Optimal FemtoCell density for Maximizing Throughput in 5G Heterogeneous Networks Under Outage Constraints

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1 Optimal emtocell density for aximizing Throughput in 5G Heterogeneous Networks Under Outage Constraints Talha ir Linglong ai Yang Yang Wenqian Shen and Bichai Wang Tsinghua National Laboratory for Information Science and Technology TNList) epartment of Electronic Engineering Tsinghua University Beijing 84 China School of Information and Communication Engineering Beijing University of osts and Telecommunications Beijing China bah5 swq3 daill Abstract Heterogeneous networks HetNets) which involve densely deployed femtocells underlaid traditional macrocell network is a promising solution to the extremely high data rate requirements of the future 5G communications In this paper we analyze the closed-form optimal deployment of femtocells in HetNets to maximize the network throughput under the outage constraints from both macrocells and femtocells Specifically we model the random distribution of macro cell users UEs) and femtocell base stations BSs) as oisson oint rocesses s) Then the closed form expressions for outage probabilities in both uplink and downlink transmissions are derived rther we study the network throughput maximization problem under the outage probability constraints inally With the help of convex optimization the interval of BS density which contains the maximum network throughput is obtained in closed form Simulation results validate the impact of the system parameters on the different optimal BS density as well as the influence of interference to the maximum network throughput Index Terms Heterogenous networks network throughput stochastic geometry convex optimization I INTROUCTION The vision of future 5G wireless communications lies in providing very high data rate significant improvement in users perceived quality of servicesqos) manifold increase in base station capacity and extremely low latency compared to current 4G LTE networks However the explosion of mobile subscribers and service demands lead to a heavy overload for traditional macro base stations BSs) Heterogeneous networks HetNets) where various femtocells can be deployed in the traditional macrocell network has been considered as a paradigm shift to offload over-burdened BSs and facilitate higher network throughput with better spectral efficiency On one hand the increasing network density can substantially improve the network capacity On the other hand densely deployed femtocells in co-channel mode cause severe interference and thus the obvious performance degradation of the macrocell network which is the key challenge for the deployment of femtocells in HetNets 3 However interference mitigation in such networks remains an open problem In order to reduce such interference some solutions have been proposed to enhance the network performance where the transmission rate is a key performance metric of HetNets Specifically based on the interference statistics between macro and femtocells the system performance of HetNet was optimized by a coalition algorithm in a single macro cell rther cooperative spectrum sharing is considered the optimization of transmission rate for femtocells in a single macro cell is investigated in 4 Then the analysis of transmission rate was extended with the consideration of quality-of-service QoS) requirement in 5 Where all analysis are based on one or multiple femto-scale macro cells However for practical HetNets it is necessary to analyze the transmission rate of large-scale networks with the random deployment of UEs and BSs as well the interference consideration from inter and intra cells In this paper by considering both the network performance optimization and random distribution of users and BSs in HetNets the statistics of interference are analyzed through stochastic geometry and the network throughput is maximized by an optimal BSs deployment The main contributions of paper can be summarized as follows: With the help of Laplace transformation the outage probability at the BS and femtocells both uplink and downlink) are derived in closed form We formulate the network throughput maximization problem of femtocells under the outage probability constraints and derive the optimal BS density to maximize the network throughput The optimal BS density is obtained in closed from for this non-convex optimization problem Simulation results discuss the outage probability and network throughput of femtocells under different system parameters The rest of the paper is organized as follows Section II describes the system model Section III presents the outage probabilities and the network throughput for femtocells Section IV shows the optimization analysis of BS density for maximizing network throughput Simulation results are discussed in Section V inally our conclusions are summarized /7/$3 7 IEEE

2 ig in Section VI The scenario of heterogeneous networks II SYSTE OEL As shown in ig we consider the HetNets where femtocells are underlaid the traditional macrocell network The uplink resources of the macrocell network are shared by femtocells We model the macro cell users UEs) as an independent homogeneous oisson oint rocess ) Π on two dimensional plane R with density λ emtocell base stations BS) also satisfy an independent homogeneous on R denoted as Π with density λ The traffic in the HetNets is assumed as full buffer The powers for UEs BSs and UEs are defined as and respectively efining uplink and down transmission probabilities in femtocells as r u r u ) and r d as r d = r u r d ) respectively According to Slivnyak s theorem 6 a typical receiver of femtocells is placed at the origin of plane R While when we consider the downlink transmission this receiver is an UE otherwise it is an BS in uplink transmission We consider following propagation model in HetNets: r = t ε tr tr ) where t and r represent the transmitter and receiver powers respectively tr is the distance and denotes path loss exponent which satisfies ε tr denotes the Rayleigh fading coefficient following an independent exponential distribution with unit mean for every communication link in the HetNets III NETWORK THROUGHUT O ETOCELLS In this section we calculate the outage probabilities in HetNets and then the network throughput for femtocells is obtained A Outage robabilities in HetNets The signal-to-interference ratio SIR) at a typical BS is γ = k Π ε k k ε ε i Π U) i Π W) ε ) where ε and denote the Rayleigh fading coefficient and the distance from the desired UE to the typical BS Similarly ε k and k represent the Rayleigh fading coefficient and the distance from node k to the origin in macrocell network while ε and are parameters for node i in femtocells Compact point sets as U and W satisfy U = x node x is the receiver in uplink transmission in femtocells} and W = y node y is the receiver in downlink transmission in femtocells} respectively Let I = ε k k I = ε and k Π i Π U) I = ε ) can be simplified as i Π W) ε γ = 3) I I I Then the following lemma shows the outage probability of typical BS in HetNets: Lemma The outage probability of a typical BS in HetNets must satisfy r u ) r d ) r γ <ζ )= e λμ λμ 4) where r ) denote the probability ζ is the SIR threshold of uplink transmission for UE μ = π ζ ) Γ ) and Γ ) represents the gamma function with the form Γz) = e t t z dt roof: rom 3) we have r γ <ζ )=rε <ζ I I I ) 5) As ζ satisfies the independent exponential distribution with unit mean 5) can be written as r γ <ζ )= E e ζ III ) = L I ζ ) L I ζ ) L I ξ ) 6) where L I ) L I ) and L I ) are Laplace transformation of I I and I respectively L I ζ )=exp λ E εk e r ) ζ dr =exp λ πζ ) Γ ) 7) L I ζ λ ) r u =exp L I ζ ) ) λ r d ) π ζ Γ ) Γ ) =exp 9) By denote μ = π ζ ) Γ ) 4) can be obtained Similarly the SIR at a typical UE and BS in uplink and downlink satisfies γ = γ = k Π k Π ε k k ε k k π ζ Γ ) Γ ) ε ε i Π U) i Π W) ε ε i Π U) i Π W) ε ε 8) ) )

3 enoting ζ and ζ as SIR thresholds for uplink and downlink transmissions in femtocells and following the same proof steps as in Lemma wehave: Lemma The outage probability of the typical UE in uplink transmission satisfies r γ <ζ ) = e λμ ) λ μ r u r d ) ) where μ = π ζ ) Γ ) Lemma 3 The outage probability of typical BS in downlink transmission satisfies r γ <ζ ) ) ) = e λμ λ μ r u r d 3) where μ = πrsd ξ ) Γ ) B Network Throughputs for emtocells In HetNets the network throughput of femtocells is defined as 7 T n λ )=λ r n R n n u d) 4) Where R n satisfies the following form 8 R n = sup W log ζ n ) r γ n <ζ n )} ζ n 5) efinition The network throughput for uplink transmission in femtocells is T λ )=Wr u λ log ζ ) ) ) λ μ r ur d e λμ 6) The network throughput for downlink transmission in femtocells is T λ )=Wr d λ log ζ ) ) ) e λμ λ μ r u r d 7) Thus network throughput for femtocells T λ ) satisfies T λ )=T λ )T λ ) 8) IV OTIIZATION O THE ETOCELLS ENSITY When femtocells reuse the frequency resources of macrocell network the reliable transmission of macrocell should be guaranteed Considering uplink and downlink transmissions in femtocells we have the following four constraints: λ λ 9) ) ) e λμ λμ r u r d φ ) ) ) e λμ λ μ r ur d φ ) e λμ ) ) λ μ r u r d φ ) where λ is the maximum density of BS in HetNets φ φ and φ are the outage probability thresholds of BS BS and UEs respectively We get the following network throughput maximization problem for femtocells: max T λ ) 3) st 9) ) rom above inequalities in )-) we have λ λ λ λ λ λ μ ln φ ) 4) r u r d μ ln φ ) 5) r u r d efine λ sup = λ λ μ ln φ ) r u r d μ ln φ ) 6) r u r d μ ln φ ) r u r d λ sup 3 = λ λ sup = μ ln φ ) r u r d Then λ sup = λ max λ sup λ sup λ sup 3 } ) Let X = W r u log ζ ) X = λ μ ) = μ r u r d Y = W r d log ζ ) ) ) Y = λ μ = μ r u r d Then we have following theorem Theorem The maximum value of function T λ ) locates at } the interval λ min λ max where λ min =min and λ max =max } roof: According to 6) and 7) we have T λ )= X λ e X λx3 and T λ )=Y λ e Y λy3 Take the first order derivative of both T λ ) and T λ )wehave T λ ) λ = X e X λx3 λ ) 7) T λ ) λ = X e X λx3 λ ) 8) ake T λ ) λ = and T λ ) λ = we get the maximum values of function T λ ) and T λ ) as and respectively When λ ) the function T λ ) increases monotonically ) and T λ ) decreases monotonically when λ Similarly the function ) T λ ) increases monotonically when λ Y3 and it ) decreases monotonically with λ

4 We denote λ min = min } λ max = max } Suppose λ min = and λ max = Then for λ ) it can be known that T λ ) < ) T and T λ ) <T ) because λ < < ) Similarly for λ ) ) T λ ) <T λ 9) TABLE I SIULATION ARAETERS arameters Abbreviations Value ath loss 4 The power of UE 5 dbm The power of BS 3 dbm r u/r d The probability of uplink/downlink communication in a femtocell 6/4 istance from BS to the typical UE m istance from UE to the typical BS 5 m istance from BS to the typical UE 6 m The same results can be obtained if we define λ min = and λ max = Therefore the maximum value of function T λ ) must locate between the interval λ min λ max Then we have following theorem Theorem The optimal BS density λ opt for maximizing the network throughput of femtocells satisfies λ opt = λsup λ sup <λ λ λ λ 3) sup where λ satisfies λ min T λ ) < λ = λ T λ ) has zero point λ max T λ ) > 3) λ =argmax T x) x λ } 3) where λ λ min λ max T λ ) means the first derivative of T λ ) with respect to λ λ is the solution T λ ) = when T λ ) has zero point on λ min λ max ) roof: rom 7) and 8) we know that the first derivative of T λ ) with respect to λ is T λ ) = X e X λx3 λ )Y e Y λy3 λ ) 33) If T λ ) < then according to Theorem we can know that T λ ) can get the maximum value as λ = λ min because T λ ) is monotonically decrease on λ min λ max ) then if T λ ) > T λ max ) is the maximum value because T λ ) is monotonically increase on λ min λ max ) Whereas we can observe that if T λ ) is a continuous bounded function on close set λ min λ max and λ λ min λ max ) which leads to T λ )= T λ ) must be the local maximum or minimum value on λ min λ max Then T λ ) is the maximum value when λ =argmax T x) x λ }Soweget λ Considering the constraints of power and the outage probabilities of both macrocell and femtocell transmissions the optimal BS density λ opt for maximizing network throughput is shown in 3) V SIULATION RESULTS In this section we evaluate our results for the network throughput of femtocells by simulations The main simulation parameters are provided in Table I Outage probability of femtocells UL λ =5x 6 UE/m =4dBm UL λ =x 5 UE/m =4dBm UL λ =x 5 UE/m L λ =5x 6 UE/m =4dBm L λ =x 5 UE/m L λ =x 5 UE/m BS density BS/m ) x 4 ig Outage probability in femtocells ig shows the outage probability of femtocells with different densities of BS Initially we can find that outage probabilities of both uplink and downlink transmissions are increasing as BS density increases This is due to the fact that high BS density causes more interference to the overall network Secondly we observe that with higher UE density the outage probabilities for femtocells is high The reason is because high UE density can generate high interference to the femtocells leading to more strict constraints in the transmission of femtocells Similarly the outage probability is increased when we enlarge the transmission power of UE which can cause more interference to the femtocells oreover the uplink transmission power is smaller than the downlink transmission power in femtocells showing that the UEs can suffer more interference as receivers in downlink transmission Therefor the outage probability of downlink transmission is smaller than that of uplink transmission In addition the probabilities of uplink and downlink transmissions in femtocells are set as 6 and 4 respectively the uplink transmission in femtocells causes more interference in a HetNets as the BS density increases Thus the outage probabilities of uplink transmission rise faster as compare to that of downlink transmission In ig 3 we illustrate the relationship between the network throughput of femtocells and BS density We observe that network throughput of femtocell is decreasing as BS density increases This increment in BS density causes more inter-

5 aximum network throughput of femtocells bit/s/hz/m ) x =3dBm =4dBm BS density UE/m ) x 6 ig 3 The maximum network throughput of femtocells vs acro cell UE density ference between femtocells and the constraints to femtocells become more strict When BS density is high enough the receivers in femtocells severely suffer interference from neighboring receivers causing network throughput values to reach ig3 further shows that high UE power also cause more interference to femtocells The maximum network throughput of femtocells is lower while the UE power is highin addition increment in BSs density the constraints to femtocells become strict which makes the optimal BS density to get only the boundary value of feasible region Then the maximum network throughput of femtocells decreases linearly aximum network throughput of femtocells bit/s/hz/m ) x 5 5 The power of UE dbm) The power of BS dbm) ig 4 aximum network throughput of femtocell vs femtocell uplink and downlink power ig 4 demonstrates the relationship between the maximum network throughput of femtocells their uplink and downlink powers Clearly the performance gain for uplink transmission is larger as compare to downlink transmission in femtocells The reasons are ) The uplink transmission distance is shorter than the downlink transmission distance which makes the signal experienced less propagation loss during uplink transmission ) Since we set the probabilities of uplink and downlink transmissions as 6 and 4 respectively it allows uplink transmissions to achieve high performance gain It can be observe that uplink transmission takes more proportion in the overall performance gain An extreme example in the above figure is when uplink and downlink transmission are 5dBm and 35dBm the maximum network throughput of femtocells has a very low value because the uplink transmission cannot bring much performance gain to the femtocells and the downlink transmission generates serious interference to the entire network VI CONCLUSIONS In this paper we optimize the BS density in HetNets for maximizing network throughput of femtocells By modeling the HetNets as homogeneous s we investigate the outage probabilities for macrocell network and femtocells The network throughput expression of femtocells is evaluated and optimization problem of BS density is then formulated with the outage probability constraints We also prove that the maximum network throughput for femtocells locates in a fixed interval of BS density inally the optimal BS density is derived in closed form for maximizing the network throughput for the femtocells in HetNets The impact of parameters such as the optimal BS density UEs power and the probability of uplink/downlink transmissions in femtocells are discussed through simulation results REERENCES W K Ng E S Lo and R Schober ultiobjective resource allocation for secure communication in cognitive radio networks with wireless information and power transfer IEEE Transactions on Vehicular Technology vol 65 no 5 pp S Yunas Valkama and J Niemela Spectral and energy efficiency of ultra-dense networks under different deployment strategies IEEE Commun ag vol 53 no pp 9 Jan 5 3 U Siddique H Tabassum E Hossain and I Kim Wireless backhauling of 5g small cells: challenges and solution approaches IEEE Wireless Commun ag vol no 5 pp 3 Oct 5 4 Z Gao L ai i Z Wang A Imran and Z Shakir mwave massive-mimo-based wireless backhaul for the 5g ultra-dense network IEEE Wireless Communications vol no 5 pp YNiuCGaoYLiLSuJinYZhuandOWu Energyefficient scheduling for mmwave backhauling of small cells in heterogeneous cellular networks IEEE Transactions on Vehicular Technology vol 66 no 3 pp Haenggi Stochastic geometry for wireless networks Cambridge University ress 7 Kamel W Hamouda and A Youssef Ultra-dense networks: a survey IEEE Communications Surveys & Tutorials vol 8 no 4 pp Nov 8 S Shalmashi E Björnson Kountouris K W Sung and ebbah Energy efficiency and sum rate when massive IO meets device-todevice communication in in roc IEEE International Conference on Communication Workshop ICC 5 Workshop) Jun 5