A Load Balancing Mehod in Downlink LTE Nework based on Load Vecor Minimizaion Fanqin Zhou, Lei Feng, Peng Yu, and Wenjing Li Sae Key Laboraory of Neworking and Swiching Technology, Beijing Universiy of Poss and Telecommunicaions, Beijing, 100876, P. R. China Email: fqzhou01@bup.edu.cn Absrac Load balancing is one of he key arge of LTE Self- Opimizaion Nework (SON). In his paper, we propose a load balancing mehod for LTE downlink nework, namely Load Vecor Minimizaion based Load Balancing (LVMLB) mehod. Load Vecor (LV) is a vecor whose elemens are he load values of cells and sored in descending order. The order of LVs is defined by he lexicographical order. The smaller he LV is, he higher he balance degree of cells load will be. As he LV has a lower bound wih oal load fixed, he balance degree of cells load would reach a local opimal. On his basis, we design he LVMLB algorihm, rying o ge he opimal soluions o load balancing problems, he proof of being opimal will also be given in his paper. Simulaion scenarios are se in a square par of Macro- mixed HeNes. Simulaion resuls show ha LVMLB ouperforms he Cell Region Expansion (or Bias) scheme, increasing he capaciies of Macro and iers a he same ime, and improving balance degree of cells load, only sacrificing a lile QoS performance. Keywords cell load vecor; lexicographical order; LTE; load balancing. I. INTRODUCTION The unbalanced load disribuion in wireless communicaion sysem is ineviable, because of he randomness of user posiion and heir service saus. The evoluion of mobile phones bring an explosion of mobile users, which challenges he capaciy of he wireless access nework and raises higher requiremens o load balancing abiliy. Boh of he wo aspecs are considered in LTE design. The densiy of base saions is grealy raised so ha resources in uni area increase. As a resul, he capaciy of he whole wireless access nework is improved. Besides, HeNes, developed in 3G, are aken as basic pars of LTE radio access nework (RAN) archiecure. Through he flexible deploymen of Low-power Base Saions (LBS), no only he raffic pressure a high-load areas can be relieved, bu also he coverage holes a he edges of macro-cells can be easily compensaed, wihou disurbing he curren seing of enodebs. The capaciy of LTE sysem is furher enhanced. To faciliae load balancing, a Cell Individual Offse (CIO) parameer is designed in LTE o affec he handover procedures of users. By adjusing CIO, he acual coverage of LTE RAN will no be grealy influenced, compared wih oher mehods, such as power uning, or anenna iling. To reduce he managemen complexiy and operaional cos, he concep of self-organizing nework (SON) is inroduced in LTE, ha he nework is auonomously operaed o reducing manual inervenion. Load balancing is one of he key arge of SON [1]. LTE nework wih SON funcions configured will ransfer load from high load cells o heir low load neighbor cells auomaically, when he load saus of he nework reaches a rigger condiion, o mainain a proper load disribuion in he This research is suppored by NSFC 6171187 and 863 Program 013AA01350. nework. The use case given in [1] proposed a load balancing mehod based on CIO adjusmen. However, i is no a frozen sandard. In order o improve he efficiency and performance of load balancing, he algorihms or mehods of load balancing are sill worh deep research. New properies of dense small cell and HeNes also raise new requiremens o he curren LB mehods. Presen works on load balancing are shown below. A load balancing mehod is proposed in [], aiming a reducing he load of high load cells o cerain hreshold. S. Yang, e al, in [3], improve he former mehod by proposing a wo-hop scheme o make up he shorcoming ha when a cluser of cells are all of high load, he cener cell will no be able o ransfer is load. Mehod in [4] is o achieve load balancing by minimizing he load gap beween wo neighbor cells o cerain hreshold. However, all he mehods above have he limiaion ha hey depends on cerain predesign load hreshold. These predesign hreshold canno adap o he load saus of he nework, so he balance degree canno be furher improved. In addiion, he above mehods considers lile abou heir applicabiliy under HeNes scenarios. In [5] opimized cell selecions are made for mobile users under proporional fairness principle, bu i pays no aenion o he order of users in raversal process, which affecs he performance of LB. In [6] LB problem is ransformed ino a convex opimizaion problem, and opimal user-bs associaions can be found by solving i. However, his paper focus on he load balancing beween differen HeNes iers, raher han he load balancing among all cells. Besides, [5] [6] give merely user-bs associaions, lacking he pracical implemenaion procedures. To overcome he shorcomings of he above LB mehods, in his paper we propose a load balancing mehod whose main idea is he balance degree of nework load can be improved he mos by minimizing he load vecor. We firs give he definiion of Load Vecor (LV) and define a balancing degree funcion of he load of all cells in he nework, and hen we prove he value of he funcion is monoonically increasing wih he decrease of LV, which will ransform he load balancing problem of minimizing he funcion value o minimizing LV. Thus, he original load balancing problem is much easier o solve. The QoS of users are guaraneed by handover margin (HOM), which sands for he limi of CIO parameers. Users are no allowed o ransfer o neighbor cells, if heir RSRP suffer from a loss more han HOM. The res of his paper are organized as follows. Secion gives he problem formulaion, in which he sysem model and some relaed conceps are inroduced. In Secion 3, we describe he LVMLB mehod, including he basic principle, he deailed procedures, and also he convergence proof of i. Simulaion seings and resuls analysis will be given in secion 4, and he whole paper will be concluded in secion 5.
II. PROBLEM FORMULATION In his secion, we give he sysem model and basic conceps of LV, and describe he original load balancing problem wih a balancing degree funcion derived from Jain s fairness index formula [7]. By analyzing he funcion, i is easy o know ha he funcion value monoonically increases wih he decrease of LV. Therefore, we naurally ge he main idea of LVMLB. A. Sysem Model Consider a Macro- cell mixed HeNes scenario, as illusraed in figure 1. N cells in he nework forms a se B, which consiss of N 1 Macro cells in B 1 and N cells B. N 1 + N = N. M mobile users forms he se U. Mobile users access cells wih bes RSRP signals by defaul. For simpliciy, we assume a cell generaes a Uni Load (UL), when a user access he nework hrough i. Due o he resricion of resource blocks, he capaciy of each cell has an upper bound ρ max. If he load of BS i B reaches he bound, new users canno be admied o i and hus be blocked. The defaul user access scheme, MaxRSRP, can be described in formula 1 as follows. CellID serv (j) = arg max i B {RSRP ij} Fig. 1 Illusraion of Macro- Mixed HeNes. In LTE Macro- mixed HeNes, Macro BS and BS differ in he ransmi power and he size of hem [8], so in his paper we assume all BSs have he same load capaciy. However, because he ransmi power of Macro BS is abou 100 imes (0dB) of ha of BS [9], he defaul cell selecion scheme will bring abou he coverage dispariy of Macro and cells, causing he unbalanced load disribuion beween differen kinds of cells. Range expansion (Bias) scheme is proposed o deal wih i [7], ha he RSPR of LBSs are biased up so ha more users are end o access LBSs. In HeNes wih Bias scheme deployed, cell selecions of users are made according o formula. CellID serv (j) = arg max i B {RSRP ij + Bias i } However, Bias scheme can balancing he load among cells in he same ier. So oher schemes are needed. B. Problem Formulaion The funcion in formula 3, derived from Jain s fairness index, is widely used o evaluae he balance degree of cells load. Wherein, he ρ i sands for he load of BS i, and N is he number of base saions. The load of a UL is represened by e, and x ij indicaes wheher here is an associaion beween user j and BS i. x ij = 1 is for yes, and 0 for no. The value of he funcion is in he range of [1/N,1], and he bigger value means he load of cells is more balanced. f(ρ ) = ( i B ρ i ) N ( ρ i B i ) s.. ρ i = e j x ij 1 user j is serving by BS i x ij = { 0 user j is no serving by BS i Load vecor indicaes he load of all cells in descending order. Wih he help of neighbor cell informaion, a possible arge cell in each ieraion of load balancing can be easily specified. User j in BS i 1, for insance, wans o handover o neighbor cell BS i should saisfy he following simplified requiremen [10]. RSRP i j + CIO i1 i > RSRP i1,j Here for simpliciy we omi he hyseresis and fixed offse. The difference of RSPR i1 j and SRP i j, denoed as Pcos i1 i j, can be expressed as Pcos i1 i j = RSRP i1 j RSRP i j, which indicaes he RSRP sacrifice afer handover and he minimum value he CIO parameer should be adjused o. Users in cell i 1 can be sored on Pcos i1 i j, and smaller value means he corresponding user j is closer o he arge neighbor cell i and is more likely o be handed over. Moreover, only users who mee he requiremen in formula 4, which also means he Pcos should be less han he curren CIO value, can be handed over o heir arge cell. So he CIO parameer should be adjused according o Pcos. A large CIO value may lead o severe QoS deerioraion, as he RSPR drops oo much for he user of big Pcos value. So an upper bound of CIO, denoed as Handover Margin (HOM) is se. Users whose Pcos value exceed HOM will no be allowed o hand over and CIO will never be se a value bigger han HOM. Bigger HOM means more users can be reallocaed in load balancing, so he load in he nework can be more balanced. Bu he QoS of users afer load balancing may no be guaraneed. HOM is a radeoff beween he wo facors, and he value of HOM should be carefully designed. Relaed works have given empirical range of i. In his paper, we adop he value derived from simulaions. C. Definiions To faciliae he explanaion of LVMLB, some relaive erms are defined here. Definiion 1. Cell Load Vecor (CLV) is a vecor consising of he load values of all cells in descending order, denoed as ρ = (ρ 1, ρ,, ρ N ). Definiion. Lexicographical Order (LO). Two vecors, W 1 = (a 1, a,, a n ) and W = (b 1, b,, b n ), if i {i i < n, i \Z + } indicaes he index of he firs elemen ha a i b i, hen a i > b i means W 1 > W ; a i < b i means W 1 < W. If no such i exiss, W 1 = W. The order of CLV can be defined as he lexicographical order. LO(ρ ) 1 < LO(ρ ) means ρ 1 < ρ. If LO(ρ ) 1 = LO(ρ ), ρ 1 = ρ. A propery of CLV is noiceable ha a CLV has a lower bound, and he ideal lower bound is a vecor consis of elemens being he average load value. So i is inuiive o ry o achieve load balance by minimizing CLV, especially when i is proved ha he balance degree funcion monoonically increases wih he decrease of CLV. So we ge he main idea of LVMLB. The deails of i will be depiced in nex secion. III. LVMLB ALGORITHM In his secion, we give he basic principle of LVMLB, and laer we prove i will converge o a local opimal. The deailed procedures of LVMLB are given laer in his secion.
A. Basic Principle of LVMLB Principle of LVMLB: Search he elemens of CLV in urn o find a cell ha can ransfer a UL o a low load neighbor cell, unil no such cell can be found. If such a cell is found, updae he user-bs associaion, he BS load and CLV, and hen search he CLV from beginning again. High load cell i 1 can ransfer a UL o a low load neighbor cell i based on wo condiions. 1) ρ i1 > ρ i and j U, Pcos i1 i j HOM; ) The UL o be ransferred will no bring abou a loop of arge cells. 1#41 1#40 1#40 A B Fig. Illusraion of UL-ransfer cell loop. The example of a load-ransfer cell loop is illusraed in Fig.. In sae A, BS1 has he highes load, so i ransfer a uni load o neighbor BS and BS urns o be he BS of he highes load. Then in sae B, BS ransfers a uni load o BS3. BS3 ransfers a uni load o BS1 in sae C, where i goes back o sae A. To avoid he endless load-ransfer loop, condiion is necessary. The firs condiion is easy o check, while he second seems no apparen. In fac, i includes wo siuaions. Siuaion 1,ρ i ρ j > e, no loop will occur. Siuaion, ρ i ρ j = e, LVM ry o guaranee no loop occurs by he following rule. I is easy o know ha he loop occurs only when ρ i ρ j = e, which also means he cells wih heir load higher han ρ i, canno have heir load ransferred according o he principle of VLMLB. Assuming cell i is seleced o ransfer a uni load o neighbor cell j, whose load is as low as possible among all neighbor cells, and ρ i and ρ j saisfy ρ i ρ j = e in an ieraion, we can use a Broad Firs Search (BFS) algorihm o search all he neighbor cells of cell i, wih load being ρ j, o find a cell k being he neighbor of neighbor cells of cell i, ha saisfy ρ j > ρ k. BFS will coninue o search mulilayer cells unil a cell k is found or all he possible searches are ried. If such a cell k is found, BFS will reurn a pah o ransfer a UL from cell i o cell k. If no, BFS will keep all he cells i searched in a se S mp, because hese cells can ransfer any UL o heir neighbor cells. They will be appended o he se S DSC, he cells in which will no be considered in he following ieraion. LVMLB will converge o local opimal soluions, which will be proved hrough he following several heorems. B. Convergence of LVMLB Theorem 1. CLV is non-increasing in each ieraion of LVMLB. Proof: The CLV is ρ afer he -h ieraion, and ρ +1 afer (+1)-h ieraion. A UL is ransferred from cell of index i in ρ o cell of index j in ρ. Then he original proposiion equals o prove ρ ρ. +1 As he order of wo equal elemens in ρ will no affec LO, so he elemens of ρ can be adjused o saisfy he condiion, ρ i > ρ (i+1). There are wo cases o be discussed. 1) ρ i > ρ j + e. I means ρ i > max {(ρ j + e), ρ k (k > i)} in ρ, and ρ i(+1) = max {(ρ j + e), ρ k (k > i)} in ρ +1. So ρ i > ρ i(+1) and herefore ρ > ρ. +1 C ) ρ i = ρ j + e. If a arge cells k is found by BFS algorihm, i is easy o know ha ρ > ρ, +1 for he same reason as in case 1. If no arge cell is found, ρ = ρ +1 is sure o be rue. So we conclude ha ρ, ρ +1 afer each -h ieraion. Theorem. If ρ ρ +1 hen f(ρ ) f(ρ ). +1 Proof: If ρ = ρ, +1 according o he propery of elemenary funcions, f(ρ ) = f(ρ ). +1 If ρ >, ρ +1 and a UL is o be ransferred from cell i o cell j, we can ge ρ i ρ j + e from he proof of heorem 1. So he inequaliy ρ i > ρ i e ρ j + e > ρ j sands. Rewrie i as a > b c > d for simpliciy and a + d = b + c sands. Le F(ρ, ρ ) +1 = f(ρ ) f(ρ ), +1 hen F(ρ, ρ ) +1 i B ) = ( i B ρ i) ( ρ (+1)j ) ( i B ρ (+1)j ) i B ( ρ j N ( i B ρ i )( j B ρ (+1)j ) = (a + d + A) (b + c + B) (c + d + A) (a + d + B) N ( i B ρ i )( j B ρ (+1)j ) = (a + d + A) (b + c a d ) N ( i B ρ i )( j B ρ (+1)j ) 1 = (a + d + A) [(b c) (a d) ] < 0 N ( i B ρ i )( j B ρ (+1)j ) Wherein A = i B ρ i a d, and B = i B ρ j a d. Thus, f(ρ ) > f(ρ ) +1 is proved. Theorem 3. If ρ s and ρ are wo CLVs from a same original sae and ρ s ρ, hen ρ s can urn ino ρ, hrough a series of CLVs {ρ (α {1,,, n})}, in which wo adjacen CLVs have only one UL ransferred, and ρ s ρ 1 ρ ρ n ρ. Proof: A serial of {ρ (α {1,,, n})} can be consruced he following way. The index of firs differen elemen in he same posiion of ρ s and ρ is i, and he las is j. ρ i ρ j. A uni load is ransferred from cell i o cell j. Updae he CLV, we can ge ρ. 1 Subsiue ρ 1 for ρ, s and go on he process, we can ge ρ. Repea he process, we will ge a series of ρ (α {1,,, n}), in which ρ n has only wo elemens differen from ρ, and afer one more ieraion, i would urn ino ρ. There mus be such a ρ. n (Proof by conradicion). If such a ρ n doesn exis, here mus be a ρ, x which has he fewes elemens ha differen from elemens in ρ. So he number of differen elemens beween ρ x and ρ n should be 1. However, we have known i is impossible. So here mus be such a ρ, n and he heorem is proved. Here he proof of heorem 3 only care abou he propery of CLV and doesn concern abou he acual handover evens. Corollary 1. ρ s and ρ are wo CLVs ha he load of he nework can be adjused o, if ρ s ρ, f(ρ ) s f(ρ ). Proof: According o he principle of LVMLB, here mus be a serial of {ρ (α {1,,, n})} ha saisfies ρ s ρ 1 ρ ρ n ρ. And according o heorem, f(ρ ) s f(ρ ) 1 f(ρ ) f(ρ ) n f(ρ ). So f(ρ ) s f(ρ ). Theorem 3. If ρ m is he resul CLV of LVMLB, no oher CLVs will be small han i on he given condiions. Proof: (by conradicion) assuming here exiss a ρ, n ρ n < ρ, m here mus be a leas wo elemens in ρ n differen from elemens in ρ. m Because if here is only one differen elemen, he oal load of ρ n and ρ m will be differen. I is impossible, because hey are from he same original sae and he oal load of ρ n and ρ m
should be he same. If here is a cell i whose load saisfies ρ mi > ρ ni, i means he LVMLB is no finished, so i is conradicion ha ρ m is he final resul of LVMLB. Therefore, he assumpion doesn sands, and he original proposiion is proved. Corollary : LVMLB ge he local opimal of original load balancing problem. Proof: LVMLB ge he smalles CLV, according o heorem 3. I is easy o know he resul CLV corresponds o he bigges f(ρ ). Thus, we ge he local opimal resoluion of original load balancing problem. C. Deails of LVMLB procedures LVMLB includes he following procedures. Prereamens: 1) Each BS ges repors from users i serves and moniors he load saus of iself; ) Each BS judges wheher he load saus of is own reach a rigger hreshold. If i reaches, inform oher BSs o sep ino he main procedure. Main procedures: Iniializaion: assign big enough value o ρ, and clear S mp, S DSC ; Sep 1: updae CLV ρ and he corresponding cell ID lis L BS ; Sep : search for a BS in L BS ha is no in S DSC and saisfies condiion 1. If such a BS is found, go o sep 3. If no such BS is found, he whole process ends; Sep 3: if BS i has a low load neighbor BS j and follows case 1, come o sep 4. If i follows case, use BFS o search a arge BS k (in mulilayer cells) ha saisfies ρ i ρ k > e, and a UL can be ransferred from i o j hrough a series of BSs. If such a BS k is found, save he pah (a series of BSs) ino S mp and go o sep 4; else save all he BSs searched ino S DSC, and back o sep 1; Sep 4: updae corresponding user-bs associaions and CIO parameers and go back o sep 1. Pseudo codes are as follows. Inpu: ρ, L BSNeib, U BSNeib, L UsroBS 1 SDSC=[ ]; ρ = Inf (1,1,,1) 1,N ; while ρ ρ && S DSC S BS 3 f 1 = 0; f = 0; ρ = ρ ; 4 for i in L BS 5 sor {j j L BSNeib (i)} on ρ j in ascending order; 6 for j in {j} 7 if U i,j is empy // no user can be ransferred in BS i 8 coninue; 9 else if ρ i > ρ j + 1 10 f 1 = 1;break; 11 else //ρ i = ρ j + 1, perform BFS 1 [S mp, f ] = BFS(i) 13 if f = 1 // find cell k 14 f 1 = 1; break; 15 else // f = 0, can find cell k 16 S DSC = S DSC S mp 17 end 18 if f 1 ==1; break; end; 19 end 0 if f 1 == 0; coninue; 1 else if f == 0 disribue load uni from i o j; 3 else //f == 1 4 disribue load uni according o S mp ; 5 S mp = [ ]; 6 updae ρ, L UsroNeib and U BSNeib 7 end Oupu: ρ, U BSNeib, L UsroBS As Broad Firs Search (BSF) is a common sraegy for searching and he space is limied, he deails of BFS is omied. IV. SIMULATION Simulaion scenario seings and resuls will be given in his secion. A. Simulaion scenario and seings The simulaion is performed in an irregular HeNes scenario, as illusraed in figure 3 below. The scenario is se according o [9]. This par of nework covers a 5000m 5000m square area. Two kinds of base saions are included, Macro BS (enodeb) and BS. A blue riangle sands for an enodeb which serves a wide area of he nework, and cyan riangle sands for a BS, which serves only a small area. The raio of he wo ypes of BSs are 1:5 and here are 30 enodebs, which means a oal of 180 BSs are in he simulaion scenario. The ransmiing powers of he wo ypes of BSs are 46dBm and 6dBm respecively. Because i is suggesed in [9] ha he ransmiing power of an enodeb is abou 100 imes of ha of a BS. Fig. 3 Illusraion of simulaion scenario. Users in he simulaion are uniformly disribued. However, as BSs are randomly disribued, he coverage of cells will differ, so i is wih he load. So load balancing is necessary. The iniial user-bs associaions are buil according o bes RSRP wih no resource resricions considered, differen o MaxRSRP. Oher simulaion assumpions are oulined in able 1. TABLE I. Iems(uni) SIMULATION PARAMETERS Values Number of BSs (Macro) 30, () 150 Sysem bandwidh(mhz) 0 Pah loss(db) Shadowing Transmission power(dbm) L(d) = 34 + 40log(d) a Lognormal shadowing wih a sandard deviaion σ s = 8dB (Macro)46, ()6 Thermal noise power(dbm) -104 Trigger LB hreshold 0.9 RSRP Bias(dB) 6 a. referring o [6].
As HOM is he upper bound of CIO, which is a radeoff beween load balancing performance and user QoS, i should be carefully se. So in his paper a proper HOM value will be chosen for LVMLB by simulaions. B. HOM value seing 1) HOM affecs Balancing Performance. Figure 6 plos he cumulaive disribuion funcion (CDF) of user SINR. MaxRSRP and RSRPBias schemes are for conras. I can be seen from he figure ha, wih he increase of HOM, SINR performance deerioraes. When HOM is 4dB, he SINR performances of LVMLB and RSRPBias are almos he same. However, when HOM is 6dB, he SINR performance of LVMLB becomes worse han RSRPBias. Because more users are ransferred among cells o achieve a more balanced load sae in LVMLB. Fig. 4 Sysem capaciy of differen HOM Figure 4 shows he sysem capaciies of differen schemes for load balancing under differen HOM seings and he number of users is fixed a a oal of 6000 in he nework, while he HOM varies from 1dB o 0dB. When HOM is small, he number of users allowed o ransfer is grealy limied, so LVMLB has poor capaciy. Wih he increase of HOM, he capaciy of LVMLB has an apparen growh unil i reaches he fixed limi of oal capaciy given by Ini scheme a 11dB. From 1dB, i improves he capaciy of he defaul MaxRSRP scheme and from 3dB i ouperforms he RSRPBias scheme. Fig. 5 Balance degree of differen HOM Figure 5 shows he balance degree of all BSs under differen HOM seings. The balance degree increases wih he rising of HOM. Low HOM means only a small limied number of users can be ransferred, which affecs he balance degree grealy and leads o he poor balancing performance. The RSRP bias facor of RSRPBias scheme is 6dB. However, as LVMLB will balance load among all cells raher han only differen iers, i performs almos he same as he bias scheme, when HOM is jus 5dB, and ouperforms he bias scheme when HOM is 6dB. ) HOM affecs user Qos Fig. 7 Balance degree of differen HOM Figure 7 depics he oal hroughpu under differen HOMs. Wih he increase of HOM, more users are ransferred ino low load cells in which free resources is possibly enough, bu he SINR performances deerioraes oo much o achieve any hroughpu gain. So he hroughpu decreases wih he raising of HOM. Afer he above analysis, we simply choose he 6dB as he value of HOM in LVMLB, which also equals o he value of RSRP facor of he RSRPBias scheme. Because i is enough for he capaciy and balance gain, while a he same ime he user QoS performances will no be sacrificed oo much. C. Performance under differen user densiy 1) Load balancing performance. Here in his paper, he erm user densiy sands for he number of users averaged o all macro cells raher han all cells, denoed as average user number (AUN). Because he Macro cells provide he basic nework coverage and cells serve only a spos in he nework, which can be reaed as supplemen o he homogeneous macro-cell nework. Assuming a cell (boh Macro and ) holds a mos 00 users, so he range of user densiy can be se from 0 o 400. Because 400 is double he capaciy of a macro cell, and i is exremely high load for a macro cell, even wih some cells providing load relief. Fig. 6 Balance degree of differen HOM Fig. 8 Sysem capaciy under differen load densiies Figure 8 shows he sysem capaciies under differen user densiies. The Ini daa give an upper bound of he sysem capaciy, i means he oal loads available under curren user densiy condiion. I is clear ha he oal capaciy increases wih
he rising of AUN, assuming LB is always riggered. However, he capaciies of differen schemes differ. When AUN is below 160, LVMLB and RSRPBias scheme have almos he same capaciy, and boh give remarkable ier capaciy gain. When AUN goes o or beyond 160, LVMLB and RSRPBias have almos he same capaciy gain from cells, while he LVMLB achieves more capaciy gain from Macro cells. Fig. 9 Balance degree under differen load densiies Figure 9 shows he balance degrees under differen load densiies. I is obvious ha he LVMLB has bigger load balance degree han RSRPBias scheme. Wih he rising of load densiy, he balance degree gap beween he wo schemes is narrowed and finally eliminaed. This is because he macro cells finally reach heir load limi and hus have he same load, and a he same ime cells in he wo schemes have almos he same load because of he same value of bias facor and HOM, so he gap is eliminaed. However his exreme case will seldom occur. ) User QoS performance (a)aun = 0 (b)aun=50 (c)aun=80 Fig. 10 Balance degree under differen user densiies Figure 10(a), 10(b) and 10(c) plo he CDF of user SINR under differen user densiies wih AUN being 0, 50 and 80 respecively. Compared wih LVMLB, he RSRPBias scheme has beer SINR performance, because of fewer LB handovers. And he SINR performance of boh schemes are worse han ha in he original sae. Fig. 11 Balance degree of differen user densiies Figure 11 shows he oal hroughpu under differen user densiies. LVMLB has lower hroughpu han he RSRPBias scheme. And he hroughpu of boh schemes are lower han ha of he original sae. Togeher wih figure 10, i is obvious ha all load balancing schemes will suffer from QoS performance loss. And i is a radeoff, beween load balancing performance and user QoS requiremen. From he simulaion resuls above, we can conclude ha, LVMLB has good load balance performance in improving he balancing degree of all cells and he capaciy of he sysem, boh in Macro ier and ier, compared wih RSRPBias scheme, only on he expense of a lile more QoS loss. V. CONCLUSION The proposed LVMLB in his paper, can achieve he goal of improving he balance degree among all cells, including boh Macro and cells, by minimizing cell load vecor, raher han merely draining load from Macro cells o cells. I also provides a handover scheme for users, which is implemened by updaing CIO parameers in he process. A he same ime, HOM parameer, which defines he range for CIO variaion, can be adjused o make a proper radeoff beween QoS requiremen and load balancing performance gain. Simulaion resuls show LVMLB has exraordinary performance gain in sysem capaciy and load balance degree, compared wih he RSRPbias scheme a he expense of a lile more QoS loss. REFERENCES [1] SOCRATES Deliverable D5.9: Final Repor on Self-Organisaion and is Implicaions in Wireless Access Neworks, EU STREP SOCRATES (INFSO-ICT-1684), Version 1.0, December 010 (Available January 011), pp.83-90. [] A. Lobinger, S. Sefanski, T. Jansen, and I.Balan, Load balancing in downlink LTE selfopimizing neworks, Proc. IEEE Vehicular Technology Conference (VTC010-Spring), Taipei, Taiwan, May 010. [3] S. Yang, W. Zhang and X. Zhao, Virual cell-breahing based load balancing in downlink LTE-A self-opimizing neworks, Inernaional Conference on Wireless Communicaions & Signal Processing (WCSP), 01, Huangshan. [4] Y. Yang, P. Li, X. Chen and W. Wang, A high-efficien algorihm of mobile load balancing in le sysem, Vehicular Technology Conference (VTC Fall), 01, Quebec Ciy, QC. [5] J.Wang, J. Liu, D. Wang, J. Pang and G. Shen, Opimized Fairness Cell Selecion for 3GPP LTE-A Macro- HeNes, Vehicular Technology Conference (VTC Fall), 011, San Francisco, CA. [6] Qiaoyang Ye and Beiyu Rong, e al. (013). User Associaion for Load Balancing in Heerogeneous Cellular Neworks, IEEE Transacions on Wireless Communicaions, 013, pp.706-716. [7] D. Chiu and R. Jain, Analysis of he increase and decrease algorihmsfor congesion avoidance in compuer neworks, Compuer Neworksand ISDN Sysems, vol. 17, no. 1, p. 1C14, 1989 [8] Damnjanovic, A. and J. Monojo, e al, "A survey on 3GPP heerogeneous neworks," in IEEE Wireless Communicaions, 011, 18(3): 10-1. [9] H. S. Dhillon, R. k. Gani, F. Baccelli and J. G. Andrews, "Modeling and Analysis of K-Tier Downlink Heerogeneous Cellular Neworks," IEEE Journal on Seleced Areas in Communicaions, 01, 30(3): 550-560. [10] 3rd Generaion Parnership Projec;Technical Specificaion Group Radio Access Nework;Evolved Universal Terresrial Radio Access (E- UTRA);Radio Resource Conrol (RRC);Proocol specificaion(release 9). 3GPP TS 36.331 V9.3.0,010(06).