Dynamic downlink aggregation carrier scheduling scheme for wireless networks

Transcription

1 Pubished in IET Communications Received on 2nd Apri 2013 Revised on 7th August 2013 Accepted on 6th September 2013 Dynamic downink aggregation carrier scheduing scheme for wireess networks Kan Zheng 1, Fei Liu 2, Wei Xiang 3, Xuemei Xin 1 ISSN Wireess Signa Processing and Network Lab, Key Laboratory of Universa Wireess Communication, Ministry of Education, Beijing University of Posts & Teecommunications, P.O. Box 93, No. 10, Xi Tu Cheng Road, Beijing , Peope s Repubic of China 2 Institute for Networked Systems, RWTH Aachen University, Kackertstrasse 9, D Aachen, Germany 3 Schoo of Mechanica and Eectrica Engineering, University of Southern Queensand, Toowoomba, QLD 4350, Austraia E-mai: zkan@bupt.edu.cn; kzheng@ieee.org Abstract: Carrier aggregation has been accepted as a means of bandwidth extension in the third generation ong-term evoutionadvanced (LTE-advanced) network, in an effort to support high data rate transmission with backwards compatibiity. Since there are two or more component carriers (CCs) to be aggregated, it is crucia to design efficient carrier scheduing schemes. In this study, the authors propose a nove dynamic aggregation carrier (DAC) scheme for downink transmission, which enabes CCs to aggregate with each other in a dynamic manner. The dynamic nature of the new scheme aows the tota capacity of a CCs to be fuy utiised to serve fows, whereas the number of aggregated suppementary CCs is decreased so as to ower the computationa compexity at user equipment (UE). Furthermore, the performances of the new scheme and two other carrier scheduing schemes are evauated thoroughy through both anaytica and simuation resuts. It is demonstrated that the DAC scheme offers good performances in terms of deay and throughput whie reducing energy consumption and the signaing overhead at UEs. 1 Introduction Wide bandwidth, that is, up to 100 MHz, is required for the third generation (3G) ong-term evoution-advanced (LTE-advanced) network, whose target is to support a peak data rate of 100 Mbps under high mobiity and 1 Gbps under ow mobiity [1]. Generay speaking, the most straightforward way to meet such requirements is to use arge contiguous bandwidth. However, such a straightforward method proves to be quite chaenging because of highy scarce radio frequency (RF) spectra avaiabe for mobie communications. On the other hand, spectra segments beonging to an operator, which may be of different sizes and not necessariy ocated contiguousy in the same frequency band, shoud sti be utiised. As a resut, carrier aggregation (CA) is adopted by the 3G partnership project (3GPP) as a soution to bandwidth extension for LTE-advanced [2]. Through CA techniques, two or more component carriers (CCs) can be aggregated to support high data rate transmission with backwards compatibiity. At present, there exist three types of spectrum configurations for CA, that is, contiguous CC, non-contiguous CC in a singe frequency band and non-contiguous CC in mutipe frequency bands. When CA was first introduced in LTE-advanced, the radio access network has to be modified or compemented in an effort to achieve high data rates whie reducing upgrade costs and impementation compexity. There are a number of technica chaenges reating to CA-based LTE-advanced systems such as upink CC seection, radio resource connection procedures, radio resource management of mutipe CCs, among which the carrier scheduing technique is the most significant in affecting the performance of CA-based LTE-advanced systems. The cross-cc scheduing functionaity in CA for improved contro channe optimisation is discussed in [3]. The performance of CA with eastic traffic is anaysed and compared with those of the independent carrier (IC) approach [4]. Then, a burst-eve carrier scheduing scheme is proposed in [5], which achieves a good trade-off between performance and compexity. In [6], two nove methods of search space design for mapping contro information on one CC are proposed, which can reduce the search space overapping of different user equipment (UE). Moreover, CA technique aso heps reducing interference among femtoces in LTE-advanced networks [7]. In CA, the base station, termed the enodeb in an LTE-advanced network, manages a avaiabe CCs by using a carrier scheduing scheme. An UE may simutaneousy receive or transmit on one or mutipe CCs depending on its capabiity. The simpest approach of managing mutipe CCs is to aocate each user onto a singe CC. The UE can receive data ony on one of the CCs at a time. This approach does not require any change to 3GPP Re-8 specifications, and above a, the UE costs and compexity are greaty reduced by not having to support bandwidth wider than 20 MHz. This is referred to as IC in the rest of this paper. However, the IC 114

2 scheme performs poory in terms of spectrum utiisation. By contrast, another straightforward way is to jointy schedue the radio resources of a the CCs, which is termed joint carrier (JC). It can attain the optima performance, but is ess practica because of overwheming signa processing compexity at the UE. It has been shown that the mean throughput of the IC approach with a random routing dispatcher is ony 1/L of that of its JC counterpart, when there are L CCs with the same bandwidth in the system, irrespective of the bandwidth of these CCs [4]. Furthermore, the performance of the IC scheme can be improved by using a smarter dispatcher [8]. As a resut, advanced carrier scheduing schemes are expected to strike a good baance between practicabiity and efficiency. However, to the best of our knowedge, this probem has not yet been we researched to date. In this paper, the performances of a variety of carrier scheduing schemes for CA-based LTE-advanced systems under eastic traffic are anaysed. Owing to the imited capabiities of UEs and the switch signaing overhead, it is better to maintain the connection of an UE with ony one CC as ong as possibe. In other words, infrequent switching between CCs is desirabe. Motivated by the couped processors in [9], we propose a nove dynamic aggregation carrier (DAC) scheme which enabes CCs to hep one another in a dynamica manner. When no CC has an empty queue, each CC serves ony its own queue. Whenever a queue of any CC becomes empty, this carrier wi be abe to hep its counterparts. By this way, the tota capacity of the carriers can be utiised to serve fows of the CCs with a non-empty queue. When the number of the CCs is greater than two, two methods, that is, serving the ongest queue (SLQ) and round robin with priority (RRP), can be used for cooperation among the CCs. Simuation and numerica resuts are presented for evauating the performances of the various schemes. The remainder of this paper is organised as foows. The system mode is introduced in Section 2. Severa carrier scheduing schemes are described in Section 3. In Section 4, the performances of different carrier scheduing schemes are discussed. Section 5 compares a of the schemes in terms of simuation and anaytica resuts. Section 6 concudes this paper. Owing to a arge number of abbreviations used in this paper, a ist of acronyms is given in Tabe 1. Tabe 1 Abbreviations 3G CA CC DAC IBS IC JC JSQ LTE PCC PS RA RR RRP RS SCC SLQ List of acronyms Descriptions third generation carrier aggregation component carrier dynamic aggregation carrier ideay baanced system independent carrier joint carrier joint shortest queue ong-term evoution primary component carrier processor-sharing random aocation round robin round robin with priority resource scheduer Secondary component carrier serving the ongest queue 2 System mode Let us consider the downink of an OFDMA-based network, which consists of a singe enb communicating with mutipe UEs in a time-sotted fashion. Athough CA can support the aggregation of both non-contiguous and heterogenous CCs, we assume for simpicity that the enb empoys L adjacent CCs in the same frequency band, and that the bandwidth of each CC is the same. A dynamic fow mode with eastic traffic is assumed, where a new fow arrives at the system with a finite-ength fie request, and eaves the system after the fie is transmitted [10]. Without oss of generaity, each UE is assumed to start a new transmission ony after the od one is finished, and each new transmission by the same UE is treated as a new fow. The arriving fow to the network foows a Poisson process with an average arriva rate of λ. The sizes of the fows are exponentiay distributed as shown beow { P F (n) } a = 1 e a/f, a [ {0, 1, 2,..., 1} (1) where F (n) is the fie ength of user n, and F = E[F (n) ] is the average size of the fows. Each CC is comprised of K resource bocks (RBs), aso known as subchannes, which span mutipe subcarriers in the frequency domain per time sot. One CC can serve mutipe UEs through its resource scheduer (RS) at the enb. Each UE is abe to receive data from mutipe CCs simutaneousy, abeit with an increased computationa compexity and power consumption at the UE. In each time sot, the RS aocates RBs to serve given UEs in accordance with a certain scheduing strategy. In this paper, an equa number of RBs are aocated to UEs in the queue circuary using the round robin (RR) strategy. The queueing mode of the RR scheduer can be modeed as a processor-sharing (PS) queue [10], where the UEs share the wireess resources of one or mutipe aggregated CCs aocated to them. For simpicity, the transmit power is assumed to the same for a RBs, that is, P,k = P T, 1 L, 1 k K. The received signa on RB k at CC of UE n is given by y (n) = PT a n h (n) x n + z (n), 1 L, 1 k K (2) where x n represents the transmitted signa from the nth UE, h (n),k denotes the independent compex fading channe gain on RB k at CC of UE n, modeed as h (n) CN (0, s2 ) [ 1 ] with s 2 = E h (n) 2, α n represents the path oss attenuation factor of UE n and z (n),k is modeed as zero-mean additive white Gaussian noise with a noise power of s 2 N. Then, the instantaneous signa-to-noise ratio (SNR) on RB k at CC of UE n can be cacuated as a = n h (n) 2 P T, 1 L, 1 k K (3) g (n) s 2 N Correspondingy, the achievabe data rate on RB k at CC of UE n is given by ( ) C (n) = W og g (n), 1 L, 1 k K (4) where W is the bandwidth of each subchanne. 115

3 [ ] Let C (n) = E C (n) be the time-averaged transmission rate on RB k at carrier of UE n, that is 1 ( ) C (n) = W og g (n) f (g (n) )dg(n), 0 (5) 1 L, 1 k K where f (g (n),k ) is the probabiity density function (pdf) of random variabe g (n),k. Under the Rayeigh fading channe, the fading coefficients foow an exponentia distribution and their pdfs can be expressed as ( ) f (g (n) ) = 1 exp (n) g g(n) g (n), 1 L, 1 k K (6) where g (n) = E[g (n),k ] = a ( n s 2 P T /s 2 ) N is the average SNR of UE n. The vaues of g (n) for the UEs at different ocations may be different. It is cear that the time-averaged transmission rate depends ony on the user ocation, that is, C (n),k = R (n),1 L, 1 k K. Hence, the tota time-averaged transmission rate for UE n per CC is given by C (n) = K k=1 C (n) = KR (n) (7) Therefore the average service rate per CC can be computed as m = [ ] 1 F(n) C (n) = 1 F [ 1 ( g g (n) ) ] d g (n) 1 0 C (n) (8) ( where g g (n) ) is the pdf of the average SNR received at UE n, which is reated to the distribution of the UE ocation. 3 Carrier scheduing schemes for CA-based networks In this section, two straightforward carrier scheduing schemes, that is, JC and IC, wi be presented first [11], foowed by an introduction to the proposed DAC scheme that possesses the advantages of improving system efficiency whie reducing power consumption. 3.1 Joint carrier In JC, each UE has access to one or more CCs, and is served across a CCs. In other words, the data of any current fows may be transmitted over a the CCs. As iustrated in Fig. 1, there is ony a singe RS at the enb, which is responsibe for jointy assigning the RBs of a the CCs to the fows. Such a joint processing mechanism can ead to maximum spectra efficiency and fu resource utiisation in the CA-based LTE-advanced system. Therefore the optima system performance can be achieved by using the JC scheme. However, with JC, each UE has to maintain simutaneous connections with a the CCs. A user needs to use mutipe fast Fourier transform (FFT) and RF units to receive data from more than one CC. Thus, the effectiveness of JC is argey constrained by the computationa compexity and power consumption that can be afforded by the UE. 3.2 Independent carrier In IC, each UE can ony use a singe CC to exchange data with the enb. When a new fow arrives at the system, a fow dispatcher immediatey assigns it to a CC, as shown in Fig. 1. Then, the data of this fow can ony be transmitted over the assigned CC. Specificay, there are one independent RS and fow queue for each CC. The RS of the assigned CC aocates RBs to its incoming fows. In an effort to baance the traffic oad across the CCs, the dispatcher needs to sensiby seect an aocation strategy, for exampe, the RR, random aocation (RA) or joint shortest queue (JSQ) method. RR is the simpest aocation method, where fows are assigned to the queues of a the CCs circuary. With the RA approach, the dispatcher assigns arriving fows to different CCs with given probabiities. As for the JSQ method, it takes into account the ength of each queue, and aocates an arriving fow to the queue with the east number of fows. 3.3 Dynamic aggregation carrier When the IC scheme is appied, a CC remains ide so ong as a its assigned fows have been transmitted, athough there may be fows assigned to other CCs that are sti being served. On the other hand, the JC approach has a better Fig. 1 Comparison of system mode of the JC scheme and IC scheme 116

4 trunking efficiency, that is, ess number of backogged user packets, than its IC counterpart at the expense of computationa compexity and energy consumption at the UE. We propose a DAC scheme which is capabe of striking an eegant baance between performance and compexity especiay for eastic traffic. In accordance with certain dispatching principes such as RR and JSQ, arriving fows are aocated by a dispatcher to the queue at each CC. An UE in the queue of a CC regards this CC as its primary CC (PCC) to transmit both signaing information and data. An UE has ony a singe PCC at a time, which is not supposed to be changed during transmission since switching the PCC is very time-consuming for 3GPP LTE-advanced systems [12]. With the proposed DAC method, each CC first serves the fows in its own queue when it is non-empty. Whenever a queue of any CC becomes empty, the CC with an empty queue, dubbed the suppementary CC (SCC), wi assist other CCs. In this way, the tota capacity of a the CCs can be fuy utiised to serve fows of the CCs with non-empty queues. Furthermore, we propose two methods for cooperation between the CCs under the DAC scheme in the foowing Serving the ongest queue: A the CCs with an empty queue, that is, the SCCs, are aggregated with the PCC having the ongest queue. If more than one PCC has the same ongest queue ength, the SCCs are aocated to any of them randomy. For iustrative purposes, an exampe of the system with four CCs using the SLQ scheme is iustrated in Fig. 2a. Assume that the queues of CCs 2 and 3 are empty, that is, the queue ength Q 2 = Q 3 = 0, whereas those of CCs 1 and 4 are non-empty. Then, CCs 2 and 3 may be used as the SCCs to hep others. CC 1 wi be aggregated with CCs 2 and 3 if the queue of CC 1 is onger than that of CC 4, that is, Q 1 > Q 4. Then, the RBs of CCs 2 and 3 are aggregated with those of CC 1, atogether serving the fows in the queue of CC Round robin with priority: The PCCs are first sorted according to their queue ength before being couped with the SCCs. The SCCs are circuary aocated to the ordered PCCs based on the RR principe. With this method, the PCC with a onger queue ength has a higher priority to be couped with one or more SCCs. Meanwhie, the PCC with a shorter queue ength aso has the opportunity to be aggregated with SCCs when there are more than one SCC. As shown in Fig. 2b, unike the SLQ scheme, CC 2 is firsty aocated to CC 1 because CC 1 has a onger queue ength. Next, CC 3 starts heping CC 4. 4 Performance anaysis of carrier scheduing schemes 4.1 Queueing performance Since each RS empoys the RR agorithm to schedue RBs, the CCs can be modeed as an L PS queueing system for both the IC and JC schemes [10]. Each CC in the IC scheme or a the CCs working as one in the JC scheme, are regarded as a processor, the capabiities of which are shared by distributing RBs to the fows in their serving queue by the RS. In consideration of arriving and departing processes, each PS queueing system is an M/G/1 system [13]. The soution of the average number of backogged users and response time is given in [14, 15], and proved Fig. 2 a SLQ b RRP Two exampes of the DAC scheme with four CCs independent of the distribution of the service time. Moreover, the steady-state resuts of the average queue ength, which are the backogged fows in an M/G/1 PS system, and the average time consumption of each fow in the system are consistent with those of M/M/1 PS [16]. Based on the above discussions, we present the average performance of the system under a variety of carrier scheduing schemes in the seque. 1. JC: with JC, the system can be formuated as a PS server with an arriva rate of λ. The average service rate of this PS server is the sum of a the CCs, that is, m = L =1 m = Lm.Define the traffic oad of the network as ρ = λ/μ. According to existing resuts on the PS mode with a state-dependent service rate [4, 10], the average queue ength, average sojourn time (AST) and average throughput 117

5 (ATP) can be cacuated by Q JC = r 1 r D JC = Q JC = 1 m j JC = E[F(n) ] D JC = F(m ) respectivey. The AST consists of two parts, namey, the waiting time and service time in a genera queueing system. However, in a PS queueing system, there is no waiting time for each user. Every packet is transmitted immediatey after its arriva. 2. IC: the system can be formuated as L parae PS servers with a state-dependent service rate, corresponding to the L CCs. The serving rate of each PS server is μ. There is a dispatcher routing fows to servers such that the arriva rate of fows on server is λ. The dispatch agorithms wi impact on the system performance as wi be anaysed in the foowing part. RA When the dispatcher empoys the RA agorithm, fows probabiisticay arrive at server independenty with probabiity β, where L =1 b = 1. Then, the arriving process at each server is sti Poisson and its rate is λ = β λ. Define the traffic oad of server as ρ = λ /μ. Speciay, when β =1/L, the average queue ength, AST and ATP of the whoe system can be derived as foows RR Q IC RA = L =1 D IC RA = Q IC RA Q = L =1 = L m j IC RA = E[F(n) ] F(m ) = D IC RA L r = Lr 1 r 1 r (9) (10) Another simpe dispatch agorithm is to aocate packets to each server using the RR approach. The interva of fow arrivas at each server is Erang distributed [13]. Thus, each CC behaves ike an E L /G/1 PS system with an average arriva rate of λ/l and average serving rate of μ/l. The anaytica performance of this queueing system is attainabe ony when the serving process satisfies certain conditions. We use the soution of the E L /M/1 PS system with the same arriva process and average serving rate as an approximation. As indicated in [13], its performance is better than that of the E L /G/1 PS system, when the serving time of process G has a arger variance than that of Poisson process M. The soution to the E L /M/1 PS queueing system can be obtained according to Ramaswami [17]. Thus, the average queue ength, AST and ATP can be derived as foows Q IC RR = L r 1 h D IC RR = Q IC RR = 1 L m 1 h j IC RR = E[F(n) ] m(1 h) = F D IC RR L (11) where η denotes the unique root in the unit circe of (14) beow. The pdf of the time interva between fows is given by p(t) = (t)l 1 (L 1)! e t, t 0 (12) The Lapace transformation of (12) is f (s) = +1 0 p(t)e st dt = ( ) L (13) + s According to the method in [17] in soving the AST in the G/M/1 PS system, (5) in [17] can be written as ( ) ( ) L h = f m m h = + m m h (14) L ( ) L = h+ m m h The minima non-negative root of (14) is the soution to η in (11). JSQ The JSQ method aocates a new arriving fow to the serving queue with the east number of fows backogged [18]. The arriva process of each processor is not independent, since the reationship of the queue engths needs to be taken into account. By using a specia singe queue approximation (SQA) method, the performance of the system based on the PS serving processors with the JSQ method can be anaysed according to Gupta et a. [19]. The performance of the M/G/L/JSQ PS system may be approximated by that of the M n /M/1 PS system. The M n (M) /G/1 PS system obtained by SQA is insensitive to the serving process, simiar to M/G/1 PS. Thus, the average queue ength and sojourn time of M (M) n /G/1 PS are the same as those of M n /M/1 PS as foows 1 C (n) = W 0 ( ) og g (n) 1 L, 1 k K f (g (n) )dg(n), (15) The average number of backogged users for various r and L can be found in Tabe 2 [20]. DAC: the system empoying the DAC scheme can be modeed as a specia M/G/K PS system. Different from the IC scheme, the number of service ines K and the capabiities of them vary depending on the CA state. According to the conservation aw for time-shared systems in [13], the average queueing performance of the DAC scheme is the same as that of the JC scheme, because no 118

6 Tabe 2 Average number of backogged users for various ρ and L in the JSQ system [20] ρ L transmission bandwidth of the carriers is wasted when there are sti fows in the queues waiting to be served. Thus, the DAC system ensures fu utiisation of carrier resources, and the average queue ength, AST and ATP can be derived as per (9). Moreover, the departing process of the DAC system is aso a Poisson one because of the insensitivity of the PS scheduing system, and that the aggregation can be regarded as a combination of Poisson processes [14 16]. The proof of the insensitivity of the M/G/1 PS queue on the distribution of the service time is detaied in the Appendix. 4.2 Number of SCCs It is we known that, to achieve the same deay and throughput performance, the ess number of SCCs used by each UE is, the more suitabe the oad baance scheme is for practica systems. Firsty, an UE served by ony the PCC has ower power consumption in comparison with one served by both PCC and SCCs. The power consumption increases with the number of CCs an UE has to receive and process because of the more FFT and RF units required and more data streams combined by the mutipexer [3]. Secondy, a ess contro signaing overhead is needed when a ess number of SCCs are aggregated with the PCC. For exampe, in the JC scheme, the channe state information of a the CCs must be estimated and transmitted for each user. This wi consume more bits than using fewer SCCs or ony the PCC. Therefore the number of active SCCs pays a crucia roe in evauating the performance of the proposed carrier oad baance schemes. For ease of anaysis, deay because of CA scheduing is not considered in this paper. The CCs with an empty queue can be immediatey aocated to users with fows by the proposed scheduing schemes. In addition, a the CCs can be used as the PCCs of different users if the number of the CCs is no ess than that of existing users in the system. Thus, a minimum number of active SCCs are needed in such a system. We ca it the ideay baanced system (IBS), whose performance can serve as a upper bound for practica systems. 3. DAC: as shown in Fig. 3, the arriving and departing fow processes in the DAC system can be modeed as a birth death process. The birth death process is a specia case of the continuous-time Markov process, where each state represents the current number of active UEs and transitions occurring between neighbouring states. This is a typica M/ M/1 process, where the arriva of users foows a Poisson distribution whie the service time is exponentiay distributed. When the number of active users is no ess than the tota number of CCs, each UE can use ony one CC as its PCC and thus does not need to aggregate SCCs in the IBS. However, when the number of active users is ess than that of CCs, to guarantee the fu utiisation of wireess resources, some UEs can use SCCs aggregated with their PCCs in accordance with a certain DAC scheme. Using a variety of DAC schemes may resut in different SCC aggregation states. A four-cc system iustrated in Fig. 3 is used as an exampe to demonstrate this fact. The steady-state probabiity of each state of this M/M/1 system can be easiy soved as foows p(0) = 1 r p(n) = (1 r)r n (16), n = 1, 2,... SLQ method There is no CC working when the system is in the ide state. When there is a singe UE in the system, that is, in state 1, the 1. JC: for the JC scheme, the number of SCCs is aways L 1, indicating P{N SCC = L 1} = 1, since there is ony a singe PCC aggregated by a the other CCs. Hence, JC can ony be used in the LTE-advanced system, in which UEs are abe to transmit data through mutipe CCs, and thus are not backward compatibe with LTE UEs. 2. IC: for the IC scheme, each CC serves UEs independenty without aggregating any other SCC, making the number of SCCs to be 0 at a times, that is, P{N SCC =0}=1. However, radio resources may be wasted without an appropriate CA scheme. Fig. 3 RRP States of the number of SCCs in four CCs IBS with SLQ and 119

7 UE wi have three SCCs aggregated with its PCC. When there are two UEs, one of them may have two SCCs, whereas the other one has no SCC with the SLQ scheme. When there are three UEs, ony one UE may have one SCC, whereas the other two have none. When the UE number is more than 3, a UEs have no SCC. The probabiities of various numbers of SCCs are cacuated as foows [ v SLQ (0) = (1 r) r 2 + 2r 3 + 4r 4 ] /(1 r) v SLQ (1) = (1 r)r 3 v SLQ (2) = (1 r)r 2 v SLQ (3) = (1 r)r (17) The normaised probabiity of SCCs aggregated by the SLQ method is given by { } P N SCC = = vslq ()/ L 1 v SLQ (m) (18) m=0 where P{N SCC = }, 0 is the probabiity of each UE using SCCs (N SCC = ) for transmission, which is a meaningfu measurement metric to assess the oad baance performance of the DAC schemes and dispatching agorithms. For a genera system with L CCs, ω SLQ (m) can be expressed as L 1 (1 r) (i 1)r i + Lr L, = 0 v SLQ () = i=2 (1 r)r L, = 1,..., L 1 (19) 5 Numerica and simuation resuts In this section, the performances of various carrier scheduing schemes in the LTE-advanced system are compared. The system main parameters are isted in Tabe 3. The urban macro (UMa) wireess channe environment is adopted for the purpose of performance studies [21]. It targets the scenario of continuous coverage for urban areas. A Tabe 3 Parameter Simuation parameters Vaue number of CC (L) 4 number of subchannes per CC (K) 25 tota bandwidth 5 MHz distance between sub-carriers (W s ) 15 KHz penetration oss 20 db tota BS TX power (P tota ) 49 dbm for 20 MHz noise figure of UE 5 db therma noise spectra density 174 dbm/hz fasting fading mode Rayeigh ength of time sot ( 1 ms average size of fows F ) n 500 Kb carrier frequency ( f c ) 2 GHz channe mode UMa defined in 3GPP [21] path oss PL = og 10 d RRP method The probabiities of various numbers of SCCs using the RRP method with four CCs are given as foows [ v RRP (0) = (1 r) 2r 3 + 4r 4 ] /(1 r) v RRP (1) = (1 r)(2r 2 + r 3 ) v RRP (2) = 0 v RRP (3) = (1 r)r (20) Aso, the normaised probabiity of SCCs aggregated by RRP is { PF (n) } a = 1 e a/f, a [ {0, 1, 2,..., 1} (21) Owing to the high compexity of RRP, a genera expression of ω RRP (m) is anayticay unattainabe. The probabiity of UEs without the use of any SCC, that is, P{N SCC = 0}, is an important performance metric. Since UEs in the LTE system cannot support CA, a higher probabiity of UEs without using SCCs means better backward compatibiity with LTE for LTE-advanced system. Fig. 4 AST and throughput with IC and JC a AST b Average throughput 120

8 hexagona depoyment is used with an inter-site distance of 500 m and antennas mounted ceary above rooftop. Non-ine-of-sight is common for this scenario. Base stations operate at 2 GHz. 5.1 Comparison of queueing performance In Fig. 4, wefirsty compare the performance of the AST and ATP of the JC and IC schemes with three dispatching agorithms. From the viewpoint of performance, the JC scheme is the best, verified by not ony the simuation resuts, but aso the anaysis in (9). For the IC scheme, its performance is poorer than that of JC and depends on the chosen dispatching agorithm, attributed to the unbaanced oad of each CC in the IC scheme. With the RA method, the AST of each fow is 4 (number of CCs) times that of JC, whereas the ATP is 1/4 exacty as given in (10). The performance of the JSQ dispatching agorithm is the best with the IC scheme, and very cose to the anaytica resuts, which are the approximation resuts given in Tabe 2. Moreover, the RR method can achieve a better performance than RA. The anaytica resuts in the E L /M/k PS system with the same mean capacity μ are used as the upper bounds of the performance achievabe by the RR method. As shown in Fig. 4, the simuated performance is poorer than the anaytica bound when the RR method is appied in the case of IC. The difference between the simuation Fig. 6 Statistica resuts of the number of SCCs a Cumuative distribution of the number of SCCs b Mean and variance of the number of SCCs Fig. 5 a SLQ b RRP AST and throughput with DAC resut and the anaytica bound increases when the traffic oad becomes heavier. However, when the arriva rate of fows is ow, the anaysis bound is very cose to the simuation resut, which can be used as a good approximation. Next, Fig. 5 shows both the simuation and anaytica resuts of the AST and throughput of the system with the SLQ and RRP methods when empoying the DAC scheme. Both the JC and two DAC schemes are abe to ensure fu utiisation of radio resources. Thus, they have the same performance in terms of the sojourn time and throughput, which is consistent with the anayses in Section 4. Unike the IC scheme, the performance of DAC is independent of the underying dispatching method. 5.2 Comparison of the number of SCCs As discussed previousy, with the JC scheme every UE is served by a the aggregated CCs simutaneousy, whie DAC can greaty reduce the need of CA. The power consumption per user increases with the number of CCs an UE has to receive and process [3]. The ess probabe each UE uses mutipe SCCs, the ess processing compexity and power the UE requires. We use (18) and (21) to cacuate the probabiity of the number of SCCs that each UE may use in the IBS, which can be used as the optima bound. 121

9 The arriva rate of fows λ is 20 s 1, impying that the average interva between arriving fows is 50 ms. The cumuative distribution curves of the numbers of SCCs are depicted in Fig. 6a. Let p{n SCC = 0} be the probabiity of an UE without using any SCCs, indicating that the UE uses ony the PCC for transmission, which is the same as LTE Re-8. The SLQ method has a higher p{n SCC = 0} than that of RRP when using the same dispatching method. In the SLQ scheme, the SCCs hep ony the PCC with the ongest queue, eaving other PCCs with a non-empty queue aone. Thus, SLQ is better backwards compatibe with the LTE system, whose UEs are unabe to communicate with mutipe CCs simutaneousy. The means and variances of the numbers of SCCs under various scheduing schemes are shown in Fig. 6b. Athough SLQ has higher p{n SCC = 0}, RRP has a smaer variance, impying better UE fairness and ess frequent carrier switching. In addition, the dispatching method aso has an impact on the probabiity of the number of SCCs, as demonstrated in Fig. 6b. More baanced traffic using certain dispatching methods wi ead to a ower possibiity that UEs use mutipe carriers. In terms of traffic baance, JSQ is the best, and performs fairy cose to the IBS. In our simuation of the four-cc system, the JC scheme makes a the UEs aways having three SCCs, more than the proposed DAC scheme as shown in Fig. 6. Therefore it incurs higher power consumption and processing compexity per user. Therefore it incurs higher power consumption and processing compexity per user. 6 Concusion In this paper, we propose a nove DAC scheme for the CA-based LTE-advanced system. The system performance, incuding the sojourn time and throughput, is anaysed using queueing theory. Among a the schemes, the JC scheme is demonstrated to perform best in terms of the sojourn time and throughput. With the IC schemes, different dispatch agorithms ead to different performances, in which the JSQ is preferred to from the performance view. On the other hand, the performances of the systems with the DAC are not independent on the dispatch agorithm. Moreover, the processing compexity of impementing CA for UEs is investigated based on the distribution of the number of secondary CCs. The DAC scheme enjoys the same fu utiisation as the JC scheme and thus provides the best transmission performance. Moreover, it is abe to reduce the energy consumption and processing compexity at the UE. The SLQ and RRP methods have their respective features. The former has a high possibiity of UEs without using any secondary CC such that it can support more LTE UEs, improving the backward compatibiity of the LTE-advanced system. The atter resuts in better fairness among UEs, athough it may use secondary CCs aggregated with PCCs more frequenty than the SLQ scheme. In addition, the JSQ dispatching method can greaty improve the baance of the traffic oad on each CC, which can enhance the performance of the IC scheme and reduce the number of secondary CCs in the DAC scheme, bringing it cose to the IBS. It is concuded that the DAC scheme has the advantages of ensuring fu resources utiisation whie reducing energy consumption as we as processing demands at the UE. 7 Acknowedgments This work was funded in part by China NSFC (no ), Program for New Century Exceent Taents in University (NCET ) and the Nationa Key Technoogy R&D Program of China under grant 2013ZX References 1 3GPP TR V10.0.0, Requirement for further advancements for E-UTRA (LTE-Advanced), Apri GPP TR V10.0.0, Feasibiity study for Further Advancements for E-UTRA (LTE-Advanced), March Pedersen, K.I., Frederiksen, F., Rosa, C., et a.: Carrier aggregation for LTE-advanced: functionaity and performance aspects, IEEE Commun. Mag., 2011, 49, (6), pp Lei, L., Zheng, K.: Performance evauation of carrier aggregation for eastic traffic in LTE-advanced systems, IEICE Trans. Commun., 2009, E92-B, (11), pp Zhang, L., Zheng, K., Wang, W., Huang, L.: Performance anaysis on carrier scheduing schemes in the ong-term evoution-advanced system with carrier aggregation, IET Commun., 2011, 5, (5), pp Li, A., Takeda, K., Miki, N., et a.: Search space design for cross-carrier scheduing in carrier aggregation of LTE-advanced system. Proc. IEEE Int. Conf. Communications (ICC), Kyoto, Japan, June 2011, pp Zheng, K., Hu, F., Lei, L., Wang, W.: Interference coordination between femtoces in LTE-advanced networks with carrier aggregation. Proc. IEEE Commun. Networking in China (CHINACOM), Harbin, China, August 2011, pp Wang, Y., Pedersen, K.I., Mogensen, P.E., Sorensen, T.B.: Carrier oad baancing methods with bursty traffic for LTE-advanced systems. Proc. PIMRC, Tokyo, Japan, September 2009, pp Fayoe, G., Iasnogorodski, R.: Two couped processors: the reduction to a Riemann-Hibert probem, Z. Wahrscheinichkeitstheor. Verwandte Geb., 1979, 47, (3), pp Lei, L., Lin, C., Cai, J., Shen, X.: Fow-eve performance of opportunistic OFDM-TDMA and OFDMA networks, IEEE Trans. Wire. Commun., 2008, 7, (12), pp Zhang, L., Liu, F., Huang, L., et a.: Traffic oad baance methods in the LTE-advanced system with carrier aggregation. Proc. IEEE Int. Conf. Communications, Circuits and Systems (ICCCS 2010), Chengdu, China, Juy 2010, pp Chang, J., Li, Y.J., Feng, S., et a.: A fractiona soft handover scheme for 3GPP LTE-advanced system. Proc. IEEE Int. Conf. Communications Workshops (ICCW2009), Dresden, Germany, June 2009, pp Keinrock, L.: Queueing systems (Wiey, 1976) 14 Sakata, M., Noguchi, S., Oizumi, J.: Anaysis of a processor-sharing queueing mode for time-sharing systems. Proc. Second Hawaii Int. Conf. System Sciences, January 1969, pp Sakata, M., Noguchi, S., Oizumi, J.: An anaysis of the M/G/1 queue under round robin scheduing, Oper. Res., 1971, 19, pp Key, F.P.: Reversibiity and stochastic network (Wiey, 1979) 17 Ramaswami, V.: The sojourn time in the GI/M/1 queue with processor sharing, J. App. Probab., 1984, 21, pp Winston, W.: Optimaity of the shortest ine discipine, J. App. Probab., 1977, 14, pp Gupta, V., Bater, M.H., Sigman, K., Whitt, W.: Anaysis of joint-shortest queue routing for web server farms. PERFORMANCE IFIP wg 7.3 Int. Symp. Computer Modeing, Measurement and Evauation, Coogne, Germany, October 2007, vo. 64, pp Gupta, V., Bater, M.H., Sigman, K., Whitt, W.: Simuation resuts for JSQ server farms with processor sharing servers, Perform. Eva., 2007, 64, (9 12), pp GPP TR , v2.0.0, Further advancements for E-UTRA, physica ayer aspects. March Appendix Insensitivity of queue M/G/1 PS on distribution of service time Firsty, we derive an auxiiary resut, which is vaid for a genera G/G/1 queue. Denote x is the number of transmitted bits of a fow; 122

10 transmission. By age x, a fraction F x (x) of the fows has departed and a fraction 1 F x (x) of them remains in the G/G/1 system. By combining (23) and (24), we arrive at Fig. 7 Subsystem defined with the amount of received bits F X (x) is the cumuative distribution function of the ength of each fow; N(x) is the average number of fows in the system with ess than x bits having been transmitted; T(x) is the average time spent in the system by the fows of which x bits have been transmitted; and n(x) =(dn(x)/(dx)) is the average fow density. We then appy Litte s theorem to a subsystem defined as foows. As shown in Fig. 7, a fow arrives at the subsystem when the amount of received bits is more than x; the fow has then spent T x in the G/G/1 system on average. A fow departs from the subsystem when the amount of received bits is more than x + Δx; the fow has then spent T(x + Δx) in the G/G/1 system on average. Then, no fows exit in the subsystem on competion of the job. Finay when Δx 0, the discreteness of bits becomes irreevant. As fows arrive at the system with rate λ and the fraction of 1 F x (x) reach the service age x, the arriva rate at the box, that is, the subsystem, is λ(1 F X (x)). The mean deay of a fow in the box is T(x + Δx) T(x). According to Litte s theorem, we have N(x + Dx) N(x) = [1 F X (x)][t(x + Dx) T(x)] (22) Divided by Δx 0, the auxiiary resut is given by n(x) = [1 F X (x)] dt(x) dx On the other hand, we can directy deduce that (23) n(x) = n(0)[1 F X (x)] (24) This is because a the fows in a PS queue are served with an equa amount of resources. As a resut, the service ages increase at the same rate. The difference in fow density with respect to the service age rises, that is, n(x), due ony to the departure of the fows on competion of their dt(x) dx = n(0) and T(x)=0ifx = 0. Then, we have (25) T(x) = n(0) x (26) which is the average time spent in the G/G/1 system by fows with age x, and aso the tota mean deay of those fows whose service demand is aso x bits, that is, the mean deay conditioned on the service requirement. Furthermore, one can deduce that im T(x) = x x 1 C(1 r) (27) where C is the service capabiity of the system, and ρ = λ/μ. The arriva of a very big job is a rare event. Such a big job stays in the system for a very ong time. Meanwhie, a other sma jobs arriving at the system pass by. The big job sees effectivey the service rate remaining from the other jobs, that is, C(1 ρ). Thus, the coefficient of x in (5) is 1/C(1 ρ) as shown beow T(x) = x C(1 r) (28) By averaging (7) for the conditiona deay with respect to the distribution of the fow ength, and then appying Litte s resut, we obtain the foowing mean resuts E[T] = 1/m, 1/m = E[X ]/C (29) 1 r E[N] = r 1 r (30) The distribution of the serving time is not assumed in the derivation process. Therefore the mean performance of the M/G/1 PS queue is insensitive. 123