WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2016; 16:264 278 Published online 12 August 2014 in Wiley Online Librry (wileyonlinelibrry.com)..2517 RESEARCH ARTICLE Distributed two-hop proportionl fir resource lloction in Long Term Evolution Advnced networs Chen Sun 1, Weidong Wng 2, Yinghi Zhng 2 nd iojun Wng 1 * 1 School of Electronic Engineering, Dublin City University, Dublin, Irelnd 2 Key Lbortory of Universl Wireless Communiction, Ministry of Eduction, Beijing University of Posts nd Telecommunictions, Beijing, 100876, Chin ABSTRACT In Long Term Evolution Advnced networs with Type I in-bnd hlf-duplex decode-nd-forwrd rely nodes, proportionl fir (PF) resource lloction is iming t gurnteeing two-hop mtch nd optimising globl proportionl firness. The twohop mtch is defined s equl dt rtes in the ccess lins nd the corresponding bchul lins. The globl proportionl firness is between ll the user equipments served by the evolved nodes B nd the rely nodes. Existing centrlised schemes chieve these trgets t the cost of enormous chnnel stte informtion (CSI) exchnge. Existing distributed schemes focus on resource prtitioning nd employ trditionl single-hop PF scheduling lgorithm in ccess lins, with less CSI exchnge. The trditionl PF scheduling lgorithm mximises single-hop proportionl firness between the dt rtes in the ccess lins rther thn two-hop proportionl firness between the end-to-end dt rtes in the two hops. In order to reduce CSI exchnge nd t the sme time to mximise the two-hop proportionl firness, distributed two-hop PF resource lloction scheme is proposed. The proposed scheme includes two-hop PF resource scheduling lgorithms nd dptive resource prtitioning lgorithms, pplied in different two-hop trnsmission protocols. Simultion results demonstrte the proposed scheme is better thn the existing distributed schemes in obtining better proportionl firness nd lrger celledge user equipment throughputs. Copyright 2014 John Wiley & Sons, Ltd. KEYWORDS LTE-dvnced; rely; proportionl fir; resource lloction *Correspondence iojun Wng, School of Electronic Engineering, Dublin City University, Dublin, Irelnd. E-mil: xiojun.wng@dcu.ie 1. INTRODUCTION In the 3rd Genertion Prtnership Project (3GPP) stndrds, Long Term Evolution (LTE) Relese 10 [1], LTE- Advnced is specified, dopting Orthogonl Frequency Division Multiple Access (OFDMA) in downlin nd relying technology for cpcity increment nd coverge extension. Type 1 in-bnd hlf-duplex decode-nd-forwrd rely node (RN), defined in the stndrds, ppers to user equipments (UEs) s n evolved node B (enb) nd performs independent scheduling. In LTE-Advnced networs with RNs, the UEs re served either directly by the enbs (direct UEs) or ttched to the RNs (rely UEs). There exist three types of lins: direct lins between the enbs nd their direct UEs, ccess lins between the RNs nd their rely UEs nd bchul lins between the RNs nd their donor enbs. In order to support in-bnd relying, time-domin multiplexing between the ccess nd bchul lins is defined in the stndrds. All subfrmes in rdio frme re grouped into bchul subfrmes nd ccess subfrmes. The bchul lins cn only occupy the resources in the bchul subfrmes, nd the rest of resources cn be llocted to the direct UEs. Besides, the direct nd ccess lins will shre or reuse the resources in the ccess subfrmes ccording to different two-hop trnsmission protocols. As n effective compromise between throughput nd firness, proportionl fir (PF) resource lloction hs been widely studied in conventionl single-hop cellulr networs [2,3], OFDMA networs [4] nd LTE networs [5]. In recent yers, the reserches on PF resource lloction in rely enhnced OFDMA networs hve been emerging, which nturlly comprise two phses: resource prtitioning phse, which ssigns resources to different types of lins, nd resource scheduling phse, which commits resources of ech lin between the UEs. There re two commonly ccepted objectives: first, gurnteeing two-hop mtch, which mens equl dt rtes of bchul lins nd their corresponding ccess lins; second, mximising 264 Copyright 2014 John Wiley & Sons, Ltd.
globl end-to-end proportionl firness of both the direct UEs nd the rely UEs. Note tht in this pper, we minly refer to the literture in two-hop in-bnd non-coopertive fixed rely enhnced OFDMA networs, which cn be esily implemented in LTE-Advnced networs with Type I RNs. A simple thought of processing two PF resource lloction phses is to pply centrlised rchitecture, in which the resource prtitioning nd the resource scheduling re executed together by the donor enbs. During the resource scheduling of ccess lins, their chnnel stte informtion (CSI) ought to be collected nd fed bc by the RNs. Single-hop resource scheduling lgorithms coupled with dptive subfrme division re utilised in the studies in [6,7]. In [8 10], two-hop resource scheduling lgorithms using the sttic hlf-to-hlf subfrme structure re proposed. An dptive power lloction nd resource scheduling scheme is designed in [11]. However, the dptive power lloction mechnism will increse the complexity of RN trnsmitters. In [12], the uthors te the two-hop proportionl firness, the dptive time division nd different reuse scenrios into considertion. Although multi-subchnnel diversity nd multi-user diversity cn be exploited using the centrlised rchitecture, enormous CSI exchnge between the enbs nd the RNs will bring hevy burden to the uplin signlling chnnels. In order to reduce CSI exchnge, some PF resource lloction schemes dopt distributed rchitecture, in which two resource lloction phses re processed by different types of serving nodes. Prticulrly, the resource scheduling of the ccess lins is executed t ech RN, which is supported by Type I rely in LTE-Advnced networs, nd the resource prtitioning is determined by the donor enbs. In the existing distributed PF resource lloction schemes, gret ttentions re pid to designing resource prtitioning lgorithms. A sttic equl resource prtitioning scheme is used in [13], resulting in the two-hop mismtch. A two-hop mtch fctor in the resource prtitioning between bchul lins nd direct lins is considered in [14] to reduce the two-hop mismtch; however, the resource prtitioning between direct lins nd ccess lins is still fixed. In [15], the two-hop mismtch is llevited by djusting the trnsmitting power of donor enb nd RNs under sttic resource prtitioning scheme. The uthors in [16] proposed n dptive resource prtitioning lgorithm bsed on the rel-time throughput nd gve setchy fixed initil pttern. An optimised initil pttern is given in [17]. However, the frequent-vrying resource prtitioning will bring burden to the decentrlised rchitecture. Therefore, two semi-sttic PF-bsed resource prtitioning lgorithms bsed on the time-verge dt rtes re designed for the orthogonl reuse pttern in [18] nd the full reuse (FR) pttern in [19] through formulting the generlised PF (GPF) problem nd solving it by the Lgrnge multiplier lgorithm. There re more centrlised nd distributed resource lloction schemes proposed in recent yers. Reference [20] proposed centrlised resource lloction scheme to ensure the proportionl firness between the dt rtes of two-hop lins. This centrlised resource lloction scheme is conducted in the time-frequency domin, while the time domin is considered in [12]. In [21], problem to jointly optimise subfrme, resource nd power lloction is formulted nd solved by centrlised optiml joint lloction lgorithm. A distributed resource lloction scheme is proposed in [22] to increse the throughput of the UEs with worst chnnel conditions. The optiml resource prtitioning in the prtil reuse (PR) pttern is determined by the rtios of the verge spectrl efficiencies in this study. Weighted PF schedulers re proposed in [23] to consider the impct of bchul lin on performnce in the FR pttern. However, these schedulers re not proposed to solve the PF resource lloction problem. The uthors in [24] proposed distributed resource lloction scheme in order to provide high cell throughput nd low outge probbility, but proportionl firness is not considered. Two-hop PF scheduling lgorithms re used in centrlised resource lloction schemes, such s [12,20,21]. The conventionl single-hop PF scheduling lgorithm proposed in [5] is commonly utilised to gurntee the proportionl firness between the dt rtes of the rely UEs in the ccess lins, which is not n optiml choice for the distributed PF resource lloction schemes. To ensure two-hop mtch, the virtul resource scheduling in bchul lins is dependent on the resource scheduling in the ccess lins. Furthermore, the PF resource lloction in the ccess lins my led to unfir distribution of the resources in the corresponding bchul lin. This is becuse the unblnced two-hop chnnel condition, tht is, unequl chnnel conditions in the ccess lins nd equl chnnel conditions in the bchul lins. Therefore, the two-hop proportionl firness between the rely UEs cnnot be mximised, becuse the proportionl firness in the bchul lins is not mximised. As it cn be found, the centrlised PF resource lloction schemes using the centrlised two-hop scheduling lgorithms cn chieve the PF resource lloction trgets but with lrge CSI exchnge, nd the distributed schemes cn decrese the CSI exchnge but cnnot mximise two-hop proportionl firness in the ccess lins using the conventionl PF resource scheduling lgorithm. Besides, the centrlised two-hop resource scheduling lgorithms cnnot be directly incorported in the distributed resource lloction schemes, becuse of the constrints of the resource prtitioning results. In this pper, distributed two-hop resource lloction scheme is proposed to ddress this problem, nd the following contributions re mde: A GPF problem is formulted nd decomposed into two interdependent sub-problems, tht is, resource prtitioning sub-problem ccording to resource scheduling results nd resource scheduling sub-problem subject to resource prtitioning. In ddition, two different two-hop trnsmission protocols re considered in the formultion. Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 265
Abbrevition 3GPP ARP CDFs CRS CSI DF enb FR GPF KKT LTE OFDMA OR OTH PF PR PRB RN SN STH UE Tble I. List of bbrevitions. Full nme The 3rd genertion prtnership project Adptive resource prtitioning Cumultive distribution function Conventionl resource scheduling Chnnel stte informtion Decode nd Forwrd Evolved Node B Full reuse Generlised proportionl firness Krush Kuhn Tucer Lone Term Evolution Orthogonl frequency division multiple ccess Orthogonl reuse Orthogonl two-hop Proportionl fir Prtil reuse Physicl resource bloc Rely node Serving node Simultneous two-hop User equipment The resource scheduling sub-problem is solved by two-hop PF resource scheduling lgorithms in timefrequency domin through the Lgrnge multiplier lgorithm. Ech lgorithm is designed for two-hop trnsmission protocol under the constrints of the corresponding resource prtitioning. The resource prtitioning sub-problem in the twohop trnsmission protocols is solved by djusting the existing dptive resource prtitioning lgorithms in [18,19] bsed on the requirements of LTE-Advnced stndrds. In order to me this pper more redble, we provide list of bbrevitions in Tble I. n ccess PRB subset N for ccess lins nd bchul PRB subset N b for bchul lins. Note tht N nd N b need to be integers, where jjmens the crdinlity of set, nd the bchul PRB size N b 0 is defined s 0 for the donor enb. The reltionship between the ccess PRBs nd the bchul PRBs cn be given by N \ N b D;, N [ N b D N, 8N 2 N, 8N b 2 N 2.2. Chnnel model ssumptions In direct lins nd ccess lins, we ssume ll UEs hve independent multipth frequency-selective Ryleigh fding chnnels, nd their instntneous chnnel gins re flt over ech PRB. In ddition, bsed on the clcultion given in [25], the Doppler time-selective Ryleigh fding chnnels result in flt chnnel gins within rdio frme, when the speeds of UEs re under 60 m/h. For bchul lins, flt fding chnnels re ssumed under the fixed line-of-sight condition, nd the instntneous dt rtes re constnt over ll PRBs. A multi-cell scenrio is considered in this pper. Through PRB pre-ssignments in subfrmes, the inter-cell interference is predictble in order to mintin stble interference environment nd me the problem formultion fesible. In ddition, fixed trnsmitting power per PRB is ssumed for ll the lins to reduce the complexity of trnsmitters. (1) 2. SYSTEM MODEL 2.1. Networ model In this pper, we consider the downlin trnsmission of n LTE-Advnced networ with Type I RNs. In the cell of interest, there re set of serving nodes (SNs) K, including donor enb nd multiple RNs. The SN. 2 K/ denotes the enb when D 0ornRNotherwise.TheRNsre connected to the donor enb vi wireless bchul lins. A set of UEs M cn be either served by the donor enb directly or vi n RN through two hops. We ssume tht ll the dt in the wireless bchul lins re decoded nd forwrded by the RNs to the rely UEs in the ccess lins, becuse the RNs re incpble of buffering excess dt. The UEs ssociting with SN crete subset M of M. Multiple SN connection nd coopertive trnsmission re not considered in this pper. Physicl resource bloc (PRB) is bsic OFDMA resource lloction unit, comprising of constnt number of subcrriers nd OFDM symbols. Assume tht there is set of PRBs N for dt trnsmission in ech rdio frme. With certin resource prtitioning pttern, SN cn obtin PRB subset N, which is further divided into Figure 1. Two-hop trnsmission protocols. 266 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
2.3. Two-hop trnsmission protocols Two typicl two-hop trnsmission protocols re considered in this pper, orthogonl two-hop (OTH) trnsmission protocol nd simultneous two-hop (STH) trnsmission protocol, which re illustrted in Figure 1. In the twohop trnsmission protocols, ech rdio frme is divided into bchul subfrmes nd ccess subfrmes. The ccess PRBs in the ccess subfrmes nd the bchul PRBs in the bchul subfrmes re llocted to the two-hop rely UEs. For the single-hop direct UEs, the reminder of the bchul subfrmes cn be used. The PRBs in the ccess subfrmes re reused or not reused by the two-hop rely UEs nd the single-hop direct UEs ccording to different two-hop trnsmission protocols. In the OTH trnsmission protocol, the single-hop direct UEs nd the two-hop rely UEs shre ll the PRBs in the ccess subfrmes without ny overlpping. No intr-cell interference is generted. An orthogonl reuse (OR) pttern in the ccess subfrmes is used. The min inter-cell interference experienced by the rely UEs is from the RNs in the djcent cells, nd the min inter-cell interference received by the direct UEs is from the surrounding enbs. The OR pttern deployed in different sectors of mcro cell is shown in Figure 2. Using the STH trnsmission protocol, FR pttern nd two PR ptterns re considered s shown in Figure 3. In the FR pttern, the whole PRBs in the ccess subfrmes re vilble for the direct lins nd the ccess lins. The intr-cell nd inter-cell interference suffered by the UEs is consistent from ll the unttched SNs. In the 2/3 PR pttern, the ccess lins re llowed to reuse 2/3 of the resources for the direct lins. In the 1/3 PR pttern, the ccess lins re llowed to reuse 1/3 of the resources for the direct lins. Thus, the intr-cell nd inter-cell interference is reduced, nd the vilble resources of the rely UEs for the ccess lins re lso diminished, compred with the FR pttern. These three ptterns deployed in different sectors of mcro cell re presented in Figure 3. The reltionship of the ccess PRBs, bchul PRBs nd direct PRBs in different two-hop trnsmission protocols cn be summrised by in the OTH protocol, in the STH protocol, K[ N D N (2) D0 K[ N b C N 0 D N D1 N 0 N 0 (3) where indictes 1, 2/3 nd 1/3 in the FR, 2/3 PR, nd 1/3 PR ptterns, respectively. 3. PROBLEM FORMULATION Without loss of generlity, we consider the trnsmission frme-by-frme. The PF resource lloction problem with dptive resource prtitioning in LTE-Advnced networs with Type I RNs is formulted s the equivlence of mximising the following utility function [26]: mx log R m (4) m2m where R m is the dt rte of UE m within rdio frme. Becuse the UE ssocition reltionship hs been decided by certin route selection lgorithm, the dt rte of UE m served by SN in rdio frme cn be expressed s R m D m,n r,m,n (5) where m,n is the binry resource lloction vrible, nd r,m,n is the instntneous dt rte chieved by UE m connected to SN on PRB n. IfPRBn is llocted to UE m ssociting with SN,then m,n D 1; otherwise, m,n D 0. Note tht only the throughputs finlly received by the UEs in the ccess PRBs should be included in the expression. Considering time multiplexing nd two-hop mtch required in the LTE-Advnced stndrds, the GPF problem in the OTH protocol cn be formulted s mx log m,n r,m,n (6) 2K m2m Figure 2. An orthogonl reuse pttern in the orthogonl protocol. Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 267
Figure 3. Full reuse, 2/3 prtil reuse nd 1/3 prtil reuse ptterns in the simultneous protocol. subject to C1 : m2m C2 :N 0 jn j m,n r,m,n D N b r 0,, 8 2 K, 0 2K, 0 N 2K, 0 N b nd the GPF problem in the STH protocol cn be formulted s mx log m,n r,m,n (7) 2K m2m subject to c1 : n2m c2 :N 0 jn j m,n r,m,n D N b r 0,, 8 2 K, 0 2K, 0 N b In different reuse ptterns, constrints C1 nd c1 re the sme, which imply the two-hop mtch. Additionlly, the constrints C2 nd c2 show how to segment the entire PRBs in rdio frme. The GPF problems (6) nd (7) re not convex optimistion problems, becuse UE s dt rtes R is not convex set with the binry vribles 2 Œ0, 1. In order to me the GPF problem trctble, the binry vribles re llowed to te ny vlue between 0 nd 1, 2 Œ0, 1,sothtR is convex set nd the GPF problems (6) nd (7) become convex [27]. The method of Lgrnge multipliers cn be used to solve the GPF problems. 4. DISTRIBUTED TWO-HOP PROPORTIONAL FAIR RESOURCE ALLOCATION SCHEME IN LONG TERM EVOLUTION ADVANCED NETWORKS In this section, our im is to solve the formulted GPF problem in different two-hop trnsmission protocols. 268 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
Using distributed rchitecture, the GPF problem cn be decomposed into two sub-problems, tht is, resource portioning problem with given scheduling results nd resource scheduling problem considering the nown twohop resource segments. 4.1. Adptive proportionl fir resource prtitioning with given resource scheduling results According to the findings in [2,4] nd the system model defined in this pper, the throughput of UE m in PF scheduler cn be pproximted by its verge dt rte per PRB, the verge llocted PRB number nd PF scheduling gin G m, compred with the round-robin scheduling. R m G m, jn j jm j Nr m, (8) where G m, depends on the chnnel sttes of ll the UEs in the scheduler nd is irrelevnt of the PRB number to be scheduled. In [18,19], the resource prtitioning problems in the OTH nd STH trnsmission protocols re simplified into PRB number-relted logrithmic sum mximistion function through substituting Eqution (8) into Equtions (6) nd (7) mx jm j log N (9) 2K Besides, the reltionship between the bchul PRB numbers nd the ccess PRB numbers cn be derived by substituting Eqution (8) to constrint C1 or c1. A bchul -to-ccess rtio is defined for every RN s D P N b m2m N D G m, Nr m, (10) jm jr 0, where indictes the rtio of the dt rtes per PRB of the bchul lin to the ggregte ccess lins of RN. Note tht the bchul-to-ccess rtios cn be estimted by the previous verge dt rtes. Two dptive resource prtitioning lgorithms in the OTH nd STH protocols hve been proposed in [18,19]. However, these lgorithms re bsed on the OFDMA networs without considering the integrted subfrme division, which is not prcticl for rely enhnced LTE- Advnced networs. In wht follows, these dptive resource prtitioning lgorithms re djusted for the LTE- Advnced networs, considering the integrted subfrme division indictor with only slight increse in complexity. In the orthogonl two-hop protocol The dptive PF resource prtitioning lgorithm in the OTH protocol is described in the following steps. Step 1: By only considering constrint C2 nd solving (9) by the Lgrnge multiplier lgorithm, perfect resource prtitioning results in the OTH protocol cn be redily derived [18]. N 0 D jm 0 jjn j N D jm jjn j.1 C / D N b, 8 2 K, 0 (11) Step 2: The bchul subfrme number is determined by the minimum integer, which fulfil ll the requirements of bchul PRB. 0 2 31 D min @T 1, jm jt A 6 1 C 2K, 0 7 (12) where T is the subfrme number in rdio frme nd de mens rounding up to the nerest integer. Step 3: The ccess subfrme number is ensured by clculting. P N 2K, 0 D 1, 8 2 K, 0 (13) 1 T jn j If the is below 1, the lgorithm ends with perfect resource prtitioning results. Otherwise, the imperfect resource prtitioning results will be obtined s N N new D N, b N b D, 8 2 K, 0 new N0 new DjNj.1 C / N 2K, 0 (14) This lgorithm hs low computtion complexity of O.K/, the sme s the lgorithm in [18]. It needs t most 2K bsic resource prtitioning opertions, when there re excessively lrge number of rely UEs occurs, s described in Eqution (13). In the simultneous two-hop protocol Through the following steps, the dptive PF resource prtitioning lgorithm in the STH protocol is described s follows: Step 1: Considering constrint c2 nd function (9), the perfect results cn be redily obtined using the Lgrnge multiplier lgorithm [19] s N 0 D jm 0 jjn j N jm jjn j D D N b, 8 2 K, 0 (15) Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 269
Step 2: The bchul subfrme number is clculted s the minimum integrted vlue to stisfy the requirements of bchul PRB. 0 2 31 D min @T 1, T jm j A 6 (16) 2K, 0 7 where de mens rounding up to the nerest integer. Step 3: In order to stisfy the PRB requirements of ccess lins, is clculted s N D, 8 2 K, 0 (17) 1 T jn j where is 1 in the FR pttern, 2/3 in the 2/3 PR pttern nd 1/3 in the 1/3 PR pttern. If of some RNs re more thn, their ccess PRB numbers re fixed t 1 T jn j nd the bchul PRB num- jn j. Then, these bers re clculted s 1 T RNs nd their bchul PRBs re excluded from the SN set K nd the bchul PRB set N b, respectively. Accordingly, the remining PRB number jn j nd the remining UE number re renewed. Step 4: Repet steps 1 nd 3 by substituting the new PRB number jn j nd the new UE number into Eqution (15), until ll the remining RNs fulfil the requirement (17). Therefore, we cn obtin the ccess PRB numbers nd bchul PRB numbers of ll SNs, N nd N b. Compred with the lgorithms in [19], our lgorithm pplies more prcticl subfrme division nd hs the sme mximum complexity. Besides, potentil shorter opertion time cn be chieved by the proposed lgorithm, becuse multiple RNs cn be delt with in prllel in Step 3. Integrl resource segments In the rel LTE-Advnced systems, the ctul PRB number should be integers. Some simple rounding opertions re required. ON D N, 8 2 K ON b D (18) N, 8 2 K, 0 where Πdenotes rounding to the nerest integers no less thn 0. 4.2. Two-hop proportionl fir resource scheduling problem with given resource segments After hving obtined resource prtitioning results, the resource scheduling sub-problem t ech SN cn be deduced from the GPF problem. Becuse the resource scheduling problem t donor enb cn be solved by the conventionl resource scheduling lgorithm [5], we focus on the resource scheduling problem t RNs, which cn be formulted s mx m2m log n2n m,n r,m,n (19) which is m,n -relted 0-1 integer progrmming problem with certin PRBs. Becuse the ccess PRBs re ssumed to be identicl for the RNs in chnnel fding chrcteristics, the problem is subject to the ccess PRB numbers, which re obtined by the resource prtitioning lgorithms. Becuse the bchul-to-ccess rtios re the vlues determined by the resource scheduling itself, no ccess PRB sizes including cn be directly used to solve the problem. In order to obtin low-complexity resource scheduling lgorithms for the OTH protocol nd the STH protocol, we solve the resource scheduling problem in PRB-by-PRB mnner. In the orthogonl two-hop protocol The two-hop PF resource scheduling problem in the OTH protocol cn be formulted s mx subject to log m,n r,m,n (20) m2m N jm jjn j N b D.1 C / D (21) m,n 1, 8n 2 N (22) m2m m,n 0, 8n 2 N, 8m 2 M (23) The ccess PRB number nd bchul PRB number of ech RN re given in Equtions (11). Both of them re relted with the bchul-to-ccess rtio nd cnnot be directly used in getting the scheduling results. It cn be observed tht the sum of the number of the ccess PRBs nd the number of the bchul PRBs is constnt without ny reltion to. Therefore, constrint bsed on two-hop resources is considered insted of Eqution (21), which is m2m m,n C m,n r,m,n r 0, jm 0jjN j (24) 270 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
For the solution of the problem (20) with constrints, Lgrngin function is written s follows: L.,,, / D log m,n r,m,n m2m 2 C 4 jm 0jjN j 3 r,m,n m,n C m,n 5 r m2m 0, 2 3 C n 41 m,n 5 m2m C m,n m,n (25) m2m where,, nd re the Lgrngin multipliers nd nonnegtive numbers to stisfy the KrushKuhnTucer (KKT) conditions. By letting the differentition of L with regrd to m,n equl 0, the following eqution cn be obtined for ech m,n. We cn find tht @L @ m,n r,m,n D Pn2N 1 C r,m,n m,nr,m,n r 0, n C m,n D 0 n m,n D 1 C r,m,n r 0, r,m,n r 0, r,m,n Cr 0, P n2n m,nr,m,n! (26) (27) We use,m,n nd,m,n to simplify the forementioned eqution. n m,n D.1 C,m,n /.,m,n / (28),m,n,m,n D r,m,n r 0, (29) D r,m,n 1C,m,n P n2n m,nr,m,n (30) Considering the KKT conditions for the Lgrngin function (25), if the m,n is chosen more thn 0, m,n should be chosen s 0. Unless only one UE is chosen in PRB n with m,n D 1, n should be chosen s 0. For different,m,n, the following expression of m,n cn be derived. 0, if,m,n < m,n D.0, 1, if,m,n (31) In order to round m,n to 0 or 1 nd to gurntee there is only one UE selected for the PRB n, the sub-optiml greedy solution in ech PRB n should be the UE m with the following mximum vlue: m D rg mx M r,m,n r 0, r,m,n Cr 0, P n2n n,mr,m,n (32) By replcing P n,mr,m,n with the history dt rte NR m,.t 1/ of UE m ssocited with RN, distributed two-hop resource scheduling lgorithm for the OTH protocol is proposed s m D rg mx M r,m,n r 0, r,m,n Cr 0, NR m,.t 1/, 8n 2 N (33) After ech time intervl, NR m,.t 1/ is updted s NR m,.t/ D 1 1 NR m,.t 1/C W 1 (34) n,m r,m,n W where W is the verge filter window length. Using the proposed resource scheduling lgorithm, the proportionl firness of end-to-end dt rtes is supposed to be mximised. Thus, bsed on the findings in [2,4], the end-to-end dt rte of ech rely UE cn be pproximted s R m G m, N C N b jm j Nr m, r 0, Nr m, C r 0, (35) where G m, is the scheduling gin of the proposed lgorithm compred with the round-robin scheduling. It cn be seen from the pproximtion in Eqution (35) tht the difference between the end-to-end dt rtes of rely UEs cn be reduced compred with the conventionl single-hop PF scheduling lgorithm. In the simultneous two-hop protocol Bsed on the dptive resource prtitioning in the STH protocol, the two-hop resource scheduling problem for the STH protocol is subject to two independent constrints: mx subject to log m,n r,m,n (36) m2m N 1 jn j (37) T N b jm jjn j (38) m,n D 1, 8n 2 N (39) m2m m,n 1, 8n 2 N, 8m 2 M (40) Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 271
In order to solve this resource scheduling problem, we consider the Lgrngin function with the KKT conditions L.,,, / D log m,n r,m,n m2m 2 3 C 4 1 jn j m,n 5 T m2m 2 3 C 4 jm 0jjN j r,m,n m,n 5 r m2m 0, 2 3 C n 41 m,n 5 m2m C m,n m,n m2m (41) where,,, nd re the Lgrngin multipliers nd non-negtive numbers to stisfy the KKT conditions. By letting the differentition of L with regrd to m,n equl 0, the following eqution cn be obtined for ech m,n. @L D @ m,n r P,m,n r,m,n n C m,n D 0 m,nr,m,n r 0, (42) If the constrint (38) is not stisfied, cn be ny number no less thn 0. We hve! n m,n D r,m,n r 0, r 0, Pn2N n,mr,m,n (43) Similr to the solution of the resource scheduling problem in the OTH protocol, the chosen UE should mximise the following vlue. r 0, m D rg mx M Pn2N (44) n,mr,m,n If the constrint (38) is stisfied, should be 0 to stisfy the KKT condition. Therefore, the UE should be chosen ccording to the following metric. m D rg mx M r,m,n Pn2N n,mr,m,n (45) In order to solve the PF scheduling problem with two constrints, two-hop schedule-nd-confirm lgorithm with two stges is proposed. Stge 1: The initil scheduling results ccounting for constrint (37) cn be obtined esily through similr procedure in the OTH protocol. As for PRB n, it is scheduled to UE m with the highest rtio of the current dt rte to the history dt rte. m D rg mx M D rg mx M r P,m,n m,n r,m,n r,m,n NR,m.t 1/ (46) nd the preliminry vrible O m,n is set to 1. For those UEs tht re not chosen, O m,n is 0. Stge 2: After ll the ccess PRBs hve been scheduled ccording to (46), they should be confirmed by the scheduling of the bchul PRBs. Becuse of constrint (38) nd.c1/, the ccess PRB n llocted to UE m is confirmed by r 0, m D rg mx P M b n,m r 0, b r (47) D rg mx P 0, M m,n r,m,n where b n,m is the resource lloction vrible in the bchul lins. If the ccess PRB scheduling is confirmed, the finl resource lloction vrible m,n nd the corresponding b n,m re set to 1; otherwise, the confirmtion of the next ccess PRB will begin. Stge 2 repets until the scheduling of ll ccess PRBs re confirmed, or ll the bchul PRBs re scheduled. After ech time intervl, NR m,.t 1/ is updted s NR m,.t/ D 1 1 NR m,.t 1/C W 1 (48) n,m r,m,n W where W is the verge filter window length. Becuse the PF resource scheduling problem in the STH protocol is constrined by the resources of both hops, the end-to-end dt rtes of rely UEs re between two vlues, R Access m nd R Bchul m R Access m, for the two hops. R Bchul m N G m, jm j Nr m, N b jm j r 0, (49) where G m, is the scheduling gin of the conventionl PF scheduling lgorithm compred with the round-robin scheduling lgorithm. The end-to-end dt rtes re closer to which vlue depends on which constrint is stricter. 272 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
Figure 4. Cellulr networ lyout nd rely node deployment. Chnnel stte informtion exchnge nlysis By using the distributed resource lloction scheme proposed in this pper, the CSI exchnge between the donor enbs nd the RNs cn be reduced significntly. In the centrlised resource lloction schemes, the chnnel informtion of the rely UEs in ll the PRBs should be trnsmitted to the donor enb periodiclly by ech RN, nd the resource scheduling decision of rely UEs in the ssigned PRBs is trnsmitted to ech RN by the donor enb. In the proposed scheme, only the sum of dt rtes of the ttched rely UEs in the ccess lins should be trnsmitted by ech RN, nd the donor enbs inform the RNs bout the PRBs prtitioned for them. Thus, the occupied resources in the control chnnels of bchul lins by the CSI exchnge using the centrlised scheme re jm j jn j times tht for the proposed distributed scheme. 5. SIMULATION RESULTS According to LTE self-evlution methodology [1], semi-sttic system-level Mtlb simultion pltform is developed to evlute downlin performnce. Using the wrp-round technique, seven 3-sectored mcro cells re generted with fixed numbers of UEs rndomly dropped in them. In ech cell, fixed number of RNs re locted t the cell edge with the sme distnce of hlf of the inter-site distnce from the enb. The simulted networ is illustrted in Figure 4. The detils of simultion prmeters re listed in Tble II. The end-to-end optiml routing strtegy [28] is utilised in this simultion. Ech UE m is connected to SN with the mximum end-to-end dt rte per PRB. SE0, SE,m D rg mx SE0,m, SE0, C SE,m (50) where SE,m represents the estimted verge dt rte per PRB between SN nd UE m, nd SE0, denotes the bchul dt rte per PRB of RN. The OR pttern in the OTH protocol nd the FR, 2/3 PR nd 1/3 PR ptterns in the STH protocol re considered s the scenrios of the performnce evlutions. Although these ptterns hve been mentioned in the previous sections, more detils bout the PRB ssignment in different sectors of mcro cell re illustrted in Figures 2 nd 3. In the OR pttern, the ccess PRBs re ssigned firstly in different sectors to void more inter-cell Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 273
Tble II. Simultion prmeters. Prmeters Vlues Crrier/bndwidth Subfrme number PRB number UE number Inter-site distnce Trnsmitting power Antenn configurtion Therml noise density Noise figure 2 GHz/FDD 10 MHz 10/rdio frme 50/subfrme 30/sector 500 m enb: 46 dbm RN: 30 dbm enb: 14 dbi, 70 directionl RN: 5 dbi, omni UE: 0 dbi, omni 174 dbm/hz 9 db t UE, 5 db t RN Chnnel model 3GPP cse 1 for rely [1] Log-norml distribution enb-rn: 6 db Shdowing stndrd devitions enb-ue: 8 db RN-UE: 10 db Fst fding model SUI-5 chnnel [29] Trffic model Full buffer AMC scheme 15 levels ccording to [30] PRB, physicl resource bloc; UE, user equipment; AMC, Adptive Modultion nd Coding. interference from the enbs in the djcent cells. In the 2/3 PR nd 1/3 PR ptterns, the ccess PRBs in different sectors re reusing different prts of the whole PRBs to reduce inter-cell interference s well s intr-cell interference. The proposed resource lloction scheme in ech reuse pttern includes two lgorithms: n dptive PF resource prtitioning lgorithm nd n end-to-end proportionl firness bsed resource scheduling lgorithm. Aprt from the PF scheduling scheme without rely, distributed PF resource lloction scheme ws considered for comprison. The distributed PF-bsed dptive resource prtitioning nd the conventionl resource scheduling (ARP + CRS) scheme used in [18,19] is the most vluble benchmr of the proposed scheme. In the ARP + CRS scheme, the resource prtitioning is similr to the proposed scheme, nd the resource scheduling lgorithm of ccess lins is given by m D rg mx M r,m,n NR m,.t 1/, 8n 2 N (51) NR m,.t/ D 1 1 NR m,.t 1/C W 1 (52) n,m r,m,n W where r,m,n is the dt rte in the ccess lins nd W is the verge filter window length. In this simultion, the performnce of ll the UEs in the mcro cell is evluted. The performnce of the rely UEs ttched to the RNs is lso ssessed. Mcro UEs re defined s the UEs in the mcro cell, including the direct UEs nd the rely UEs in the sme mcro cell. The metrics of the evlution include the GPF fctor, the verge UE throughput nd the 5% worst UE throughput. Besides the GPF fctor is required to show the effectiveness of the solutions to the GPF problem in 4, it is commonly used metric [2] to show the trde-off between verge throughput nd Figure 5. Generlised proportionl firness fctor (mcro user equipments) versus rely node number per cell. firness, which is expressed s GPF fctor D 1 m2m log R m (53) The 5% worst UE throughput is the lrgest throughput of the 5% UEs with worst throughputs, s defined in 3GPP stndrd [1]. This metric is lso used to indicte the celledge performnce. Figure 5 shows the GPF fctors using different schemes versus the RN number in the OR, FR, 2/3 PR nd 1/3 PR ptterns. When the number of RNs per cell is 12, the mximum GPF fctor chieved in the OR pttern is lrger thn tht without rely by 0.3 nd by less thn 0.1 in the FR pttern, which is equivlent to gins of 30% nd 10%, respectively. The GPF fctors in the 2/3 PR nd 1/3 PR ptterns re between the fctors in the OR nd FR ptterns. Reduced intr-cell interference leds to lrger GPF fctors in the 1/3 PR pttern thn in the FR pttern. However, less resources for the ccess lins imply less GPF fctor in the 1/3 PR pttern thn in the 2/3 PR pttern, when the RN number per cell is lrge nd mny UEs re ssocited with RNs. In ll ptterns, the proposed scheme outperforms the ARP + CRS scheme in getting better trde-off between throughput nd firness. It lso cn be noticed tht when the resources for the ccess lins re getting less in the 2/3 PR nd 1/3 PR ptterns, the GPF fctor improvement obtined by the proposed scheme is getting less, compred with the FR pttern. This is becuse stricter resource constrints of the ccess lins me the proposed resource scheduling lgorithm in the STH protocol closer to the conventionl PF scheduling lgorithm. In Figure 6, it is illustrted tht long with RN number in ech cell, most of the verge UE throughputs using different schemes rise except the sitution when the number of RN goes up from 9 to 12 per cell in the FR pttern. In the OR pttern, the benchmr scheme cn obtin lrger verge throughput for the UEs thn the proposed scheme. The throughputs chieved by the two schemes cn hrdly be differentited in the FR, 2/3 PR nd 1/3 PR ptterns, 274 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
Figure 6. Averge mcro user equipment throughput versus rely node number per cell. Figure 7. 5% worst mcro user equipment throughput versus rely node number per cell. becuse the throughputs of rely UEs re constrined by the bchul PRB numbers ssigned by the common dptive resource prtitioning lgorithm of these two schemes. When the number of RNs in cell is 3, the throughput of the 2/3 PR pttern is lmost the sme s tht in the 1/3 PR pttern. When the number of RNs in cell is 12, the throughput of the 2/3 PR ptter is much lrger thn tht in the 1/3 PR pttern. The throughputs in the 2/3 PR nd 1/3 PR ptterns re significntly more thn those in the FR with ny numbers of RN per cell, becuse of less intr-cell interference between direct lins nd ccess lins. The 5% worst throughputs of Mcro UEs re demonstrted in Figure 7. In the OR pttern, the rpidly incresing 5% worst throughput chieved by the proposed scheme obtins mgnificent gin compred with the vlue chieved by the ARP + CRS scheme, which is lower thn tht of LTE-Advnced networs without rely when the RN number is below 9 per cell. The 5% worst throughputs in the FR pttern re ll less thn tht using the PF scheduling lgorithm without RN, in which the proposed scheme is performing mrginlly better thn the ARP + CRS scheme. The reson of this sitution is tht ll the UEs in the mcro cell re fully reusing ll the PRBs in the ccess subfrmes nd thus re experiencing severe intr-cell interference from the enb nd the RNs. With llevited intr-cell interference in the 2/3 PR nd 1/3 PR ptterns, the 5% worst throughputs re lrger thn the single-hop networs without rely. It cn be observed tht the difference between the proposed scheme nd the ARP + CRS scheme is the smllest in the 1/3 PR pttern. For some UEs ttched to the RNs, their performnce differs from the UEs in the mcro cell. As is displyed in Figure 8, the GPF fctors in the FR pttern re lrger thn those in the OR pttern. The proposed scheme cn chieve more GPF fctors of rely UEs thn the benchmr scheme in both ptterns, nd their difference in the FR pttern is bigger thn tht in the OR pttern. When the RN number is no less thn 12 per cell, the rely UE GPF fctor drops becuse of the ggrvting inter-rn interference brought by the incresing number of RNs. With only 1/3 resources Figure 8. Generlised proportionl firness fctor (rely user equipments) versus rely node number per cell. in the 1/3 PR pttern, the rely UE GPF fctors re less thn those in the FR nd 2/3 PR ptterns, the rely UE GPF fctor gins chieved by the proposed scheme re lso less thn those in the FR nd 2/3 PR ptterns. However, the rely UE GPF fctors re incresed significntly when the RN number per cell grows from 9 to 12, becuse of less intr-cell interference. It cn be observed from Figure 9 tht the verge rely UE throughputs chieved by the proposed scheme nd the ARP + CRS scheme in the FR, 2/3 PR nd 1/3 PR ptterns re lmost identicl nd exceed those in the OR pttern except the 1/3 PR pttern. In the OR pttern, the benchmr hs slightly lrger men rely UE throughput thn the proposed scheme. When the number of RNs is 12 per cell in the FR pttern, the verge UE throughputs fll owing to the sme reson for the GPF fctors. Figure 10 depicts the 5% worst throughput of rely UEs ginst different RN numbers. The 5% worst throughputs increse with more RNs per cell. They re rised shrply in the OR pttern nd slowly in the FR pttern. With more RNs in cell, cell-edge UEs with bd chnnel conditions hve more chnces of choosing one of multiple RNs to Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd. 275
Figure 9. Averge rely user equipment throughput versus rely node number per cell. Figure 11. Cumultive distribution function of rely user equipment throughput. lins nd ccess lins in the FR pttern. However, the performnce of rely UEs is better in the FR pttern thn in the OR pttern. With less intr-cell interference nd less resources for the ccess lins in the 1/3 PR pttern, the performnce is better thn tht in the FR pttern using the proposed scheme nd the benchmr scheme. The performnce gin chieved by the proposed scheme compred with the benchmr scheme is smll. As the compromise between the FR nd 1/3 PR ptterns, the 2/3 PR pttern cn chieve better performnce nd significnt performnce gin using the proposed scheme. Figure 10. 5% worst rely user equipment throughput versus rely node number per cell. improve their performnce. However, in the FR pttern, incresing intr-cell interference cused by multiple RNs weens the diversity gin of routing between multiple RNs. When the intr-cell interference decreses, the 5% worst throughputs using the ARP + CRS scheme re better in the 2/3 PR nd 1/3 PR ptterns thn in the FR pttern with smll RN number per cell. Using the proposed scheme with 12 RNs per cell, the 5% worst throughput in the FR pttern is lrger tht in the 2/3 PR nd 1/3 PR ptterns. The cumultive distribution functions of rely UE throughputs with six RNs per cell in the OR nd FR ptterns re shown in Figure 11. For the 40% rely UEs with worst throughputs, they cn chieve better throughputs in the proposed scheme. For the rely UEs with top 20% throughput, the ARP + CRS scheme performs significntly better thn the proposed scheme in the OR pttern but hs no dvntge in the FR pttern. In summry, the proposed resource lloction scheme hs better GPF fctors nd better 5% worst UE throughputs, in different RN numbers for ll the reuse ptterns. The performnce of mcro UEs in the OR pttern is better thn tht in the FR pttern, becuse extr intr-cell interference is generted by reusing the sme PRB in direct 6. CONCLUSIONS The existing distributed PF resource lloction schemes, using the conventionl single-hop PF scheduling lgorithm t RNs, fil to ensure the two-hop end-to-end proportionl firness of rely UEs. This pper proposes distributed resource lloction scheme tht cn chieve better two-hop end-to-end proportionl firness in LTE-Advnced networs with Type I RNs. Our contributions re tht the GPF problem is formulted nd decomposed into two relted sub-problems, tht is, resource prtitioning nd resource scheduling; orthogonl nd STH trnsmission protocols re considered in solving the sub-problems; the existing dptive resource prtitioning lgorithms re djusted for LTE-Advnced networs; nd two lgorithms re proposed for two-hop resource scheduling subject to different resource prtitioning constrints. The simultion results show tht the proposed resource lloction scheme hs better compromise between throughput nd firness. REFERENCES 1. 3GPP TR 36.814 Evolved Universl Terrestril Rdio Access(E-UTRA) Further dvncements for E-UTRA physicl lyer spects. 276 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.
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25. Rppport TS. Wireless Communictions: Principles nd Prctice (2nd ed.) Prentice Hll PTR: Upper Sddle River, N.J, 2002. 26. Kelly FP. Chrging nd rte control for elstic trffic. Europen Trnsctions on Telecommunictions 1997; 8: 33 37. 27. Wong CY, Cheng RS, Ltief KB, Murch RD. Multiuser OFDM with dptive subcrrier, bit, nd power lloction. IEEE Journl on Selected Ares in Communictions 1999; 17(10): 1747 1758. 28. Pr WH, Bh S. Resource mngement policies for fixed relys in cellulr networs. Computer Communictions 2009; 32(4): 703 711. 29. Erceg V, Hri KVS, Smith MS. Chnnel models for fixed wireless pplictions. Technicl Report, 2001. IEEE 802.16.3c-01/29r4. 30. Iuno JC, Wrulich M, Rupp M. System level simultion of LTE networs. In 2010 IEEE 71st Vehiculr Technology Conference (VTC 2010-Spring), Tipei, 2010;1 5. AUTHORS BIOGRAPHIES Chen Sun ws born on 24 My 1985. He received his BEng from Beijing University of Posts nd Telecommunictions (BUPT) in 2006 nd his MEng in 2009 lso from BUPT. He is now studying for his PhD degree under the supervision of Dr. iojun Wng in the School of Electronic Engineering of Dublin City University from 2010. His reserch interests include rdio resource mngement, rely nd heterogeneous networ. Weidong Wng ws born on 23 Mrch 1967. He got his PhD degree from Beijing University of Posts nd Telecommunictions in 2002. He is now the professor nd deputy director of Informtion nd Electronics Technology Lb in Beijing University of Posts nd Telecommunictions. He tes the role of expert of Ntionl Nturl Science Foundtion nd member of Chin Assocition of Communiction. His reserch focuses on Rdio Resource Mngement in Telecommuniction System, Internet of Things, Intelligent Trnsporttion, Cognitive Rdio nd Mobile Terminls. Yinghi Zhng got his PhD degree from Beijing University of Posts nd Telecommunictions in 2007. He is now full professor of Beijing University of Posts nd Telecommunictions. He lso tes the role of Chirmn of the Acdemic Committee of BUPT. His reserch res include Mobile/Wireless communictions, Communiction networs nd Internet of Things. He hs been engged in plenty of Ntionl nd Interntionl projects nd hs published more thn 40 cdemic ppers nd five cdemic boos. He ws honored to be the Chirmn of ICCTA2009 nd ICCTA2011 funded by IEEE nd IET. iojun Wng received his BEng in Computer nd Communictions from Beijing University of Posts nd Telecommunictions (BUPT) in Chin in 1984 nd his MEng in computer pplictions in 1987 lso from BUPT. iojun ws employed s ssistnt lecturer/lecturer in BUPT from 1987 to 1989. He received his PhD from Stffordshire University in 1993 for reserch in the re of high level logic synthesis. He joined the School of Electronic Engineering of Dublin City University s n ssistnt lecturer in November 1992, becme permnent stff in 1995 nd is now senior lecturer. He is the hed of the Networ Innovtions Center in the Rince Institute. Dr. Wng is interested in the following reserch res: Energy efficient ICT, rdio resource mngement, informtion nd networ security nd FPGA hrdwre ccelertion. 278 Wirel. Commun. Mob. Comput. 2016; 16:264 278 2014 John Wiley & Sons, Ltd.