A Proportional Fair Resource Allocation Algorithm for Hybrid Hierarchical Backhaul Networks

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1 A Proportional Fair Reource Allocation Algorithm for Hybrid Hierarchical Backhaul Network Intitute of Communication and Information Sytem, Hohai Univerity, Nanjing, , China Guoping Tan Intitute of Communication and Information Sytem, Hohai Univerity, Nanjing, , China gptan@hhu.edu.cn Yandan Zhu Intitute of Communication and Information Sytem, Hohai Univerity, Nanjing, , China yandanzhu_zyd@163.com Guomin Wu, Yueheng Li Intitute of Communication and Information Sytem, Hohai Univerity, Nanjing, , China guomin.wu@wico.h; yueheng_li@hhu.edu.cn In order to improve the total ytem throughput by analyzing the reource allocation problem in backhaul link and acce link of bae tation in ultra-dene network (UDN), a proportional fair reource allocation (PFRA) algorithm wa deigned for the wirele hybrid hierarchical backhaul network in thi paper. Firt, the bae tation were tratified and the frame tructure of each bae tation in different layeie wa re-deigned.then, the objective function wa contructed baed on the proportional fair utility function to optimize the ytem throughput. Finally, an iterative algorithm wa derived baed on Lagrange Multiplier algorithm to obtain the optimal olution of pectrum reource allocation in hybrid hierarchical backhaul network. The performance of the PFRA algorithm ha been imulated and the reult how that the PFRA algorithm can improve network throughput effectively at the cot of loing a certain network coverage rate. In the future, PFRA need to be optimized to reach the bet balance between network throughput and network coverage rate. CENet July 2017 Shanghai, China 1 Speaker 2 Correponding Author 3 Thi work wa upported by Fundamental Reearch Fund for the Central Univeritie (2015B18914; 2014B33114), Key Laboratory of Wirele Senor Network and Communication, Shanghai Intitute of Microytem and Information Technology, Chinee Academy of Science ( ) and Graduate tudent cientific reearch innovation project in jiangu province (KYLX_0436). Copyright owned by the author() under the term of the Creative Common Attribution-NonCommercial-NoDerivative 4.0 International Licene (CC BY-NC-ND 4.0).

2 A Proportional Fair Reource Allocation Algorithm for HHBN 1. Introduction Complex network have been widely tudied in recent year and different interconnected network model are propoed to olve the cacading failure caued by overload [1-4]. A a new heterogeneou network architecture, ultra-dene network (UDN) i different from the deployment cenario of traditional macro-cell. UDN provide a efficient energy-aving olution to the wirele mobile data ervice that grow rapidly in the future [5]. Under thi network architecture, the number of mall-cell bae tation (SBS) i increaed and the coverage area of ingle cell i reduced with dener deployment. Therefore, the load of macro-cell bae tation (MBS) can be hared, the phyical ditance between the ender and the receiver hortened and low latency and reliable uer experience achieved. Meanwhile, UDN reduce the intallation cot of the network infratructure deployment and the operating cot of the bae tation ignificantly [6]. However, the complexity of the network tructure make inter-cell interference more eriou. Beide, the pectrum reource and backhaul network capacity i contrained [7]. How to allocate the pectral reource in backhaul and acce link of bae tation effectively i an important problem in UDN. How to allocate reource to reach the mot total network throughput and pectral highet efficiency will be tudied in thi paper. Thu, a proportional fair reource allocation (PFRA) algorithm i deigned. The objective function to maximize the network throughput in hybrid hierarchical backhaul network i contructed. And an iterative algorithm i derived baed on Lagrange Multiplier algorithm to obtain the optimal allocation of pectrum reource. In addition, PFRA algorithm i compared with traditional tatic allocation algorithm and imulated by MATLAB oftware repectively. The performance in interm of total network throughput and edge uer throughput are compared and the experimental reult are analyed. 2. Sytem Model Hybrid hierarchical backhaul network i a new network tructure a propoed in UDN. In actual deployment, the bae tation in the next layer only need to etablih a backhaul link with the bae tation in the upper layer to achieve plug and play. In order to implify and keep general nature, three-hop hybrid hierarchical backhaul network cenario i ued in thi paper, a hown in Figure 1. MBS in the firt-level backhaul layer (the following i called firt layer) i denoted by SN 0 and SBS in the econd-level backhaul layer (the following i called econd layer) i denoted by SN ( S, 0). S i the et of bae tation in the firt and econd layer. SBS in the third-level backhaul layer (the following i called third layer) i denoted by SN c ( S, c C). C i the et of bae tation in the third layer. The et of Uer Equipment (UE) i denoted by U. The et of UE connected to the bae tation in the firt and the econd layer i U, in the third layer i U c. UE i connected to one bae tation at mot at ome point to communicate without conidering the cooperative tranmiion. Since only downlink tranmiion i conidered in thi paper, the data packet that SBS tranmit to UE are generally ent by MBS to SBS. During thi period, the data packet tranmitted from the upper layer are decoded by SBS, and queued in the buffer of SBS, waiting for the cheduler to be tranmitted to the correponding target UE in turn. According to the definition of frame tructure in 3GPP LTE [8], the reception and tranmiion of SBS can t be carried out at the ame time o a to avoid the ignal interference. 2

3 A Proportional Fair Reource Allocation Algorithm for HHBN Therefore, a radio frame i divided into the acce ubframe and the backhaul ubframe. The MBS and SBS in each layer imultaneouly multiplex the ubframe frequency band and tranmit data to their own UE at the ame time in the acce ubframe. The MBS orthogonally allocate frequency band to UE for backhaul link in backhaul ubframe. The ubframe allocation change upon the cene, the UE' need or higher configuration. A baic OFDMA reource allocation unit can be named a a reource block (RB), which i compoed of reource element in column [9]. RB i ued a the mallet indepedant reource allocation unit in thi paper. Wirele backhaul link Wired backhaul link Acce link Macro Pico UE Figure 1: Hybrid Hierarchical Network Framework Core network 3. Proportional Fair Reource Allocation Algorithm Macro coverage (firt layer) Microcellular coverage (econd layer) Microcellular coverage (third layer) The PFRA algorithm re-deign the frame tructure of bae tation in different layer baed on hybrid hierarchical network framework. The frame tructure of SBS in the econd layer i the ame a MBS and oppoite to SBS in the third layer. How many RB are allocated to each bae tation i derived from the following algorithm. The algorithm take a utility function baed on proportional fairne [10]: max u U log R u, =max u U S ρ u, log( j J w j,u r j,u ) (3.1) R u, i the received data rate of a UE (denoted by u) which connected to the SN on a radio frame. If u i directly connected to the SN, ρ u, =1, otherwie ρ u, =0. w j,u =1 mean that the jth RB i aigned to u, otherwie w j,u =0. The r j,u refer to the intantaneou data rate received by u at the jth RB. J i the um of RB in a radio frame. (3.1) meet following condition: S ρ u, =1, ρ u, {0,1}, u U u U w 1, w {0,1}, j J, S Main layer reource allocation Secondary layer reource allocation (3.2) 3.1 Main Layer Reource Allocation The main layer reource allocation i that the MBS allocate the RB to their own UE and the SBS in the econd layer. Only the acce reource of the MBS and the acce and backhaul reource of the SBS in the econd layer are conidered. We aume that the data ervice and ervice queue of the UE under the MBS are of full buffer. Therefore, UE belonging to the MBS can conume all the allocated acce reource J a. The average data rate of u connected to SN 0 i 3

4 A Proportional Fair Reource Allocation Algorithm for HHBN R u,0 J a U 0 f ( γ u,0 )G(U 0 ) (3.3) The cheduling gain G(U 0 ) =1 due to the Round-Robin (RR) cheduling cheme ued. The key idea of the RR cheduling i that the UE in the cell have the ame priority, and each UE i periodically cheduled with equal opportunity. f(γ u,0 ) denote the linear mapping function of ignal to interference plu noie ratio (SINR) in the acce link that from u to SN 0, calculated by f ( γ u,0 )=log 2 ( 1+ R N 0 + I ) (3.4) R refer to the ignal UE received. N 0 i the Gauian white noie. I mean the interference UE received which i an accumulated value. And the SBS in the econd layer not only provide acce ervice to their own UE, but alo provide backhaul ervice to the SBS in the third layer. A demotrated below, the average data rate of the u connected to SN ( S, 0) i R J a u, U +U ' f ' ( γ u,) (3.5) The SBS in the econd layer can t ue J a fully unle the link from SN 0 to SN can provide enough tranfer rate. Therefore, the acce reource J a that SBS allocated i a part of J a. U' repreent the et of UE connected to SBS in the third layer, U '= S U c. If u U, f'(γ u, )= f(γ u, ). If u U', f'(γ u, )=f(ϕ c ). f(ϕ c ) i the linear mapping function of the SINR in the backhaul link that goe from SN c to SN, calculated a (3.4). Therefore, the cumulative average data rate R a obtained on the allocated acce ubframe of SN i calculated by R a = R uϵ (U +U ' ) u,. Correpondingly, the cumulative average data rate R b obtained on the allocated backhaul ubframe of SN i calculated a R b = J b f ( ϕ ). J b i the required backhaul reource where SN 0 tranmit data to SN. In order to avoid packet congetion, the cumulative average data rate of each bae tation hould match each other on the acce ubframe and the backhaul ubframe, o, R a = R b. We ubtitute (3.3) and (3.5) into (3.1) to obtain the object function of PFRA: max( U +U ' log J a + ρ u, log f '( γ u,) S u U S (3.6) U +U ' ub-formula 1 ub-formula 2 ) When the SINR of the communication link i unchanged at the period of reource allocation, the ratio η of the backhaul reource to the acce reource of each bae tation can be determined. So, the ub-formula 2 in (3.6) i a definite value. (3.6) can be olved only when the ub-formula 1 i conidered and two condition are met a below: S η J a = J (3.7) J a J a, S The ub-formula 1 can be tranformed by uing the equal ign contraint: max U t +U t ' log J a + U +U ' log J a (3.8) t D S, D The ubet D i defined a a et of bae tation that can fully ue the acce reource. The Lagrange multiplier formula i ued to olve (3.8) and λ (λ 0) i the Lagrange multiplier. 4

5 A Proportional Fair Reource Allocation Algorithm for HHBN L( J a,λ )= U t +U t ' log J a + U +U ' log J a t D S, D λ ( t J a + η J a t Dη S, D J ) The acce reource J a of SN can be obtained with derivative in (3.9). J a ={ U +U ' η J, S, D U U t +U t ' t D J,t D η t U t D (3.9) (3.10) The reult of reource allocation mut be in the form of integer, o the acce reource of SN i J a = max(1, J a ), S,( U +U ' ) 0. The iterative algorithm i ued to find the mallet number of SBS in ubet D. Firt, the ubet D only contain the MBS. Then, make P a a et of SBS in the econd layer when acce reource calculated by (3.10) do not atify the contraint condition (3.7). Finally, if the et P i nonempty, the SBS with mot acce reource i elected from the et P and added to the ubet D which i updated. The proce repeat until the et P i empty. 3.2Secondary Layer Reource Allocation The econdary layer reource allocation i that the SBS in the econd layer allocate RB to their UE and the SBS in the third layer. After the acce reource J a of SN ha been calculated, the backhaul reource J b i obtained by J b =η J a, S. c The backhaul link cumulative rate R b of u connected to SN c i J R c b = R u, c a u U c u U c U +U ' f ( ϕ c) (3.11) c The backhaul reource J b of SN c i J b c = The acce reource J a c of SN c i J a c = u U c R c b f ( ϕ c ) = u U c J a U +U ' f ( ϕ c ) f ( γ u,c ) U 2 c U +U ' J a (3.12) (3.13) It hould be enured that J a c i le than backhaul reource J b of SN 0, otherwie, reduce the J a c. Thu by now, the reource allocation of the acce and the backhaul link have been completed. 4. Matlab Simulation Analye The imulation i performed under a ingle cell. There i only one MBS in the cell divided into three ector. The coverage ditance of the MBS i [-1/3km, 1/3km]. We mainly imulate the downlink performance gain, focuing on the data from the core network to the UE. 5

6 A Proportional Fair Reource Allocation Algorithm for HHBN It can be oberved from Figure 2 that the uer rate of non-mall-cell-tation reource allocation (NSRA) algorithm i more concentrated, and that of PFRA algorithm and fixed reource allocation (FRA) algorithm i relatively cattered. PFRA algorithm i the bet of the three cheme to improve the uer rate. On the one hand, tt can reduce the number of uer with low rate and increae the number of uer with high rate. On the other hand, PFRA algorithm enure that the number of uer in the bottom layer i conitent with the allocation of backhaul reource, and the data rate of the backhaul link i greater than or equal a the um of rate of the acce uer. The mallet reource allocation unit ued in thi cheme i RB with large granularity. Therefore, the rate will ignificantly be decreaed by reducing one RB. If the mallet egmentation unit with maller granularity i ued, uch a carrier [11] [12], the uer throughput performance will be better. Uer throughput comparion graph Uer throughput CDF Throughput/Mbp (a) Cumulative Ditribution NSRA FRA PFRA (b) Probability Denity Ditribution Figure 2: Comparion of Uer Throughput Ditribution for Different Algorithm (with 5 SBS in the econd layer and 2 SBS in the third layer) PDF Throughput/Mbp Figure 3 how that the edge uer throughput of PFRA algorithm and FRA algorithm i le than that of the NSRA algorithm. Compared with NSRA algorithm, in PFRA algorithm, while the addition of the mall bae tation make total throughput ignificantly increae, the interference will relatively increae. RR cheduling cheme ued in thi paper without conidering the quality of uer channel and the tranmiion rate may lead to mall network coverage rate of PFGA algorithm NSRA FRA PFRA (a) Different number of SBS in the Third Layer (b) Different number of SBS in the Second Layer Figure 3 : Edge Uer Throughput of Different Layer and SBS 6

7 A Proportional Fair Reource Allocation Algorithm for HHBN 5. Concluion The PFRA algorithm i deigned in thi paper for wirele hybrid hierarchical backhaul network to improve the total network throughput. The imulation reult how that the PFRA algorithm i effective in improving the network throughput compared with the traditional NSRA algorithm and FRA algorithm. However, the edge uer throughput of PFRA algorithm i not very atifactory when compared with NSRA algorithm. RR cheduling cheme ued may lead to the reduction of the network coverage rate. The proportional fair cheduling cheme which take uer fairne and uer rate into account will probably olve thi problem and improve the network performance. That' the further tudy we need to do. Reference [1] Hong S, Lv C, Zhao T, Wang B, Wang J, Zhu J. Cacading failure analyi and retoration trategy in an interdependent network[j]. Journal of Phyic A Mathematical & Theoretical, 2016, 49(19): [2] Hong S, Zhang X, Zhu J, Zhao T, Wang B. Suppreing failure cacade in interconnected network: Conidering capacity allocation pattern and load reditribution[j]. Modern Phyic Letter B, 2016, 30(05): [3] Hong S, Wang B, Ma X, Wang J, Zhao T. Failure cacade in interdependent network with traffic load[j]. Journal of Phyic A Mathematical & Theoretical, 2015, 48(48): [4] Hong S, Yang H, Zhao T, Ma X. Epidemic preading model of complex dynamical network with the heterogeneity of node[j]. International Journal of Sytem Science, 2016, 47(11): [5] Hwang I, Song B, Soliman S S. A holitic view on hyper-dene heterogeneou and mall cell network [J]. Communication Magazine, IEEE, 2013, 51(6): [6] Yu S M, Kim S L. Downlink capacity and bae tation denity in cellular network[c]. Modeling & Optimization in Mobile, Ad Hoc & Wirele Network (WiOpt), th International Sympoium on. IEEE, Japan, Aug, 2013: [7] Wang C X, Haider F, Gao X, You X H, Yang Y, Yuan D, et al. Cellular architecture and key technologie for 5G wirele communication network [J]. Communication Magazine, IEEE, 2014, 52(2): [8] Acce E U T R. Phyical channel and modulation[j]. 3GPP TS, 2009, : V [9] 3GPP long term evolution: principle and ytem deign [M]. The People' Pot and Telecommunication Pre (Pot & Telecom Pre), [10] Kelly F. Charging and rate control for elatic traffic [J]. European tranaction on Telecommunication, 1997, 8(1): [11] Song Q, Huang Y, Ning Z, Wang F. Subcarrier allocation in multi-hop orthogonal frequency diviion multiple acce wirele network[j]. Computer & Electrical Engineering, 2014, 40(2): [12] Kim B G, Lee J W. Joint opportunitic ubchannel and power cheduling for relay-baed OFDMA network with cheduling at relay tation[j]. Vehicular Technology, IEEE Tranaction on, 2010, 59(5):