QoS-Based Power-Efficient Resource Management for LTE-A Networks with Relay Nodes

Transcription

1 QoS-Based Power-Efficient Resource Management for LTE-A Networks with Relay Nodes Kai-Ten Feng, Tzu-Hao Su, and Tain-Sao Chang Department of Electrical and Computer Engineering National Chiao Tung University, Hsinchu, Taiwan and Abstract This paper investigates the resource management problem in the relay-enhanced long term evolution advanced LTE-A systems The challenges of this resource allocation problem arise from the complication of assigning transmission links to the multicast broadcast single frequency network MBSFN subframe within the numerous physical resource block PRB pair Existing research work does not fully consider all the influential factors to achieve power efficiency for the LTE-A networks In this paper, a power-efficient QoS-based resource management PERM scheme is proposed to allocate MBSFN subframes, PRB pairs, and transmission power The proposed PERM scheme is targeting at power efficiency with the consideration of both QoS requirements of user equipment UE and direct/two-hop communications Moreover, the heuristic PERM H-PERM scheme is designed to provide efficient resource allocation for the LTE-A systems compared to the original PERM scheme Simulation results show that the proposed schemes can provide power efficiency with consideration of UE s QoS requirements for the LTE-A systems I INTRODUCTION Due to the rise of smart phones in recent years, the demand for high-speed mobile networks rapidly increase The 3GPP long term evolution Advanced LTE-A [1] is a standard for next generation wireless communication systems to provide higher data rate services The orthogonal frequency division multiplexing access OFDMA technology is a mutli-user version of original OFDM for LTE-A downlink, which divides the wideband channel into numerous subchannel in order to both provide high spectral efficiency and alleviate frequencyselective fading Based on the OFDMA technique, multiuser diversity can be achieved by opportunistic scheduling which appropriately allocates the subsets of subchannels to individual user equipment UE However, excessive power consumption can be induced when the wireless network operator intends to provide quality-of-service QoS for UEs In particular, UEs may inevitably be assigned to operate under a worse channel for data transmission which can result in additional power consumption Therefore, relay node RN is introduced to provide an alternative path between evolved nodeb enb and the UEs Data transmission will have the flexibility to be conducted in either the original direct path from enb to UE or via the RN Therefore, it is important to provide feasible 1 This work was in part funded by the Aiming for the Top University and Elite Research Center Development Plan, NSC E MY3, the MediaTek research center at National Chiao Tung University, and the Telecommunication Laboratories at Chunghwa Telecom Co Ltd, Taiwan resource management for relay-enhanced communications in order to both fulfill the QoS requirements of UEs and preserve network energy Related research in [2] focuses on subchannel assignment and path selection by comparing the effective data rates between relay-based and direct transmissions A void filling algorithm is proposed in [3] as a heuristic joint path selection and subchannel allocation scheme for throughput enhancement However, these two schemes are designed with constant power allocation for UEs The suboptimal solutions are obtained by jointly considering the subchannel and power allocation with QoS consideration for direct transmission [4] and relay-based network [5] Furthermore, the two transmission phases within a subchannel are assigned to a single UE by these [2; 3; 5], ie, the RN receives data from enb in the first transmission phase and utilizes the same subchannel to forward the data in the second phase On the other hand, heuristic switching assignments between the two transmission phases are considered in [6] for power allocation and in [7] for opportunistic power scheduling However, QoS constraints from UEs have not been addressed in these two schemes Moreover, the coexistence of both direct and relay-based communications in the network has not been investigated in most of existing research A QoS-based resource allocation scheme is proposed in [8] which provides optimal assignments of two transmission phases considering both direct and relay-based links Note that most of the existing studies are designed based on either generic OFDMA networks or IEEE systems For LTE-A standard, a heuristic resource allocation scheme has been proposed in [9] that utilizes the relay zone to ensure the transmission of RN-UE links to a specific portion of the entire resource allocation Feasible throughput performance of the entire network can be achieved However, it is noticeable to observe that most of the existing research focuses on maximization of network throughput Since most UEs in a wireless network are battery-powered, power efficiency is considered one of the principal issues to prolong the lifetime of UE Moreover, energy conservation of network components, including RNs and enbs is crucial from green energy perspective Therefore, a powerefficient QoS-based resource management PERM scheme is proposed in this paper to solve the resource allocation problem for LTE-A systems According to the further advancemet of LTE-A standard [10], the multicast broadcast

2 single frequency network MBSFN subframes are defined to specifically reserve for transmissions of enb-rn links All the remaining transmission links can only be allocated to those subframes other than MBSFN Moreover, instead of adopting two transmission phases in most of existing research work, total of ten subframes can be individually allocated for each UE in the LTE-A systems Note that each subframe consists of two physical resource block PRB, ie, denoted as a PRB pair Therefore, the resource allocation problem for the LTE-A network is considered more challenging with both the constraint from MBSFN subframes and the additional degree of freedom to allocate the PRB pairs for UEs An optimization problem is formulated by the proposed PERM scheme to acquire resource allocation for MBSFN subframes, PRB pairs, and transmission power Moreover both the QoS requirements from UEs and direct/two-hop communications are considered in the PERM scheme Owing to the NPhard nature of the original optimization problem for resource allocation, the Lagrangian formulation is adopted to obtain the suboptimal solution based on the continuous relaxation [11] for PRB pair and MBSFN subframe assignment However, intensive computation is required for solving the proposed PERM scheme due to the complication of resource allocation for the ten PRB pairs Therefore, a heuristic PERM H- PERM scheme is proposed to efficiently resolve the resource allocation problem for LTE-A systems Hungarian algorithm [12] is adopted to heuristically perform resource allocation for MBSFN, PRB pair, and transmission power Simulation results show that the proposed PERM scheme can provide better power efficiency than conventional direct transmission With slightly sacrificing power saving performance, the proposed H-PERM method effectively reduces computation complexity of the original PERM scheme II SYSTEM MODEL AND PROBLEM FORMULATION As shown in Fig 1, a downlink scenario of relay-enhanced LTE-A system is considered There exists an enb, R fixed RNs, and U UEs in a single cellular network The total channel bandwidth is equally divided into N subcarriers each with B Hz The downlink transmission frame is equally divided into T = 10 subframe as shown in Fig 2 According to the LTE-A specification [10], a PRB pair is the basic unit of resource which consists of two time slots in the time domain and N c consecutive subcarriers in the frequency domain Note that each PRB pair can only be allowed to allocate one transmission link In the relay-based LTE-A system, a two phase half-duplex transmission mode is adopted To facilitate the operations of RNs in the network, each subframe is classified as either MBSFN subframe or normal subframe Following relay-based LTE-A specification [13], the MBSFN subframe is possible to be assigned at number 1, 2, 3, 6, 7, and 8 subframe The MBSFN subframe can be only assigned to the enb-rn links and the normal subframe can be assigned to either enb-ue links or RN-UE links, as shown in Fig 2 Noted that the enb-ue link represents direct communication channel Hz RN 4 1 subframe 1 ms RN 3 RN 5 UE 1 BS UE 3 RN 2 RN r UE u RN 1 Fig 1 Downlink relay-based LTE-A system 1 frame 10 ms #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 enb- RN link MBSFN enb- UE link RN- UE link Fig 2 Schematic diagram of ten subframes transmission for downlink relaybased LTE-A system between the enb and the UE where the RNs are not involved in data transmission Let L be denoted as the transmission link from relay r to UE u L r,0 and L 0,u respectively denote transmission links of enb to RN r link and enb to UE u link The relay selection function is defined as Ωu = r if a UE u is served by the RN r; while Ωu = 0 if a UE u is operated in direct transmission The parameter θ τ is defined as the MBSFN subframe binary assignment variable for assigning MBSFN subframe at τ {1,, T }th subframe, ie, { θ τ 1, if τth subframe is the MBSFN subframe = 1 0, if τth subframe is the normal subframe Moreover, {0, 1} denotes the PRB pair assignment indicator for L on the τth subframe of PRB pair n as either assigned = 1 or not assigned = 0 The other two PRB pair assignment indicators 0,u {0, 1} and ρ r,0 {0, 1} can also be defined in a similar manner Before each downlink transmission, the enb can obtain all the channel state information CSI, eg, the channel gain, of both the RNs and UEs based on their corresponding feedback mechanisms It is also assumed that the channel gains of all the communication links remain constant in one downlink transmission frame The normalized data rate C of L on PRB pair n of τth subframe can be acquired as C = 1 θ τ log 2 1 p g, 2

3 where p is the transmission power, g = Hn 2 ΓBN 0 with H n as the channel gain of L, and N 0 is the power spectral density of additive white Gaussian noise AWGN The parameter Γ = ln5ber/15 is obtained from [14] given the target bit error rate BER and the continuous-rate M- ary quadrature amplitude modulation Based on the normalized data rate C obtained from 2, an optimization problem with the objective to minimize the sum power of entire system can be formulated as min 3a θ,ρ,p n=1 τ=1 L p s t θ τ, {0, 1}, n, τ, r, u; 3b 1 θ τ p 0,u θτ p r,0 P enb, max τ; 1 θ τ θ τ R τ=1 n=1 0,u 1 θτ [ n=1 3c p P max r, r, τ; 3d 0,u ] 1, n, τ; 3e C R QoS, L ; 3f where θ, ρ and p are defined as the sets of θ τ, and p for all n, τ, r, and u, respectively The expression in 3b states each communication link can be either assigned with a PRB pair, ie, = 1, or not assigned, ie, = 0 The constraints in 3c indicate that the transmission power of enb should be smaller than maximum transmission power of the enb, ie, PeNB max The constraint in 3d ensures that RN r s transmission power cannot exceed Pr max for all r, where Pr max is the maximum transmission power of RN r at each subframe 3e is utilized to denote that each PRB pair is allocated with at most one communication link in each subframe The condition in 3f indicates that each UE is required to satisfy its QoS constraint, where the parameter R QoS is the minimum required transmission rate of UE u and RN r according to its QoS requirement It can be observed that the optimization problem in 3a is a mixed integer programming which is in general considered as an NP-hard problem and does not exist efficient algorithm to acquire the optimal solution except by adopting the exhausted search algorithm Note that the complexity of [ exhausted search ] algorithm to allocate PRB pairs is O T U R U N Moreover, The optimization problem in 3a is not considered as convex due to the discrete manner of θ τ and assignment indicators, ie, can only be assigned with either 0 or 1 value In the case that the constraint can be released as stated in [11], the indicators θ τ and will be allowed to be any value within the interval [0, 1] Let ε be defined as the effective transmission power as ε = p, the normalized data rate C C = 1 θ τ log 2 1 ε of L in 2 can be rewritten as, 4 g By defining ε as the set of ε for all n, τ, r, and u, the set θ, ρ, p in 3a will be replaced with θ, ρ, ε, and the constraints in 3b-3d can be modified as θ τ, [0, 1], n, τ, r, u, 5a 1 θ τ ε 0,u θτ ε r,0 P BS max ; 5b 1 θ τ n=1 ε P max r 5c As a result, the optimization problem for resource management in 3a can be converted into a convex optimization problem by replacing 3b-3d with 5a-5c Moreover, the convex optimization problem can be solved by applying the Lagrange Multiplier method III PROPOSED POWER-EFFICIENT QOS-BASED RESOURCE MANAGEMENT PERM SCHEME In this section, the proposed PERM scheme will be described Let λ τ 1 and λ τ 2,r be defined as the Lagrangian multipliers of 5b and 5c, respectively The parameters λ 2,r, η, and µ τ are the Lagrangian multipliers of the rth RN s constraint in 5c, the τth subframe of nth PRB pair s constraint in 3e, the uth UE s constraint and the rth RN s constraint in 3f, respectively Moreover, Φ is defined as the set of all Lagrangian multipliers Hence, the Lagrangian function Lθ, ρ, ε, Φ of modified optimization problem in 3a along with the convex properties as in 5a-5c can be formulated as Lθ, ρ, ε, Φ = τ=1 λ τ 1 τ=1 τ=1 n=1 ε n=1 τ=1 L 1 θ τ λ τ 2,r η 1 θ τ θ τ 0,u ] 1 R ε 0,u θτ n=1 ε Pr max 0,u 1 θτ [ µ τ τ=1 L ε r,0 P enb max N n=1 C R QoS Furthermore, the Karush-Kuhn-Tucker KKT conditions of modified convex optimization problem for obtaining the optimal solution are given by Lθ, ρ, ε, Φ ε { 0, if ε = 0 = 0, if ε > 0 6 7a

4 { Lθ, ρ, ε, Φ 0, if ρ = 0 = 0, if > 0 { Lθ, ρ, ε, Φ 0, if θ τ = 0 θ τ = 0 if θ τ > 0 Equation 7a can further be expressed as Lθ, ρ, ε, Φ ε = λ τ r µτ θ τ g ε g where 1 λ τ λ τ 1 1 θ τ, if r = 0 and u 0 r = 1 λ τ 2,r 1 θ τ, if r 0 and u 0 1 λ τ 1,rθ τ if r 0 and u = 0 7b 7c, 8 Therefore, according to 7a and 8, the effective transmission power ε can be written as µ τ θ τ ε = λ τ r 9 1 g n 10 It is noted that the expression x in 10 indicates x = x if x 0 and x = 0 if x < 0 Furthermore, 7b can also be similarly derived as Lθ, ρ, ε, Φ = η θ τ µ τ [θ τ log 2 1 ε g θτ ε g ε g ] 11 By substituting 10 into 11, the parameter D µ τ,λ τ 1,λ τ 2,r can be defined as D µ τ, λ τ 1, λ τ 2,r θ = µ τ [θ τ τ µ log 2 { η, if = 0, = η, if > 0 g n λ τ r 1 λ τ ] r θ τ µ g n 12 As a consequence of above formulation, given the ˆnth PRB pair and the ˆτ th transmission subframe, there exists a link L r,u such that r, u = arg max Dˆn,ˆτ µˆτ, λˆτ 1, λˆτ 2,r 13 If there exists a unique L r,u to achieve the maximal value of D µ τ,λ τ 1,λ τ 2,r, the optimal resource allocation can be obtained such that ρˆn,ˆτ r,u = 1, ρˆn,ˆτ = 0, r r or u u 14 As mentioned before, the PRB pair assignment indicator is relaxed from the original two distinct values, ie, {0, 1}, into a continuous set of values in the interval of [0, 1] Therefore, the resulting optimal solution can happen if the indicator is a fractional value between [0, 1] In such case, suboptimal and non-unique solutions with link L r,u that satisfy 13 can be acquired by constraining to be either 0 or 1 As a result, the τth subframe of nth PRB pair will be assigned with the link that has the largest value of D µ τ,λ τ 1,λ τ 2,r The allocation for all the subframes can also be determined in a similar manner Similarly, 7c can be derived as N N ε 0,u Lθ, ρ, ε, Φ θ τ = λ τ 1 N λ τ 2,r ε [ U R η n=1 µ τ n=1 { 0, if θ τ = 0 = 0, if θ τ > 0 log 2 0,u 1 ε n=1 g n ε r,0 r,0 ] 15 Moreover, in order to obtain the suboptimal solution for 13, the values of Lagrangian multiplier are required to be obtained An iterative approach that exploits the subgradient method as in [15] is utilized to update the value of each Lagrangian multiplier For example, considering that µ τ,i is defined as the ith iteration of µ τ,i, its updating process can be expressed as µ τ,i1 = µ τ,i s i R QoS n=1 C, 16 where s i = α/ i is the step size and α is a tunable constant The updating processes for the other Lagrangian multipliers can also be obtained similarly The complexity of proposed PERM algorithm can be obtained as ONURT I where I denotes the number of total iterations It can be seen that the proposed scheme can provide more efficient computation than the exhaustive search algorithm especially under large number of PRB pairs IV PROPOSED HEURISTIC POWER-EFFICIENT QOS-BASED RESOURCE MANAGEMENT H-PERM SCHEME In this section, a low complexity H-PERM scheme which adopts the Hungarian algorithm [12] is designed to heuristically solve the optimization problem in 3a The Hungarian algorithm is an optimal algorithm for solving the one-toone assignment problem In other words, a square-matrix relationship is required between input and output by adopting the Hungarian algorithm The proposed H-PERM scheme is to heuristically form square matrix from the original formulation in order to apply the Hungarian method First of all, the required number of MBSFN subframes can be calculated by U M N = RQoS Ωu 0,u, 17 NC τ where C τ = log 2 1 κn, 18

5 QoS κn = 2 R BN 1 19 Note that κn is a pre-defined rate adjustment threshold, which depends on the both uth UE s required data rate and the number of PRB pairs N Moreover, the number of normal subframes which are assigned to L for u 0 links can be obtained as T M N In order to formulate the square matrix for Hungarian algorithm, the matrix H τ N N is defined for the τth subframe as H τ N N = g 1,1 Ω1,1 g 1,2 Ω1,1 g 1,mr,1 Ω1,1 g 1,m r,u ΩU,U g 2,1 Ω1,1 g 2,m r,1 Ω1,1 g N,1 Ω1,1 g N,2 Ω1,1 g N,mr,1 Ω1,1 g N,m r,u ΩU,U, 20 where N = U m Ωu,u and m Ωu,u is denoted as the number of PRB pairs that are allocated to uth UE which is served by Ωuth RN For example, the elements in H τ N N matrix g N,1 Ω1,1 represents the channel gain of the Nth assigned PRB pair in the first subframe from the Ω1th relay to UE 1 Similarly, m r,0 represents the number of PRB pairs that are assigned to rth RN which is served by enb In the proposed H-PERM scheme, same data rate across all the PRB pairs is assumed for each subframe The operations of proposed H-PERM algorithm for normal subframes is described as follows 1 Initialize m Ωu,u = N/U, u 2 Apply the Hungarian algorithm to H τ N N, and then obtain the allocation matrix I N N Note that the ith row element of I N N represents that the corresponding UE is assigned with the ith PRB pair if its value is equal to 1 3 For τ = 1 While U m Ωu,u < N m 1 Ωu,u ḡ u = I N N i,j H τ N N i,j 21 m Ωu,u j=u i=1 p m Ωu,u = m Ωu,u ḡ u κm Ωu,u u m Ωu,u 1 ḡ u κm Ωu,u 1 22 = arg max u p m Ωu,u 23 m Ωu,u = m Ωu,u 1 24 End while Update H τ N N and repeat 2 End for 4 For τ = 2 : T M N While U m Ωu,u < N τ Calculate ḡ u and p m Ωu,u by 21 and 22, respectively Obtain u by 23 and update m Ωu,u by 24 End while Update H τ N N and repeat 2 End for Note that the ḡ u in 21 is defined as the average channel gain for UE u over the m Ωu,u allocated PRB pairs The parameter pm Ωu,u in 22 represents the net power reduction while the UE u is assigned with an additional PRB pair Equation 23 is utilized to acquire the UE that can result the maximum power reduction with an additional PRB assignment Moreover, since the complexity of Hungarian algorithm is ON 3, that of the proposed H-PERM scheme can be obtained as OT N 3 Compared to the PERM algorithm as described in previous section, it can be observed that smaller computational complexity can be obtained by adopting the H-PERM scheme if N 2 URI, which is considered valid since significant amount of iteration number I is required for obtaining Lagrangian multipliers V PERFORMANCE EVALUATION In this section, the performances of proposed PERM and H-PERM schemes will be compared with direct transmission Considering a relay-enhanced network, there exists one enb with radius of transmission range equal to 1732 meters, several numbers of RNs are located at the cell edge which are /3 from the enb, and 10 UEs which are randomly distributed within the transmission range of enb The largescale fading model composed of both path loss and shadowing is adopted from urban macro scenario Moreover, for smallscale fading model, Rician distributions for line-of-sight LOS environments are considered in enb-rn links, and Rayleigh distributions for non-los scenarios are adopted in RN-UE as well as enb-ue links The system parameters and configurations are listed in Table 1 as below TABLE 1 : SYSTEM PARAMETERS Parameter Value Number of PRB pairs N 50 Number of subframes T 10 Bandwidth of PRB B 180 KHz Channel noise density 174 dbm/hz Maximum transmission power of enb PeNB max 46 dbm Maximum transmission power of RN Pr max 37 dbm Target bit error rate BER 10 5 Fig 3 shows power consumption in enb-ue, enb-rn, and RN-UE links versus the number of MBSFN subframes under the minimum required data rate R QoS = 2Mbps left plot and 5Mbps right plot for proposed H-PERM scheme with 6 RNs in the network It can be observed that power consumption in enb-rn links decreases as the number of MBSFN subframes is augmented since channel capacity is a non-linear logarithmic function In other words, more power consumption in enb-rn links is obtained when less MBSFN subframes are provided On the other hand, the power consumption in enb-ue and RN-UE links increases with larger number of

6 Power consumptionw R QoS = 2Mbps enbue enbrn RNUE Number of MBSFN subframe Power consumptionw R QoS = 5Mbps Number of MBSFN subframe Fig 3 Performance evaluation of proposed H-PERM scheme: power consumption in enb-ue, enb-rn, and RN-UE links versus the number of MBSFN subframes under the minimum required data rate R QoS = 2Mbps left plot and 5Mbps right plot System power Consumption W Without RS HPERM Method with 3 RS HPERM Method with 4 RS HPERM Method with 5 RS HPERM Method with 6 RS PERM Method with 6 RS UE s data rate requirement R QoS Mbps Fig 4 Performance comparison: system power consumption versus the minimum required data rate of each UE R QoS MBSFN subframes Moreover, it can be seen that the system power consumption is minimum when the number of MBSFN subframes is set to one under R QoS = 2Mbps For the case of R QoS = 5Mbps, setting the number of MBSFN subframes as two can achieve the optimal system performance It is intuitive to explain the results since more MBSFN subframes are required for the data transmission in enb-rn links in order to acquire larger R QoS As shown in Fig 4, system power consumption versus the minimum required data rate of each UE R QoS is demonstrated for performance comparison between proposed H- PERM/PERM schemes and direct transmission Note that the cases with different numbers of RNs are conducted for the H-PERM scheme Intuitively, system power consumption increases as R QoS is augmented It can be seen that the proposed PERM scheme can provide better performance compared to both H-PERM scheme and direct transmission owing to its optimal formulation By observing the H-PERM scheme, system power consumption can be further reduced by setting more RNs to improve UEs channel qualities The power consumption of H-PERM mechanism is almost the same as that of PERM scheme in the case that the number of RNs is equal to 6 The proposed PERM scheme is served as a performance upper bound; while the H-PERM scheme can be implemented in a computation-efficient manner The merits of both PERM and H-PERM schemes can be observed VI CONCLUSION In this paper, power-efficient quality-of-service-based QoSbased resource management PERM scheme is proposed for the relay-enhanced long term evolution advanced LTE-A networks The proposed PERM scheme is formulated as an optimal resource allocation for multicast broadcast single frequency network MBSFN subframes, physical resource block PRB pairs, and transmission power considering QoS requirements of user equipment Compared with existing works, the factors of MBSFN subframe and PRB pairs are considered in order to meet the practical LTE-A systems For the purpose of implementation, the simplified version of PERM named as heuristic PERM H-PERM scheme is proposed to reduce computational complexity Numerical results show that the proposed H-PERM scheme with lower computational complexity can achieve almost the same performance as PERM mechanism from the perspective of power consumption REFERENCES [1] 3GPP TS V920, Overall Description Stage 2 Release 9, Dec 2009 [2] B Can, H Yanikomeroglu, F A Onat, E De Carvalho and H Yomo, Efficient Cooperative Diversity Schemes and Radio Resource Allocation for IEEE 80216j, in Proc IEEE WCNC, Mar 2008 [3] L Wang, Y Ji, and F Liu, Resource Allocation for OFDMA Relay- Enhanced System with Cooperative Selection Diversity, in Proc IEEE WCNC, Apr 2009 [4] N U Hassan and M Assaad, Resource Allocation in Multiuser OFDMA System: Feasibility and Optimization Study, in Proc IEEE WCNC, Apr 2009 [5] Z Tang and G Wei, Resource Allocation with Fairness Consideration in OFDMA-Based Relay Networks, in Proc IEEE WCNC, Apr 2009 [6] L Huang, M Rong, L Wang, Y Xue, and E Schulz, Resource Allocation for OFDMA Based Relay Enhanced Cellular Networks, in Proc IEEE VTC, Apr 2007 [7] B G Kim and J W Lee, Opportunistic Power Scheduling for OFDMA Cellular Networks with Scheduling at Relay Stations, in Proc IEEE WCNC, Apr 2009 [8] W P Chang, J S Lin, and K T Feng, QoS-based Resource Allocation for Relay-Enhanced OFDMA Networks, in Proc IEEE WCNC, Apr 2011 [9] B G Choi, S J Bae, K-y Cheon, A-S Park, and M Y Chung, Relay Selection and Resource Allocation Schemes for Effective Utilization of Relay Zones in Relay-Based Cellular Networks, IEEE Commun Lett, Apr 2011 [10] 3GPP TR36814 v900, Further Advancements for E-UTRA Physical Layer Aspects Release 9, Mar 2010 [11] C Y Wong, R S Cheng, K B Lataief, and R D Murch, Multiuser OFDM with Adaptive Subcarrier, Bit, and Power Allocation, IEEE J Sel Areas Commun, vol 17, pp , Oct 1999 [12] H W Kuhn, The Hungarian Method for the Assignment Problem, Naval Research Logistics Quarterly, vol 2, no 1, pp 83 97, 1955 [13] 3GPP TS V1000, Physical Channels and Modulation Release 10, Dec 2010 [14] M S Alouini and A Goldsmith,, Adaptive Modulation over Nakagami Fading Channels, Wireless Personal Communications, vol 13, pp , 2000 [15] N Z Shor, K C Kiwiel, and A Ruszcayǹski, Minimization Methods for Non-differentiable Functions Springer-Verlag, 1985