of failures i HetNets ca be classified ito three categories as follows. 1) The first category is equipmet malfuctio, which may occur due to hardware or power outage. 2) The secod category is lik outage due to the failure of the SC back-haul that prevets the SC from relayig traffic to the core etwork. 3) Outage may occur due to the limited capacity ad coverage capabilities of SCs that may become cogested by overwhelmig traffic from ed users or chael impairmets. Due to its importace, the self-healig fuctioality has bee itroduced as oe of the mai fuctioalities of the self orgaizig etworks (SON) [3]. Usig the SON framework, selfhealig procedures ca be triggered to perform the proper remedy whe fault tolerace plaig is implemeted to restore the service iterrupted by ay failure from the above three failure categories. I the model of this paper, we cosider the self-healig fuctioality i the case i which at most oe SC might fail at a certai time. It could be ay SC amog the used SCs. With a adequate level of service, the SC should be repaired before aother SC fails. This assumptio (allowig oly oe SC to fail) also allows keepig the cost of the system reasoable. The proposed model is flexible to accommodate the umber of assumed failig SCs, albeit with a icreased capital expediture (CAPEX). To provide fault tolerace, we defie for each user a full bit rate ad a backup bit rate. Whe there is o failure amog the SCs, users receive service at the full bit rate. However, i the case of a failure, we cosider that offerig service to affected users at a reduced rate is better tha o service at all. Thus, i the case of a SC failure, the users receive service at the backup rate. This defiitio also allows users who primarily deped o the Iteret for busiess to have a backup rate that ca be made equal to the full rate. Thus, these users will fuctio without service degradatio eve i the case of a SC failure. The iput to our problem is the locatio of the BS/eNB, the potetial locatios of the SCs, the locatio of the users (MSs/UE), ad their respective demads represeted by the bit rate. To reduce the problem complexity, groups of users are represeted by traffic poits (TP). For example, if there are several offices located close to each other with demads of 50, 100, ad 150 Mb/s, they could be represeted by a TP (located i a cetric poit to the offices) with a demad equal to the total MSs/UE demads of 300 Mb/s. The plaig solutio we preset i this paper aims at placig the SCs i the etwork to achieve several goals. The specific goals are as follows. 1) All the service area should be covered with coectio to the etwork. The service area is defied through the TPs; thus, by providig coectivity betwee all the TPs ad the BS/eNB, the service area will be covered. 2) The throughput demad of all the TPs should be satisfied. There should be a coectio betwee the TP ad the BS/eNB, with a flow equal to the predefied demad of the correspodig TP. The coectios are assumed to be withi the licesed carrier s spectrum. 3) The umber of SCs placed by our solutio should be miimized to reduce the equipmet, istallatio, ad operatio cost, i.e., both CAPEX ad OPEX. 4) I case a SC i the etwork fails, the etwork should cotiue to operate ad provide service to the TPs at a predefied level of service, which we call the backup service rate. Thus, our plaig method provides fault tolerace ad resiliece to sigle SC failures. B. Cotributio Self-healig is the mai fuctioality of the SON framework that provides fault-tolerat operatio. Self-healig mechaism through cooperative clusters is proposed i [4] to deploy ad maage the icreasig umber of small-cell etworks. Resource utilizatio performace i both ormal ad failure modes of a small-cell etwork is evaluated ad the authors show that their proposed mechaism outperforms other covetioal mechaisms. The study i [5] provided a relay statio (RS) plaig solutio i WiMAX that satisfies oly the first three goals listed above. There was o fault tolerace provisio i the approach used. Thus, if a RS fails, there is o guaratee that the level of service provided would be adequate to the subscribers. I additio, the authors studied oly WiMAX relayig without cosiderig the applicable dow-lik chaels iterferece as oly out-bad trasmissio was cocered. Hece, i this paper, we exted the approach to icorporate the i-bad SCs plaig with fault tolerace i a differet etwork architecture by modelig the problem of i-bad iterferece i HetNets. The ew approach will esure that users are served adequately i the case of a SC failure i 4G/5G HetNets. There are several papers i the literature that address the problem of placig relay odes i 4G etworks. These are reviewed i the ext sectio. However, to the best of our kowledge, there is o work o plaig the locatios of SCs i HetNets with fault tolerace. There have bee some approaches o placig relays i a fault-tolerat maer i other types of etworks, such as wireless sesor etworks (WSN). We formulate the SCs plaig problem usig a mixed iteger liear program (MILP). We preset umerical results by solvig our model with CPLEX. We believe that solvig the model directly to obtai results is a valid approach sice plaig is ot a real-time operatio. The problem is solved ad the allocatio is made usig both out-bad (o iterferece) ad i-bad (iterferece due to dow-lik resources sharig) trasmissio modes. To address the i-bad mode, a iterferece model is itroduced ad the maximum lik rates are calculated while takig the iterferece ito cosideratio. Sice the iterferece model results i a oliear formulatio of the problem, we mapped the formulatio to a biary liear formulatio by expadig the state space, hece avoidig oliearities. We preset umerical results that show how our model fids the umber ad locatios of SCs. Our model also specifies all the liks that are used ad gives the rate o each lik. Also, for every SC that is used i the mai topology (used whe o SC is

3 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5271 i a failure coditio), the model gives a correspodig backup topology i case this SC fails. The rest of this paper is orgaized as follows. Sectio II presets the related work ad Sectio III presets the etwork model. The optimizatio model with fault tolerace is provided i Sectio IV for out-bad mode ad i Sectio V for i-bad operatioal mode. Numerical results are give i Sectio VI ad the coclusios are give i Sectio VII. II. RELATED WORK This sectio presets earlier work i the literature that is related to the problem of plaig the SC locatios with fault tolerace. a) Plaig Locatios i LTE The i-bad mode is addressed by authors i [6] as oe of the strategies used i 5G HetNets to share the etwork resources betwee the enb ad the SCs. This study shows the importace of creatig a iterferece model like the oe proposed i this paper to address this issue i HetNets by usig i-bad strategy. Eguizabal ad Heradez [7] proposed a i-bad strategy to multiplex traffic to several relay odes i LTE. Iterferece coordiatio is proposed to icrease coverage ad improve capacity. However, fault tolerace ad self-healig was ot discussed by the authors. A i-bad mode performace evaluatio for differet deploymets is ivestigated by the authors i [8]. Differet scearios are preseted to show the performace of relayig i LTE etworks, ad results show that relayig is strogly affected by the back-haul. However, fault tolerace is ot addressed i the study to show the effect of failure o etwork plaig. A clusterig algorithm based o uiform cluster cocepts is proposed i [9] to select the BS ad RS locatios from cadidate positios, depedig o the traffic demads. The authors itroduce a scheme that makes adaptive decisio for selectig the deploymet sites of the BS ad RS. Simulatio results show that the scheme achieves good performace i terms of etwork throughput ad coverage. Li ad Ho preset aother RS placemet solutio i [10], wherei the cooperative trasmissio paradigm is used i multihop relayig for the purpose of rage extesio. Also, Li et al. [11], [12] presets a RS placemet solutio that uses the cooperative trasmissio techique for the purpose of capacity ehacemet. b) Plaig Locatios i WiMAX Our previous work i [5] presets a model for plaig the RS locatios i a WiMAX etwork. However, i the previous work, there was o guaratee of service if a RS fails sice fault tolerace was ot cosidered. I this paper, we exted our model to provide resiliece to relay failures. A plaig model is preseted i [13] to fid the locatios of BSs ad RSs i the etwork. The model is formulated as a optimizatio problem usig iteger programmig. I this model, there is at most oe RS betwee the SS/MS ad the BS, ad a maximum of two hops is allowed. Sice the stadard does ot have a limit o the umber of hops goig through the RSs, this assumptio may impose uecessary restrictios. Yu et al. preset a extesio of their work i [14]. I this paper, they cosider a large coverage area that icreases the computatio time of the model. To reduce the computatio time, they divide the area ito clusters ad apply the approach above to every cluster. The, the cases o the boudaries of the clusters are solved to fid the overall solutio. This paper similarly limits the umber of hops to two. I [15], a model is preseted to fid the locatios of RSs that exted the rage of a BS i a WiMAX etwork. This work defies preset topologies ad fids the RS placemet for these topologies; i compariso, our model i this paper ad i [5] ca work with ay topology. This work also cosiders RS locatio plaig for sector-based topology. Each sector uses a frequecy that is differet from adjacet sectors to reduce iterferece. I [16], a RS placemet model is preseted. This work is based o cooperative trasmissio betwee the source ode ad the relay ode to provide a better sigal to the destiatio ode. They cosider the decode-ad-forward scheme ad the compress-ad-forward scheme for cooperative trasmissio. This model is differet from our work sice it cosiders the placemet of a sigle RS to serve multiple MSs. I [17], the problem of joit BS ad RS deploymet is cosidered ad a optimizatio model is preseted. Due to the large size of the problem, the model takes a log time to solve. Thus, the authors also preset a efficiet heuristic algorithm to fid the problem suboptimal solutio. I [18], the problem of RS placemet i the WiMAX etwork is cosidered. The locatio of the RSs ad the badwidth allocatio to users are foud. This work assumes that users demads could chage due to fluctuatios i traffic demads ad due to mobility. Thus, the optimizatio of the RS locatios is foud o a log-term basis ad the badwidth allocatio to users is foud o a short-term basis. Chag et al. [19] cosider usig relays for the purpose of capacity ehacemets as follows. There is a BS, a area that ca be totally covered by the BS, ad a give umber of relays. This work decides where to place the relays to maximize the system capacity. I [20], the followig paradigm is cosidered for the placemet of RSs i WiMAX etworks. The umber ad locatios of BSs are give. The goal of the problem is to place RSs that use the trasparet mode. I this mode, the RSs do ot trasmit cotrol iformatio; the cotrol iformatio are oly trasmitted by the BS. The RSs are thus i rage of the BS ad the goal of the RS placemet is capacity ehacemet. Other approaches used i BSs ad RSs placemet are preseted i [21], [22], with the goal of ehacig the overall etwork capacity. c) Plaig Locatios i WSN There are approaches i the literature that provide relay locatio plaig with fault tolerace. But these approaches have bee desiged for WSNs ad ot for WiMAX etworks. I [23], a Iteger Liear Program model is preseted for placig relays i sesor etworks to provide fault tolerace i case some odes fail. The mai issue was coectivity, regardless of badwidth requiremets, which implies that all relay odes may be operatioal all the time. Bari et al. preset a extesio of their work i [24], which takes ito cosidera-

4 5272 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 tio the routig strategy to reduce battery cosumptio. Other approaches o fault-tolerat placemet of relay odes are give i [25] [32]. The approaches preseted i this sectio cosider a multitude of issues ad cofiguratios for traffic relayig used i broadbad ad WSNs. There are multiple approaches for plaig the placemet of odes that is discussed i these etworks, some of them, specifically i WSNs, address the plaig of relay odes locatios with fault tolerace. However, oe of this work is applicable to broadbad wireless HetNets. To the best of our kowledge, there is o approach that provides the plaig of SCs locatios operatig withi the same frequecy bad (i-bad mode) i HetNets with fault-tolerace. Moreover, either the approaches itroduced for WSNs that discussed fault tolerace or our previous work i [5] cosidered the iterferece caused due to the i-bad trasmissio mode. Usig the SON framework, the proposed approach ca be implemeted as a self-healig fuctioality to compesate for HetNet failures. However, the offered service i case of failures is dowgraded to the backup rates. Hece, our paper is the first to propose such solutios that map from oliear to liear iterferece usig state space trasformatio as a approach to perform HetNet SCs recovery i a i-bad trasmissio mode ad to guaratee the busiess cotiuity eve i case of partial failures by usig the proposed fault tolerace plaig. III. NETWORK MODEL This sectio presets the etwork model that we cosider i this paper. A. Small Cells Offloadig Modes The 4G/5G HetNets defies two modes of macrocells to SCs offloadig operatio modes: a trasparet mode ad a otrasparet mode. I the trasparet mode, the users (MSs/UE) are uaware of the presece of a SC. The SC does ot trasmit cotrol iformatio (such as dow-lik map ad up-lik map). These are trasmitted by the BS/eNB. Thus, all the MSs/UE are withi rage of the BS. However, the SCs are used i the trasparet mode for the purpose of capacity ehacemet. I the otrasparet mode, the SCs perform all fuctios eeded for a stadaloe cell ad trasmits cotrol iformatio as well as data to the MSs/UE it serves. Multi-hop routes are allowed i the otrasparet mode. The goal for usig otrasparet SCs is to exted the rage of the etwork ad to also ehace the capacity. Curretly this mode is widely used for SCs deploymet ad is the mode cosidered i our study. B. Duplexig Mode Whe SCs are used, trasmissios from two statios that are i rage should be duplexed either i the frequecy domai (FDD) or i the time domai (TDD) to avoid iterferece. The 4G stadards allow the use of differet frequecies for SCs servig the same BS. Thus, we make the assumptio that the SCs duplex their trasmissio usig the frequecy divisio duplex (FDD) mode. For example, o a two-hop route enb-sc-ue, we ca have a trasmissio of rate r o the enb- SC hop ad aother trasmissio of the same rate o the SC-UE TABLE I OFDMA RATES (IN MBPS) FOR VARIOUS MODULATION SCHEMES USING 7 MHZ BANDWIDTH QPSK QPSK 16-QAM 16-QAM 64-QAM 64-QAM / / / / / / hop. This happes if the two hops are usig differet frequecies. With time divisio duplex (TDD), the two hops will alterate i trasmissio usig the same frequecy chael. However, each hop will have a larger badwidth sice the badwidth is ot divided aymore. We use FDD for simplicity, but our model is logically equivalet to TDD. For more geeralizatio of the studied problem, we also assumed the utilizatio of oorthogoal physical layer multiplexig approaches (e.g, CDMA, FDMA). The proposed model ca beefit from adoptig frequecy partitioig ad reuse techiques whereby the same chaels ca be reallocated to differet small cells if they are geographically distributed so that the itercell iterferece betwee them does ot egatively impact their trasmissio rates. C. Lik Capacity Our model allocates a rate o each lik that is used i the produced topology. The allocated rate o a lik is bouded by the maximum capacity of the lik. The maximum capacity of a wireless lik ca be modeled with the Shao Hartley equatio as give i [33]. It is give by the equatio: C = B. log 2 (1 + SINR), where C is the capacity i bit/s, B is the chael badwidth i Hz. The sigal to iterferece plus oise ratio ca be calculated as SINR = S/ [N 0 + I], where S is the received sigal power, N 0 is the oise power, ad I is the sigal power received from all iterferers, j. The capacity chages with the distace sice the SINR degrades whe the distace icreases. The SINR ca be expressed as βp i SINR i = [ (d) α N 0 + (1) j i p j /(d) α] where p i is the sigal trasmissio power, d is the Euclidea distace betwee the trasmitter ad receiver, α>2 is the path loss expoet, ad β is the atea gai. Other factors also affect the lik capacity, such as the codig ad modulatio schemes. Whe a high SINR is measured o the lik, codig, ad modulatio schemes with high rates are used. However, whe the SINR is low, robust codig ad modulatio schemes are preferred to limit the bit error rate (BER), although they provide low data rates. Table I shows the achievable bit rates for the Orthogoal Frequecy-Divisio Multiple Access (OFDMA) physical layer as give i the stadard [34]. Quadrature Phase Shift Keyig (QPSK) is more robust but achieves a small rate. O the other had, 64-QAM is less robust but achieves a high rate. The factors that affect a lik s capacity ca be combied i a equatio. For ay lik i, the maximum rate is: m i = Γ(SINR i,χ,cod, Mod), where χ is the upper-boud o the

5 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5273 TABLE II ABBREVIATIONS TABLE III LINK RATES OUT-BAND MODE Parameters Descriptio Distace (uit) Lik Rate (Mb/s) R T B L x i F x r i, rb i k S T Variables dr, dbr, dbtdrt, drr fbr, fbt, frt, frr BR, BT, RT, RR mbr, mbt, mrt, mrr cbr, cbt, crt, crr dbr, dbt, drt, drr, Ix j,yx Fx vbr, vbt, vrt, vrr wbr, wbt, wrt, wrr X i,z ij,xi k,zk ij Set of cadidate sites for SC Set of TPs that represet the user traffic Base Statio Set of liks that ca iterfere with lik i Sets of active iterferece liks to lik i Rate requiremet, backup rate requiremet Backup topology umber Total umber of SCs Total umber of SCs i backup topology Descriptio Decisio variables Traffic flow Number of subcarriers Maximum lik capacity Actual lik capacity Biary variables Variables Auxiliary variable BER, Cod is the codig scheme, ad Mod is the modulatio scheme. Γ is the fuctio that maps all the three parameters to the maximum rate. Ay defiitio of the fuctio Γ ca work with our model. However, for simplicity, we assume that the maximum rate chages with distace. I real-life scearios, there is usually a field survey that precedes the etwork deploymet [35] [37]. The lik rates are selected based o the liks characteristics, such as the SINR, fadig, the specifics of the terrai, ad iterferece with other wireless systems. D. Defiitio of Fault Tolerace The plaig model we preset i this paper allows the failure of a SC without iterruptig service to the users, albeit at a reduced bit rate, hece toleratig equipmet failure. We assume that oly oe SC will fail at a give time. This is a reasoable assumptio sice usually i the time it takes the SC to be repaired, there is a very small probability that aother SC will fail. This is true sice the umber of operator supported SCs (e.g, Pico Cells) supportig a BS/eNB will typically be a small umber of SCs. This assumptio will keep the cost of SCs small, sice toleratig the failure of two or more SCs at the same time requires istallig may extra SCs, which is ot a cost-effective approach. For every set of customers represeted by a TP, a tuple {r i,rb i } defies the requested service rates. Whe all the SCs are operatioal, the full rate for a TP i, give by r i is provided. However, whe there is a SC failure, a reduced rate that is the backup rate rb i, is provided, with rb i r i. Users who request the same service rate, eve i the case of a SC failure, will have rb i = r i. IV. OPTIMIZATION MODEL: THE OUT-BAND MODE This sectio presets the optimizatio model for the SC plaig problem with fault tolerace i the out-bad mode. The model takes the followig as iput. if distace <= 1 rate = 10 else if distace <= 2 rate = 5 else if distace <= 3 rate = 2 else if distace <= 4 rate = 1 else rate = 0 1) the possible sites where a SC ca be istalled; 2) the locatios of the TP that represet the users traffic; 3) the rates (full ad reduced) i Mb/s of each TP. The full rate is provided whe all the SCs are operatioal, ad the reduced rate is guarateed whe there is a SC failure; ad 4) the model takes as a iput the maximum rate o ay lik: enb-sc, SC-TP, SC-SC, ad SC-TP, which depeds o the lik characteristics such as distace, SINR, ad badwidth. Table III helps to clarify the otatios i this paper. The output of our model is the full-rate (mai) topology ad the reduced-rate (backup) topologies. The full-rate topology is defied by the umber of SCs used, their positios, the liks used, the rate o each lik, ad fially, the coectio ode for each TP (either the enb or a SC). Each of the backup topologies correspods to a failure i oe of the SCs used i the mai topology. For example, if the mai topology uses SC 1, SC 3, ad SC 8, the there will be three backup topologies that are used i case ay of these SCs fails. For ay TP (TP i ), the full rate is desigated by r i ad the reduced backup rate is desigated by rb i, which is the miimum acceptable rate i the case of failure. Let R = {SC 0,...,SC N 1 } be the set of cadidate sites for SC with cardiality R = N. Similarly, let T = {TP 0,...,TP M 1 } be the set of TPs that represet the user traffic with cardiality T = M. A. Decisio Variables The followig decisio variables defie the full-rate topology { 1; a SC is deployed i site SCi dr i = 0; otherwise (i R) { 1; a lik is used betwee the enb ad SCi dbr i = 0; otherwise(i R) { 1; TPi is assiged to the enb dbt i = 0; otherwise (i T ) { 1; a lik is used betwee the SCi ad SC drr ij = j 0; otherwise (i, j R) { 1; TPj is assiged to the SC drt ij = i 0; otherwise (i R, j T ). We also defie variables that are similar to the above to specify the backup topologies. These variables are: dr k i, dbr k i, dbt k i, drr k ij, ad drt k ij. The term k idicates

6 5274 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 the backup topology umber used whe SC k i has failed. For example, whe k = 3, these variables defie the backup topology that is used whe SC 3 fails. We also defie decisio variables that desigate the assiged flow (i Mb/s) o each lik. Although the previous variables were biary, the flow variables take cotiuous values. I the full-rate topology, the variables fbr i ad frr ij desigate the flow o the liks from enb to SC i ad SC i to SC j, respectively, where i ad j are idexes of SCs (i, j R). Similarly, i the backup topology, the variables fbr k i ad frr k ij desigate the flow o the liks from enb to SC k i ad SC k i to SC k j, respectively, where i, j are idexes of SCs, k is the idex of the backup topology whe SC k fails, ad (i, j, k R). B. Topology Costraits The followig costraits defie the topology of the SCs domai. They esure that whe a lik is used i the solutio, the two ed odes of the lik exist (i.e., the SCs are selected). They also esure that a TP is coected either directly to the enb or to oly oe SC; we use this coditio to ot add complexities to the UEs. First, whe there is a lik betwee the enb ad SC i, there should be a SC deployed at site SC i. This is esured by the followig costraits i the full-rate ad the backup topologies dbr i dr i i R (2) dbr k i dr k i i k i, k R. (3) Whe there is a lik betwee SC i ad SC j, two SCs should be istalled at sites SC i ad SC j. This is esured by the followig costraits: drr ij dr i + dr j 2 i, j R (4) drr k ij drk i + drk j i k, j k i, j, k R. (5) 2 Whe there is a lik betwee SC i ad TP j, a SC should be deployed at site SC i. This is esured by the followig costraits: drt ij dr i i R j T (6) drt k ij dr k i i k, j k i, k R j T. (7) The followig costraits sed all the traffic of a TP either through a direct lik with the enb or through a sigle SC: dbt i + drt ji = 1 i T (8) dbt k i + j R j R, j k drt k ji = 1 i T. (9) C. Flow Costraits The flow costraits esure that the amout of data that is trasported is balaced ad sufficiet for the demads of all the TPs. 1) Flow Balace at the BS: I the mai topology, the total traffic goig out of the enb should be equal to the sum of the full rates r i of all the TPs. This coditio is esured by the followig equatio: fbr i dbr i + r j dbt j = r j (10) i R j T, mbt j r j j T where ( mbt j,mrt j ) are the upper bouds of the rates o the liks for the mai topology which are iput parameters to the problem ad are calculated i Sectio V-A At a backup topology, the rate provided to TP i is greater tha or equal to rb i. The, this coditio is used fbr k i dbr k i + rb j dbt k j = rb j. i R, i k j T, mbt j rb j j T (11) We are iterested i keepig the system liear. Thus, we use the followig trasformatio ad substitute i (10): X i = fbr i dbr i where X i is a auxiliary variable. Equatio (10) therefore becomes X i + r j dbt j = r j. i R j T, mbt j r j j T (12) X i ca be evaluated usig the followig set of liear costraits, where Q is a large umber such that Q>max(fBR i ) iɛr: X i Q dbr i Q + fbr i i R (13) X i fbr i i R (14) X i 0 i R (15) X i Q dbr i i R. (16) Similarly, we use the followig trasformatio for (11): Xi k = fbr k i dbr k i i k i, k R. (17) Hece, (11) becomes Xi k + rb j dbt k j = rb j. j T, mbt j rb j j T (18) i R, i k Xi k is evaluated like X i was evaluated i (13) (16). 2) Flow Balace at a SC: At ay SC, the amout of traffic that is comig from the enb ad from upstream SCs is equal to the amout of traffic that is goig to dowstream SCs ad to TPs that are directly coected to the SC. This is esured by the followig costrait: fbr i dbr i + frr ji drr ji j R = frr ij drr ij + r y drt iy i R. j R y T, mrt j r y (19) The equatio above is made liear by usig the trasform Z ij = frr ij drr ij ad becomes X i + Z ji = Z ij + r y drt iy j R j R y T, mrt iy r y i R. (20)

7 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5275 For the backup topologies, the flow coservatio at the SC is esured by the followig equatio: fbr k i dbr k i + frr k ji drr k ji = j R, j k frr k ij drr k ij + j R, j k y T, mbt iy rb y rb y drt k iy i k i, k R. (21) The equatio above is made liear by usig the trasform Zij k = frrk ij.drr k ij ad it becomes Xi k + Zji k = + j R, j k j R, j k y T, mbt iy rb y rb y drt b iy i k i, k R. (22) Z ij ad Zij k are evaluated similar to how X i was evaluated i (13) (16). 3) Flow Balace at a TP: I the mai topology, the amout of traffic betwee the enb or the SC ad the TP should be equal to the full-rate, r i of the TP. This is esured by the followig costrait: i r i dbt i + r i drt ji = r i i=i, mbt i r i j R, mrt ji r i i T. (23) For the backup topologies, the amout of traffic at the TP should be equal to rb i. This is esured by the followig costrait: i rb i dbt k i + rb i drt ji = rb i i=i, mbt i rb i j R,j k,mrt ji rb i Z k ij i T,k R. (24) V. OPTIMIZATION MODEL A. I-Bad Model The model that we have so far assumes the out-bad mode, ad i this case the maximum capacity of lik BR i,rr i,bt i, ad RT i are mbr i,mrr i,mbt i, ad mrt i respectively. To accommodate the i-bad mode, the capacity o lik i depeds o the activity of other liks j, which may iterfere with lik i. We will eed to set the capacity o lik i so that it correspods to the capacity that is subject to iterferece with other active liks i the system. Rather tha usig a oliear formulatio, we use a liear formulatio that comes at the cost of a expaded space state. The basic idea of the trasformatio is to precompute the capacity of the target lik i for all possible cases of iterferece. This ca be doe offlie, ad outside the optimizatio formulatio. The, for each of the iterferece cases, we have a biary variable that is equal to 1 if this case is valid. Multiple iterferece cases may occur at the same time, e.g., if two liks iterfere with the target lik, the there are three cases of Fig. 1. Example for lik iterferece. iterferece, oe for each lik ad the third for both liks. The, the optimizatio problem by determiig the iterferece cases ca select the correspodig capacity as the miimum capacity for all valid iterferece cases. The expasio i the state space is the result of the use of the biary variable correspodig to the iterferece cases. It is worth metioig that the coversio of the iterferece oliear characteristics to liear is developed without chagig the parameters of the origial problem (e.g., o. of subcarriers allocated for a SC). This is doe by usig a biary liear formulatio i which the capacity of lik i is defied as follows. 1) Assume that the maximum umber of other liks that ca iterfere with lik i is a i, ad the set of such liks is Lx i = l 1,l 2,...,l a i where x {BR, RR, BT, RT}. 2) The capacity of lik i, give that liks i the th subset Fx Lx i are active, icludig the empty subset, is give by cx Fx ad is precomputed. A example is show i Fig. 1 for the iterferece sets ad subsets to explai the iterferece that a lik may suffer. To fid out which combiatio of liks are active, a biary variable Ix j is defied as beig equal to 1 if lik j is active. The umber of active liks i each Fx is evaluated as follows: = Ix j Fx Lx i. (25) Ax Fx j F x The, to fid the combiatio that has all of its member liks active. We defie a biary variables Yx Fx, which will be equal to 1 oly if all liks i the subset Fx are active. Yx Fx ca be evaluated usig the followig costraits: mbt i FBT i mrr ijk FRR ijk Yx Fx Ax Fx Fx + 1 (26) Yx Fx Ax Fx + δ Fx + δ (27) where δ is a small umber. The additio of δ to both the umerator ad deomiator is to iclude the case of empty subset, i which case both Fx ad Ax Fx are zeros. Therefore, the maximum capacity of a lik ca be evaluated as the miimum for all cases i which Yx Fx = 1. The upper bouds o the rates o this lik (mbr i,mrr ij, FBR i FRR ij, mrt ij ) for mai topology ad (mbr ik, FRT ij FBR ik,mbt ik FBT ik,mrt ijk FRT ijk ) for backup topologies are

8 5276 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 iput parameters to the problem ad are calculated as follows: mbr i FBR i mrr ij FRR ij mbt i FBT i mrt ij FRT ij mbr ik FBR ik = cbr i YBR i FBR i FBR i = crr ij YRR ij FRR ij FRR ij = cbt i YBT i FBT i FBT i = crt ij YRT ij FRT ij FRT ij = cbr ik YBR ik FBR ik FBR ik +(1 YBR i ) M FBR i (28) +(1 YRR ij ) M FRR ij (29) +(1 YBT i ) M FBT i (30) +(1 YRT ij ) M FRT ij (31) +(1 YBR ik ) M FBR ik (32) mrr ijk = crr ijk YRR ijk +(1 YRR ijk FRR ijk FRR ijk FRR ijk mbt ik FBT ik = cbt ik YBT ik FBT ik FBT ik FRR ijk ) M (33) +(1 YBT ik ) M FBT ik (34) mrt ijk = crt ijk YRR ijk +(1 YRT ijk FRT ijk FRT ijk FRT ijk FRT ijk ) M (35) where M is a very large umber. I (28), if subset FBR i is active, hece YBR i is 1, the the capacity of lik i is equal to FBR i cbr i. Otherwise, the effect of subset FBR i FBR i is excluded by havig this capacity equal to a very large umber, M. Equatios (29) (35) follow similar reasoig. The maximum flow that ca be trasmitted o a lik i is limited by the trasmissio power, the lik distace, ad the codig ad modulatio schemes. The maximum rate that ca be assiged o the lik from the enb to SC i,fbr i, is limited by mbr i, where mbr i is the maximum rate o this FBR i FBR i lik. A similar otatio is used for all the other liks, ad the costraits that esure the upper boud are the followig: C fbr i BR i mbr i FBR i FBR i C frr ij RR ij mrr ij FRR ij FRR ij C fbr k i BR ik mbr ik FBR ik FBR ik C frr k ij RR ijk mrr ijk FRR ijk FRR ijk C fbt i BT i mbt i FBT i FBT i C frt ij RT ij mrt ij FRT ij FRT ij FBR i LBR i (36) FRR ij LRR ij (37) FBR ik LBR k i (38) FRR ijk LRR k ij (39) FBT i LBT i (40) FRT ij LRT ij (41) C fbt k i BT ik mbt ik FBT ik FBT ik FBT ik LBT k i (42) C frt k ij RT ijk mrt ijk FRT ijk FRT ijk FRT ijk LRT k ij (43) i k, j k, i, j, k R where the variable BR i {0, 1,..., C} correspods to FBR i the umber of subcarriers allocated to ay SC i out of a total of C subcarriers, which is a iput parameter, ad C is assumed to be a itegral power of 2 (e.g., C = 512) 1. To avoid further complexity of the modeled problem, we assumed that the orthogoality amog subcarriers is maitaied ad that there is o itercarrier iterferece betwee trasceivers of differet liks. The costrait i (36) is a oliear costrait with BR i FBR i a discrete variable ad mbr i a cotiuous variable. The FBR i followig equatios are used to trasform it to a liear form. A ew variable vbr i = BR i mbr i is defied FBR i FBR i FBR i ad a biary expasio [38] for BR i is performed as FBR i BR i FBR i dbr ir FBR i = The vbr i F BR vbr i FBR i where ρ 2 r dbr ir FBR i r=0 FBR i LBR i,i R (44) ρ = log 2 (C) (45) {0, 1} (46) = ca be rewritte as ρ 2 r wbr ir FBR i r=0 wbr ir FBR i FBR i LBR i,i R = dbr ir mbr i FBR i FBR i (47) FBR i LBR i,i R. (48) Now the costrait i (36) is coverted ito oliear costrait but with dbr i a biary variable ad mbr i a FBR i FBR i cotiuous variable, which ca be liearized usig the same approach used i (13) (16). Similarly, the same coversio is used for variables (vbt i, vrr ij, vrt ij ) ad the backup topologies FBT i FRR ij FRT ij variables (vbr ik, vbt ik, vrr ijk, vrt ijk ). Also, FBT ik FBT ik FRR ijk FRT ijk whe a SC fails, the rate o all the liks icidet o it is zero. B. Out-Bad Model For out-bad mode, the iterferece betwee the liks are ot cosidered, ad the maximum rate that ca be assiged o the lik from the BS to SC i,fbr i, is limited by fbr i mbr i. Similarly for all the other liks, the costraits that esure the upper boud are calculated accordig to fbr i mbr i frr ij mrr ij i R i, j R fbr k i mbr i i k, i, k R frr k ij mrr ij i k, j k, i, j, k R. 1 Without loss of geerality, ad to reduce the model complexity, we cosider C to be a power of 2.

9 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5277 C. Objective Fuctio The primary objective of our solutio is to miimize the total umber of SCs used. This will miimize the cost of SC istallatio. We defie the variable S i, which idicates if a SC is istalled at site SC i either i the mai topology or i ay other topology S i dr i i R (49) S i dr k i i k, i, k R. (50) To miimize the total umber of SCs that are istalled, iɛr S i should be miimized. We also aim at reducig the umber of SCs used i backup topologies. Miimizig the umber of SCs used i every topology allows us to remove legthy paths. For example, if a TP ca coect to the enb by goig through oe SC oly, it is better ot to use two SCs for this TP. Thus, miimizig the umber of SCs i the backup topologies will make a TP use the miimum ecessary umber of SCs it eeds to coect to the enb. The variable T k desigates the umber of SCs used i the backup topology whe SC k fails. We have the followig costrait: T k dr k i k R. (51) i R, i k For a similar reaso to the above, we aim to miimize the umber of SCs that is used i the mai topology, desigated by the term V. We have the costrait V dr i. (52) i R The term Obj combies the terms above. The mai term from the above is iɛr S i, sice it gives the umber of SCs that should be istalled. It should be give a higher weight tha the other terms. The maximum value of kɛr T k is N 2 ad the maximum value of V is N. Thus, we give the weight N 2 + N to the term with S i Obj =(N 2 + N) S i + T k + V. (53) i R k R The, the objective fuctio is Miimize Obj. (54) Implemetig a system with multihop relays icreases the operatioal complexity, ad also solvig the problem with wireless back-haulig ad multihop topology adds more complexity to the problem. However, usig more tha two hops has advatages i terms of performace, such as rage of coverage ad bit rate. This is why we opted to develop a geeric model that ca accommodate ay umber of hops. To accommodate the case of oly two hops, we ca force all the RR, frr, drr, mrr, ad wrr to zero. VI. NUMERICAL RESULTS This sectio itroduces umerical results based o the plaig models preseted above. First, we show examples of plaig without fault tolerace i a WiMAX etwork. I these examples, whe a SC fails, there is o guaratee of service Fig. 2. Plaig SC locatios without fault-tolerace for out-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio. to the TPs. Secod, we show examples with fault tolerace, where service will be guarateed eve i case of failure of a SC. We cosider both the out-bad ad i-bad operatio i solvig the locatio plaig MILP problem i a WiMAX HetNet. By usig CPLEX, which rus o a moder multicore machie, we obtaied solutio times i terms of hours for realistic scearios that shows a reasoable computatio time for practical cases. The solutio of the optimizatio problem for the proposed model is feasible as log as proper desig parameters are selected to support the required resources for a certai etwork desig sceario. A. Plaig SC Locatios For Out-Bad Mode 1) Plaig Without Fault Tolerace: This sectio presets the iitial results of plaig the SC locatios without fault tolerace. I this sectio, where o fault tolerace is cosidered, the variables ad costraits i the model that are used for fault tolerace are omitted. These are all the variables that have a idex k, which are: dr k i,dbr k i,dbt k i,drr k i,fbr k i,fbr k i, ad frr k ij. Also, the objective fuctio will chage. For the case i which we do ot have fault tolerace, the objective is simply to miimize the total umber of SCs used. The, the objective fuctio

10 5278 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 Fig. 3. Plaig SC locatios with fault-tolerace for out-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio: The mai topology. (c) Solutio: Backup topology whe SC2 fails. (d) Solutio: Backup topology whe SC5 fails. (e) Solutio: Backup topology whe SC7 fails. is mi dr i. (55) i R a) Theoretical Model: The followig is a SC plaig example that uses our solutio. The problem is show i Fig. 2(a). The plaig area is made discrete by the use of a square grid. The BS locatio is o the top lie of the grid, as show i the figure. We select this settig sice we cosider that the BS is at the edge of the coected area. The area below the BS does ot have the coectio, ad we pla to coect this area through the BS. Without loss of geerality, we ca use ay topology with our model. The potetial sites for a SC are the corers of a grid square. I the 4 4 grid, the SC sites are umbered 0 to 15, as show i the figure. The possible site of a TP is i the ceter of a square. The TPs are umbered 0 to 9. I the figure, the TP umbers are TP (2,4,5,6,8). The umber show i the figure ext to each TP is its traffic demad i Mb/s. The maximum rate o the liks is show i Table III. The distace uit is the side legth of a square i the grid. The table shows the feasible rate for the correspodig distace iterval (per the model i Sectio III). The solutio to this plaig example is show i Fig. 2(b). The shaded SC sites are the Descriptio TABLE IV SYSTEM PARAMETERS Value Bad Width 5 MHz Trasmitter Power 46 dbm / (39.81 W) path loss expoet (α) 2 Receiver Noise 104 dbm Coverage area 12 KM 12 KM Number of SC sites 8 oes that have bee selected. Three SCs are eeded for this problem, which are SC 1,SC 5, ad SC 7. The solid lie liks are the BS-SC ad SC-SC liks. The dashed lies are the BS-TP ad SC-TP liks. The uderlied umbers are the lik rates allocated by the solutio. The rates of the dotted liks are equal to the correspodig TPs rates. The arrows o the liks show the flow of traffic i the dow-lik to facilitate iterpretig the results. However, the traffic may go i the up-lik or dow-lik directio. We ote the followig observatios from this example. 1) The distace from the TP to the BS does ot ecessarily idicate a direct or relayed coectio. For example, the TP with demad of 2 Mb/s is the farthest from the BS.

11 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5279 Fig. 4. Plaig SC locatios with fault tolerace for i-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio: The mai topology. (c) Solutio: Backup topology whe SC0 fails. (d) Solutio: Backup topology whe SC3 fails. (e) Solutio: backup topology whe SC5 fails. (f) Solutio: Mai topology for out-bad mode (o iterferece). However, its demad is relatively low, which ca be satisfied by a sigle lik. O the other had, TPs that are closer to the BS have higher demads ad require the use of a SC. 2) Secod, the SC-to-SC liks help i reducig the umber of SCs i the HetNet. I our example, there is more traffic to the right of the BS ( = 14) tha the left (5) ad the middle (6). Thus, i the solutio, the diagoal ad horizotal liks, both with rate of 2 Mb/s, betwee SCs (1,7) ad (5,7), respectively, relay the traffic from the right side to the less cogested left side. If this was ot the case, more SCs would be eeded o the right side. 2) Plaig With Fault Tolerace: I this part, we preset plaig results with fault tolerace. The problem iput is show i Fig. 3(a), ad it has the same TP locatios ad rates as the example i Fig. 2(a). I this case, there are also backup rates for each TP, which are smaller tha or equal to the the mai rate. Fig. 3(b) shows the mai topology that supports the mai rates of the TPs. This topology, similar to that i Fig. 2(b), supports the same ormal operatio rates ad also uses three SCs. However, ulike the topology i Fig. 2(b), it uses SC 2, SC 5, ad SC 7. Moreover, it also requires the istallatio of a additioal relay at site SC 10. Eve though SC 10 is ot used i the mai topology, it is required i case oe of the three used SCs fails. I Fig. 3(b), the TPs with rates of 4 ad 2 Mb/s coect directly to the BS sice their direct lik ca support the required rate. This is similar to Fig. 2(b). Each of the other TPs coects to the SC that is closest to it. Fig. 3(c) shows the backup topology that is used whe SC 2 fails. I this topology, the backup rates are supported, which are smaller tha the mai rates i this example. Due to the lower rates, ow three TPs are able to have a direct coectio to the BS (compared to two i the mai topology). The other two TPs coect through SCs. I this topology, SC 10 is also ot used

12 5280 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 Fig. 5. Plaig SC locatios with fault tolerace for i-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio: The mai topology. (c) Solutio: Backup topology whe SC0 fails. (d) Solutio: Backup topology whe SC3 fails. (e) Solutio: Backup topology whe SC5 fails. sice SC 5 ad SC 7 are able to support the TPs demads, which makes the recovery from SC 2 failure faster, sice SC 10 eed ot be used. The topology i Fig. 3(d) is the case i which SC 5 fails. I this case, three SCs are eeded to support the TPs. Notice that i the previous topology, SC 5 was strategically located betwee the BS ad the TP i the lower-left corer. Sice SC 5 has failed, there is o SC that ca satisfy this TP. Thus, two SCs are used to coect this TP. I Fig. 3(e), the topology that is used whe SC 7 fails is show. Now the TP i the lower-left corer is able to coect via SC 5. However, the TP with demad 6 Mb/s, which was 9 previously relyig o SC 7 caot coect with oly oe SC. The, SC 2 ad SC 10 covey the traffic of this TP i this case. However, the TP coects oly to SC 10, ad SC 10 coects to both the BS ad SC 2 to receive the data. Fially, whe SC 10 fails, we ca cotiue to use the mai topology as i Fig. 3(b) sice this topology does ot use SC 10. We compared our proposed solutio to provide fault tolerace to the oe without fault tolerace. The results i Fig. 3(e) shows that with oe extra SC for achievig fault tolerace, the trasmissio rates achieved is about 68% of the rates achieved i the mai topology. Fig. 3(b) shows that i case of SC 5 failure ad without fault tolerace plaig oly 44% of the rate ca be provided ad 40% of the TPs will have o service at all. This trasmissio performace ca defiitely guaratee busiess cotiuity i case of failures. However, this comes o a icrease of 25% of the capital cost for acquirig the additioal SC. B. Plaig SC Locatios for I-Bad Model For i-bad mode, the iterferece betwee differet liks is take ito cosideratio ad the maximum rate that ca be assiged o ay lik is calculated accordig to the iterferece model listed i Sectio V-A. I the followig plaig case, we are tryig to preset the effect of the iterferece cosideratio o the allocatio of SCs usig the plaig with fault tolerace model ad compare it with out-bad model. Plaig results for the i-bad with fault tolerace model are preseted to show the iterferece effect o the plaig process. Iterferece is modeled such that the trasmissio from

13 OMAR et al.: FAULT-TOLERANT SMALL CELLS LOCATIONS PLANNING IN 4G/5G HETEROGENEOUS WIRELESS NETWORKS 5281 each BS to aother SC or TP is iterfered by trasmissio from other SCs withi 1 uit grid, similarly the trasmissio from each SC to a SC or TB may suffer from iterferece by the SCs withi the 1-by-1 grid distace. Two scearios usig differet umbers of TPs are preseted to examie the etwork load coditios. The rate requiremets chage i each sceario to show the effect of the load coditios o the SCs allocatio. The parameters used i the simulatio are show i Table IV. 1) Sceario 1 (8 TPs): a) Homogeeous Rate Requiremets: Fig. 4(a) shows the locatios of the TPs ad SCs. I this i-bad case, eight SCs ad eight TPs are used. For the case of i-bad mode, the differet maximum lik rates are calculated accordig to (28) (43) ad the SINR is calculated accordig to (1). The mai (r i ) ad backup rate (rb i ) requiremet for each TP are show i Fig. 4(a), where backup rates are smaller tha the the mai topology required rates. Fig. 4(b) shows the mai topology that supports the mai rates to the TPs. This topology supports the equal homogeeous rates for all TPs (10 Mb/s), ad uses three SC (SC 0,SC 3,SC 5 )to satisfy all the TPs rate requiremets. I Fig. 4(c,d,e) the backup topology for the i-bad mode is preseted, i case of ay SC failure i the mai topology, the etwork will implemet the backup solutio usig two SCs (SC 2,SC 6 ). Both SCs will operate to support the backup rates (8 Mb/s) to the TPs. The solutio shows that the BS supports TP 2,SC 2 supports TP (0,1,3,4,7) ad SC 6 supports TP (5,6) i both backup plas for (SC 0 ad SC 3 ). However i backup pla for SC 5,TP (0,1,2) are supported by the BS. SC 6 supports TP (5,6,7) ad SC 2 supports TP (3,4).Theicrease i the umber of SCs ad the diversity of their locatios ad which TPs they serve are due to the cosideratio of the iterferece caused by the i-bad mode. Results i Fig. 3(f) for the mai topology without iterferece cosideratios shows that the TPs rate requiremets are all satisfied by direct liks from the BS. The reaso is that the BS to TPs liks maximum rates are capable of deliverig the TPs rate requiremets without ay relayig. This compariso shows that modelig the problem with iterferece costraits requires SCs implemetatio, but i case of igorig the iterferece i the model o relayig is required to support the TPs with same rate requiremets. The compariso clearly shows the importace of cosiderig the iterferece effect i plaig the SCs placemet. b) Heterogeeous Rate Requiremets: Fig. 5(a) shows the mai ad backup rate requiremet for each TP. The rate requiremets for the TPs i this heterogeeous case are differet, ad the same umber of SCs are eeded to satisfy a smaller total rate requiremets (64 Versus 80 Mb/s) tha that of the homogeeous case. The results for the mai topology i Fig. 5(b) show that SC 0 supports TP (0,1,2,3,4),SC 3 supports TP 6, ad SC 5 supports TP (5,7). Fig. 5(c) shows a the backup pla whe SC 0 fails, oly backup SC 2 is activated to support TP (0,1,2,3),SC 3 still supports TP 6, ad SC 5 is supportig TP (4,5,7). Results i Fig. 5(d) show the backup pla whe SC 3 fails, both backup SC (2,6) are activated where SC 2 supports TP (0,1,2,3,4,5,7) ad SC 6 is supportig TP 6. Fig. 5(e) shows the backup pla whe SC 5 fails, also both backup SC (2,6) are activated but SC 2 supports TP (0,1,3,4,5,7),BS Fig. 6. Plaig SC locatios with fault tolerace for i-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio: The mai topology. (c) Solutio: Backup topology whe SC4 fails. supports TP 2, ad SC 3 still supports TP 6. It is also oticed that ot all SCs from either the mai or backup SCs are used i all backup plas sice part of the objective is to use the miimum amout of SCs i ay idividual pla. 2) Sceario 2 (16 TPs): a) Homogeeous Rate Requiremets: I this sceario, the umber of TPs is icreased to 16 TPs to show more isight about the distributio of the etwork load i the etwork. The case show i Fig. 6(a) presets the locatios ad homogeeous rate requiremets for all TPs. Oly two SCs are eeded i this sceario, Fig. 6(b) shows the mai topology where TPs 0 to 7 are supported by the BS ad TPs 8 to 15 are supported by TP 4. Oce TP 4 has failed, the backup topology activates SC 3, which supports the TPs 8 to 15 ad the BS keeps supportig TPs 0to7. The results show the capability of the BS to support the TPs whe their rate requiremets decrease from 10 Mb/s i the first sceario to 6.4 Mb/s i this sceario. The reaso is that the maximum lik capacities are able to support the required rates to the upper SCs without ay relayig. b) Heterogeeous Rate Requiremets: Fially, the heterogeeous case of the 16 TPs, i which the TPs have differet rate requiremets, as show i Fig. 7(a). The mai topology show i Fig. 7(b) requires two SCs to satisfy the TPs. SC 0 supports TP (0,1,2,3,4,6,8,11,12), ad SC 0 supports the rest of the TPs. Fig. 7(c) ad 7(d) show the backup solutio i case of SC 0

14 5282 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 6, JUNE 2017 model ca deal with these obstacles ad pla the etwork aroud them effectively. REFERENCES Fig. 7. Plaig SC locatios with fault tolerace for i-bad model. (a) Problem (mai rates ad backup rates i Mb/s). (b) Solutio: The mai topology. (c) Solutio: Backup topology whe SC0 fails. (d) Solutio: Backup topology whe SC4 fails. or SC 4 failure, respectively. I case of SC 4 failure, multihop relayig occurs from SC 0 to SC 1 for 11.2 Mb/s to be relayed to TP (0,2). This result shows that for this sceario, although the TPs total required rate is less tha the homogeeous case (96.4 Versus Mb/s), the plaig still eeds more SCs to serve the TPs. This icrease i the umber of the SCs is clearly due to the heterogeeity i the rate requiremets that causes more iterferece ad requires more relayig. VII. CONCLUSION I this paper, we cosidered the problem of plaig the SC locatios i the WiMAX etwork i a fault-tolerat maer. 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Available: Tamer Omar received the B.S. degree i electrical egieerig from Ai Shams Uiversity, Cairo, Egypt, i 1999, the MBA degree with emphasis o MIS from the Arab Academy for Sciece ad Techology, Alexadria, Egypt, i 2004, ad the Ph.D. degree from the Electrical Egieerig Departmet, Iowa State Uiversity, Ames, IA, USA, i He is a Assistat professor i the Departmet of Techology Systems, East Carolia Uiversity, Greeville, NC, USA. His research iterests iclude wireless etworks architecture, resources allocatio i wireless etworks, heterogeeous etworks, self-orgaized etworks, big data implemetatio ad aalysis, RDBMS, ad decisio support systems. Dr. Omar has six years of experiece i academia ad more tha 10 years of idustrial experiece i differet ICT positios. Zakhia Abichar received the B.S. ad Ph.D. degrees i computer egieerig from Iowa State Uiversity, Ames, IA, USA. He is a Lecturer i the Departmet of Electrical ad Computer Egieerig, Uiversity of Cetral Florida, Orlado, FL, USA. His teachig experiece is i the udergraduate computer egieerig classes, ad his research experiece is i the area of wireless etworks ad mobile computig. His research iterests iclude STEM educatio ad developig effective teachig techiques ad cotets to spread computig learig beyod higher educatio istitutios. He also has experiece i egieerig assessmet ad has worked o udergraduate computer egieerig program assessmet. Ahmed E. Kamal (S 82 M 87 SM 91 F 12) received the B.Sc. (distictio with hoors) ad the M.Sc. degrees both from Cairo Uiversity, Cairo, Egypt, i 1978 ad 1980, respectively, ad the M.A.Sc. ad Ph.D. degrees from the Uiversity of Toroto, Toroto, ON, Caada, i 1982 ad 1986, respectively, all i electrical egieerig. He is a Professor i the Departmet of Electrical ad Computer Egieerig, Iowa State Uiversity, Ames, IA, USA. His research iterests iclude wireless etworks, cogitive radio etworks, optical etworks, wireless sesor etworks, Iteret of Thigs, ad performace evaluatio. Dr. Kamal received the 1993 IEE Hartree Premium for papers published i Computers ad Cotrol i IEE Proceedigs, ad the Best Paper Award of the IEEE Globecom 2008 Symposium o Ad Hoc ad Sesors Networks Symposium. He chaired or co-chaired Techical Program Committees of several IEEEsposored cofereces, icludig the Optical Networks ad Systems Symposia of the IEEE Globecom 2007 ad 2010, the Cogitive Radio ad Networks Symposia of the IEEE Globecom 2012 ad 2014, ad the Access Systems ad Networks track of the IEEE Iteratioal Coferece o Commuicatios He is also the Chair of the IEEE Commuicatios Society Techical Committee o Trasmissio, Access ad Optical Systems for 2015 ad He is o the editorial boards of the IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, the Computer Networks joural, ad the Optical Switchig ad Networkig joural. He served as a IEEE Commuicatios Society Distiguished Lecturer i 2013 ad He is a seior member of the Associatio of Computig Machiery. J. Morris Chag (SM 08) received the Ph.D. degree from North Carolia State Uiversity, Raleigh, NC, USA, i He is a Professor i the Departmet of Electrical Egieerig, Uiversity of South Florida, Tampa, FL, USA. His past idustrial experieces iclude positios at Texas Istrumets, Microelectroic Ceter of North Carolia, ad AT&T Bell Labs. I the last five years, his research projects o cyber security have bee fuded by DARPA. His research iterests iclude cyber security, wireless etworks, ad eergy-efficiet computer systems. Dr. Chag received the Uiversity Excellece i Teachig Award at Illiois Istitute of Techology, i He is curretly a Hadlig Editor of the Joural of Microprocessors ad Microsystems ad the Associate Editor-i-Chief of the IEEE IT PROFESSIONAL. Mohammed Abdullah Aluem received the M.Sc. degree i distributed systems ad etworks from the Uiversity of Bradford, Bradford, U.K., i 2005, ad the Ph.D. degree i mobile computig ad etworks from the School of Iformatics, Uiversity of Bradford, i He is a Associate Professor i the College of Computer ad Iformatio Scieces, Kig Saud Uiversity, Riyadh, Saudi Arabia. His research iterests iclude computer etworks (wired ad wireless), mobile ad hoc ad sesor etworks, cloud computig, ad distributed systems. He has published a umber of research papers i peerreviewed cofereces ad jourals. His research is fiacially supported by several grats.