Proportional Fair Resource Partition for LTE-Advanced Networks with Type I Relay Nodes

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1 Proportional Fair Resource Partition for LTE-Advanced Networks with Type I Relay Nodes Zhangchao Ma, Wei Xiang, Hang Long, and Wenbo Wang Key laboratory of Universal Wireless Communication, Ministry of Education, Beijing University of Posts and Telecommunications, China Faculty of Engineering and Surveying, University of Southern Queensland, Australia mzc.bupt@gmail.com Abstract In 3GPP LTE-Advanced networks deployed with type I relay nodes (RNs), resource partition is required to support in-band relaying. This paper focuses on how to partition system resources in order to attain improved fairness and efficiency. We first formulate the generalized proportional fair (GPF) resource allocation problem to provide fairness for all users served by the evolved node B (enb) and its subordinate RNs. Assuming traditional proportional fair scheduling is executed independently at the enb and each RN to achieve local fairness, we propose the proportional fair resource partition algorithm to tackle the GPF problem and ensure global fairness. Through system level simulations, the proposed algorithm is evaluated and compared with both non-relaying and relaying systems with the fixed resource partition approach. Simulation results demonstrate that the proposed algorithm can achieve a good trade-off between system throughput and fairness performance. I. INTRODUCTION Relaying has been seen as one of the most promising techniques towards the next generation of mobile communication systems. LTE-Advanced, as a major enhancement of the 3GPP Long Term Evolution (LTE) standard, incorporates relaying technology to improve cell coverage and throughput in cell border areas. There are mainly two types of relay nodes (RNs) defined in LTE-Advanced networks to support relaying [1]. The type I RN, featuring independent scheduling capability, is able to transmit its own synchronization signals, reference signals and physical control channels. Thereby from the perspective of its associated user equipments (UEs), the type I RN can be viewed as a full-functional enb (evolved Node B, i.e., the LTE base station), except that it uses a wireless backhaul to connect to the core network via the donor enb. The type II RN does not have own control signals. It is transparent to the UEs, with the main objective of assisting and enhancing the donor enb s signal. Featuring better implementation feasibility and backward compatibility, the type I RN has been extensively advocated by telecommunications operators and manufacturers. The network incorporating type I RNs also poses new challenges. To support the in-band relaying function, the radio frames need to be partitioned into two types of subframes (SFs), i.e., the backhaul SFs and the access SFs. The enb can only schedule data packets to/from the RNs in the backhaul SFs, while the enb and RNs can both independently schedule transmissions to/from their associated UEs in the access SFs. With this decentralized scheduling architecture, how to partition system resources affects not only the system spectral efficiency but the overall fairness performance. The majority of work on resource allocation for relay-enhanced cellular systems is usually based on the assumption that the two phases of relaying transmission occupy equally partitioned resources [2]-[4]. Although adaptive time domain resource partition is suggested in [3], their scheme merely focuses on maximizing throughput without concerning the impact of fairness. Moreover, the authors assume that the partition pattern can be altered in a frequent frame-by-frame manner, which is impractical for a decentralized system. In this paper, a proportional fair (PF) based scheduling approach is proposed to achieve throughput gains and fairness at the same time. The generalized proportional fair (GPF) problem to optimize the sum of logarithmic user data rates is formulated for downlink Orthogonal-frequency-divisionmultiple-accessing (OFDMA) systems with multiple fixed RNs. Based on the proposed resource partition method, we provide an efficient resource allocation scheme in the sense of PF for the network with type I RNs. The remainder of this paper is organized as follows. The system model is described in Section II, while the GPF resource allocation problem is formulated in Section III. The PF resource partition algorithm is presented in Section IV and Section V presents the simulation results. Finally, concluding remarks are drawn in Section VI. II. SYSTEM MODEL We consider a downlink two-hop relay-enhanced cellular network. In the cell of interest, there are a set of UEs U and a set of serving nodes (SNs) S, comprised of an enb and a number of RNs. The SN s (s S) denotes the enb when s =0, or an RN otherwise. The UE can either communicate with the enb directly or via an RN. A UE can be associated with at most one SN at a time, and no cooperative transmission is considered for simplicity. The UEs associated with SN s are a subset U s of U. The RNs perform in-band half-duplex relaying through layer 3 [1]. All the three types of links, i.e., enb RN, RN UE and enb UE operate within the same frequency band. The received data packets through the enb RN link are decoded and queued up in the service buffer at the RN, /11/$ IEEE

2 y c n e u q e r F B One radio frame, T frame = 10 ms SF #0 SF #1 SF #2 SF #9 Access enb RN 1 UE UE RN 2 UE RN s UE Fig. 1. Time Access Backhaul Access enb RN 1 enb RN 2 enb RN s T RB = 1 ms RB 1 RB 2 RB j Illustration of frame structure model waiting to be forwarded to the target UE through the RN UE link. In order to avoid self-interference, the enb RN and RN UE transmission can not occur simultaneously. Based on the frame structure defined in 3GPP LTE [5], a radio frame is further partitioned as access SFs and backhaul SFs as shown in Fig. 1. In the access SFs, the enb UE and RN UE transmissions can take place simultaneously with full frequency reuse. In the backhaul SFs, the enb allocates orthogonal resources for different enb RN transmission. The access/backhaul partition pattern repeats with a certain period until it is changed by a higher layer configuration. A basic OFDMA resource allocation unit is called a resource block (RB), consisting of a constant number of subcarriers and OFDM symbols (12 14 in 3GPP LTE). We assume each radio frame contains a set J of RBs for data transmission. With a certain resource partition scheme, the access and backhaul SFs occupy RB subsets J a and J b of J, respectively. Note that for the sake of simplicity, we relax the frame structure constraint that J a and J b need to be an integer multiple of the number of RBs per subframe, where means the cardinality of a set. At the SN UE link, we suppose all UEs have independent multipath Rayleigh fading channels and their instantaneous channel gains are flat over each RB. We further assume the interference from all surrounding enbs and RNs always exists and can be factored into additive white Gaussian noise. For each UE u associated with SN s, its instantaneous signal-tointerference-plus-noise ratio (SINR) on the jth RB is given by γ j,u,s = γ j,u,s H j,u,s 2, where H j,u,s CN(0, 1),γ j,u,s and H j,u,s are the average SINR and the complex channel gain of UE u on RB j, respectively. We suppose all SNs allocate equal power over the RBs. Then, UE u obtains the same average SINR over each RB j, i.e., γ j,u,s = γ u,s, j J a. For the enb RN link, the flat fading channel is assumed under a fixed line-of-sight (LOS) condition. Then the instantaneous SINR of RN s is constant for all RBs, i.e., φ j,s = φ s, j J b, where φ s is the average SINR of the enb RN s link. III. PROBLEM FORMULATION It has been shown in [6] that the PF resource allocation problem amounts to optimizing the following logarithmic utility function max log R u (1) u U where R u is the data rate achieved by UE u. Let ρ u,s be a binary association variable, i.e., ρ u,s =1if UE u is associated with SN s, 0 otherwise. Let ω j,u be the binary resource allocation variable, i.e., ω j,u =1if the RB j is allocated to UE u, 0 otherwise. Then for the UE u associated with SN s, its instantaneous data rate achieved in a radio frame can be represented as R u,s = j J ω j,ur j,u,s, where r j,u,s is the instantaneous data rate achieved by UE u on RB j. Next, we can formulate the generalized proportional fairness (GPF) problem for the relay-enhanced system as max ( ) ρ u,s log ω j,u r j,u,s (2) j J s.t. ρ u,s =1,ρ u,s {0, 1}, u U u Us ω j,u 1,ω j,u {0, 1}, j J, s S (3) The first constraint guarantees each UE can only associate with one SN at a time. The second constraint ensures that the UEs associated with the same SN are scheduled with disjoint RBs. IV. PROPORTIONAL FAIR RESOURCE PARTITION AND SCHEDULING The problem described in (2), which aims at optimizing the GPF objective in a frame-by-frame manner, is not only NP-hard in its computation complexity, but impractical due to the need for joint processing of global network information. Therefore, we consider a two-step solution to simplify the problem. First, the enb partitions the system resources for the enb and RNs. Next, the enb and RNs independently schedule their associated UEs within the partitioned resource area. The first step can be performed semi-statically based on the long-term averaged system information, while the second step is performed in every subframe. In this way, the system performance can be effectively improved with a low complexity. A. Resource Partition We assume the user association relationship has been determined with certain routing algorithm. The resource partition pattern can remain constant for a period of time, possibly in the order of several seconds. Meanwhile, we suppose each SN s schedules its associated set of UEs, i.e., U s,usingthe traditional PF algorithm within the partitioned access SFs. In this case, we can utilize existing analytical results about PF scheduling to simplify the analysis. According to [7], assuming Rayleigh fading and the data rate are linear functions of the SINR, which is approximately accurate when the SINR is not too high [8], the resulting scheduling gain of the PF algorithm, which accounts for the throughput gain over round-robin scheduling, can be simply expressed as G = U. s We further assume all UEs have elastic traffic and service queues at the enb are always backlogged. Hence, the UEs associated with the enb can always consume all the resources of the access SFs, i.e., J a. Then the average data rate of UE u when associated with the enb can be estimated as R u,0 J a U 0 f(γ u,0)g( U 0 ) (4)

3 where f( ) represents the linear mapping function from the SINR to the data rate achievable on one RB. However, for the UEs associated with RNs, the data rates are constrained by not only the resources of the access SFs but the limited capacity of the enb RN link. The RN can not make full use of the resources of J a unless the enb RN link supplies enough service data. Thus we assume RN s can only schedule on a RB subset Ja s of J a. Furthermore, we assume certain UE-specific scheduling mechanism for the enb RN link is implemented, so that the amount of data delivered for each UE u (u U s ) through the enb RN s link can deliberately satisfy the requirement of the RN s UE u link scheduled with the PF algorithm. Then the average data rate of UE u associated with RN s can be approximated as R u,s J s a f(γ u,s)g(). (5) Therefore, the aggregate data rate of RN s achieved within the access SFs, denoted as R s a, can be represented as R s a = u U s R u,s. (6) Correspondingly, we assume the set of RBs required for the enb RN s transmission in the backhaul SFs is Jb s of J b. Since the enb RN s channel is assumed to be flat, there is no multi-user scheduling gain achievable. Hence, the average data rate on the enb RN s link, denoted as R s b, can be estimated as R s b = Jb s f( φ s ). (7) The data rates achieved in the backhaul and access SFs should be balanced so as to avoid congestion at the RNs. By setting R s a = R s b, we can attain the backhaul-to-access resource allocation ratio for RN s as follows η s = J b s f( γ u,s )G() Ja s = u U s f( φ, s S,s 0. (8) s ) Under the total RB constraint of one radio frame, we have,s 0 J s b + J a = J. For ease of exposition, let η 0 = 1, J 0 a = J a for the enb. We then have η s J s a = J. Substituting (4) and (5) into (2), the GPF resource allocation objective function can be rewritten as ρ u,s log J a s f( γ u,s )G(). (9) With = u U ρ u,s, the GPF objective function in (9) can be transformed to log Ja s + ρ u,s log f( γ u,s)g(). (10) We assume the average SINRs of the related links, i.e., γ u,s (s S) and φ s (s S,s 0), remain constant during the resource partition cycle. As a result, the backhaul-toaccess resource allocation ratio η s is also determined. Then, as the second term of (10) is a deterministic quantity, the GPF resource allocation problem amounts to max log Ja s (11) s.t. η s Ja s = J (12) Ja s J a 0, s S (13) With the inequality constraint in (13), it is difficult to obtain the optimal solution to the above problem. Therefore, we assume a subset L of S can be determined in advance, which includes the enb and all the RNs that can fully utilize the access SFs, i.e., Ja s = J a, s L. Then, the above problem can be transformed to an optimization problem with equality constraints only max log J a + log Ja s (14) s.t. η s J a + η s Ja s = J (15) This problem can be readily solved through the Lagrange multiplier algorithm as L( Ja s,λ)= log J a + log Ja s ( λ η s J a + ) η s Ja s J (16) where λ 0 is the Lagrangian multiplier. We relax Ja s to real values, denoted by Jˆ a s. We then take the derivatives of (16) with respect to Jˆ a s and set their values equal to zero. Further considering constraint (15), the following results can be obtained J, Jˆ η a s s U = l L U l l L η l J U, (17) Since the resource partition results should be integers, we need to round up the results in (17) and ensure a minimum RB number for the RNs that have active users associated. We then ˆ have Ja s = max(1, Ja s ), s S, 0, where means rounding up to the nearest integer. Likewise, the related resource partition in the backhaul SFs can also be determined as Jb s = η s Ja s. In order to satisfy the total resource constraint in (15), further refinement to the resource partition results might be required. Now, the only remaining problem for resource partition is how to decide the set L. We adopt an iterative algorithm trying to minimize the number of RNs in L. Initially, only the enb is included in the set L, and then corresponding resource partition is predicted using (17) as Ja s. Denote by E = {s Ja s > Ja 0,s S}the set consisting of the RNs that violate the constraint (13). If E is not empty, we select the

4 RN with the largest access SF requirement from E and add it into the set L. With the renewed L, this process is iterated until all RNs satisfy the constraint (13). The algorithm is described in greater detail below Algorithm 1 Obtain the set L Input: L = {0}, U s, η s, s S repeat { With (17), E = s Us l L η s > if E is not empty then s = arg max s E L = {L,s } end if until E is empty U s η s U l η l l L },. Algorithm 1 requires S times of iterations at most. Since the computational complexity for each iteration is O( S ), the maximum complexity for algorithm 1 is O( S 2 ), which is quite tolerable considering the number of RNs deployed per cell should not be very large. However, it should be noted that if the algorithm 1 terminates at the first loop, the resulting solution is optimal to the resource partition problem in (11). If further iterations are required, the optimality of the solution can not be guaranteed. B. User Scheduling After the enb determines the resource partition pattern, the enb and RNs can carry out the scheduling procedure in each subframe. In the access SFs, each SN independently schedules its associated UEs using the traditional PF algorithm [9]. Each RB j of J a is allocated to UE u with the highest ratio of instantaneous achievable rate over the average data rate u r j,u,s = arg max (18) u U s R u,s (t 1) where R u,s (t 1) denotes the average data rate of UE u before the current scheduling subframe t. The average data rate of UE u is updated according to the following rule R u,s (t) =(1 1 T )R u,s(t 1) + 1 T R u,s (t) (19) where T is the average window length. In the backhaul SFs, the enb performs a queue-based scheduling scheme to ensure that each UE associated with an RN can achieve the matched data rates on the enb RN and RN UE links. Let the service queue of UE u (associated with RN s) at the enb be Q 0,u, and the corresponding service packet queue at RN s be Q s,u. The difference between Q 0,u and Q s,u can reflect the service demand of each UE u on the enb RN link according to [2]. We suppose the RN can feedback the queue information of each associated UE to the enb. The enb then schedules to UE u each RB of the given resource area partitioned for RN s according to the following rule u = arg max{l(q 0,u ) L(Q s,u )} (20) where L( ) indicates the queue length. V. SIMULATION RESULTS In this section, we evaluate the proposed PF resource allocation algorithm through system level simulations. We configure a network with two circles of cells surrounding the one of interest, i.e., a total of 19 hexagonal cells are considered. The enb is located at the center of each cell, equipped with 120 o sectorized antennas. The inter-site distance, i.e., the nearest distance between two enbs, is set to 500 meters. Twenty-five UEs and a fixed number of RNs are both randomly dropped within each sector following a uniform spatial distribution. The system carrier frequence and bandwidth are set to 2 GHz and 10 MHz, respectively. The enb and the RN are both fitted with single antenna, transmitting with a total power of 46 dbm and 30 dbm, respectively. The path-loss models are according to 3GPP TR [1]. The shadow fadings of enb-rn, enb- UE and RN-UE links follow log-normal distributions with standard variances of 6 db, 8 db and 10 db, respectively. The fast fadings of enb-ue and RN-UE links are modeled with the ITU Pedestrian A channel model at 3km/h. To guarantee the high efficiency of the enb RN link, the RN is equipped with two antenna sets, i.e., a 30 o directional antenna pointing toward the donor enb and an omni-directional antenna for the RN UE link. We compute full interference from two circles of surrounding cells, assuming that the activities in each of these surrounding cells are identical to those in the cell of interest. The routing algorithm is consistent with the linkoptimal policy, which has been extensively utilized in previous work [10]. The proposed scheme with PF resource partition, referred to as scheme 1, is compared with both the scheme without relaying and the relaying scheme with fixed resource partition, denoted as scheme 2, where the backhaul and access SFs are configured so that each group of SFs occupies half of the total resources, consistent with the assumptions commonly found in previous work [2]-[4]. The routing and scheduling algorithms adopted by both relaying schemes are the same. In the ensuing discussions, the system spectral efficiency (SE) is calculated as the sector throughput normalized by the system bandwidth. The GPF factor is the sum of the logarithmic average throughputs of all served UEs normalized by the UE number, which is used as the metric for fairness measurement. Figs. 2 and 3 show the system SE and the GPF factor achieved by different schemes versus the number of RNs, respectively. It is demonstrated that both the efficiency and fairness performance of the proposed scheme 1 are better than in the case without relaying. Moreover, the gains increase with the number of RNs. It is also shown in Table. I that the fraction of the backhaul SFs increases along with the fraction of r- UEs (i.e., the UEs associated with the RNs) when more RNs are deployed under PF resource partition. Since the RNs are randomly located, the enb RN link can maintain the same SINR distribution with different RN numbers, and thus the fraction of the backhaul SFs directly indicates the capacity of the enb RN link. Apparently, the backhaul SF allocation

5 Fig. 2. Spectral efficiency vs. RN number. Fig. 3. GPF factor vs. RN number. Fig. 4. CDF of UE throughput. TABLE I STATISTICS OF UE ASSOCIATION AND RESOURCE PARTITION. RN number R-UE percentage Backhaul SF percentage can adapt to the varying load of r-ues with the proposed PF resource partition algorithm, and thus the resulting system SE and fairness performance under scheme 1 is able to increase with the number of RNs. In comparison to scheme 2, scheme 1 only achieves better system SE while the RN number is increased to more than 4 RNs/sector as shown in Fig. 2. In contrast, the GPF factor of scheme 1 is consistently better than that of scheme 2. In particular, when the RN number is less than 4 per sector, the GPF factor of scheme 2 even falls below the level achieved by a non-relay system, as shown in Fig. 3. This is because resource partition under scheme 2 is in a fixed half-to-half pattern, irrespective of how the load of r-ues varies. When the RN number is small ( 4), it allows a few r-ues (less than 30%) to utilize a large part of the system resources through excessively allocated backhaul SFs. As a result, only a small portion of UEs can achieve extremely high throughputs, whereas the majority of UEs served by the enb suffer throughput degradation due to reduced access SF resources. Consequently, the overall fairness performance is severely degraded. Furthermore, when the RN number increases, the traffic demand from the r-ues grows such that the limited backhaul SF allocation cannot supply enough service data and thus becomes the bottleneck. While the r-ues data rates are constrained by the backhaul SF resources, the interference level caused by RNs increases with the number of RNs. Hence, the system SE begins to drop with more than 3 RNs/sector deployed. Moreover, when the RN number exceeds 8 per sector, the r-ues which are constrained by the backhaul SFs become the majority (more than 50%), and then the system GPF factor also begins to decrease. Fig. 4 plots the the cumulative density function (CDF) curves of UE throughputs under schemes 1 and 2. Scheme 1 is shown to achieve a significantly higher throughput than the scheme 2 for more than 80% UEs, although scheme 2 performs better at the high throughput region. In regard to the throughputs at 5% CDF, which indicate the cell-edge UEs performance, the proposed scheme 1 always outperforms scheme 2, which is even worse than the case without relaying. The results verify that the scheme with PF resource partition can achieve a good trade-off between throughput and fairness. VI. CONCLUSION This paper focuses on the LTE-Advanced networks where the enb and the type I RNs can both independently schedule their associated UEs using the traditional proportional fair (PF) algorithm. Although local fairness for the UEs associated with the enb or an RN can be ensured, the decentralized scheduling approach can lead to unfairness for the UEs belonging to different serving nodes. We formulate a generalized proportional fair (GPF) problem and propose an efficient resource allocation strategy which integrates PF resource partition to tackle the GPF problem and to ensure global fairness. The simulation results demonstrate that when compared with fixed resource partition, the PF resource partition algorithm can achieve a better throughput-fairness trade-off. ACKNOWLEDGMENT This work was supported in part by the China NSFC under Grant , and National Key Technology R&D Program of China under Grant 2009ZX REFERENCES [1] 3GPP TR v1.4.1, Further Advancements for E-UTRA Physical Layer Aspects, Sep [2] M. Salem, A. Adinoyi, H.Yanikomeroglu, et al, A Fair Radio Resource Allocation Scheme for Ubiquitous High-data-rate Coverage in OFDMAbased Cellular Relay Networks, in Proc. GLOBECOM 2009, Honolulu, HI, Dec [3] M. Kaneko, P. Popovski, and K. Hayashi, Throughput-Guaranteed Resource-Allocation Algorithms for Relay-Aided Cellular OFDMA System, IEEE Trans. Veh. Technol., vol. 58, no. 4, pp , May [4] W. Liping, J. Yusheng, and L. Fuqiang, A Semi-distributed Resource Allocation Scheme for OFDMA Relay-Enhanced Downlink Systems, in Proc. IEEE GLOBECOM Workshops, New Orleans, LO, Dec [5] 3GPP TS V8.2.0, Physical Channels and Modulation, Mar [6] F. P. Kelly, Charging and Rate Control for Elastic Traffic, European Transactions on Telecommunications, vol. 8, no. 1, pp , [7] L. Lei, L. Chuang, C. Jun, et al, Flow-level Performance of Opportunistic OFDM-TDMA and OFDMA Networks, IEEE Trans. Wireless Commun., vol. 7, no. 12, pp , Dec [8] S. C. Borst, User-level performance of channel-aware scheduling algorithms in wireless data networks, in Proc. INFOCOM, San Francisco, CA, April [9] H. Kim, Y. Han, A proportional fair scheduling for multicarrier transmission systems, IEEE Commun. Lett., vol 9, no. 3, pp , Mar [10] E. Kwon, J. Lee, M. Do, and K. Jung, Comparison of symmetric and asymmetric routing for fixed two-hop cellular relaying network, IEEE Commun. Lett., vol. 11, no. 5, pp , May 2007.