Performance Analysis of Small Cells Deployment under Imperfect Traffic Hotspot Localization

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1 Performance Analysis of Small Cells Deployment under Imperfect Traffic Hotspot Localization Aymen Jaziri +, ida Nasri, Tijani Caed + Orange Labs, + Telecom Sudparis {aymen.jaziri, rida.nasri}@orange.com, tijani.caed@telecom-sudparis.eu arxiv:68.7v [cs.ni] 3 Aug 6 Abstract Heterogeneous Networks HetNets, long been consided in operators roadmaps for macrocells network improvements, still continue to attract intest for 5G network deployments. Understanding te efficiency of small cell deployment in te psence of traffic otspots can furter draw operators attention to tis featu. In tis context, we evaluate te impact of imperfect small cell positioning on te network performances. We sow tat te latter is mainly impacted by te position of te otspot witin te cell: in case te otspot is near te macrocell, even a perfect positioning of te small cell will not yield improved performance due to te interfence coming from te macrocell. In te case we te otspot is located far enoug from te macrocell, even a large error in small cell positioning would still be beneficial in offloading traffic from te congested macrocell. Index Terms Heterogeneous networks, Traffic otspot localization, Small cell positioning, Performance analysis, Mean user trougput, Offloading gain. I. INTODUCTION Heterogeneous Networks HetNets, composed of small cells micro, pico, emote adio Heads H, lay and femto cells witin macro-cell coverage, ave been sown to be efficient in improving network performance [], [], mostly by covering traffic HotSpots HS and coverage oles. Te sulting enanced network performance depends among oter parameters on te location of te small cells deployment, and tis is te focus of our psent work we we study te impact of imperfect small cells deployment on te overall network performance. Te analysis of Small Cell SC deployment was te subject matter of many works but mostly using simplified network topology models wic yields eiter optimistic or pessimistic sults. For instance, autors in [] [3] consided a HetNet network wit diffent tiers to evaluate diffent performance metrics suc as te coverage probability, te average acievable rate and te average load per tier. Te network structu in eac tier is based on a spatial Poisson Point Process PPP wic is well suited for SC networks, we te Base Station BS positions a mo irgular tan for te Macro Cell MC layout. Eac tier differs from te oter by te average transmit power, te base station density and te supported data rate. Using PPP model allows for simple and tractable analytical expssions but it mains quite diffent from te al network layout, mainly for macro tier wic is close to te exagonal grid wit imperfections [4]. Moover, te deployment of SCs sould be made based on te traffic distribution as well. Considering small cell distribution as a PPP model implies tat te traffic HS - in case it is te ason for deploying SCs - follows also a PPP model wit a constant traffic value in eac HS wic is not te case, as sown in [5]. Tis random spatial model can owever be improved by incorporating new parameters suc as te minimum separation distance between BSs and/or te spatial traffic distribution. A diffent approac was used in [6] we te autors used a fluid model in order to study te impact of SC location on te performance and Quality of Service QoS in HetNets. A closed-form expssion of te Signal plus Interfence to Noise atio SIN is found for eac position in te network and is used, along wit te trougput distribution in bot MC and SC layers, in order to assess te impact of SC location on te network performance. Te quite gularity of al networks and non-omogeneous spatial traffic distribution a owever not taken into consideration in fence [6]. In general, it is commended to perform analysis in a exagonal network layout because of te fact tat radio engineers start te design of te network based on a exagonal model. Te deviation of te al network structu from te exagonal model is basically linked to te constraints imposed by engineering rules, field imperfections and government carters. Following tis approac, we derive and evaluate, in te psent work, several performance metrics in an infinite exagonal MC network for te diffent scenarios: wit MCs only, wit perfectly deployed SCs and wit SCs deployed wit considering imperfections in te positioning. Te former does not involve any SC deployment and so interfence comes only from neigboring MCs. Te second scenario assumes tat a SC is perfectly deployed in te peak of te traffic HS. Te last scenario involves errors in te positioning of SCs lative to te position of te traffic HS. Te main contributions of tis paper a twofold. First, we evaluate te gain tat can be generated from te deployment of a SC considering an error in HS localization, as compad to perfect HS localization. Second, we identify te tsold of HS localization errors tat can be tolerated

2 in operational tasks mainly for HetNet design. Te mainder of tis paper is organized as follows. In te next section, we psent te downlink system model. In section III, we detail te performance analysis for te above-mentioned scenarios. Numerical sults a igligted in section IV, and, in section V, we conclude wit a brief discussion of te sults of tis paper. II. DOWNLINK SYSTEM MODEL A. System setup and BS location model We consider a cellular network wit an infinite number of omni-sectorial MCs, eac one transmitting wit power level P. Te location of te MCs is drawn following a exagonal grid layout see Fig. wit inter-site distance denoted by δ. Next, we add a SC located in s, θ s as illustrated in Fig.. Te transmit power level of te SC is P s = αp wit α <. Fig. : Network layout. A given User Equipment UE wit polar coordinates m = r, θ is served by eiter te central MC or te deployed SC, depending on te lative signal stngt coming from bot antennas, and te st of te cells play te role of interfering ones. In order to evaluate te efficiency of deploying SCs, we consider a traffic HS wit polar coordinates, θ. Witout loss of generality, we assume tat tis HS is located inside te central MC of te network. Tis means 3 tat is smaller tan te radius of te cell = δ π defined by te radius of te disk aving te same aa as te exagon. Ten, a Gaussian distribution defines te UE location distribution inside te HS and its measu is given by dtr, θ = r + r cosθ θ πσ e rdrdθ σ psents te standard deviation of te distribution. In simulations, σ is equal to. and an example of te Te radio design based on te disk aving te same aa as te exagonal cell, avoids te over-overlapping between cells and te appearance of coverage oles wen te network is deployed. lative spatial distribution is plotted in Fig.. y=r/δ sin θ UEs BS.5.5 x=r/δ cos θ Interfering BS Fig. : Distribution of UEs in a Normal HS wit σ =. in =.44δ, θ = π 3. As indicated in te introduction, we consider te scenarios: In Scenario, te network is composed of MCs only. Tis scenario psents a bencmark allowing te comparison of a network containing SCs wit a network witout SCs. Scenario adds one SC inside te central MC. Tis SC is perfectly deployed and its position matces exactly wit te HS s position. In Scenario 3, we consider a SC deployed inside te central MC as in Scenario but we introduce some errors in te HS localization so tat te positions of te HS and te SC a not te same. To model te wiless cannel, we consider a distance based patloss metric wit a standard function given by a m C b, we m C is te distance between te UE m and any cell C in te network, wic can be eiter a MC or a SC. a is a patloss constant wic depends on te type of te environment lative to te type of te cell indoor, outdoor, rural, urban... and b > is te patloss exponent coefficient. Based on te proposed patloss model, te UE located in m = r, θ is served by te SC only if te SP efence Signal eceived Power [9] of te SC is iger tan te SP coming from te MC. Tis can be expssed by te following inequality P s iθ se iθs b > P r b If te constraint in is not satisfied, te UE will be connected to te MC. Based on inequality, we evaluate te absorption coefficient denoted by µ wic flects te percentage of mobile locations generated according to a given traffic distribution tat can be served by te SC. Tis performance metric is given by µ = I P s iθ se iθs b > P r b dtr, θ 3 S S we S is te coved aa by te central MC and te deployed SC. S = dtr, θ 4 S Witout loss of generality, we consider tat te transmit power levels P and P s include as well te patloss constant a, antenna gain, cable loss, UE antenna gain and body loss.

3 B. SIN VS Trougput: Link level capacity curve Te SIN ceived at te UE and its trougput a spectively denoted by γr, θ and ηr, θ indexed wit m if it is ceived from te MC and wit s if it is ceived from te SC. Te lation between γ in linear scale and η in Mbps depends on te UE capacity, te available bandwidt, te radio conditions, te type of te service etc... Tis lation is often modeled by a modified Sannon formula as stated in [], η = mink W ln + γ, η 5 we K and a two variables depending on transmission conditions fogoing and can be adapted for eac UE; W is te used bandwidt; η is te maximum trougput psenting te capability of te target UE category. For te psent paper, we consider UE category equal to 3 working at MHz and we find out tat, under labs measument conditions, η = 98Mbps, K =.85 and =.9. III. PEFOMANCE ANALYSIS In te psence of a HS in te central MC, we define te mean user trougput MUeT in te gion S, coved by te MC and te deployed SC as follows we η = η m + η s 6 η m = I P s iθ se iθs b < P r b S S mink W ln + γ mr, θ, η dtr, θ 7 η s = I P s iθ se iθs b > P r b S S mink W ln + γ sr, θ, η dtr, θ 8 and dtr, θ is te measu psenting te spatial traffic distribution flecting te psence of a HS. As mentioned in II-B, γ m and γ s a te SINs ceived at a UE wit polar coordinates r, θ and served spectively by te MC and te SC. Hence, γ m and γ s a expssed as follows γ mr, θ = fr + α iθ se iθs b r b + P 9 N P r b γ sr, θ = Ps iθ se iθs b fr + P r b + P N we P N is te termal noise power and fr psents te interfence factor in a network composed of only MCs. It is defined by te ratio between te power coming from all te interfering MCs and te ceived power from te serving MC. In order to evaluate te impact of infinite number of interfering MCs, we ave establised and validated in [7] an efficient and simple expssion of te interfence factor for te consided exagonal network model. Tis formula is expssed as follows: + b fr 6x b x x + ωb b wit ωb = 3 b ζb ζb, 3 ζb, 3 we x = r δ, ζ. and ζ.,. a spectively te iemann Zeta and Hurwitz iemann Zeta functions. We notice tat te performance analysis in Scenario is equivalent to te case of Scenario 3 but wit deploying a SC far enoug from te MC and HS positions. For instance, s can be taken as equal to +. Hence, te inequality in will be never satisfied for UEs located inside te HS and it follows tat η = η m and η s = 3 On te oter and, Scenario is illustrated by te equality s, θ s =, θ knowing tat 4 Scenario 3 is eventually depicted by te following conditions s, θ s, θ and s 5 A. Scenario : wit macro-cells only deployment As mentioned befo, we take s = and so all te UEs in te HS, following dtr, θ defined in, a served by te MC. In tis case, te mean user trougput is equal to η = K W S σ e r ln = K W S σ e r ln + + max ρ, gr π π r cosθ e σ drdθ r I max ρ, gr σ dr 6 we ρ is equal to e η, K W I. is te first order of te modified Bessel function of te first kind [] and gr = fr + P N P rb 7 Function g alizes a continuous incasing function from [, ] to [, g]. And so, it is possible to explicitly inverse g using series version or also by switcing numerically te axes x and y. A simple and accurate inverse function of g is provided in [8]. Using te monotonicity of g, te expssion of η is furter simplified: η = S K W K W S σ e ln min,g ρ σ e + K ρ r I r σ dr+

4 min,g ρ r ln + K r I gr σ dr B. Scenario : wit perfectly deployed small cell 8 In Scenario, UEs a served eiter by te MC or by te SC depending on te igest ceived SP. So, te mean trougput of UEs served by te MC is η m = K W S π σ e r r cosθ e σ cos r ln + max ρ, gr + αr b iθ b drdθ 9 we π r = s + r α b r r s r if < r < r = if r < if r > and P s iθ s e iθs b < P r b is only verified wen cosθ θ s < r. wit r = cos r = s +α b and r = { cos r if r < r < r oterwise s α b And so we obtain te following expssion η m = K W S π ln + σ e [, r ] [r, ]. r π max ρ, gr + αr b iθ b r cosθ e σ drdθ + K W r π S π σ e r r cosθ e σ r cos r ln + max ρ, gr + αr b iθ b drdθ 3 Following te same steps to obtain 3, te mean trougput of UEs served by te SC is η s = K W r cos r S π σ e r r cosθ e σ r ln + max ρ, gr + α r b iθ b drdθ 4 C. Scenario 3: wit introducing te impact of imperfect otspot localization In Scenario 3, te SC is deployed near te HS but it does not cover exactly te traffic in tis HS. And so, mo UEs will be served by te MC but te interfence in tis case will be mo significant. Te expssion of η m in 3 can be easily transformed to η m = K W S π σ e π ln + [, r ] [r, ] r r cosθ θ +θs r cosθ+θ θs e σ + e σ max ρ, gr + αr b iθ s b drdθ + S K W π π cos r ln + σ e r r r r cosθ θ +θs r cosθ+θ θs e σ + e σ max ρ, gr + Ps P rb iθ s b Likewise, η s becomes η s = S K W π cos r ln + σ e e r r r r cosθ θ +θs σ drdθ 5 r cosθ+θ θs + e σ max ρ, gr + α r b iθ s b drdθ 6 IV. NUMEICAL ESULTS In order to assess te numerical sults of te studied scenarios, we propose to alize two kind of simulations we te most important parameters a sown in Table. In te first simulation, te position of te HS canges wit varying at first and ten θ. Furtermo, we consider te error of SC positioning to be constant lative to te position of te HS. We fix an error of meters perfect HS localization, 6 meters accuracy provided in [], [3] and meters curnt accuracy wen using probes spectively between te variables and s and we suppose tat θ s is equal to θ equal to π 3. Ten, te mean user trougputs and te absorption coefficients a calculated as a function of. Next, we take s = =.4 Km, and we consider te error between θ and θ s to be equal to, π/6 and π/3 spectively and we evaluate te same performance metrics as in te first part of te simulations. In te second simulation, we fix te position of te HS

5 in.35e i π 6 and.5e i π spectively. Ten te mean user trougputs and te absorption coefficients a plotted as a function of te SC position wit varying s wit θ s = θ at first and ten θ s wit s =. Table : Simulation parameters. Macro deployment infinite exagonal wit δ = Km Association UE associated to igest SP Patloss model MtoUE log d Km Patloss model StoUE log d Km BS power Macro:46dBm, Small:3dBm Antenna gain wit cable loss Macro:8dBi, Small:6dBi Fquency/Bandwidt.6 Gz / Mz Termal noise per Hertz -74dBm/Hz Noise figu 8dB UE category/trougput 3 / η = 98Mbps, K =.85, =.9 UE antenna gain/body loss db / db From Fig. 3a, we observe tat deploying a SC near te MC does not generate additional capacity gains since te interfence in tis case is very ig comparing to te SN ceived eiter from te serving SC or MC. In fact, for a HS in position of less tan 3 meters far from te MC, te evaluation of te impact of bad localization of te traffic HS is wortless and not justified because te offloading gain 3 is negative even wit a perfect positioning. Hence, te deployment of a SC near te MC does not elp to offload te traffic and it deteriorates te trougput in te MC. However, te deployment of a SC improves significantly te overall performance of te MC in te psence of te HS in cell edge. In te latter case, te SC still generates positive offloading gains even wen its position does not matc exactly wit te position of te HS. Moover, from Fig. 3b, it is clear tat wen te HS is MUeT in Mbps η in Scenario η Sc in Scenario η in Scenario η Sc in Scenario η in Scenario 3 error of 6m η in Scenario 3 error of m in Km a µ in % in Scenario in Scenario 3 error of 6m in Scenario 3 error of m in Km b Fig. 3: Te MUeT a and te absorption coefficient b for diffent locations of te HS wit varying. in te center of te cell, te SP ceived from te MC is often iger tan te SP ceived from te SC. As a sult, te absorption coefficient lative to te psence of te SC is very small even wit a perfect positioning of te SC. Tis coefficient is mo important wen te HS is in te cell edge. Moover, deploying a SC wit errors in te positioning mains a useful solution to offload an 3 Te offloading gain is te extra capacity effectively exploited in te deployed SC and it is defined by ρ = η Scenario,3 η Scenario η Scenario important percentage of traffic located in te cell edge. We also notice tat for a HS in te cell center, a small percentage of mobile locations can be offloaded by te SC but te mean trougput in te SC denoted by η Sc in Scenario is not improved comparing to te mean trougput in Scenario denoted by η Sc wic means tat te mean user trougput is calculated only in te same gion as te served aa by te SC in Scenario. Tis is due to te ig interfence in te center between te SC and te MC. Tis observation is deduced from te extra curves psented wit triangles for η Sc and dotted line for η Sc in Fig. 3a. We observe in Fig. 4a tat te mean trougput in Scenario is iger tan tat in Scenario. However, wen we introduce an error of π/6, te mean trougput becomes lower because most of te traffic is served by te MC and te SC will play te role of interfering cell. So far, wen te error is taken iger tan π/6, te mean user trougput is improved since te interfence is mo attenuated. Fig. 4: Te MUeT a and te absorption coefficient b for diffent locations of te HS wit varying θ. Fig. 4b sows tat wen θ is diffent from θ s, te absorption coefficient is duced as compad to te case of a perfectly deployed SC, especially if tis diffence is ig. In Fig. 5a, we compa te mean user trougput in te psence of a traffic HS and wit varying te position of te SC. Wen te SC is deployed near te MC, te traffic located in te cell center HS located at.35km far from te MC and served by te MC will be significantly interfed by te SC. If tis SC is deployed near te HS, most of te traffic will be offloaded by te SC and te mean user trougput is improved. However, we observe also tat wen te distance between s and incases, te mean user trougput is approximately constant function of and its value is equal to te mean user trougput of a network witout SCs offloading gain near %. Tis means tat wen te SC is deployed far from te HS and te MC, te performance of Scenario is approximately te same as tat of Scenario 3. On te oter and, we observe tat wen te HS is in te cell edge, te SC is an appropriate solution to offload te congesting traffic and errors of SC positioning a mo tolerated comparing to te case of a HS in te center. In

6 MUeT in Mbps in Scenario for a HS in.5e iπ/ in Scenario 3 for a HS in.5e iπ/ in Scenario for a HS in.35e iπ/6 in Scenario 3 for a HS in.35e iπ/ s in Km a µ in % wit a HS in.5e iπ/ wit a HS in.35e iπ/ in Km s b Fig. 5: Te MUeT a and te absorption coefficient b for diffent locations of te SC lative to te HS position wit varying s. fact, for a traffic HS in 5m far from te MC, te SC still improve te mean user trougput in te MC even wit an error of HS localization of 6m wic is not te case for a HS in 35m far from te MC. In suc scenarios, some traffic HS localization tecniques [], [3] can be implemented and used in operational SC planning tools. esults in Fig. 5b sow tat mo traffic locations a served by te SC wen its coordinates approaces tose of te HS. Te absorption coefficient is iger for a HS in te cell edge and is duced wen te HS gets near to te MC. Fig. 6a sows tat wen te HS is in te cell edge, te performance of te MC is improved wit deploying a SC wit θ s θ less tan a certain tsold. Tis can be explained by te fact tat UEs in bad radio conditions and taken in carge by te MC a offloaded to te SC wic is near to te HS. Moover, we observe tat te impact of error lated to θ s is very important and may cause significant degradation of te system performance wen te distance between te HS and te MC incases. Tis can be explained by te fact tat te distance between te SC and te HS is proportionally incased wit te diffence between θ s and θ. MUeT in Mbps in Scenario for a HS in.5e iπ/ in Scenario 3 for a HS in.5e iπ/ in Scenario for a HS in.35e iπ/6 in Scenario 3 for a HS in.35e iπ/ θ s in rad a µ in % wit a HS in.5 e iπ/ wit a HS in.35 e iπ/ θ s in rad Fig. 6: Te MUeT a and te absorption coefficient b for diffent locations of te SC lative to te HS position wit varying θ s. Fig. 6b consolidates te diffent observations in Fig. 6a and it furter sows tat te absorption coefficient is mo important wen te HS is in te cell edge and te error of SC positioning is mo tolerated. b V. CONCLUSION We studied in tis paper te impact of deploying a SC in te psence of traffic HS inside a MC. Our sults sow tat te efficiency of deploying SCs to offload traffic in te congested MC depends mainly on te HS s position witin te cell as well as te SC s position wit spect to te MC location. Wen te HS is in te cell center, even a perfect positioning of te SC is not beneficial for te user trougput and does not bring offloading gain. However, wen te HS is in cell edge, errors of HS localization a mo tolerated and te system performance is improved by deploying SCs as compad to a network composed of MCs only. Furtermo, our sults sow tat for SC deployments wit positive gains, te mean user trougput and te absorption coefficient essentially depend on te distance between te SC and te HS. As a futu step, we a considering analytical modeling of te system performance at te flow level, in a dynamic configuration we users arrive to te network at random time epocs and leave it after a finite service duration. Moover, we would like to incorporate oter parameters, suc as sadowing, tri-sectorial sites and antenna masks. EFEENCES [] H. S. Dillon,. K. Ganti, F. Baccelli, and J. G. Andws, Modeling and analysis of K-tier downlink eterogeneous cellular networks, IEEE Journal on Sel. Aas in Communications, vol. 3, no. 3, p ,. [] H. S. Dillon, M. Kountouris and J. G. Andws, Downlink MIMO HetNets: Modeling, Ordering esults and Performance Analysis, IEEE Trans. On Wiless Communications, vol., no., 3. [3]. W. Heat, M. Kountouris, and T. Bai, Modeling eterogeneous network interfence using Poisson point processes, IEEE Trans. on Signal Processing, vol. 6, no. 6, p , 3. [4] A. Guo and M. Haenggi, Spatial stocastic models and metrics for te structu of base stations in cellular networks, IEEE Trans. on Wiless Communications, vol., no., p , 3. [5] D. Lee, S. Zou, X. Zong, et al., Spatial modeling of te traffic density in cellular networks, IEEE Wiless Communications, vol., no, p [6] J. M. Kelif, S. Senecal and M. Coupecoux, Impact of small cells location on performance and QoS of eterogeneous cellular networks, in Proc. IEEE PIMC, 3. [7]. Nasri and A. Jaziri, On te Analytical Tractability of Hexagonal Network Model wit andom User Location, Arxiv Pprint Accepted in IEEE Trans. on Wiless Communications. [8]. Nasri and A. Jaziri, Tractable Approac for Hexagonal Cellular Network Model and its Comparison to Poisson Point Process, accepted in IEEE Globecom 5. [9] 3GPP TS 36.4, Evolved Universal Terstrial adio Access E- UTA; Pysical layer; Measuments, version.., elease,. [] P. Mogensen, W. Na, I. Z. Kovacs, et al. LTE capacity compad to te sannon bound, in Proc. IEEE Veicular Tecnology Confence, p Spring 7. [] A. P. Prudnikov, A. B. Yu, and O. I. Maricev, Integrals and Series, Volume 5: Inverse Laplace Transforms, Gordon and Bac, New York 99. [] A. Jaziri,. Nasri and T. Caed, Traffic Hotspot localization in 3G and 4G wiless networks using OMC metrics, in Proc. IEEE PIMC, p. 7-74, 4. [3] A. Jaziri,. Nasri and T. Caed, Tracking traffic peaks in mobile networks using statistics of performance metrics, submitted to IEEE Trans. on Mobile Computing.