Performance Analysis of the Idle Mode Capability in a Dense Heterogeneous Cellular Network

Transcription

1 Performance Analysis of the Idle Mode Capability in a Dense Heterogeneos Celllar Network Chan Ma, Ming Ding, Senior Member, IEEE, David ópez-pérez, Senior Member, IEEE, Zihai in, Senior Member, IEEE, Jn i, Senior Member, IEEE, and Goqiang Mao, Fellow, IEEE Abstract In this paper, we stdy the impact of the base station BS idle mode capacity IMC on the network performance of mlti-tier and dense heterogeneos celllar networks HCNs with both line-of-sight os and non-line-of-sight NoS transmissions. Different from most existing works that investigated network scenarios with an infinite nmber of ser eqipments UEs, we consider a more practical set-p with a finite nmber of UEs in or analysis. Moreover, in or model, the small BSs SBSs apply a positive power bias in the cell association procedre, so that macrocell UEs are actively encoraged to se the more lightly loaded SBSs. In addition, to address the severe interference that these cell range expanded UEs may sffer, the macro BSs MBSs apply enhanced inter-cell interference coordination eicic, in the form of almost blank sbframe ABS mechanism. For this model, we derive the coverage probability and the rate of a typical UE in the whole network or a certain tier. The impact of the IMC on the performance of the network is shown to be significant. In particlar, it is important to note that there will be a srpls of BSs when the BS density exceeds the UE density, and ths a large nmber of BSs switch off. As a reslt, the overall coverage probability, as well as the area spectral efficiency ASE, will continosly increase with the BS density, addressing the network otage that occrs when all BSs are active and the interference becomes os dominated. Finally, the optimal ABS factors are investigated in different BS density regions. One of major findings is that MBSs shold give p all resorces in favor of the SBSs when the small cell networks go ltra-dense. This reinforces the need for orthogonal deployments, shedding new light on the design and deployment of the ftre 5G dense HCNs. This work is spported in part by the National Natral Science Fondation of China nder Grant 6778,6538, in part by the Jiangs Provincial Science Fondation nder Project BK5786, in part by the Specially Appointed Professor Program in Jiangs Province, 5, in part by the Fndamental Research Fnds for the Central Universities nder Grant 3965, and in part by the Open Research Fnd of National Mobile Commnications Research aboratory, Sotheast University, nder grant No. 7D4. The associate editor coordinating the review of this paper and approving it for pblication was Marco Di Renzo. Correspondence Athor: Jn i. C. Ma is with the School of Electrical and Information Engineering, The University of Sydney, Sydney, N.S.W. 6, Astralia and Data6, CSIRO, Astralia chan.ma@sydney.ed.a. M. Ding is with Data6, CSIRO, Astralia Ming.Ding@data6.csiro.a. D. ópez-pérez is with Nokia Bell abs david.lopez-perez@nokiabell-labs.com Z. in is with the School of Electrical and Information Engineering, The University of Sydney, Sydney, N.S.W. 6, Astralia zihai.lin@sydney.ed.a. J. i is with the School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, CHINA. He is also with the National Mobile Commnications Research aboratory, Sotheast University, Nanjing, CHINA, and with the Department of Software Engineering, Institte of Cybernetics, National Research Tomsk Polytechnic University, Tomsk, 6345, RUSSIA. jn.li@njst.ed.cn. G. Mao is with the School of Compting and Commnication, The University of Technology Sydney, Astralia and Data6, CSIRO, Astralia g.mao@ieee.org. Index terms os and NoS transmissions, IMC, HPPP, Ultra dense network I. INTRODUCTION To meet the explosively increasing demand for more mobile data traffic [], commercial wireless networks are evolving towards higher freqency rese by deploying more and more small cells []. A major part of the mobile throghpt growth has already been spplied by the so-called network densification dring the past few years, and this trend is expected to contine in the years to come. Ths, the emerging fifth generation 5G celllar network deployments are envisaged to be heterogeneos and dense. Sch a dense heterogeneos celllar network HCN will be comprised of a conventional celllar network overlaid with a variety of small cells, metro, pico and femtocells. This will greatly help to realize the 5G reqirement of a x increase in mobile network throghpt with respect to the crrent 4G one [3]. In this context, the co-channel deployment of macro cell BSs MBSs and small cell BSs SBSs in HCNs, i.e., all BS tiers operating on the same freqency spectrm, have recently attracted considerable attention, e.g., [4], [5] and [6]. Andrews et al. in [7] first analyzed the coverage probability of a single-tier small cell network by modeling BS locations as a homogeneos point Poisson process HPPP. That stdy conclded that the coverage probability of the network does not depend on the density of BSs in interference-limited scenarios. Following [7], Dhillon et al. in [8] also reached the same conclsion for each BS tier in a mlti-tier HCN. In contrast, sing a different modelling that considered a dal slope path loss model, Zhang et al. in [9] demonstrated that the coverage probability strongly depends on the BS density. In the same line, sing a mlti-slope path loss model and the smallest path loss association rle, the athors in [] showed that the coverage probability first increases with the BS density and then decreases, while the area spectral efficiency ASE will grow almost linearly as the BS density goes asymptotically large. In [], a stretched exponential path loss model was proposed for the short-range commnication, and they proved that the ASE is non-decreasing with the BS density and converges to a constant for high densities. However, it is important to note that the aforementioned stdies assmed an nlimited nmber of ser eqipment UE in the network, which implies that all BSs wold always be active and transmit in all time and freqency resorces. Obviosly, this may not be the case in practice, especially c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

2 in ltra-dense networks UDNs. To attain a more practical network performance, ee et al. in [] first analyzed the coverage probability of a single-tier small cell network with a finite nmber of UEs, and derived the optimal BS density accordingly. This was done considering the tradeoff between the performance gain and the resltant network cost. Moreover, a system-level analysis of celllar networks with respect of the density of BSs and blockages was condcted in [3], which show the validity for the footprints of bildings in dense rban environments. A trackable performance analysis was proposed in [4], and they fond that the increasing trend of the ASE is highly related to the density of BSs and UEs. Recently, the athors in [5] stdied the coverage probability and ASE of a single-tier small cell network with probabilistic line-ofsight os and non-os NoS transmissions, in which the UE nmber is finite and the small cell BS has an idle mode capability IMC. More specifically, if there is no active UE within the coverage area of a certain BS, that BS will be trned off and will not transmit. The IMC switches off nsed BSs, and ths can improve the UEs coverage probability and network energy efficiency as the network density increases. This is becase UEs can receive stronger signals from the closer BSs, while the interference power remains constant or even decreases thanks to the IMC. This conclsion in [5] - the coverage probability depends on the density of BSs in a interference-limited network - is fndamentally different from the previos reslts in [7] and [8], and presented new insights for the design and deployment of 5G networks. Nevertheless, althogh of importance, none of the above works considered that the original association/coverage areas of the SBSs tend to be mch smaller than those of the MBSs in a HCN de to the large power difference, and ths the UE poplation that is offloaded to small cells may be limited. To encorage UEs to take advantage of the large amont of resorce at the SBSs, cell range expansion CRE was introdced in long term evoltion TE networks to proactively offload UEs from MBSs to SBSs. This is done by adding a positive offset to the pilot RSS of the SBSs dring the cell selection procedre []. CRE allows UE not associating with the BS that providing the strongest signal strength, bt with those with more resorces. Intitively speaking, more UEs will be offloaded to the SBSs with a larger range expansion bias REB. CRE withot interference management has been shown to increase the sm capacity of the macrocell UEs de to the offloading, bt decrease the overall throghpt of the network de to strong cell-edge interference [6]. The offloaded UEs do not connect to the strongest cell anymore. To address this cell-edge performance isse, the se of enhanced intercell interference coordination eicic schemes was also introdced in TE networks [7], [8]. One sch eicic strategy implemented in the time-domain, called almost blank sbframe ABS, received a lot of attention. No control or data signals bt only reference signals are transmitted in an ABS. Ths, when a MBS schedles ABSs, SBSs can schedle their offloaded UEs in sbframes overlapping with the MBS ABSs. This significantly redces interference towards those the offloaded UEs. To the best of or knowledge, the theoretical stdy of dense HCNs with a realistic path loss model, a finite nmber of UEs as well as CRE together with ABSs has not been condcted before, althogh some preliminary simlation reslts can be fond in [] and [9]. Motivated by this theoretical gap, in this paper, we analyze for the first time the coverage probability and ASE of a HCN with i two BS tiers, ii a general and practical path loss model, iii a finite nmber of UEs, iv an IMC at small cell BSs, and v a flexible cell association strategy with CRE and ABS. This reslts in a completely new modelling and analysis, throgh which we provide the following theoretical contribtions: We calclate an analytical expression to derive the density of active BSs in a two tier HCN. Based on this, we compte the analytical expressions of the coverage probability and ASE for sch two tier HCN, while considering the IMC. The optimal ABS factor, i.e., the ratio between the nmber of ABS to the nmbers of total sbframes, is showed nmerically and obtained by simlations for schedling in MBSs for different SBS density regions. Moreover, we prove that ASE can achieve the maximm vale if the ABS factor is set to one when the small cell networks go ltra-dense. 3 We perform an extensive simlation campaign to validate the accracy of the analytical reslts. Both simlation and analytical reslts match and shed new insights on the design and deployment of BSs in 5G UDNs. One important finding is that MBSs shold give p all resorces in favor of the SBSs when the small cell network goes ltra-dense. This reinforces the need for orthogonal spectrm assignments for macrocell and ltra-dense small cell deployments. The rest of the paper is strctred as follows. We introdce the system model in Section II, and derive the activated BS density in a two tier HCN in Section III. In Section IV, we obtain the analytical expressions of the coverage probability and ASE for this network. Then, we validate the accracy of the analytical reslts throgh extensive simlations and discss the network performance in Section V, and conclde the paper in Section VI. II. SYSTEM MODE In this paper, we assme a wireless network consisting of two BS tiers. The locations of the BSs of the kth tier k =, are modeled as a two-dimensional HPPP Φ k with a density λ k. Withot loss of generality, we denote the macrocell tier and the small cell tier as tier and tier. The locations of UEs denoted by U in the network are modeled as another independent HPPP Φ with a density λ. In most existing works, λ was assmed to be sfficiently large, so that each BS in each tier always has at least one associated UE. However, in or model with finite BS and UE densities, a BS might serve no UE, and ths be trned off thanks to the IMC. The mobility of UEs is not considered in the work. It is worth noting that if mobility is present, MBSs may not be trned off easily, as the MBSs need to spport the UE handover. Several works considering the mobility can be fond in [] and [] c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

3 3 The SINR of the typical UE with a random distance r to its associated BS in the kth tier is given by Fig.. A network scenario consisting of two BS tiers. Each UE is connected to the BS that provides the strongest average signal, which is marked by the designed signal. BSs with no UE associated are in idle mode. Following [], we adopt a general and practical path loss model, in which the path loss ζr associated with distance r is calclated as { ζk ζ k r = r =A k r k, os: Pr k r; ζk N r =AN k r N k, NoS: Pr N k r= Pr kr, where A k and AN k are the path losses at a reference distance r =for the kth tier and for the os and the NoS cases, respectively, and k and N k are the path loss exponents for the kth and for the os and NoS cases, respectively. Moreover, Pr kr is the os probability fnction that a transmitter and a receiver separated by a distance r has a os path. For example, as recommended by the 3GPP, Pr kr is can be compted as Pr kr = min.8/r, exp r/.63+exp r/.63, when k=;.5 min.5, 5exp.56/r+min.5, 5exp r/.3, when k=. Moreover, we consider a cell association based on the maximm received power, where a UE is associated with the strongest BS: X k = P k ζ k rd k, 3 where P k and D k denote the transmit power and the REB of absinthekth tier, where D =db for the macrocell tier and D = D db for the small cell tier. Since UEs are randomly and niformly distribted in the network, we adopt a common assmption that the activated BSs in each tier also follows an independent HPPP distribtion Φ i, the density of which is denoted by λ i BSs/km [], [3]. Finally, we assme that each UE/BS is eqipped with an isotropic antenna, and as a common practice in the field, that the mlti-path fading between an arbitrary UE and an arbitrary BS is modeled as independently identical distribted i.i.d Rayleigh fading. Part of this work was pblished in IEEE WCNC 8 [3]. SINR k r = P k h k ζ k r K j= i Φ\b P j h ji ζ j Y ji +σ, 4 where h k and h ji are the exponentially distribted channel power with nit mean from the serving BS and the i-th interfering BS in the j-th tier, respectively, Y ji is the distance from the activated BS in the j-th tier to the origin, and b is the serving BS in the k-th tier. Note that only the activated BSs in Φ\b inject effective interference into the network, since the other BSs are trned off thanks to the IMC. In Fig., we show an illstration of the proposed network, which consists of two BS tiers. In this case, UE is offloaded from the MBS to the SBS becase of the REB. The other SBS is in idle mode since there is no UE associated to it. III. DENSITY OF THE ACTIVATED BSS To evalate the impact of the IMC on the performance of each BS tier, we first analyze the probability of having a given average nmber of UEs in each cell. Then, we derive expressions for the density of active BSs in each tier. A. Average Nmber of UEs in Each Cell The coverage area of each small cell is a random variable V, representing the size of a Poisson Voronoi cell. Althogh there is no known closed-form expression for V s probability distribtion fnction PDF, some accrate estimates of this distribtion have been proposed in the literatre, e.g., [4] and [5]. In [4], a simple gamma distribtion derived from Monte Carlo simlations was sed to approximate the PDF of V for the kth BS tier, given by f Vk x =bλ k q x q exp bλ kx, 5 Γq where q and b are fixed vales, Γx = + t x e t dt is the standard gamma fnction and λ k is the BS density of the kth BS tier. Remind here we assme the coverage area of each cell has not been considered the associating relation to sers, where each ser may be covered by mltiple BSs in different tiers, and the average nmber of UEs in each cell may be a litter larger than the actal one. This inaccracy is shown to be ignorable in the Sec. V-A. If the association probability is considered here, sch that each ser can only be covered by one BS, then the Poisson Voronoi cell will change to be a weighted cell, and the shape of cell will become irreglar. The works in [6] show how to calclate the weighted Poisson Voronoi cell and are sefl for frther discssion. Since the distribtion of UEs follows a HPPP with a density of λ, given a Voronoi cell with size x, the nmber of UEs located in this Voronoi cell is a Poisson random variable with c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

4 a mean of λ x. Denoting by N k the nmber of UEs located in a Voronoi cell of the kth BS tier, we have that P[N k = n] = a = + Γn + q Γn +Γq λ x n exp λ xf Vk xdx n! n q λ bλk, n λ + bλ k λ + bλ k 6 where step a is compted by sing the definition of the gamma fnction. B. Probability of a UE Associated to the kth Tier According to 3, each BS tier density and transmit power determine the probability that a typical UE is associated with a BS in this tier. The following emmas provide the per-tier association probability, which is essential for deriving the main reslts in the seqel. If one UE connects to one MBS k =, this MBS can be a MBS with an os path or a NoS path. In the following, we provide the probability that one sch UE is associated with an os MBS in emma. emma. The probability that the UE is associated with a os MBS can be written as P = where p r = exp Δ r = AN A N r N, and p r =exp Δ r Δ r = DPA p 3r =exp P A p r p r p 3r f rdr, 7 Δ r Pr N πλ d, Pr πλ d, Δ 3 r DPA N P A r, and Pr N N πλ d, Δ 3r = r N, respectively, and f r is the PDF of that the UE is associated with a os MBS, which can be written as { r } f r =exp Pr πλ d Pr rπλ r. 8 Proof: See Appendix A. Following the same logic, we provide the probability that the UE is associated with a NoS MBS in emma. emma. The probability that the UE is associated with a NoS MBS can be written as P N = p N r p N r p N 3 r f N rdr, 9 where p N r = exp Δ N r Pr πλ d, Δ N N r =A A N, and p N r =exp Δ N r, Δ N r = DPA P A N Pr πλ d N, and p N 3 r =exp Δ N 3 r Pr N N N πλ d, Δ N 3 r = DPA N P A N N, respectively, and f N r is the PDF that the UE is associated with a NoS MBS, which can be written as { r } f N r =exp Pr N πλ d Pr N rπλ r. Proof: See Appendix B. 4 If one UE connects to one SBS K =, this SBS can also be a SBS with an os path or a NoS path. Similarly, the corresponding UE association probabilities are derived in emma 3 and emma 4. emma 3. The probability that the UE is associated with a os SBS can be written as P = p r p r p 3r f rdr, where p r =exp Δ Pr N πλ d, DP A Δ r = PA, and p r =exp Δ Pr πλ d, Δ r = PAN DP A N r N, and p 3r =exp Δ 3 Pr N πλ d, Δ 3r = AN A N N, respectively, and f r =Pr rπλ r exp { r Pr πλ d }. emma 4. The probability that the UE is associated with a NoS SBS can be written as P N = Δ N r = PA p N r p N r p N 3 r f N rdr, where p N r =exp Δ N Pr πλ d, N, and p N DP A N r =exp Δ N Δ N DP A N Pr N N πλ d, N N PAN r =, and p N 3 r =exp Δ N 3 Pr πλ d, Δ N N 3 r =A A N, respectively, and f Nr =exp{ r PrN πλ d } Pr N rπλ r. Proof: The proofs of emma 3 and emma 4 are similar with emma and emma, so the proof are omitted here. C. Density of activated BSs in the kth tier After attaining the probability of one UE associating to a BS in the kth tier, we are ready to derive the density of active BSs in the kth tier c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

5 5 Defining by P off k n the probability that a BS in the kth tier is inactive when there are n UEs in its coverage, then P off k n can be calclated by P off k n =P[N k = n] A k n, 3 where P[N k = n] is the probability of having n UEs located in a cell of the kth tier, which can be obtained from 6, and A k = P k + PN k, which denotes the per-tier association probability. With this reslt, the density of active BSs in the kth tier λ k can now be derived as λ k = λ k P off k n, 4 n= where P off k n is the probability that the kth tier is inactive when there are n UEs in its coverage. IV. MAIN RESUTS Recall that in this paper, The REB for the first tier macro tier is D =db and that for the second tier is simply denoted by D, where D db. With or modelling, a UE U belongs to the following six disjoint sets: { U, The UE connects to a os MBS; U U N ; The UE connects to a NoS MBS; U, The UE connects to a os SBS withot power bias; U U N ; The UE connects to a NoS SBS withot power bias; U3, The UE is offloaded from a MBS to a os SBS; U 3 U3 N ; The UE is offloaded from a MBS to a NoS SBS, 5 where U U U3 = U. The set U is the set of macrocell UEs and the set U is the set of nbiased small cell UEs. The UEs offloaded from macrocells to small cells de to CRE constitte set U 3, and are referred to as range expanded RE UEs. Moreover, an ABS approach to eicic is considered, in which MBSs sht their transmissions on certain fraction of time/freqency resorces, and SBSs schedle their RE UEs on the corresponding resorces, which are free from macrocell interference. Definition. η: The resorce partitioning fraction η is the fraction of resorces on which the MBSs are inactive, where <η<. η is also known as the ABS factor. Ths, with resorce partitioning, η is the fraction of resorces that the MBSs and the SBSs allocate to UEs in U and U, respectively, while η is the fraction of resorces in which the MBSs do not transmit and the SBSs can schedle UEs in U and U 3. In Fig., we show an illstration of the proposed network when the ABS framework is in place. When the MBS schedles ABSs and mtes its transmission, UE 3 and UE 4 will Fig.. MBS schedles ABSs, and the UEs associated with it cannot get service in sch sbframes. not receive any signal from their serving MBS. In contrast, the UEs associated with the SBS, i.e., UE the RE SBS UE and UE the native SBS UE, can be served withot the interference from the MBS. As a reslt of resorce partitioning, the SINR of a typical UE, when it belongs to U k, can be written as SINR = k, P kh k, ζ k r k= I k + σ +k, 3P h, ζ r I + σ, 6 where A is the indicator of the event A, and I k is the interference from the kth tier. A. The Coverage Probability et s define the coverage probability S as the probability that the instantaneos SINR of a randomly located UE is larger than a target SINR τ. Since the typical UE is associated with at most one BS, the coverage probability can be calclated by 3 3 S = S k = PSINR k >τ. 7 k= k= The reslts of the coverage probability is presented in Theorem shown on the top of next page. In Theorem, I s in are the aplace transform of I agg evalated at s for os or NoS transmissions in each BS tier, respectively. For clarity, they are presented in the following emmas. emma 5. In Theorem, I /Ns are given by I s =exp π λ Pr d x + S x τs exp π λ Pr N Δ x d + S x τs N exp π λ Pr d Δ x + S x τs exp π λ Pr N Δ 3 x d, + S x τs N c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

6 6 Theorem. Coverage Probability For a typical UE in the presented framework, the SINR coverage probability is Sτ =S τ+s N τ+s τ+s N τ+s3 τ+s3 N τ, 8 where S /N τ = [ ] S /N xh Pr I agg+σ >τ F /N xdx, S /N τ = θ [ ] S /N xh Pr I agg +σ >τ F /N xdx + θ [ ] S /N xh Pr I agg +σ >τ F /N xdx, and S3 /N τ = [ ] S /N 3 xh Pr I agg+σ >τ F /N 3 xdx, where θ represents the ABS fraction, and θ = η. Moreover, F /N xdx, F /N xdx and F3 /N xdx are represented by F /N x =p /N x p /N x p /N 3 x f /N x, F /N x =p /N x p /N x p /N 3 x f /N x, F3 x =p x p x p 3x p x+p N x f x, and F3 N x =p N x p N x p N 3 x p x+p N x f N x. [ ] [ ] [ ] S /N xh S /N In addition, Pr I agg+σ >τ, Pr xh S /N I agg, +σ >τ and Pr 3 xh I agg+σ >τ are respectively compted by [ ] S /N xh Pr I agg + σ >τ =exp σ τ τ S /N x I /N S /N x, [ ] S /N xh Pr I agg + σ >τ =exp σ τ S /N x I /N τ S /N x, [ ] S /N xh Pr I agg + σ >τ =exp σ τ S /N x I /N τ S /N, and x [ ] S /N 3 xh Pr I agg + σ >τ =exp σ τ τ I /N 3 Proof: See Appendix C. S /N x S /N x. 9 and I N s =exp π λ Pr N x exp π λ Pr Δ N x exp π λ Pr Δ N x exp π λ Δ N 3 x Pr N d + SN x τs N d + SN x τs d + SN x τs d + SN x τs N. emma 6. In Theorem, I /N s and I /N s are given by I s =exp π λ Pr d Δ x + S x τs exp π λ Pr N Δ x d + S x τs N exp π λ Pr d x + S x τs exp π λ Pr N Δ 3 x d. + S x τs N 3 In emma 5, the interference from a os/nos channel foraue U is represented by and, respectively. Moreover, the interference for I is composed of for parts, which are from other os MBSs, NoS MBSs, os SBSs and NoS SBSs as showed in, and I N is shown as the similar components. I s =exp π λ Pr d x + S x τs exp π λ ; Δ 3 x Pr N + S x τs N d c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

7 7 and I N I N s =exp π λ Pr Δ N x exp π λ Pr N Δ N x exp π λ Pr Δ N 3 x exp π λ Pr N s =exp π λ Pr Δ N 3 x exp π λ Pr N x x d + SN x τs d + SN x τs N d + SN x τs d + SN x τs N, d + SN x τs d + SN x τs N 5. 6 In emma 6, the interference from a os/nos channel for a UE U is represented in 3-6, respectively. Moreover, from 4 we can find that when the ABS is working, only the interference from the other SBSs is valid. This is becase all the MBSs are not transmitting in the ABS, and this brings abot two parts of interference in 4. Similar components are shown in 5 and 6. emma 7. In Theorem, I /Ns are given by 3 I 3 s =exp π λ Pr d x + S x τs exp π λ Pr N Δ 3 x d, + S x τs N 7 and I Ns =exp π λ 3 Pr d Δ N 3 x + SN x τs exp π λ Pr N. x d + SN x τs N 8 In emma 7, the interference from a os/nos channel foraue U 3 is represented in 7 and 8, respectively. Similar with 4 and 6, the components of them are two pars, as the interference only comes from SBSs. It is important to note that the impact of the tier and BS selection on the coverage probability is measred in 9, the expressions of which are based on λ and λ. This is becase all the BSs can be chosen by the UEs. Moreover, the impact of the interference on the coverage probability is measred in emma 5, 6 and 7. Note that instead of λ and λ, we se λ and λ. This is becase we se the IMC, and ths only the activated BSs emit effective interference into the network. B. Area Spectral Efficiency In this sbsection, we investigate the network capacity performance in terms of the area spectral efficiency ASE in bps/hz/km, which is defined as R = U k η k R k, 9 k,,3 where A is the indicator of the event A, η = η, η 3 = η, and η = η when ABS is engaged, while η = η when ABS is not engaged. Then, the per tier R k is defined by R k λ E x {E SINRk [log + SINR k x]}. 3 It is important to note that the average is taken over both the spatial PPP and the channel fading distribtion. The ASE is first averaged on the condition that the typical UE is at a distance x from its serving BS in the kth tier. Then it is averaged by calclating the expectation over the distance x. The following Theorem on the top of next page gives the ASE over the entire network. Althogh the reslts for the coverage probability and ASE are not in closed-form, they can be nmerically evalated in a simple form. Moreover, they can be presented in closed-form expressions in several cases, for example, the 3GPP Case mentioned in []. C. Special Case for ASE In this sbsection, we se a special case to show the analysis reslts for the ASE, and obtain insights from it. We consider a very dense network that λ +, then the signal comes from the NoS BSs can be neglected, and all UEs can be assmed to connect with BSs in a os channel. Ths, the ASE for the considered very dense network does not actally depend on the os and NoS propagation, and it can be described as the following emma. emma 8. In a very dense network that λ +, the ASE can be shown as R = R + R + R 3 38 = ηλ Θ +Θ +ηλ Θ +Θ 3, where Θ = Θ = Θ = x= ρ x= ρ x= ρ exp σ tρ S x exp σ tρ S x exp σ tρ S x I tρ I tρ S xdρf xdx, 39 S xdρf xdx, 4 I tρ S xdρf xdx, c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

8 8 Theorem. Area Spectral Efficiency For a typical ser in the setp, the ASE is compted by where the conditional rate coverage R k is given by the following eqations: R = ηλ exp σ tρ S x R N = ηλ R = ηλ + ηλ R = R + R N + R + R N + R 3 + R N 3, 3 x= R N = ηλ + ηλ x= R 3 = ηλ R N 3 = ηλ x= ρ x= ρ x= ρ ρ x= ρ ρ x= ρ x= ρ exp exp σ tρ S x exp σ tρ S x σ tρ S x exp σ tρ S N x exp σ tρ S Nx exp σ tρ S x exp σ tρ S N x I tρ I N S xdρf xdx; 3 S N tρ xdρf xdx; 33 I tρ S xdρf xdx I tρ I N I N S xdρf xdx; tρ N S N xdx; xdρf tρ N S N xdx xdρf I 3 tρ I N S xdρf 3 xdx; 36 tρ N 3 S N 3 xdx, 37 xdρf where ρ =log τ +, defined the minimm working SINR, and tρ = ρ and the PDFs in each eqation are given in Theorem. Proof: See Appendix D. and Θ 3 = x= ρ exp σ tρ S x I 3 tρ S xdρf 3 xdx. 4 Besides, to compte the interference power for different tiers, I tρ S x, I tρ S x, I tρ S x, and I3 tρ S we propose emma 9. x, emma 9. The interference power for different tiers can be calclated by I tρ S x = exp π λ ρ,,tρ x,x exp π λ ρ,, P A P A tρ x, Δ. x, 43 I tρ S x = exp π λ ρ,, P A P A tρ x, Δ. x exp π λ ρ,,tρ x,x, 44 and I tρ S x = I3 tρ S x = exp π λ ρ,,tρ x,x, where ρ, β, t, d = [ ] [ d β F t β, β + β + ; ; td 45 ], >β+, 46 where F [, ; ; ] is the hyper-geometric fnction [7]. Proof: See Appendix E c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

9 9 TABE I TABE I: PARAMETER VAUES SUMMARY Parameter Vales Macro BS transmit power P 46 dbm Micro BS transmit power P 4 dbm Macro BS density λ BSs/km User density λ 3 UEs/km A.34.4 A N 3. N 4.8 A.38.9 A N 4.54 N 3.75 Power bias allocation D 5dB Noise Power σ -95 dbm q = b 4.8 [5] Resorce partitioning fraction η.4 From emma 8 and 9, the expression of the special case can be obtained, where the expressions of the interference power are mch simpler than in the general case. To get more insights, we provide emma to show that the ASE achieves the maximm vale when the ABS factor is set to one. emma. In a very dense network, ASE achieves the maximm vale when the ABS factor is set to one. Proof: Take the derivative of R with respect to η, then we get ΔR Δη =Θ +Θ 3 Θ Θ.Astheλ +, for the UE associated with a MBS, the interference power is increasing while the sorce power keeps stable. For the UE associated with a SBS, the UE can get stronger signal from a closer SBS. So intitively speaking, Θ +Θ 3, which represents the UE connecting the SBS and receiving interference only from SBSs, shold larger than Θ +Θ, which sffers interferences from all BSs. As a reslt, ΔR Δη > and the optimal ABS factor shold be one to get the maximm ASE. The probability of active BSs The macrocell tier Sim. The macrocell tier Ana.. The small cell tier Sim. The small cell tier Ana.. 3 Micro base station density λ [BSs/km ] Fig. 3. The active BS probability for each tier The Coverage probability Overall Ana. The macrocell tier Ana. The small cell tier-contribted by the nbiased UEs Ana. The small cell tier-contribted by the RE UEs Ana. Simlation 5 V. SIMUATION AND DISCUSSION In this section, we se nmerical reslts to establish the accracy of or analysis, and frther stdy the performance of dense HCNs. A. Validation and Discssion on the Active BS Probability We consider the -tier HCN, following the 3GPP definitions [8], to show the accracy of or analysis. Table I smmarizes the most important assmptions and parameter vales. In Fig. 3, we plot P on i verss λ, where λ [, ] BSs/km. As can be observed from this figre, or analytical reslts match well with the simlation reslts. Moreover, they also show that, within the 5 db power bias allocation to the small cell BSs, i the probability of a BS being active in the small cell BS tier decreases with λ, when λ is a finite vale, and that ii the BSs with a lower transmit power have lower activation probability. For example, more than 6% of the BSs in the small cell BS tier are idle when λ > 3 BSs/km. This means that a large nmber of UEs are associated with the 3 Micro BS density [BSs/km ] Fig. 4. The coverage probability with respect to small cell BS density λ BSs in the macrocell tier, as they can provide stronger signals to these UEs. B. Validation and Discssion on the Coverage Probability In this sbsection, we first validate the accracy of Theorem. As in the previos sbsection, the network consists of tiers of BSs, representing as U and U, respectively, and U 3 is defined by the small cell tier, contribted by the range expanded RE UEs. All the simlation reslts are represented by the solid line. In Fig. 4, we show the reslts of S with respect to λ.as can be seen from the figre, there are some small misalignment between the simlation and analytical reslts in each tier. For example, there is abot.5% inaccracy when λ is abot c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

10 BSs/km as shown in Fig. 4. With the increasing nmber of BSs in the small cell tier, the error becomes negligible. The reason of sch error is that the spatial correlation in the UE association process is not considered in or analysis. More specially, when performing simlations, nearby UEs have a high probability of being covered and served by the same BS. However, for tractability, we consider the BS association of different UEs as independent process in 3 in or analysis, which nderestimates the active BS density, as their no channel correlation. Since the accracy of S is good enogh, abot.5%, we will only se analytical reslts of S for the figres in the seqel. Fig. 4 also shows that with the increasing nmber of BSs in the small cell tier, the coverage probability of U decreases while that of U increases. The coverage probability of U 3 first increases to a peak point and then decreases afterwards. As a reslt, the overall coverage probability first increases, then decreases, and finally increases again. The reason behind this phenomenon is that: The overall coverage probability first increases becase UEs can connect to the stronger BSs. Then, the overall coverage probability decreases since the interference power grows faster than the signal power as many interfering paths transit from NoS to os. Finally, the overall coverage probability performance continosly increases as the network densifies. The intition is that the interference power will remain constant when the BS density is large enogh larger than the UE density, thanks to the IMC 3, while the signal power will continosly grow de to the closer proximity of the serving BSs, as well as the larger pool of BSs to select from. C. Validation and Discssion on the ASE In this sbsection, we first validate the accracy of Theorem, and then discss the optimal ABS factor in different BS density regions. In Fig. 5, we can observe that the analytical reslts on the per tier ASE match well with the simlation reslts. Moreover, the reslts show that with an increasing nmber of BSs in the small cell tier, the ASE of U decreases, while ASE of U increases. The ASE performance decrease of U is becase the interference power grows, as the BSs in the small cell tier get closer and transition to os, while the signal power remains constant. There is no densification in the macrocell tier. The ASE performance increase of U is becase the signal power grows, as the UE is served by a stronger link in the small cell tier, while the interference power remains constant. This becase the BS density is larger than the UE density and de to the IMC in the small cell tier. In contrast, the offloaded UE in U 3 will first benefit from the network densification, bt 3 The interference power will become constant eventally when there is large nmber of BSs. This is becase of the IMC, which makes the nmber of active BSs at most eqal to the nmber of UEs. Ths, from the viewpoint of the typical UE, the interference from other active BSs can be regarded as the aggregate interference generated by BSs on a HPPP plane with the same intensity as the UE intensity. Sch aggregate interference is bonded and statistically stable [7]. ASE [bps/hz/km ] Overall Ana. The macrocell tier Ana. The small cell tier contribted by the nbiased UEs Ana. The small cell tier contribted by the RE UEs Ana. Simlation 3 Micro BS density λ [BSs/km ] Fig. 5. The reslts of ASE with respect to the small cell BS density λ ASE [bps/hz/km ] Micro Density λ [BSs/km ] Fig. 6. The system throghpt with respect to the SBS density λ 3 η=. η=.4 η=.6 η=.8 η= later they get a more severe interference from the increasing nmber of BSs in the small cell tier, whereas they do not have a large serving BS pool to select from. In Fig. 6, the ASE is showed as a fnction of the BS density in the small cell tier for for different ABS fractions η. Note that λ = 3 UEs/km. We can draw the following conclsions from Fig. 6: The ASE almost monotonically grows as the network densifies. In more detail, the system throghpt first increases qickly when λ goes from BSs/km to BSs/km. Then, the ASE sffers from a slow growth or even a decrease when λ [, 9] BSs/km. Finally, the ASE monotonically grows again when λ > 9 BSs/km. Different ABS factors shold be applied in different BS c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

11 75 8 System Throghpt [bps/hz/km ] λ = λ =3 λ = λ = ABS fraction η ASE [bps/hz/km ] Micro Density λ [BSs/km ] η=. η=.4 η=.6 η=.8 η= Fig. 7. The system throghpt with respect to the ABS factor η Fig. 8. The system throghpt with respect to the SBS density λ density regions. In the region of λ < 9 BSs/km, most sers are associated with the MBSs and the less the nmber of ABSs, i.e., smaller η, the larger the ASE. However, when λ 9 BSs/km, the more the nmber of ABSs, i.e., lager η, the larger the ASE, since there are more sers associated with the SBSs. The demarcation point, 9 BSs/km, shold be strongly related to the REB, which in this case is 5 db. In Fig. 7, we verify the observations from Fig. 6 by comparing the system throghpt as a fnction of the ABS fraction for for different BS densities in the small cell tier λ. Note that λ = 3 UEs/km. For SBS densities are considered in this figre to show the varios trends of the ABS fraction. As can be fond from the figre, more channel resorce shold be allocated to the BSs in the macrocell tier when the network is sparse, e.g., λ = BSs/km and λ = 3 BSs/km. When the network is denser, althogh the service to the macrocell UEs will get affected, for the benefit of the whole system, a larger η shold be applied. It is important to note that MBSs shold give p all resorces, all sbframes are ABSs, when the small cell networks go ltra-dense. The intition is that most UEs are associated with small cell BSs at close proximity in UDNs, and the density of small cell BSs is very large. As a reslt, the cost of activating a MBS is high, since it will severely interfere with a large nmber of small cell BSs. Therefore, sing a higher η, i.e., macrocell BSs giving p more sbframe resorces, is helpfl to achieve a better overall system throghpt. This reveals an important conclsion: to maximize network capacity, ltra-dense small cell networks shold operate in a different freqency spectrm from the macrocell ones. In other words, the orthogonal deployment is sperior to the co-channel deployment for ltra-dense small cell networks in ftre wireless networks. The intition is that the additional spatial rese of spectrm in the co-channel deployment is over-shadowed by the large interference emitted from the macrocell tier to the ltra-dense small cell tier. In Fig. 8, we compare the crrent reslts with the bonded path loss model in [9] as follows, ζ kr = ζk r =A k + r k, os: Pr kr; ζk N r =AN k + r N k, NoS: Pr N k r = Pr kr. 47 From Fig. 8 we can find that there are two main differences with previos reslts. The first one is the crossing point, which is abot BSs/km, is a little bigger than that in Fig. 6. This is becase of the application of the bonded path loss model, which makes the receive power smaller than the previos one, especially for the SBS UEs. Ths, more resorces shold be allocated in the MBSs when the density of small cell BSs is not very large, and the crossing point shifts right. The second difference is that the ASE will first increase and then decrease with the density of the SBS, and shold finally keep constant [3]. The intition is that the received signal from BSs is bonded while the interference power keeps increasing, so the ASE will decay for the denser BSs. When the network goes into ltra-dense, becase of the limited nmber of UEs and the IMC of the BSs, the ser signal power and the interference power are both bonded, so the ASE will keep constant at end. Similarly, the same conclsion can be fond from the reslts of the ASE performance: MBSs shold give p all resorces when the small cell networks go ltra-dense. VI. CONCUSION In this paper, we have stdied the impact of the IMC, cased by the finite nmber of UEs, on the network performance in a dense two-tier HCN with os and NoS transmissions. Moreover, to address the nder-tilization of SBSs, CRE and eicic via ABSs are adopted in this work. Or reslts show that c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

12 as the BS density in the second tier srpasses the UE density, for the considered path loss model, the coverage probability and the ASE will continosly increase in this dense twotier HCN, addressing the isse cased by the NoS to os transition of interfering paths. Moreover, it is important to note that more ABSs are needed to enhance the performance of range expanded UEs as the small cell BS density grows, indicating that ltra-dense small cells shold operate in a different freqency spectrm from the macrocell ones. This conclsion enlightens the new design and deployment of dense HCNs in 5G and beyond. APPENDIX A PROOF OF EMMA In this proof we first derive the conditions that the UE is associated with a os MBS, which the os MBS provides stronger power than other BSs. UE is associated with a os MBS with no NoS MBS inside: p r =Pr P A r >P A N = Pr a r > A N A N N = PrNo NoS MBS closer than Δ =exp Δ r r N Pr πλ d, 48 where step c is given by Δ 3r = P N P N. A N A N D N According to [7], the CCDF of r the distance that the nearest BS with a os path to the UE is written as F R r = exp r Pr πλd. Taking the derivative of - F R r with regard to r, we can get the PDF of r as: { r } f r =exp Pr πλ d Pr rπλ r. 5 So the probability that the UE is associated with a os MBS can be written as P = p r p r p 3r f rdr. 5 APPENDIX B PROOF OF EMMA Following the same logic with emma, the conditions that the UE is associated with a MBS with the NoS path can be derived as: UE is associated with a NoS MBS with no os MBS inside: p N r =exp Δ N r Pr πλ d, 53 where step a is given by Δ r = AN A N N. UE is associated with a os MBS with no os SBS inside: p r =Pr P A r >P A r D A = Pr r > D P P b A = PrNo os SBS closer than Δ =exp Δ r Pr πλ d, A A 49 where step b is given by Δ r = D P P. UE is associated with a os MBS with no NoS SBS inside: p 3r =Pr P A r >P A N r N D A N N = Pr r > A D N P N P c = PrNo NoS SBS closer than Δ 3 Δ 3 r =exp Pr πλ d, N 5 where Δ N N r =A A N. UE is associated with a NoS MBS with no os SBS inside: p N r =exp p N 3 r =exp Δ N r Pr πλ d, 54 where Δ N r = A D A N P N P. UE is associated with a NoS MBS with no NoS SBS inside: Δ N 3 r Pr N πλ d, N 55 where Δ N 3 r = A N A N D N N N. So the probability that the UE is associated with a NoS MBS can be written as P N = P P N p N r p N r p N 3 r f N rdr, 56 where f N r is the PDF that the UE is associated with the NoS MBS and can be written as f N r =exp { r Pr r πλ r. Pr } πλ d c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

13 3 APPENDIX C PROOF OF THEOREM In this proof we first analyze the case that {U, U }, where the derivation process follows the same approach. We first derive the distribtion of the distance between the typical ser and the tagged BS. et X l denote this distance, then PX l >x=px l >x U l = PrX l >x U l. Pr U l 58 Based on Sec. II-B and [], the corresponding PDFs are where F x =p x p x p 3x f x; F N x =p N x p N x p N 3 x f N x; F x =p x p x p 3x f x; F N x =p N x p N x p N 3 x f N x, and p x =exp Δ x Pr πλ d, Δ x = P p P A x =exp Δ Δ x = P p N P N A x Pr N A x ; πλ d, N AN x N, x =exp Δ N x Pr πλ d, Δ N x =P p N P A x =exp Δ N Δ N x =P P N A N x Pr N A N x N ; πλ d, N AN x N N, respectively. Then we focs on the derivation of the SINR. Take the case U for example, for the typical ser, the coverage probability of the os MBS is given as S { τ =E x P[SINR x >τ] } = P[SINR x >τ]f xdx. 6 The UE SINR in 6 is rewritten as γx = S xh, I agg+σ, where S x =P A x and Iagg denotes the aggregative interference, which comes from the other active MBSs and SBSs. So the CCDF of the typical ser SINR at distance x from its associated os MBS is given as { P[γx >τ] =P h, > I x + σ } τ S x 63 =exp σ τ S x I τ S x, and the aplace transform of I x is shown on the top of next page. The reslts from other cases that {U N } can be obtained by the similar approach. For the case that {U, U N}, the SINR consittes parts. The first part follows the same logic with that {U } and constittes a θ proportion of the whole nit, while the second part does not consider the mtal interference from the MBSs. In the following, we trn to the case that U 3. Following the same approach, we first show how to compte the PDF F 3 x in 9. To this end, we define two events as follow. Event Biased-SB : The nearest biased small BS with a os path to the UE is located at distance X with no other BSs otperforming the associated BS. According to the proof of emma, the PDF of X is written as f Xx =p x p x p 3x f x. 65 Event MB conditioned on the vale of X : Given that X = x, the UE is associated with a biased os small BS with distance X, which is offloaded from a macro BS with a os path at distance y Event MB or a macro BS with a NoS path at distance y N Event MB N. Event MB conditioned on the vale of X : To make sre that the UE was associated with the os MB with distance y before the power biasing process, there shold be no other BSs having stronger signal than the associated one. Sch conditional probability of MB on condition of X = x is p x= y p y p y p 3y f y dx, 66 where y satisfies y =arg{s y D = S x}. Event MB N conditioned on the vale of X : Similar to the event MB, the conditional probability is p N x = y N p N y N p N y N p N 3 y N f N y N dx, 67 where y N satisfies y N = arg{s y N S Nx}. Ths, the expression of F3 x can be written as F3 x =p x p x p 3x p x+p N x f x. 68 Similarly, the expression of F3 N x is written as F3 N x= p N x p N x p N 3 x p x+p N x f N x, 69 where p x = y p y p y p 3y f ydx, and y satisfies y = arg{s Ny D = S x}, and p N x = y N p N yn pn yn pn 3 yn N f yn dx, and y N satisfies y N =arg{s NyN D = SN x}. The calclation of SINR for U 3 is similar with other cases and it only consider the interference from the SBSs, ths the rest proof is omitted. Therefore, the overall SINR coverage of a typical ser cab then be obtained sing the law of total probability to get Sτ = l S lτ. APPENDIX D PROOF OF THEOREM From 3, the ASE of the k-th tier is R k = {E SINRk [log + SINR k x]}f k xdx, c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

14 4 The aplace transform of I x is shown as follows: τ a I S =exp { π λ Pr x x { exp π λ Pr Δ { x exp π λ Pr Δ x exp { π λ π λ Δ [ E [g] exp gτs S x 3 x Pr [ E [g] exp ] } d [ E [g] exp gτs S x [ E [g] exp =exp Pr d + x + S x τs exp π λ Pr d + Δ x + S x τs where step a states that the closest interferer from each type of BSs. gτsn S x ] d gτsn S x Δ x Pr N Δ 3 x Pr N ] } d } ] } d d + S x τs N d, + S x τs N 64 where F k x is given in Theorem. Since E[R] = P[X > x]dx for X>, we can obtain E SINRk [log + SINR k x] = = P {log [ + SINR k x] >ρ} dρ log τ+ P SINR k x > ρ dρ 7 The rest proof is similar with Appendix A, and the reslt is obtained from plgging τ = ρ, conditioned on the SINR k x >τ. For the sers belong to U, becase of the resorce partitioning, they can be served in all time-slots. Ths, the calclation of their ergodic rate is composed of two parts. When the macro BS schedle ABSs, the sers in U wold not get interference from tier BSs and they share the η fraction of channel resorce with range expanded UEs, whereas the mtal interference wold be considered when the macro BSs are working, in which η fraction of resorce is allocated to the sers in U and U. APPENDIX E PROOF OF EMMA 9 As λ +, all the UEs are assmed to be connect to BSs with os channel, so the path loss ζr can be rewritten as ζ k r =ζ k r =A kr k, os: Pr k r=. 7 Ths, the components for the NoS part in R, which are R N, R N and R N 3, can be neglected. Frthermore, the interference power I tρ S x can be written as I s =exp π λ x d + S x τs P A τx exp π λ d Δ x + S x τs =exp π λ x + d τ x exp π λ d. x P + A 73 In order to evalate 73, we define the following integral fnctions according to [7], β ρ, β, t, d = d +t d [ ] [ d β = F t β, β + β + ; ; td >β+, ], 74 where F [, ; ; ] is the hyper-geometric fnction [7]. Or proof is completed by plgging 74 into 73, and the calclations of I tρ S x, I tρ S x, and I3 tρ S x are following similar procedre, and is omitted here. REFERENCES [] Cisco, Visal networking index forecast, 5, c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

15 5 [] D. ópez-pérez, M. Ding, H. Classen, and A. H. Jafari, Towards gbps/e in celllar systems: Understanding ltra-dense small cell deployments, IEEE Commnications Srveys & Ttorials, vol. 7, no. 4, pp. 78, 5. [3] B. Zhang, D. Go, and M.. Honig, Energy-efficient cell activation, ser association, and spectrm allocation in heterogeneos networks, IEEE Jornal on Selected Areas in Commnications, vol. 34, no. 4, pp , April 6. [4] Q. Ye, B. Rong, Y. Chen, M. Al-Shalash, C. Caramanis, and J. G. Andrews, User association for load balancing in heterogeneos celllar networks, IEEE Transactions on Wireless Commnications, vol., no. 6, pp , Jne 3. [5] M. Di Renzo, Stochastic geometry modeling and analysis of mltitier millimeter wave celllar networks, IEEE Transactions on Wireless Commnications, vol. 4, no. 9, pp , 5. [6] M. Di Renzo, A. Gidotti, and G. E. Corazza, Average rate of downlink heterogeneos celllar networks over generalized fading channels: A stochastic geometry approach, IEEE, vol. 6, no. 7, pp , 3. [7] J. G. Andrews, F. Baccelli, and R. K. Ganti, A tractable approach to coverage and rate in celllar networks, IEEE Transactions on Commnications, vol. 59, no., pp ,. [8] H. S. Dhillon, R. K. Ganti, F. Baccelli, and J. G. Andrews, Modeling and analysis of k-tier downlink heterogeneos celllar networks, IEEE Jornal on Selected Areas in Commnications, vol. 3, no. 3, pp , April. [9] X. Zhang and J. G. Andrews, Downlink celllar network analysis with mlti-slope path loss models, IEEE, vol. 63, no. 5, pp , 5. [] M. Ding, P. Wang, D. ópez-pérez, G. Mao, and Z. in, Performance impact of los and nlos transmissions in dense celllar networks, IEEE Transactions on Wireless Commnications, vol. 5, no. 3, pp , 6. [] A. AlAmmori, J. G. Andrews, and F. Baccelli, Sinr and throghpt of dense celllar networks with stretched exponential path loss, arxiv preprint arxiv:73.846, 7. [] S. ee and K. Hang, Coverage and economy of celllar networks with many base stations, IEEE Commnications etters, vol. 6, no. 7, pp. 38 4,. [3] M. D. Renzo, W., and P. Gan, The intensity matching approach: A tractable stochastic geometry approximation to system-level analysis of celllar networks, IEEE Transactions on Wireless Commnications, vol. 5, no. 9, pp , Sept 6. [4] S. M. Y and S.-. Kim, Downlink capacity and base station density in celllar networks, in Modeling & Optimization in Mobile, Ad Hoc & Wireless Networks WiOpt, 3 th International Symposim on. IEEE, 3, pp [5] M. Ding, D. opez-perez, G. Mao, and Z. in, Stdy on the idle mode capability with los and nlos transmissions, arxiv preprint arxiv: , 6. [6] H.-S. Jo, Y. J. Sang, P. Xia, and J. G. Andrews, Otage probability for heterogeneos celllar networks with biased cell association, in Global Telecommnications Conference GOBECOM, IEEE. IEEE,, pp. 5. [7] A. Damnjanovic, J. Montojo, Y. Wei, T. Ji, T. o, M. Vajapeyam, T. Yoo, O. Song, and D. Malladi, A srvey on 3gpp heterogeneos networks, IEEE Wireless Commnications, vol. 8, no. 3,. [8] D. opez-perez, I. Gvenc, G. De la Roche, M. Kontoris, T. Q. Qek, and J. Zhang, Enhanced intercell interference coordination challenges in heterogeneos networks, IEEE Wireless Commnications, vol. 8, no. 3,. [9] M. Ding and D. ópez-pérez, On the performance of practical ltra-dense networks: The major and minor factors, arxiv preprint arxiv:7.7964, 7. [] Y. i, B. Cao, and C. Wang, Handover schemes in heterogeneos lte networks: challenges and opportnities, IEEE Wireless Commnications, vol. 3, no., pp. 7, 6. [] R. Balakrishnan and I. Akyildiz, ocal anchor schemes for seamless and low-cost handover in coordinated small cells, IEEE Transactions on Mobile Compting, vol. 5, no. 5, pp. 8 96, 6. [] H.-S. Jo, Y. J. Sang, P. Xia, and J. G. Andrews, Heterogeneos celllar networks with flexible cell association: A comprehensive downlink sinr analysis, IEEE Transactions on Wireless Commnications, vol., no., pp ,. [3] C. Ma, M. Ding, H. Chen, Z. in, G. Mao, and D. opez-perez, On the performance of mlti-tier heterogeneos celllar networks with idle mode capability, arxiv preprint arxiv:74.76, 7. [4] J.-S. Ferenc and Z. Néda, On the size distribtion of poisson voronoi cells, Physica A: Statistical Mechanics and its Applications, vol. 385, no., pp , 7. [5] A. Hinde and R. Miles, Monte carlo estimates of the distribtions of the random polygons of the voronoi tessellation with respect to a poisson process, Jornal of Statistical Comptation and Simlation, vol., no. 3-4, pp. 5 3, 98. [6] S. Singh, H. S. Dhillon, and J. G. Andrews, Offloading in heterogeneos networks: Modeling, analysis, and design insights, IEEE Transactions on Wireless Commnications, vol., no. 5, pp , 3. [7] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and prodcts. Academic press, 4. [8] 3GPP, TR 36.88: Frther enhancements to TE Time Division Dplex TDD for Downlink-Uplink D-U interference managemnet and traffic adapataion, Jne. [9] J. i, M. Sheng,. i, and J. i, Effect of densification on celllar network performance with bonded pathloss model, IEEE Commnications etters, vol., no., pp , 7. [3] M. Ding, D. ópez-pérez, G. Mao, and Z. in, Ultra-dense networks: Is there a limit to spatial spectrm rese? arxiv preprint arxiv:74.399, 7. Chan Ma received the B.S. degree from the Beijing University of Posts and Telecommnications, Beijing, China, in 3. Now, he is crrently prsing his Ph.D in Telecommnication from the University of Sydney. His research interests with Dr. Ding and Dr. in i inclde stochastic geometry, device-to-device commnication, wireless caching networks and machine learning. Ming Ding M -SM 7 received the B.S. and M.S. degrees with first class Hons. in electronics engineering from Shanghai Jiao Tong University SJTU, Shanghai, China, and the Doctor of Philosophy Ph.D. degree in signal and information processing from SJTU, in 4, 7, and, respectively. From April 7 to September 4, he worked at Sharp aboratories of China in Shanghai, China as a Researcher/Senior Researcher/Principal Researcher. He also served as the Algorithm Design Director and Programming Director for a systemlevel simlator of ftre telecommnication networks in Sharp aboratories of China for more than 7 years. Crrently, he is a senior research scientist at Data6, CSIRO, in Sydney, NSW, Astralia. He has athored more than 5 papers in IEEE jornals and conferences, all in recognized venes, and abot 3GPP standardization contribtions, as well as a Springer book Mlti-point Cooperative Commnication Systems: Theory and Applications. Also, as the first inventor, he holds 5 CN, 7 JP, 3 US, KR patents and co-athored another + patent applications on 4G/5G technologies. He is or has been Gest Editor/Co-Chair/Co-Ttor/TPC member of several IEEE top-tier jornals/conferences, e.g., the IEEE Jornal on Selected Areas in Commnications, the IEEE Commnications Magazine, and the IEEE Globecom Workshops, etc. For his inventions and pblications, he was the recipient of the President s Award of Sharp aboratories of China in, and served as one of the key members in the 4G/5G standardization team when it was awarded in 4 as Sharp Company Best Team: TE 4 Standardization Patent Portfolio c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.

16 6 David pez-prez M SM 7 is crrently a member of Technical Staff at Nokia Bell aboratories. Prior to this, David received the B.Sc. and M.Sc. degrees in telecommnication from Migel Hernandez University, Spain, in 3 and 6, respectively, and the Ph.D. degree in wireless networking from the University of Bedfordshire, U.K., in. David was also a RF Engineer with Vodafone, Spain, from 5 to 6, and a Research Associate with King s College ondon, U.K., from to. David has athored the book Small Cell Networks IEEE/Wiley Press, 7, as well as over book chapters, jornal, and conference papers, all in recognized venes. He also holds over 4 patents applications. David received the Ph.D. Marie-Crie Fellowship in 7 and the IEEE ComSoc Best Yong Professional Indstry Award in 6. He was also a finalist for the Scientist of the Year prize in The Irish aboratory Awards in 3 and 5. He is an editor of IEEE TRANSACTION on WIREESS COMMUNICATIONS since 6, and he was awarded as Exemplary Reviewer of the IEEE COMMUNICATIONS ETTERS in. He is or has also been a Gest Editor of a nmber of jornals, e.g., the IEEE JOURNA ON SEECTED AREAS IN COMMUNICATIONS, the IEEE Commnication Magazine and the IEEE Wireless Commnication Magazine. Goqiang Mao S 98-M -SM 8-F 8 joined the University of Technology Sydney in Febrary 4 as Professor of Wireless Networking and Director of Center for Real-time Information Networks. Before that, he was with the School of Electrical and Information Engineering, the University of Sydney. He has pblished abot papers in international conferences and jornals, which have been cited more than 5 times. He is an editor of the IEEE Transactions on Wireless Commnications since 4, IEEE Transactions on Vehiclar Technology since and received Top Editor award for otstanding contribtions to the IEEE Transactions on Vehiclar Technology in, 4 and 5. He is a co-chair of IEEE Intelligent Transport Systems Society Technical Committee on Commnication Networks. He has served as a chair, co-chair and TPC member in a large nmber of international conferences. He is a Fellow of IEEE and IET. His research interest incldes intelligent transport systems, applied graph theory and its applications in telecommnications, Internet of Things, wireless sensor networks, wireless localization techniqes and network performance analysis. Zihai in S 98-M 6-SM received the Ph.D. degree in Electrical Engineering from Chalmers University of Technology, Sweden, in 6. Prior to this he has held positions at Ericsson Research, Stockholm, Sweden. Following Ph.D. gradation, he worked as a Research Associate Professor at Aalborg University, Denmark and crrently at the School of Electrical and Information Engineering, the University of Sydney, Astralia. His research interests inclde sorce/channel/network coding, coded modlation, MIMO, OFDMA, SC-FDMA, radio resorce management, cooperative commnications, small-cell networks, 5G celllar systems, IoT, etc. Jn i M 9 received Ph. D degree in Electronic Engineering from Shanghai Jiao Tong University, Shanghai, P. R. China in 9. From Janary 9 to Jne 9, he worked in the Department of Research and Innovation, Alcatel cent Shanghai Bell as a Research Scientist. From Jne 9 to April, he was a Postdoctoral Fellow at the School of Electrical Engineering and Telecommnications, the University of New Soth Wales, Astralia. From April to Jne 5, he is a Research Fellow at the School of Electrical Engineering, the University of Sydney, Astralia. From Jne 5 to now, he is a Professor at the School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China. He served as the Technical Program Committee member for several international conferences sch as GlobeCom5, ICC4, VTC4 Fall, and ICC4. His research interests inclde network information theory, channel coding theory, wireless network coding and cooperative commnications c 8 IEEE. Personal se is permitted, bt repblication/redistribtion reqires IEEE permission. See for more information.