COST EFFICIENCY OPTIMIZATION OF 5G WIRELESS BACKHAUL NETWORKS

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1 COST EFFICIENCY OPTIMIZATION OF 5G WIRELESS BACKHAUL NETWORKS Xaohu Ge, Senor Member, IEEE, Song Tu, Guoqang Mao 2, Senor Member, IEEE, Vncent K. N. Lau 3, Fellow, IEEE, Lnghu Pan School of Electronc Informaton and Communcatons Huazhong Unversty of Scence and Technology, Wuhan 4374, Hube, P. R. Chna. Emal: {xhge, songtu, 2 School of Computng and Communcatons The Unversty of Technology Sydney, Australa. Emal: 3 Department of Electronc and Computer Engneerng Hong Kong Unversty of Scence and Technology, Hong Kong. Emal: Abstract The wreless backhaul network provdes an attractve soluton for the urban deployment of ffth generaton (5G) wreless networks that enables future ultra dense small cell networks to meet the everncreasng user demands. Optmal deployment and management of 5G wreless backhaul networks s an nterestng and challengng ssue. In ths paper we propose the optmal gateways deployment and wreless backhaul route schemes to maxmze the cost effcency of 5G wreless backhaul networks. In generally, the changes of gateways deployment and wreless backhaul route are presented n dfferent tme scales. Specfcally, the number and locatons of gateways are optmzed n the long tme scale of 5G wreless backhaul networks. The wreless backhaul routngs are optmzed n the short tme scale of 5G wreless backhaul networks consderng the tme-varant over wreless channels. Numercal results show the gateways and wreless backhaul route optmzaton sgnfcantly ncreases the cost effcency of 5G wreless backhaul networks. Moreover, the cost effcency of proposed optmzaton algorthm s better than that of conventonal and most wdely used shortest path (SP) and Bellman-Ford (BF) algorthms n 5G wreless backhaul networks. Index Terms wreless backhaul networks, two-scale, cost effcency, multple gateways, mllmeter-wave. INTRODUCTION Wth the exponentally ncreasng demand for wreless data traffc n recent years, t has become evdent that tradtonal macro cellular networks can not handle ggabtlevel data traffc n an economcal and envronmental frendly way []. The ffth generaton (5G) small cell network, adoptng massve multple nput multple output (MIMO) and mllmeter wave transmsson technologes, s emergng as a promsng soluton [2]. In order to reduce the cell coverage sharply to acheve a hgh spatal The authors would lke to acknowledge the support from Natonal Key R & D Program of Chna wth Grant No. YS27YFGH842. spectrum effcency, a large number of small cells have to be deployed to acheve a seamless coverage of urban regons and form 5G ultra-dense cellular networks [3]. However, t s uneconomcal and cost-prohbtve for every small cell to be connected va the fber to the cell (FTTC). As a consequence, wreless backhaul network becomes an ndspensable part of 5G ultra-dense small cell network solutons [4]. To promote the deployment of 5G wreless backhaul networks, the cost effcency optmzaton of 5G wreless backhaul networks s an nevtable problem. Consderng the sgnfcance of 5G wreless backhaul networks, some studes were dscussed n [5] [9]. The dfferences compared wth the conventonal massve MIMO for rado access networks and the benefts of the wreless backhaul employng massve MIMO were dscussed n [5]. In [6], Zhang et al. provded a state-of-the-art survey on large-scale (LS)-MIMO studes and proposed a jont group power allocaton and pre-beamformng scheme to substantally mprove the performance of LS-MIMO-based wreless backhaul for heterogeneous wreless networks. Based on the beam algnment technque usng adaptve subspace samplng and herarchcal beam codebooks, the mllmeter wave beamformng transmsson technology was developed for both wreless backhaul and access n small cell networks [7]. Dat et al. proposed and expermentally demonstrated a seamlessly converged rado-over-fber (RoF) and mllmeter-wave system at 9 GHz for hghspeed wreless sgnal transmsson [8]. An n-band soluton,.e., multplexng backhaul and access on the same frequency band, was proposed to solve the backhaul and nter base staton (BS) coordnaton challenges [9]. The above results confrmed the potental for employng

2 2 mllmeter wave transmsson technologes n wreless backhaul networks. Snce mllmeter wave transmsson technologes employng 6 GHz and 7 8 GHz are usually used for lne-of-sght (LOS) lnks n short ranges [], [], multhop transmssons s needed for long-range transmssons n wreless backhaul networks adoptng mllmeter wave transmsson technologes. Connectvty s an mportant ssue to make all the nodes n mult-hop networks nterconnected and reachable [2]. Some studes nvolved wth the connectvty of wreless backhaul networks were explored n [3] [6]. Amed at the jont maxmzaton of energy and spectrum effcency n wreless backhaul networks, a user assocaton scheme was developed for heterogeneous wreless network where small cells forward ther traffc through backhaul lnks to neghborng small cells untl t eventually reaches the core network [3]. Consderng the backhaul channel condtons and the qualty of servce requrements, an optmal jont routng and backhaul lnk schedulng scheme was proposed for a dense small cell network usng 6 GHz mult-hop backhaul lnks [4]. Utlzng d- ual connectvty establshment methods, a self-organzed mult-hop backhaul establshment procedure was developed to support autonomous bdrectonal beam algnments for heterogeneous wreless backhaul networks [5]. Extended from a graph theoretc clque dea, a new adaptve backhaul archtecture was proposed n [6] whch allows changes to the overall backhaul topology and each ndvdual backhaul lnk can vary ts frequency to meet traffc demand. To avod the blockage or lnk falure n mult-hop wreless backhaul networks, a group of super-bss was confgured to robustly relay backhaul traffc and mnmze the resource cost on gateways [7]. When wreless backhaul networks are provded by multple moble network operators (MNOs), a framework was proposed to optmze the route of wreless backhaul traffc based on the wreless channel condtons and economc factors among dfferent MNOs [8]. Hgher capacty and energy consumpton are requred to aggregate and forward the wreless traffc nto the next hop for aggregaton nodes closng to the core network, such as the gateways. Therefore, the backhaul capacty bottleneck exsts at the sngle gateway. However, the deployment of multple gateways n wreless backhaul networks has not been consdered n [4] [8]. In our prevous work [9], energy effcency of small cell backhaul networks was studed. Furthermore, a basc wreless backhaul network archtecture wth multple gateways confguratons was proposed n [2]. How to optmze the number and postons of multple gateways n 5G wreless backhaul networks s stll an open ssue. Besdes, the jont optmzaton of the multple gateways deployment and wreless backhaul lnks has not been nvestgated n 5G wreless backhaul networks. Moreover, the total cost effcency optmzaton for 5G wreless backhaul networks s surprsngly rare n the open lterature. Motvated by the above observatons, n ths paper we propose a two-scale cost effcency optmzaton soluton for 5G wreless backhaul networks. The contrbutons and noveltes of ths paper are summarzed as follows. ) In tradtonal network cost models, the gateway was fxed and the cost of wreless backhaul network was optmzed by the nterference management n wreless lnks [2]. To avod the performance loss due to the sngle objectve optmzaton, the multple performance aspects were formulated and optmzed wth a varety of system constrants n the mcrowave-based wreless backhaul network [22], [23]. To balance the wreless backhaul traffc n multple gateways, we propose a cost effcency model for 5G wreless backhaul networks consderng multple gateways deployment and mllmeterwave MIMO channel condtons. Snce the mllmeter wave transmsson dstance s short, the connectvty probablty and non-solaton probablty (probablty that all small cell are not solated) of 5G wreless backhual networks s analyzed. 2) To optmze the cost effcency of 5G wreless backhaul networks, a two-scale jont optmzaton soluton has been proposed. In the long tme scale, the number and postons of gateways are optmzed by the long tme optmzaton (LTO) algorthm. In the short tme scale, the wreless backhaul routngs are optmzed by the maxmum capacty spannng tree (MCST) algorthm. 3) Numercal results show that there exsts an optmal number of gateways for maxmzng the cost effcency of 5G wreless backhaul networks and the proposed algorthms are better than the conventonal and wdely used shortest path (SP) algorthm. The rest of ths paper s organzed as follows. Secton II descrbes the system model of 5G wreless backhaul networks. The cost effcency of 5G wreless backhaul networks s formulated n Secton III. Furthermore, a two-scale jont optmzaton soluton s proposed for the cost effcency optmzaton of 5G wreless backhaul networks n Secton IV. Smulaton analyss s presented n Secton V. Fnally, Secton VI concludes ths paper. 2 SYSTEM MODEL 5G dense small cell networks equpped wth massve MIMO antennas and mllmeter wave transmsson technology provde abundant resources, e.g. antennas and bandwdth, for wreless backhaul transmssons. In ths paper, the user capacty requrements are assumed to be fully satsfed and the cost effcency study therefore focuses on wreless backhaul networks. Consderng the large path loss fadng n mllmeter wave propagatons, the maxmum dstance of every hop n 5G wreless backhaul networks s lmted to D meters. The basc transmsson models studed n ths paper are descrbed

3 3 FTTC lnk Mllmeter wave lnk Control lnk macro cell BS connected wth each small cell BS Connecton cluster Fg.. System model. To core network Macro cell BS Small cell BS Specal small cell BS gateway n Fg.. To facltate readng, the notatons and symbols used n ths paper are lsted n Table. 2. Connecton Cluster Model The coverage of a macro cell BS (MBS) s assumed to be a crcle wth a radus R and a total of n small cell BSs (SBSs) are deployed n the coverage of the MBS. The MBS takes charge of the control plane and SBSs take charge of traffc transmsson n ths system. In ths paper, the 5G wreless backhaul network comprses of SBSs n the coverage of a MBS. The dstrbuton of SBSs s assumed to be governed by a Posson pont process wth densty µ. Every SBS can connect wth other SBSs wthn the dstance D. The dstance D s the maxmum transmsson dstance between two SBSs whch s determned by the SBS transmsson power. The set V ncludes n SBSs and s dvded nto connecton clusters. A group of SBSs s put nto a connecton culster f and only f these SBSs form a connected subnetwork. A par of SBSs are connected f the dstance between them s smaller than or equal to D. A set of SBSs form a connected subnetwork f and only f there s a path between any SBSs n the set to any other SBSs n the set. Let B be the total number of connecton clusters. There s no lnk between two connecton clusters. The algorthm for formng connecton clusters s gven n Algorthm. Usng the algorthm of formng connecton clusters, n SBSs are dvded nto B connecton clusters. To guarantee the forwardng of wreless backhaul traffc to the core network, every connecton cluster must have at least one SBS confgured as a gateway to connect wth the core network. Therefore, the number of gateways must be larger than or equal to the number of connecton clusters,.e., M B. 2.2 Network Transport Capacty Model Wthout loss of generalty, we assume that there are M SBSs out of the total n SBSs confgured as gateways, whch connect to the core networks by FTTC lnks. It follows that the number of the rest non-gateway SBSs s equal to N = n M. In ths study we focus on the wreless backhaul traffc,.e., the traffc transmtted from N SBSs to the M gateways, as the FTTC lnks connectng the gateway SBSs to the core network are consdered to have ample bandwdth. Let N χ,j,t be the number of bts transmtted by the SBS SBS and whch reached,.e., successfully receved by, the respectve gateway GW j durng a tme nterval [, T ], wth T beng an arbtrarly large number. The superscrpt χ Ω represents the spatal and temporal schedulng algorthm used n the wreless backhaul network and Ω denotes the set of all schedulng algorthms. We focus on the optmzaton of wreless backhaul networks. Thus, n ths paper the spatal and temporal schedulng algorthm nvolves the selecton strategy of backhaul gateways and wreless backhaul routngs n 5G networks. If the same bt s transmtted from a SBS to multple gateways, e.g., n the case of multcast, t s counted as one bt n the calculaton of N χ,j,t. It s assumed that the wreless backhaul network s stable. A wreless backhaul network s called stable f and only f the long-term ncomng traffc rate nto the wreless backhaul network equals the long-term outgong traffc rate. It s further assumed that there s no traffc loss caused by queue overflow. The transport capacty of network usng the spatal and temporal schedulng algorthm χ n a connecton cluster wth M gateways and N SBSs, denoted by C χ (M, N), s defned as: C χ (M, N) = lm T N M N χ,j,t = j= T. () In ths paper the transport capacty of network s focused on the wreless backhaul traffc n 5G dense small cell networks, whch s calculated by the number of bts successfully transmtted among dfferent SBSs [24]. Hence, the transport capacty of network wth M gateways and N SBSs n the wreless backhaul network s defned by C(M, N) = max χ Ω Cχ (M, N). (2) Consderng M gateways deployed n the wreless backhaul network, the average throughput of each gateway s gven by C(M, N) = C(M, N) M. (3) 2.3 Lnk Traffc Model Assume that there exst K types of wreless traffc n the wreless backhaul network. The set ncludng all types of wreless traffc, such as vdeo stream and voce traffc, s denoted as K := {,..., τ,..., K} and the set of all lnks s denoted as L for the wreless backhaul network. Wthout loss of generalty, the τ th type of wreless traffc s assumed to be transmtted by the lnk l L(τ) and the average transmsson rate of the τ th wreless traffc s

4 4 TABLE Notatons and symbols Notaton Descrpton V The set of n SBSs B The total number of connecton clusters n, M, N The number of small cell BSs (SBSs), the number of SBSs confgured as gateways, and the number of the rest non-gateway SBSs, respectvely χ χ Ω represents the spatal and temporal schedulng algorthm used n the wreless backhaul network and Ω denotes the set of all schedulng algorthms N χ The number of bts transmtted by the SBS SBS and whch reached,.e., successfully receved,j,t by, the respectve gateway GW j durng a tme nterval [, T ] C χ (M, N) The transport capacty of network usng the spatal and temporal schedulng algorthm χ n a connecton cluster wth M gateways and N SBSs C(M, N) The transport capacty of network wth M gateways and N SBSs n wreless backhaul network C(M, N) The average throughput of each gateway K The set of all types of wreless traffc L The set of all lnks for the wreless backhaul network a τ, a τ The average transmsson rate of the τ th wreless traffc and the th SBS SBS wth the τ th wreless traffc, respectvely rj τ, rτ q The ncomng and outgong transmsson rates of the SBS SBS wth the τ th traffc type d τ The destnaton for the τ th traffc L n, Lout The set of nput lnks and the set of output lnks at the SBS SBS, respectvely V n, V out V n = {SBS j : (SBS, SBS j ) L n }, Vout = {SBS j : (SBS, SBS j ) L out }, denote the set of nput SBSs and the set of output SBSs wth respect to the SBS SBS, respectvely c l The capacty of the lnk l rl τ The transmsson rate of the τ th traffc at the lnk l Ψ The large scale fadng over the mllmeter wave lnk H The wreless channel matrx of SBSs η The number of path between transmtter and the recever α u The small scale fadng over the u th path θu, r θu t The angle of arrval (AOA) and the angle of departure (AOD) for the u th path, respectvely a r (θu), r a t (θu) t The recevng and transmttng antenna array response vectors, respectvely s The sgnal vector for the SBS SBS NS,T The number of data streams at every SBS x, y q The transmtted sgnal at the SBS SBS and the receved sgnal at the SBS SBS q P The transmsson power at the SBS SBS n The addtve whte Gaussan nose (AWGN) wth varance σ 2 N(A) The number of SBSs n the specal coverage of the MBS wth the area A D n The maxmum value of the set of {D }, where D s the dstance between a SBS SBS, n, and ts closest SBS D con The longest lnk n the mnmal spannng tree when all SBSs n the coverage of the MBS are connected by a mnmal spannng tree W,W S The transmsson rate of wreless backhaul traffc at the SBS SBS and the transmsson rate of backhaul traffc generated by a gateway, respectvely Y χ (M, N) The average number of transmssons for transmttng a bt to a gateway Ξ j The set of SBSs assocated wth the gateway GW j t χ,j,k,l The tme requred to transmt b,j,k n the l - th transmsson ymax χ The maxmum number of hops n all routes of wreless backhaul network wth the spatal and temporal schedulng algorthm χ α A small postve constant, ndependent of T e(m, N) The cost effcency of 5G wreless backhaul network wth M gateways and N SBSs The total emboded energy and the total operaton energy of wreless backhaul network, the E EM,E OP,E G addtonal expense used for deployng the gateway, respectvely W The average transmsson rate of wreless backhaul traffc n the lfetme of the SBS P OP, P OP 2 The total operaton energy consumed by gateways and SBSs, respectvely N, M The set of non-gateway SBSs and gateway SBSs, respectvely SE l The spectrum effcency over the lnk l B (c) 28 IEEE. s The bandwdth of lnk l Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

5 5 Algorthm The generatng algorthm of connecton cluster. Input: The locaton of all the small cell BSs {(x p, y p ), SBS p V}, n ) Intalzaton: The connecton cluster Υ =, the number of clusters s B =, the temporary cluster s Θ =, v =, t =. 2) whle v < n do Θ = ; v v + ; t f B > then for = : B do for j = : Φ do The dstance between small cell BS SBS v and SBS j s D vj : D vj (x v x j ) 2 + (y v y j ) 2 ; end f end for end for end f f D vj D then f t == then else Θ = Θ + {SBS p, SBS p Φ } ; t t + ; break; B B + ; Φ B = {SBS v } ; Φ B = {SBS q, SBS q Θ} + {SBS v } ; Delete the clusters whch have been put nto Φ B and label the elements n Υ n the orgnal order. end f end whle Output: Connecton clusters Υ = {Φ }, =, 2,...B. assumed as a τ. The average transmsson rate of the th SBS SBS wth the τ th wreless traffc s denoted as a τ, whch s used to evaluate the ncomng traffc rate and outgong traffc rate n a network. Hence, f the SBS SBS s the traffc source of the τ th traffc then a τ = aτ. If the SBS SBS s the traffc destnaton of the τ th traffc then a τ = aτ. If the SBS SBS s the relayng SBS of the τ th traffc then a τ =, whch ndcates the SBS nether ncome the τ th traffc nor outgo the τ th traffc n the wreless backhaul network. The formulaton of a τ s expressed by a τ = a τ, f SBS s source of τ th traffc a τ, f SBS s destnaton of τ th traffc, otherwse (4) The ncomng and outgong transmsson rates of the SBS SBS wth the τ th traffc type are denoted as r τ j and r τ q, respectvely. When the SBS SBS s confgured as the source or relay SBS, the nput traffc of the τ th traffc, ncludng the ncomng traffc and the generated traffc. a τ, s equal to the output traffc of the τ th traffc at the SBS SBS [25], whch s expressed by a τ + SBS j V n r τ j = SBS q V out r τ q, SBS V, SBS d τ, τ K, (5) where d τ s the destnaton for the τ th traffc, the set of nput lnks and the set of output lnks at the SBS SBS s denoted by L n and L out, the set of nput SBSs and the set of output SBSs wth respect to the SBS SBS are denoted by V n = {SBS j : (SBS, SBS j ) L n } and V out = {SBS j : (SBS, SBS j ) L out }, respectvely. The capacty of the wreless lnk l s denoted as c l. The transmsson rate of the τ th traffc at the lnk l s denoted as rl τ. When dfferent types of wreless traffc are multplexed over the same lnk l, the sum transmsson rate of dfferent types of wreless traffc should be less than or equal to the capacty of wreless lnk l whch s

6 6 expressed as rl τ c l, l L. (6) τ K 2.4 Wreless Transmsson Model Every SBS s equpped wth N T and N R antennas for wreless transmsson and recepton, respectvely. The mllmeter wave frequency s adopted for wreless transmsson n the wreless backhaul network. The large scale fadng over the mllmeter wave lnk s expressed by wth Ψ=β+γlog + S, β = 2log ( 4π λ (7a) ), (7b) where λ s the wave length, γ s the path loss coeffcent, s the dstance between the transmtter and recever, S s the shadowng fadng effect followng a Gaussan dstrbuton wth zero mean and varance ξ 2,.e., S N (, ξ 2). Assume that the mllmeter wave transmsson of S- BSs s lmted to lne-of-sght (LOS) transmssons. The wreless channel matrx of SBSs s expressed by [26] N T N R η H = Ψ η α u a r (θu)a r t (θu) t u= (8a) N T N R = Ψ η A RDA T, wth A R = [ a r (θ r ) a r (θ r 2)... a r (θ r η) ], A T = [ a t (θ t ) a t (θ t 2)... a t (θ t η) ], D = dag {α, α 2,..., α η }, (8b) (8c) (8d) where η s the number of paths between the transmtter and the recever, α u s the small scale fadng over the u th path and s a complex normally dstrbuted random varable wth zero mean and unt varance, θ r u s the angle of arrval (AOA) and θ t u s the angle of departure (AOD) for the u th path, a r (θ r u) and a t (θ t u) are the recevng and transmttng antenna array response vectors, respectvely. θ r u and θ t u are assumed to be unformly dstrbuted n the range of [, 2π] and then a r (θ r u) and a t (θ t u) are extended by [5] a r (θ r u) = NR [, e j2πd sn(θr u )/λ,..., e j2π(n R )d sn(θ r u )/λ] T, (9) a t (θu) t = [, e j2πd sn(θt u )/λ,..., e j2π(n T )d sn(θ t )/λ] T u, NT () where d s the dstance among antennas. The mllmeter wave MIMO transmsson system n the 5G wreless backhaul network s llustrated n Fg. 2. For the mult-pont to sngle-pont transmsson lnk l n 5G wreless backhaul network, the transmtters nclude Small cell BS p N p S, T Dgtal precodng Dgtal precodng T N RF Analog precodng Analog precodng NT Mm Wave MIMO channel N N R R Analog combnng n p q out R N N RF S, R N S, T N T Dgtal combnng Small cell BS Addtonal stream Dgtal precodng Dgtal precodng T N RF Analog precodng Analog precodng N T Mm Wave MIMO channel Small cell BS q R q N N RF N R S, T Fg. 2. The mllmeter wave MIMO transmsson system. Q SBSs each equpped wth N T antennas and the recever s a SBS equpped wth N R antennas. Moreover, the number of antennas at recevers s assumed to be no less than Q tmes of the antenna number at transmtters [27],.e., N R QN T, for spatal multplexng. The numbers of rado frequency (RF) chans at the transmtter and recever are NRF T and N RF R, respectvely. For the SBS SBS, the sgnal vector s consstng of NS,T data streams s processed by the dgtal precodng P D N T RF N S,T and then transmtted nto NRF T RF chans. Furthermore, the sgnal passed through RF chans s transmtted nto N T transmsson antennas by the analog precodng P A N T N T RF. Hence, the transmtted sgnal at the SBS SBS s expressed by x = P A P D s. When the dgtal and analog precodng methods s adopted for the beamformng n mllmeter wave wreless transmssons, the nterference from the wreless backhaul transmsson of adjacent SBSs s assumed to be gnored n ths paper. When x s receved by the SBS SBS q wth N R receve antennas, the receved sgnal s expressed by y q = P H l P A P D s + n, () where P s the transmsson power at the SBS SBS, n s the addtve whte Gaussan nose (AWGN) wth varance σ 2. Furthermore, the sgnal y q s processed by the analog decodng F A C N R N R RF and the dgtal decodng F D C N R RF N S,T. In the end, the receved data streams are expressed by ỹ q = P F DF AH l P A P D s + F DF An. (2) 3 COST EFFICIENCY FORMULATION 3. Connectvty Probablty and the Probablty of Nodes Beng Non-solated The probablty that there exst n SBSs n a specal coverage wth area A s expressed by µa (µa)n P r [n SBSs n A] = e. (3) n! Based on the system model n Fg., n ths paper all SBSs are coveraged by a MBS. In ths case, a SBS s solated when the SBS can not establsh a backhaul lnk Analog combnng Dgtal combnng

7 7 2 R D R D D 2 D 2 r D ' r (a) (b) (c) Fg. 3. Coverage regons of the MBS and SBSs R Probablty P(non-so SBS), NUM P(non-so SBS), MC P(con), MC (/km 2 ) /( R ) wth other SBSs n the gven coverage of the same MBS. As shown n Fg. 3(a), the coverage area of a MBS s dvded nto a crcular regon A wth a radus R D (blue dsk) and a annulus A 2 wth an nner radus of R D and an outer radus of R (yellow rng). When a SBS s located n the crcular regon A, the coverage area of the SBS n the coverage area of the MBS s A (r) = πd, 2 whch s depcted n Fg. 3(b). When a SBS s located n annulus A 2, the coverage area of the SBS n the coverage area of the MBS s A (r) = D 2 arccos r2 +D 2 R2 2D r + R 2 arccos r2 D 2 +R2 2Rr 2 ξ, R D r R, wth ξ = (r + D + R)( r + D + R)(r D + R)(r + D R), whch s presented n Fg. 3(c). Based on the llustraton n Fg. 3, the probablty that a SBS s solated s expressed by P (SBS s solated) = P (SBS s solated SBS s n A ) P (SBS s n A ) +P (SBS s solated SBS s n A 2 ) P (SBS s n A 2 ) =e µa(r) π(r D ) 2 πr 2 + R R D e µa (r) 2πr dr πr 2. (4) Furthermore, the probablty that there s no solated SBS n the coverage of the MBS s expressed by P (non so SBS) = ( P (SBS s solated)) E(N(A)) = ( P (SBS s solated)) µπr2, (5) Where E( ) s the expectaton operaton, N(A) s the number of SBSs n the specal coverage of the MBS wth the area A. The probablty that all SBSs are connected n the coverage of the MBS s denoted by P (con). The event that there s no solated SBS n the coverage of the MBS s the necessary condton for the event that all SBSs are connected n the coverage of the MBS. Hence, we can get a constran as P (con) P (non so SBS). To valdate ths constran, P (con) and P (non so SBS) are smulated by Monte Carlo (MC) and numercal (Num) methods n Fg. 4, where the radus of coverage of the MBS s R = 5 meters and the radus of SBS s D = 2 meters. From Fg. 4, the numercal and the MC results of P (non so SBS) are concdent. Ths result mples that the expresson of P (non so SBS) s reasonable. When the value of SBSs densty µ s larger than or equal to 26, P (non so SBS) s approxmated wth P (con). Therefore, we derve the followng Theorem. Fg. 4. P (non so SBS) and P (con) Theorem : When the coverage radus of the MBS R and the coverage radus of SBSs D are gven, f the densty of SBSs s large enough (for example, / ( πr 2) can be one of the thresholds, as shown n Fg. 4), the probablty that there s no solated SBSs n the coverage of the MBS and the probablty that all SBSs are connected n the coverage of the MBS have the followng relatonshps:p (non so SBS) P (con), P (non so SBS) and P (con). Proof: When the densty of SBSs dstrbuton s confgured as µ, the dstance between a SBS SBS, n and ts closest SBS s D, the maxmum value of the set of {D } s denoted as D n, whch s the mnmum value for satsfyng the constrant that there s no solated SBS n the coverage of the MBS. When all SBSs n the coverage of the MBS are connected by a mnmal spannng tree, the longest lnk n the mnmal spannng tree s denoted as D con, whch s the mnmal value for satsfyng the constrant that all SBSs are connected n the coverage of the MBS. Based on results n [28], when the densty of SBSs n a square area s large enough, the value of D n wll approach to the value of D con,.e., lm P n (Dn = D con ) =. When the densty µ of SBSs n a crcular area s large enough and the value of D s fxed, we can derve a smlar result,.e., P (non so SBS) P (con), P (non so SBS) and P (con). Based on Theorem, we can use the value of P (non so SBS) to replace the value of P (con) n the followng smulaton analyss when the densty of SBS n the coverage of the MBS s large enough, e.g., / ( πr 2). 3.2 Network Transport Capacty of Wreless Backhaul Networks The optmzaton of wreless backhaul network can be acheved by the optmzaton of every connecton cluster n the wreless backhaul network. Therefore, we propose the Theorem 2 to defne the network transport capacty of a connecton cluster n the wreless backhaul network. Theorem 2: In the wreless backhaul network, the network transport capacty of a connecton cluster consstng of M gateways and N SBSs satsfes:

8 8 N W = C(M, N) mn max χ Ω Y χ (M, N) + M W S, M W G, M < n, (6a) W = a + r j. (6b) SBS j V n where W, N s the transmsson rate of wreless backhaul traffc at the SBS SBS, whch ncludes the generated traffc a from the SBS SBS and the ncomng transmsson rate at the SBS SBS. The SBS j V n generated traffc a from the SBS SBS s calculated by =, where K s the set ncludng all types of a a τ τ K wreless traffc. rj τ s the ncomng transmsson rates of the SBS SBS wth the τ th traffc, whch s calculated by r j = rj τ. Y χ (M, N) s the average number of τ K transmssons for transmttng a bt to a gateway. W S s the transmsson rate of backhaul traffc generated by a gateway, whch s confgured to be the same for every gateway. W G s the gateway maxmum transmsson rate of backhaul traffc whch ncludes the forwardng rate of wreless backhaul traffc generated from other SBSs and the transmsson rate of backhaul traffc generated by a gateway. The set of SBSs assocated wth the gateway GW j,.e., forwardng wreless backhaul traffc nto the gateway GW j, s denoted as Ξ j. Consderng the functon of gateway n wreless backhaul network, the sum of the forwardng rate of wreless backhaul traffc generated from other SBSs and the transmsson rate of backhaul traffc generated by a gateway should be less than or equal to the gateway maxmum transmsson rate,.e., W + W S W G, GW j V. SBS Ξ j Proof: Let b,j,k be the k - th bt transmtted from the SBS SBS to ts destnaton gateway GW j, h χ,j,k be the number of transmssons requred to delver b,j,k to ts destnaton gateway when the spatal and temporal schedulng algorthm χ Ω s adopted. The average transmsson number for transmttng a bt nto a gateway s derved by Y χ (M, N) = lm T r j N M N χ,j,t h χ,j,k = j= k= N M N χ,j,t = j=. (7) Consderng the stablty of wreless backhaul networks, the backhaul traffc at all SBSs are less than or equal to the backhaul traffc at all gateways. In ths case, the backhaul traffc at all SBSs at a tme slot s denoted by N W n the wreless backhaul network. The average = backhaul traffc of a SBS s denoted by N W = N n the wreless backhaul network. Let t χ,j,k,l, l hχ,j,k, be the tme requred to transmt b,j,k n the l - th transmsson n the wreless backhaul network and s derved by t χ,j,k,l = N. N W = Remark. The total transmsson tme s frst consdered as the amount of traffc transmtted, measured n bts, multpled by the tme requred to transmt each bt, n the wreless backhaul network on the ndvdual SBS. Moreover, the total transmsson tme n the wreless backhaul network can also be calculated on the network level by evaluatng the number of smultaneous transmssons n the entre wreless backhaul network. Obvously, the two values of total transmsson tme consderng at SBSs and network level must be equal. On the bass of ths observaton, the Theorem 2 can be establshed. At tme T, the total transmsson tme T total durng [, T ] ncludes the transmsson tme T gate for backhaul traffc that has reached ts gateway and the transmsson tme T norm for backhaul traffc stll n the transt at SBSs,.e., T total = T gate + T norm. Moreover, the transmsson tme T gate s calculated by T gate = N M N χ,j,t = j= k= = h χ,j,k l= = N N M N W = j= N χ,j,t k= t χ,j,k,l h χ,j,k. (8) Let ymax χ be the maxmum number of hops n all routes of wreless backhaul network wth the spatal and temporal schedulng algorthm χ, obvously ymax χ N. Snce the wreless backhaul network s stable, there exsts a small postve constant α, ndependent of T, such that the total amount of backhaul traffc n transt s bounded by αn. Hence T norm y χ maxαnt χ,j,k,l αn 2 t χ,j,k,l = αn 3. N W = (9) On the other hand, the total transmsson tme durng [, T ] calculated on the network level equals T total = N T. Therefore, N N M N W = j= = N χ,j,t k= h χ,j,k + T norm = N T. (2) When the tme nterval of [, T ] s suffcently large and the wreless backhaul network s stable, the amount of traffc n transt s neglgbly small compared wth the amount of traffc that has already reached ts gateway.

9 9 Furthermore, we can obtan the followng result: N M N χ,j,t h χ,j,k = j= k= lm T N W T = =. (2) Based on (), (7) and (2), the transport capacty usng the spatal and temporal schedulng algorthm χ n a connecton cluster wth M gateways and N SBSs s derved by N W = C χ (M, N) = Y χ (M, N) + M W S. (22) Based on (2), the network transport capacty of a connecton cluster conssted of M gateways and N SBSs s derved by C(M, N) = max χ Ω N W = Y χ (M, N) + M W S. (23) Consderng the maxmum forwardng capacty of M gateways M W G and the stablty of wreless backhaul networks, the network transport capacty of a connecton cluster conssted of M gateways and N SBSs satsfes: mn max χ Ω N W = Y χ (M, N) + M W S, M W G. (24) 3.3 Formulaton and Decomposton of Cost Effcency Optmzaton Wth the massve MIMO and mllmeter wave communcaton technologes adoptng at 5G SBSs, SBSs have enough transmsson rates used for wreless backhaul transmssons. However, the cell sze of SBSs s obvously reduced, e.g. the coverage radus of 5 meters. To guarantee the seamless coverage of 5G small cell networks, SBSs have to be deployed by an ultra-dense deployment soluton. Hence, there exst a large number of SBSs n the 5G wreless backhaul network. Based on the Theorem, SBSs n a gven coverage, e.g. the coverage of a macro cell, are formed nto one connecton cluster f the densty of SBSs s larger than a specfc threshold. Consderng that SBSs are ultra-densely deployed n the 5G wreless backhaul network, all SBSs are assumed to be formed nto one connecton cluster n 5G wreless backhaul network. Based on the Theorem 2, the network transport capacty of wreless backhaul network ncreases wth the ncrease of the number of gateways. However, the cost of wreless backhaul network s mproved wth the ncreasng of the number of gateways. Hence, t s a key ssue for telecommuncaton provders to optmze the total cost effcent of 5G wreless backhaul networks. Based on the result of Theorem 2, the cost effcency of 5G wreless backhaul network wth M gateways and N SBSs s defned as: e(m, N) C(M, N) ζ (E EM + E OP ) + M E G, E OP = (P OP + P OP 2 ) T Lfetme, P OP = M (a P Norm W G /W + b), P OP 2 = N (a P Norm W / W + b), (25a) (25b) (25c) (25d) where E EM s the total emboded energy of wreless backhaul network whch s fxed as the 2% of whole energy consumpton of wreless backhaul network n the lfetme [], E OP s the total operaton energy of wreless backhaul network, whch s calculated by the total operaton energy consumed by gateways P OP and the total operaton energy consumed by SBSs P OP 2 n the lfetme of gateways and SBSs, W s the average transmsson rate of wreless backhaul traffc n the lfetme of the SBS, whch s a constant. P Norm s the normalzed transmsson power assocated wth the normalzed transmsson rate W at the gateway and SBS, a and b are fxed coeffcents for computng the operaton energy consumpton [], ζ s the converson factor between the energy consumpton and cost expense, E G s the addtonal expense used for deployng the gateway. Furthermore, the cost effcency optmzaton of 5G wreless backhaul networks s formulated as max e(m, N) M,W,χ Ω s.t. () W c l, l L out, SBS N (2) a τ + rp τ = SBS p V n SBS q V out SBS V, SBS d τ, τ K (3) P P max, SBS N, r τ q, (26) where N s the set of non-gateway SBSs(and M, appearng n the next formula, s the set of gateway SBSs), P max s the maxmum transmsson power at the SBS. To keep the stable of wreless backhaul networks, the flow balance constrant,.e., (5) must be satsfed for the transport capacty of network n evaluatng the cost effcency of 5G wreless backhaul networks. To optmze the cost effcency of wreless backhaul networks, the optmzaton of gateways and wreless backhaul routes need to be solved for wreless backhaul networks. In general, the optmzaton of gateways, ncludng the confguraton of the number and locatons of gateways, can stay for a long tme after the wreless backhaul network has been deployed. Hence, the optmzaton of gateways n wreless backhaul networks can be updated n a long tme scale. When the number and locatons of gateways are fxed, based on (25b), (25c) and (25d), W G and W can be confgured as constants for the cost effcency of 5G wreless backhaul networks n the long tme scale. In ths case,

10 the energy consumpton of wreless backhaul network s assumed to be changeless. Furthermore, the optmzaton of cost effcency s smplfed to the optmzaton of wreless backhaul transport capacty of network, whch benefts from the optmzaton of wreless backhaul routes. On the other hand, n the short tme scale, the wreless backhaul routes are changed consderng that the wreless channel capacty over every hop of wreless backhaul network s tme-varyng. As a consequence, a wreless backhaul routng scheme χ should be optmzed n the short tme scale of wreless backhaul networks. Based on the optmzaton requrements of wreless backhaul network n the long tme and short tme scales, a two-scale jont optmzaton soluton s formulated as follows: max e(m, N) M,W,χ Ω { max e(m, N), n long tme scale; M max W Cχ (M, N), n short tme scale.,χ Ω max e(m, N) M s.t. M N = V, M N = ϕ. max W,χ Ω Cχ (M, N) s.t. W c l, l L a τ + rp τ = SBS p V n SBS q V out SBS V, SBS d τ, τ K P P max, SBS N, r τ q, (27a) (27b) (27c) where and are operatons of unon and ntersecton on two sets, respectvely. Moreover, the channel status nformaton (CSI) s mportant for optmzng the wreless backhaul routes n wreless backhaul networks. Wthout loss of generalty, the followng assumptons of CSI s declared n ths study: ) Every SBS can obtan the local CSI whch ncludes the CSI over every wreless channel assocated wth the local SBS; 2) The macro cell BS can obtan all CSI of wreless channels n the wreless backhaul network; The spectrum effcency over the lnk l s expressed by ( IN SE l = log 2 S,T ) + P F σ 2 NS,T D F A H l P AP D P D P A H l F AF D. (28) Here, the nterference from other lnks s assumed to be gnored as [3]. Moreover, the transmsson capacty of the lnk l s derved by c l = B s SE l ( IN = B s log 2 S,T ) + P F σ 2 NS,T D F A H l P AP D P D P A H l F AF D, (29) where B s s the bandwdth of lnk l. Based on the precodng/decodng optmzaton algorthms n [29], the maxmum transmsson capacty of the lnk l can be acheved. As a consequence, the optmzaton of wreless backhaul route can be acheved by maxmzng the wreless transmsson capacty of every lnk n wreless backhaul networks. 4 OPTIMIZATION SOLUTION OF WIRELESS BACKHAUL NETWORKS In ths secton, we gve two algorthms to solve the twoscale jont optmzaton soluton of (27), respectvely. 4. Soluton of Long tme Scale Gateways Optmzaton When BSs ncludng the MBSs and SBSs are deployed n 5G dense small cell networks, the number and locatons of BSs are per-determned. In ths study, we frst select the number and locatons of gateways from the determned SBSs for maxmzng the cost effcency of wreless backhaul networks n long tme scale. For a connecton cluster wth n SBSs, we propose a new algorthm to obtan the optmal number and locaton of gateways when the locatons {(x, y ), n} of SBSs SBS are known. To easly desgn the optmzaton algorthm n the long tme scale, the transmsson rate of wreless backhaul traffc at SBSs s confgured as the maxmum transmsson rate W,.e., W = W, N. The network transport capacty of a connecton cluster s smplfed as C(M, N) max χ Ω NW Y χ (M, N) + M W S. (3) To optmze the cost effcency of wreless backhaul networks e(m, N), the network transport capacty of a connecton cluster needs to be maxmzed. To acheve the maxmum network transport capacty of a connecton cluster, the optmal soluton can be mplemented by a complete traversal method,.e., all combnaton of SBSs are consdered to fnd the optmal gateways, whch can be proposed n our prevous studes [2]. Consderng the system model n ths paper, the computaton complexty of optmal algorthm n [2] s O(nM+3). Thus, t wll cost much tme for a large number of teratons. Algorthm 2 proposed here s a more effcent traversal algorthm whch confgures an ntal set of gateways and then traverses the rest of gateways to replace the ntal gateways for maxmzng the network transport capacty. Compared wth the optmal algorthm n [2], the proposed Algorthm 2 s the suboptmal soluton to maxmze the network transport capacty of a connecton cluster. Algorthm 2 s developed as follows. The complexty of Algorthm 2 s analyzed n the followng. The core functons of Algorthm 2 nclude the functons of KnowGateway() and UnknowGateway(). The calculaton space of functons of KnowGateway() and UnknowGateway() depends on the number of SBSs n the coverage of MBS. The functons of KnowGateway() and UnknowGateway() must be convergent when

11 Algorthm 2 Long Tme Optmzaton Soluton. (Part I) Input: MAX_M, n, the locaton of all the small cell BSs {(x p, y p ), SBS p V} Output: M opt, PS M. for M = : MAX_M do The mnmum average hop number of wreless backhaul traffc n the M gateways macro cell s: The poston of M gateways are: mn Y χ (M, N) UnknowGateway ({(x p, y p ), SBS p V}, M) ; χ Ω end for Choose M makng energy effcency to be the bggest: PS M = {(x q, y q ), SBS q Φ G } ; M opt arg max e(m, N); M functon UnknowGateway ({(x p, y p ), SBS p V}, M) ) Intalzaton: Put all the small cell BSs nto the set of small cell BS Φ S and empty the set of gateway Φ G. 2) whle Φ G < M do Array = zeros for SBS : SBS Φ S do Put small cell BS SBS nto set Φ G : Φ G = Φ G + {SBS } ; Call functon KnowGateway, then save the result returned by KnowGateway nto an array Array: Array KnowGateway ({(x p, y p ), SBS p V}, Φ G, {(x q, y q ), SBS q Φ G }) ; Remove the small cell BS SBS out of set Φ G : Φ G = Φ G {SBS } ; end for Put the small cell BS SBS makng Array to be the bggest nto set Φ G, and remove t from the set of small cell BS Φ S : end whle 3) f M > then for SBS j : SBS j Φ G do k arg mn Array Φ G = Φ G + {SBS k } ; Φ S = Φ S {SBS k } ; Array = zeros, Array j KnowGateway ({(x p, y p ), SBS p V}, Φ G, {(x q, y q ), SBS q Φ G }) ; for SBS : SBS Φ S do Exchange SBS j wth SBS (Put SBS j nto the set of small cell, and remove t out of the set of gateway; Put SBS nto the set of gateway, and remove t out of the set of small cell), then Array KnowGateway ({(x p, y p ), SBS p V}, Φ G, {(x q, y q ), SBS q Φ G }) ; Exchange back SBS j wth SBS ; end for k arg mn Array Φ G = Φ G + {SBS k } ; Φ S = Φ S {SBS k } ; f k j then Exchange SBS j wth SBS k ; end f end for end f end functon

12 2 Algorthm 2 Long Tme Optmzaton Soluton. (Part II) functon KnowGateway({(x p, y p ), SBS p V}, M, {(x q, y q ), GW q M}) ) Intalzaton: For all the small cell BSs, state() =, SBS V M; All the gateways are hop BSs. 2) for GW j : GW j M do Empty all the sets Φ h, varable h ; Put gateway GW j nto Φ : Φ h = Φ h + {GW j } ; whle Φ h do for SBS k Φ h do for SBS V M do The dstance between small cell BS SBS and SBS s D k : D k (x x k ) 2 + (y y k ) 2 ; f state() == &&D k D then The mnmum hop number between small cell BS SBS and gateway GW j s h +, then put small cell BS SBS nto set Φ h+ and change the state of small cell BS SBS state() nto : hop(, j) h + ; Φ h+ = Φ h+ + {SBS } ; end f end for end for Search the small cell BSs whose mnmum hop number backhaulng to gateway GW j s h + : h h + ; end whle end for 3) The routng lnk wth mnmum hop number s selected for relayng the wreless backhaul traffc between the small cell BS SBS and the correspondng gateway: hop() mn hop(, j); GW j M 4) The mnmum average hop number of wreless backhaul traffc n the macro cell s calculated by: hop() 5) return mn χ Ω Y χ (M, N). end functon mn Y χ (M, N) χ Ω SBS V M V M ; the coverage of MBS s lmted. Hence the Algorthm 2 must be convergent. For the functon of KnowGateway() n the Algorthm 2, the worst case occurs when there s only one SBS n the range of one hop. In ths case, the complexty of functon KnowGateway() s O(n 3 ). Moreover, the functon KnowGateway() s called by the functon UnknowGateway() wth O(n) tmes. Furthermore, the total complexty of Algorthm 2 s O(n 4 ). 4.2 Soluton of Short Tme Scale Routes Optmzaton After the number and locatons of gateways are optmzed n the long tme scale, wreless backhaul routes of wreless backhaul networks can be optmzed n the short tme scale. Based on system model n Fg., all SBSs report the local CSI to the macro cell BS n a tme slot. The macro cell BS works out the optmal backhaul route nformaton and then sends the optmal backhaul route nformaton to all SBSs n the next tme slot, as depcted n Fg. 5. Based on the CSI reported by N SBSs, a drectonal connected graph wth weght G = (V, L) s formed for the wreless backhaul network wth M gateways, where V s the set of SBSs and L s the lnk set of wreless backhaul routes. A SBS can have multple nput lnks but only one output lnk n the weghted drectonal connected graph, where the weghts of drected lnks correspond to the traffc rates. In the end, the wreless backhaul route has a tree topology wth the root node at a gateway. If there are multple gateways n the wreless backhaul network, the wreless backhaul routes are represented by multple tree topologes n the wreless backhaul network,.e., every tree topology has a root

13 3 c l Macro cell BS Small cell BS N _ hop and W of small cell BS SBS of the lnk l, l Fg. 5. Wreless backhaul route schedule process node at a gateway. In ths case, the short tme scale optmzaton soluton s obtaned by frst translatng the weghted drected connected graph nto multple tree topologes. Moreover, the generated tree topology can maxmze the network transport capacty of a connecton cluster and satsfy three constrans: a) the root node of the tree topology s a gateway; b) the transmsson rate of SBS wreless backhaul traffc, whch corresponds to the weght of correspondng drected lnk, s less than or equal to the wreless channel capacty; c) the wreless backhaul traffc need to be balanced at SBSs. Furthermore, the average transmsson number s calculated by Y χ (M, N) = N hop = out N, (3) where hop s the hop number between the SBS SBS and the gateway. Thus, the network transport capacty of wreless backhaul network s calculated by N N W = C(M, N) = max. (32) χ Ω N hop = Based on three constrans and (32), a maxmum capacty spannng tree (MCST) algorthm s developed to obtan the tree topology wth maxmum network transport capacty T = (U, T L), where U s the set of nodes, T L s the lnk set. The detal MCST algorthm s llustrated n Algorthm 3. The calculaton space of Algorthm 3 depends on the set whch ncludes all gateways n the coverage of MBS. The Algorthm 3 must be convergent when the number of gateways s lmted n the coverage of MBS. The complexty of Algorthm 3 s O(n2). To optmzaton the cost effcency of 5G wreless backhaul networks, the number and locatons of gateways can be adjusted by Algorthm 2 per month/year and then the wreless backhaul routes can be adjusted by Algorthm 3 per hour/day. 5 SIMULATION RESULTS AND DISCUSSION Based on the proposed two-scale jont optmzaton algorthm, the effect of varous system parameters on the cost effcency and transport capacty of network s analyzed Cost effcency(mbps/ ) Cost effcency(mbps/ ) M= M=2 M=3 M=4 M=5 M=6 M=7 M=8 M=9 M= n (a)cost effcency of 5G wreless backhaul networks wth respect to the number of total SBSs wth dfferent number of gateways n (b) Cost effcency of 5G wreless backhaul networks wth respect to the number of total SBSs. Fg. 6. Cost effcency of 5G wreless backhaul networks wth respect to the number of total SBSs wth dfferent number of gateways. and compared by numercal smulatons n ths secton. Wthout loss of generalty, the number of data streams NS,T at every SBS s confgured to be the same. The maxmum transmsson rate of wreless backhaul traffc at every SBS s confgured as W = Gbps consderng the mllmeter wave technology. The detaled parameters of smulaton system are llustrated n Table 2. Fg. 6 llustrates the cost effcency of 5G wreless backhaul networks wth respect to the number of total SBSs wth dfferent number of gateways. When the number of gateways s fxed n Fg. 6(a), the cost effcency of 5G wreless backhaul networks ncreases wth the ncrease of the number of SBSs. When the number of total SBSs s fxed n Fg. 6(a), there s a maxmum cost effcency n 5G wreless backhaul networks wth dfferent number of gateways. The reason of exstng the maxmal value s that the cost of 5G wreless backhaul networks ncreases lnearly wth the ncrease of the number of gateways, but the transport capacty of network does not always substantally ncrease. Moreover, the number of gateways correspondng to the maxmum cost effcency ncreases wth the ncrease of the number of total SBSs n 5G wreless backhaul networks. Fg. 6(b) descrbes the cost effcency of 5G wreless backhaul networks wth respect to the number of total SBSs when the number of gateways s equal to 6. The results of Fg. 6(b) mply that the cost effcency approach to an upper lmt,.e.,.78 Mbps/, when the densty of SBSs s larger than 35.

14 4 Algorthm 3 MCST Algorthm. Input: The set of gateways M and the set of SBSs N, wreless channel capactes over all wreless lnks n the wreless backhual netwok. ) Intalzaton: The set of node U = M, the set of canddate lnks CL ncludng all lnks between nodes Z j M, j M and Z N, j N, the hop number between the gateway and the node Z j M s, empty the set of lnk T L. 2) whle V U do Traverse the lnk n the set of canddate lnks ((Z j, Z v ), Z j U, Z v V U), then choose the lnk makng ( U M +) Z U M ( ) W +W v,tmp Z U M hop +hop v,tmp to be the bggest capacty (where hop v,tmp hop j + s the number of hop between the gateway and a temporary node Z v,tmp V U, W and W v,tmp are restrcted by the constrans of b) and c)), then Put (Z j, Z v ) nto the set of lnks T L; Put Z v nto U: U=U+{Z v }; The number of hop hop v between the gateway and the node Z v s one more than the number hop j of hop between the gateway and the node Z j : hop v hop j + ; The next hop node N_hop v between the gateway and the node Z v s assgned by Z j : N_hop v =Z j ; Update the canddate lnks n CL: The set of canddate lnks CL only ncludes all lnks between nodes Z j U and Z v V U end whle Output: T L, N_hop. TABLE 2 Default parameters of smulaton systems Parameters Default values The maxmum dstance of every hop D 2 meters [3] The radus of macro cell R 5 meters The densty of SBSs n a wreless backhaul network µ / ( πr 2 km 2) The converson factor ζ /kwh [3] Lfetme of SBS T Lfetme 5 years [32] The fxed coeffcent a 7.84 The fxed coeffcent b 7.5 Watt The normalzed transmsson power at SBS P Norm Watt The normalzed transmsson rate at SBS W Gbps The addtonal expense used for deployng the gateway E 39 [33] Wave length of mllmeter wave λ 5 mllmeters Path loss coeffcent γ 2 Dstance among antennas d 2.5 mllmeters Number of transmsson antennas at SBS N T 6 Number of receve antennas at SBS N R 28 Number of RF chans at a transmtter NRF T 4 Number of RF chans at a recever NRF R 4 Number of data stream NS,T 2 The maxmum transmsson power P max Watt [34] The maxmum forwardng capacty of the gateway W G Gbps Bandwdth of SBSs B s GHz

15 Cost effcency(mbps/ ) M= M=2 M=3 M=4 M=5 M=6 M=7 M=8 M=9 M= W G (Gbps) Cost effcency(mbps/ ) x -4 M=3 M=4 M=5 M=6 M= SNR(dB) Fg. 7. Cost effcency of 5G wreless backhaul networks wth respect to the gateway maxmum transmsson rate consderng dfferent number of gateways. Fg. 9. Cost effcency of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. Network transport capacty(gbps) M=3 M=4 M=5 M=6 M= SNR(dB) Fg. 8. Network transport capacty of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. Fg. 7 shows the Cost effcency of 5G wreless backhaul networks wth respect to the gateway maxmum transmsson rate consderng dfferent number of gateways. When the number of gateways s fxed, the cost effcency of 5G wreless backhaul networks decreases wth the ncrease of the gateway maxmum transmsson rate. When the gateway maxmum transmsson rate s fxed, the cost effcency of 5G wreless backhaul networks frst ncreases wth the ncrease of the number of gateways and then decreases wth the ncrease of the number of gateways after the cost effcency reaches the gven maxmum. Fg. 8 shows the network transport capacty of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. When the number of gateways s fxed, the network transport capacty of 5G wreless backhaul networks ncreases wth the ncrease of SNR values over wreless channels. When the SNR value s fxed, the network transport capacty of 5G wreless backhaul networks ncreases wth the ncrease of number of gateways. Fg. 9 descrbes the cost effcency of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. When the number of gateways s fxed, the cost effcency of 5G wreless backhaul networks ncreases wth the ncrease of the SNR values over wreless channels. When the SNR Cost effcency (Mbps/ ) M=,MCST M=,BF M=,SP M=5,MCST M=5,BF M=5,SP SNR(dB) (a) Increment of cost effcency (Mbps/ ) M=,MCST-BF M=,MCST-SP M=5,MCST-BF M=5,MCST-SP SNR(dB) Fg.. Cost effcency of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. value s fxed over wreless channels, there s a maxmum cost effcency n 5G wreless backhaul networks wth dfferent number of gateways. Moreover, the optmal number of gateways correspondng to the maxmum cost effcency s 5. To compare the ncrement of cost effcency mproved by the MCST algorthm, the ncrement of cost effcency among the MCST, Bellman-Ford (BF) [35] and shortest path (SP) [36], [37] algorthms wth respect to the SNR values consderng dfferent numbers of gateways s llustrated n Fg. (b), n whch the ncrement between the MCST and BF algorthms s labelled as "MCST-BF" and the ncrement between the MCST and SP algorthms s labelled as "MCST-SP". When the number of gateway s confgured as, the maxmum ncrement of cost effcency are 94% and 38% between the MCST and BF algorthms and between the MCST and SP algorthms n Fg. (b), respectvely. When the number of gateways s 5, the maxmum ncrement of cost effcency are % and 3% between the MCST and BF algorthms and between the MCST and SP algorthms n Fg. (b), respectvely. Fg. descrbes the network transport capacty of 5G wreless backhaul networks wth respect to the MCST, BF and SP algorthms consderng dfferent SNR values. Based on the results n Fg. (a), the network transport capacty of MCST algorthm s always larger than that of BF and SP algorthms n 5G wreless backhaul networks. The reason of ths result s that the MCST algorthm can (b)

16 6 Network transport capacty(gbps) M=,MCST M=,BF M=,SP M=5,MCST M=5,BF M=5,SP SNR(dB) (a) Increment of network transport capacty(gbps) M=,MCST-BF M=,MCST-SP M=5,MCST-BF M=5,MCST-SP SNR(dB) Fg.. Network transport capacty of 5G wreless backhaul networks wth respect to the SNR over wreless channels and dfferent number of gateways. dynamcally change the routes as the wreless lnk states are changed. As a consequence, the wreless channel capacty of the routes scheduled by the MCST algorthm s larger than or equal to the wreless channel capacty of the routes scheduled by the BF and SP algorthms. When the number of gateway s confgured as, the maxmum network transport capacty of the proposed MCST algorthm s mproved by 77% and 38% compared wth the BF and SP algorthms n Fg. (b), respectvely. When the number of gateway s confgured as 5, the maxmum network transport capacty of the proposed MCST algorthm s mproved by % and 3% compared wth the BF and SP algorthms n Fg. (b), respectvely. Fg.6 and Fg. 7 analyze the mpact of number and locatons of gateways mplemented by Algorthm 2 on the cost effcency of 5G wreless backhaul networks. Consderng the number of SBSs and the gateway maxmum transmsson rate, the optmal number and locatons of gateways can be selected by Algorthm 2 whch can acheve the maxmum cost effcency of 5G wreless backhaul network n a long tme scale. Fg. 9 and Fg. nvestgate the mpact of wreless channel condtons mplemented by Algorthm 3 on the cost effcency of 5G wreless backhaul networks. When the optmal number of gateways s fxed by Algorthm 2, the wreless backhaul route can be selected by Algorthm 3 based on the wreless channel condtons,.e., SNR values n a short tme scale. Moreover, the ncrement between the Algorthm 3 and conventonal BF and SP algorthms s llustrated n Fg.. Based on the results of Fg. 6, Fg. 7, Fg. 9 and Fg., the cost effcency of 5G wreless backhaul networks can be mproved by Algorthm 2 and Algorthm 3. 6 CONCLUSIONS In ths paper, a two-scale cost effcency optmzaton algorthm s proposed for 5G wreless backhaul networks. In the long tme scale, the number and postons of gateways are optmzed by the LTO algorthm. In the short tme scale, the transport capacty of network s optmzed by the MCST algorthm. Numercal results show that there s an optmal number of gateways for the maxmum cost effcency of 5G wreless backhaul (b) networks and the MCST algorthm can sgnfcantly mprove the cost effcency of 5G wreless backhaul networks. Our results provde useful gudelne for the deployment and optmzaton of 5G wreless backhaul networks. REFERENCES [] I. Humar, X. Ge, L. Xang, J. Ho, and M. Chen, "Rethnkng energyeffcency models of cellular networks wth emboded energy," IEEE Network, vol.25, no.3, pp.4 49, Mar. 2. [2] N. Bhushan, J. L, D. Mallad and R. Glmore, "Network densfcaton: the domnant theme for wreless evoluton nto 5G," IEEE Commun. Mag., vol. 52, no. 2, pp , Feb. 24. [3] X. Ge, S. Tu, G. Mao, C.-X. Wang and T. Han, "5G Ultra-Dense Cellular Networks," IEEE Wreless Commun., vol. 23, no., pp.72 79, Feb. 26. [4] X. Ge, H. Cheng, M. Guzan and T. Han, "5G wreless backhaul networks: challenges and research advances," IEEE Network, vol. 28, no. 6, pp. 6, Nov. 24. [5] Z. Gao, L. Da, D. M, Z. Wang, M. A. Imran and M. Z. Shakr, "MmWave massve-mimo-based wreless backhaul for the 5G ultra-dense network," IEEE Wreless Commun., vol. 22, no. 5, pp.3 2, Oct. 25. [6] Z. Zhang, X. Wang, K. Long, A. V. Vaslakos and L. Hanzo, "Large-scale MIMO-based wreless backhaul n 5G networks," IEEE Wreless Commun., vol. 22, no. 5, pp.58 66, Oct. 25. [7] S. Hur, T. Km, D. J. Love, J. V. Krogmeer, T. A. Thomas and A. Ghosh, "Mllmeter wave beamformng for wreless backhaul and access n small cell networks," IEEE Trans. Commun., vol. 6, no., pp , Oct. 23. [8] P. T. Dat, A. Kanno, K. Inagak and T. Kawansh, "Hgh-capacty wreless backhaul network usng seamless convergence of radoover-fber and 9-GHz mllmeter-wave," J. Lghtwave Technol., vol. 32, no. 2, pp , Oct. 24. [9] R. Taor and A. Srdharan, "Pont-to-multpont n-band mmwave backhaul for 5G networks," IEEE Commun. Mag., vol. 53, no., pp. 95 2, Jan. 25. [] L. We, R. Hu, Y. Qan, and G. Wu, "Key elements to enable mllmeter wave communcatons for 5G wreless systems," IEEE Wreless Commun., vol. 2, no. 6, pp , Jan. 25. [] K. Zheng, L. Zhao, J. Me, M. Dohler, W. Xang, and Y. Peng, " Gb/s Hetsnets wth mllmeter-wave communcatons: Access and networkng Challenges and protocols," IEEE Commun., vol. 53, no., pp , Jan. 25. [2] X. Ta, G. Mao and B. D. Anderson, "On the gant component of wreless multhop networks n the presence of shadowng," IEEE Trans. Veh. Technol., vol. 58, no. 9, pp , Jun. 29. [3] A. Mesodakak, F. Adelantado, L. Alonso, M. D Renzo and C. Verkouks, "Energy and spectrum effcent user assocaton n mllmeter wave backhaul small cell networks," IEEE Trans. Veh. Technol., vol. PP, no. 99, pp., May. 26. [4] E. Pateromchelaks, M. Sharat, A. Ul Quddus and R. Tafazoll, "Jont routng and schedulng n dense small cell networks usng 6 GHz backhaul," n Proc. IEEE ICCW 25, pp , Jun. 25. [5] H. Mao and M. Faerber, "Self-organzed mult-hop mllmeterwave backhaul network: Beam algnment and dynamc routng," n Proc. IEEE EuCNC 25, Pars, pp , 25. [6] W. N, I. B. Collngs, X. Wang and R. P. Lu, "Mult-hop pont-topont FDD wreless backhaul for moble small cells," IEEE Wreless Commun., vol. 2, no. 4, pp , Aug. 24. [7] Y. H. Chang and W. Lao, "mw-herback: A Cost-Effectve and Robust Mllmeter Wave Herarchcal Backhaul Soluton for Het- Nets," IEEE, vol. 6, no. 2, pp , Dec. 27. [8] O. Semar, W. Saad, M. Benns and Z. Dawy, "Inter-Operator Resource Management for Mllmeter Wave Mult-Hop Backhaul Networks," IEEE Transactons on Wreless Communcatons, vol. 6, no. 8, pp , Aug. 27. [9] X. Ge, S. Tu, T. Han, Q. L, G. Mao, "Energy effcency of small cell backhaul networks based on GaussšCMarkov moble models," IET Networks, vol. 4, no. 2, pp , Mar. 25.

17 Ths artcle has been accepted for publcaton n a future ssue of ths journal, but has not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TMC , IEEE 7 [2] X. Ge, L. Pan, S. Tu, H. Chen and C. Wang, "Wreless backhaul capacty of 5G ultra-dense cellular networks," n Proc. IEEE VTCFall, Montreal, Sep. 26. [2] Taghzadeh, Omd, et al. "Envronment-Aware Mnmum-Cost Wreless Backhaul Network Plannng wth Full-Duplex Lnks." arxv preprnt arxv: (28) [22] Y. L, A. Ca, G. Qao, L. Sh, S. K. Bose and G. Shen, "MultObjectve Topology Plannng for Mcrowave-Based Wreless Backhaul Networks," IEEE Access, Vol. 4, pp , 27 [23] Y. L, G. Qao, A. Ca, L. Sh, H. Zhao and G. Shen, "Mcrowave backhaul topology plannng for wreless access networks," 24 6th Internatonal Conference on Transparent Optcal Networks (ICTON), Graz, 24, pp. -4. [24] G. Mao, Z. Ln, X. Ge and Y. Yang, "Towards a smple relatonshp to estmate the capacty of statc and moble wreless networks," IEEE Trans. Wreless Commun., vol. 2, no. 8, pp , August 23. [25] A. Lu, V. K. N. Lau, F. Zhuang and J. Chen, "Two tmescale jont beamformng and routng for mult-antenna D2D networks va stochastc cuttng plane," IEEE Sgnal Process., vol. 63, no. 8, pp , Sep. 25. [26] M. N. Kulkarn, A. Ghosh and J. G. Andrews, "A comparson of MIMO technques n downlnk mllmeter wave cellular networks wth hybrd beamformng," IEEE Trans. Commun., vol. 64, no. 5, pp , May 26. [27] G. Mao, "Energy-effcent uplnk mult-user MIMO," IEEE Trans. Wreless Commun., vol. 2, no. 5, pp , May 23. [28] M. D. Penrose, "The longest edge of the random mnmal spannng tree," Annals of Appled Probablty, vol. 7, no. 2, pp ,997. [29] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. P and R. W. Heath, "Spatally sparse precodng n mllmeter wave MIMO systems," IEEE Trans. Wreless Commun., vol. 3, no. 3, pp , Mar. 24. [3] S. Sun, T. S. Rappaport, R. W. Heath, A. Nx and S. Rangan, "Mmo for mllmeter-wave wreless communcatons: beamformng, spatal multplexng, or both?" IEEE Commun. Mag., vol. 52, no. 2, pp. 2, Dec. 24. [3] B. Lee and S. Km, "Characterzng energy and deployment effcency relatons n cellular systems," n Proc. IEEE ICSPCS 22, Gold Coast, QLD, pp. 5, Dec. 22. [32] X. Ge, B. Yang, J. Ye, G. Mao, C.-X. Wang and T. Han, "Spatal Spectrum and Energy Effcency of Random Cellular Networks," IEEE Trans. Wreless Commun., vol. 63, no. 3, pp. 9 3, March 25. [33] K. Johansson, "Cost effectve deployment strateges for heterogeneous wreless networks," Ph.D. dssertaton, KTH Info. and Commun. Tech., Stockholm, Sweden, Nov. 27. [34] X. Ge, Y. Sun, H. Gharav and J. Thompson, "Jont optmzaton of computaton and communcaton power n mult-user massve MIMO systems," IEEE Trans. Wreless Commun., vol. 7, no. 6, pp , Jun. 28. [35] B. Awerbuch, A. Bar-Noy, M. Gopal, "Approxmate dstrbuted Bellman-Ford algorthms." IEEE Trans. Commun., vol. 42, no. 8, pp , Aug [36] I. Banerjee, I. Roy, A. R. Choudhury, B. D. Sharma and T. Samanta, "Shortest path based geographcal routng algorthm n wreless sensor network," n In Proc. IEEE CODIS 22, Kolkata, pp , Dec. 22. [37] R. C. Prm, "Shortest connecton networks and some generalzatons," The Bell System Techncal Journal, vol. 36, no. 6, pp , Nov Xaohu Ge (M 9-SM ) s currently a full Professor wth the School of Electronc Informaton and Communcatons at Huazhong Unversty of Scence and Technology (HUST), Chna. He s an adjunct professor wth wth the Faculty of Engneerng and Informaton Technology at Unversty of Technology Sydney (UTS), Australa. He receved hs PhD degree n Communcaton and Informaton Engneerng from HUST n 23. He has worked at HUST snce Nov. 25. Pror to that, he worked as a researcher at Ajou Unversty (Korea) and Poltecnco D Torno (Italy) from Jan. 24 to Oct. 25. Hs research nterests are n the area of moble communcatons, traffc modelng n wreless networks, green communcatons, and nterference modelng n wreless communcatons. He has publshed more than 2 papers n refereed journals and conference proceedngs and has been granted about 25 patents n Chna. He receved the Best Paper Awards from IEEE Globecom 2. Dr. Ge served as the general Char for the 25 IEEE Internatonal Conference on Green Computng and Communcatons (IEEE GreenCom 25). He serves as an assocate edtor for IEEE Wreless Communcatons, IEEE Transactons on Vehcular Technology and IEEE ACCESS, etc. Song Tu receved hs B.E. degree and Master degree from Huazhong Unversty of Scence and Technology (Chna) n 24 and 27. Now he works n Huawe. Technologes Co. Ltd. Hs research nterests are n the area of green communcatons and publc cloud networks. Guoqang Mao (S 98-M 2-SM 8-F 8) joned the Unversty of Technology Sydney n February 24 as Professor of Wreless Networkng. Before that, he was wth the School of Electrcal and Informaton Engneerng, the Unversty of Sydney. He has publshed about 2 papers n nternatonal conferences and journals, whch have been cted more than 6 tmes. He s an edtor of the IEEE Transactons on Wreless Communcatons (snce 24), IEEE Transactons on Vehcular Technology (snce 2) and receved Top Edtor award for outstandng contrbutons to the IEEE Transactons on Vehcular Technology n 2, 24 and 25. He s a co-char of IEEE Intellgent Transport Systems Socety Techncal Commttee on Communcaton Networks. He has served as a char, cochar and TPC member n a number of nternatonal conferences. He s a Fellow of IET. Hs research nterest ncludes ntellgent transport systems, appled graph theory and ts applcatons n telecommuncatons, Internet of Thngs, wreless sensor networks, wreless localzaton technques and network performance analyss.

18 8 Vncent K. N. Lau obtaned B.Eng (Dstncton st Hons) from the Unversty of Hong Kong ( ) and Ph.D. from the Cambrdge Unversty ( ).He joned Bell Labs from and the Department of ECE, Hong Kong Unversty of Scence and Technology (HKUST) n 24. He s currently a Char Professor and the Foundng Drector of Huawe-HKUST Jont Innovaton Lab at HKUST. He s also elected as IEEE Fellow, HKIE Fellow, Croucher Senor Research Fellow and Changjang Char Professor. Vncent has publshed more than 3 IEEE journal and conference papers and has contrbuted to 5 US patents on varous wreless systems. Hs current research focus ncludes robust cross layer optmzaton for wreless systems, Massve MIMO, Compressed Sensng, Networked Control Systems as well as PHY Cachng for Wreless Networks. Lnghu Pan receved her B.E. degree and M.S. degree n communcaton engneerng from the Huazhong Unversty of Scence and Technology (HUST), Wuhan, Chna, n 25 and 28 respectvely. Her research nterests nclude the area of 5G networks and green communcatons.