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allocation with frequency reuse in multicell OFDMA networks. The architecture ... In systems where adaptive modulation and coding (AMC) techniques are ...
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Dynamic Frequency Allocation in Fractional Frequency Reused OFDMA Networks Syed Hussain Ali, Member, IEEE, and Victor C. M. Leung, Fellow, IEEE

Abstract—This paper proposes a dynamic fractional frequency reused cell architecture that simplifies the problem of subcarrier allocation with frequency reuse in multicell OFDMA networks. The architecture divides the cell surface into two overlapping geographical regions and orthogonally allocates subcarriers, which are called super and regular group of subcarriers, to the regions. The proposed architecture allows a frequency reuse factor of 1 with reduced inter-cell interference and increased trunking gain, while satisfying minimum data rate requirements. We also propose an efficient hierarchical solution to realize the proposed architecture. The solution first allocates subcarriers to the groups so that long term performance is maximized and next opportunistically schedules subcarriers to the users. The opportunistic scheduling is performed at the base stations considering the fairness requirements of the users. Simulation results illustrate the performance improvements of the proposed solution in comparison to the traditional frequency allocation schemes. Index Terms—Wireless communication, mobile communication systems, cellular networks, 3G, cross-layer adaptation, opportunistic scheduling, data networks.

I. I NTRODUCTION

O

RTHOGONAL frequency division multiplexing (OFDM) is a popular multi-carrier modulation scheme. It provides immunity to intersymbol interference and frequency selective fading by dividing the frequency band into a group of mutually orthogonal subcarriers, each having a much lower bandwidth than the coherence bandwidth of the channel. In a multi-user environment, multiple access of OFDM can be achieved by employing Time Division Multiple Access (OFDM-TDMA) or Code Division Multiple Access (OFDM-CDMA). For both of these multiple access schemes, a user transmits over the entire spectrum, which leads to lowering of the performance as the user may experience deep fades and narrow band interference [1]. As an alternative, OFDM subcarriers can be time- and frequencydivision multiplexed among multiusers, which is referred as orthogonal frequency division multiple access (OFDMA). It Manuscript received August 25, 2008; revised December 29, 2008; accepted February 12, 2009. The associate editor coordinating the review of this paper and approving it for publication was H.-H. Chen. S. H. Ali is with Research In Motion, 295 Phillip St., Waterloo, ON Canada N2L 3W8 ([email protected]). V. C. M. Leung is with the Department of Electrical and Computer Engineering, University of British Columbia, 2332 Main Mall, Vancouver, BC Canada V6T 1Z4 (e-mail: [email protected]). This work was supported by a grant from TELUS and by the Canadian Natural Sciences and Engineering Research Council under grant CRDPJ 341254-06. Parts of this work are submitted to the 4th IEEE Workshop on Broadband Wireless Access, co-located with IEEE GLOBECOM 2008, Nov 2008, New Orleans, USA. Digital Object Identifier 10.1109/TWC.2009.081146

forms traffic channels which are based on one or a cluster of OFDM subcarriers. Each user is assigned a subset of the traffic channels at any given time. Thus, OFDMA provides a degree of freedom by allowing dynamic assignment of channels/subcarriers1 to different users at different time instances, to take advantage of the channel response variations among different users on different channels [2]. These features have resulted in the adoption of OFDM/OFDMA technology for high-speed wireless communication systems, e.g., digital video broadcasting (DVB-T), wireless LAN (IEEE 802.11a), fixed and mobile wireless metropolitan area networks (IEEE 802.16 and 802.16e) [3], [4], and the 3GPP’s Evolved Universal Terrestrial Radio Access (E-UTRA) [5]. Dynamic subcarrier assignments (DSA) to multiple users improve the system data rate of an OFDMA system [6]. This improvement is due to the multiuser diversity gain as the channel characteristics for different users are independent of one another. Thus, a subcarrier under a deep fade for one user at a given time may not be in a deep fade for other users. Therefore, every subcarrier may have a good channel response for some users in a multiuser environment. In systems where adaptive modulation and coding (AMC) techniques are employed, a better channel response results in a higher data rate. Furthermore, it is expected that adaptive power allocation (APA) to different subcarriers can further improve the system data rate. Due to these reasons, downlink DSA and APA for single cells have attracted considerable research interests (see [6], [7], [8], and references therein). In principle, allocating different power levels to individual subcarriers should improve performance. However, previous studies [6] and [7] have shown that the performance improvements are marginal over a wide range of signal-to-noise ratios (SNR’s) due to the statistical effects. Therefore, a simpler solution involving DSA with equal power per subcarrier is preferred over more complex joint DSA and APA solution. In this research, we consider the downlink DSA problem in multicell OFDMA networks with frequency reuse, which has not been investigated extensively. Multicell OFDMA DSA with frequency reuse was first studied in [1], which proposed a semi-distributed resource allocation where allocation decisions are divided between the radio network controller (RNC)2 and the base stations (BSs). 1 The

terms subcarriers and channels are interchangeably used in this paper. E-UTRA, there is no RNC node. However, we still employ Release 99 terminology in this paper as there is no central node in the E-UTRA specification that performs Inter-Cell Radio Resource Management (RRM) [9]. The RNC in this paper refers to a virtual node that performs Inter-Cell RRM. This virtual node could reside in one of the base stations or be added as an independent node in future E-UTRA architecture. 2 In

c 2009 IEEE 1536-1276/09$25.00 

ALI and LEUNG: DYNAMIC FREQUENCY ALLOCATION IN FRACTIONAL FREQUENCY REUSED OFDMA NETWORKS

Fig. 1. Fractional frequency reused (FFR) architectures (a) static (b) dynamic.

The RNC algorithm runs at the super-frame level, coordinates inter-cell interference, and assigns subcarriers to the BSs. It also recommends user assignment for every subcarrier. The BS algorithm runs at the frame level and performs subcarrier allocations to the users. It is possible that the BS does not follow the RNC recommendation on user assignment. According to [1], in this case the RNC algorithm does not remain optimal for that frame. Furthermore, when all the users served by a BS have traffic to send then the BS algorithm follows RNC recommendations. In this case, the BS algorithm has a reduced multiuser diversity gain. Generally, users near the cell boundary of a cellular network receive lower data rates because of increased path loss and inter-cell interference. This problem of low cell edge bitrate has recently received considerable attention for OFDMA systems due to the advances in new standards such as IEEE 802.16e [4] and E-UTRA [5]. In particular, for E-UTRA, inter-cell interference co-ordination is considered for the downlink [10]. Several frequency reuse schemes have been suggested. Notable among those are soft frequency reuse [11] and partial frequency reuse [12]. However, [13] reported large performance losses due to the frequency reuse schemes and suggested a frequency reuse factor of 1. Our proposed scheme falls within the broader recommendation of [13]. It dynamically assigns carriers to different regions, allocates them to different users and maintains a frequency reuse factor of 1. Which subcarriers are assigned to a user depends on the signal-to-interference-noise ratio (SINR) of the subcarrier and the fairness requirements of the users. Fractional frequency reuse (FFR) offers a simpler alternative to the frequency reuse problem in multicell OFDMA networks [14]. The FFR scheme statically partitions the cell surface into two distinct geographical regions: the inner cell area and the outer cell area near the cell edge. The set of

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users present in the inner cell area is identified as the super group, whereas the set of users located in the outer cell area is called the regular group. The regular group users are further partitioned according to the cell sectors. The set of subcarriers to service these groups of users are also called super and regular group subcarriers, respectively. We identify the original FFR as the static FFR scheme. The boundary between the super and regular groups is statically set on the basis of the distance from the serving BS or the SINR threshold. Similarly, the set of subcarriers to serve each group are selected randomly and their numbers are proportional to the ratio of users in the geographical region to the total number of users in the cell. The set of subcarriers assigned to the groups are reused in the adjacent cells. Fig. 1(a) shows the partitioning into groups and corresponding frequency allocation of the static FFR scheme for 3 cells. The set of subcarriers assigned to the super group are reused in every cell’s inner areas. The regular group subcarriers are divided into sectors and reused in the outer regions of the corresponding sectors of all the adjacent cells. The static FFR scheme has several shortcomings. First, it divides users in two groups on the basis of static distance or SINR thresholds. This partitioning reduces the trunking gain of each group because only a fraction of the total cell population is part of a group. Second, it partitions the available subcarriers randomly into the groups. The number of subcarriers assigned to a group is proportional to the number of users in the group. The subcarrier partitioning does not consider their radio channel states. We feel that FFR could benefit if only subcarriers are partitioned into groups and users in a cell are virtual members of both the groups. This way the users will be able to get access to the subcarriers of both groups and result in increased trunking gain. Furthermore, FFR can also benefit if subcarriers are partitioned on the basis of whether their presence in a particular group, that is, super group or a sector within the regular group, benefits the overall system performance or not. The motivation for dynamically distributing subcarriers into groups comes from the fact that a user may experience different SINR values on different subcarriers due to the subcarrier specific multipath and interference profiles. Therefore, it is possible for the network to find a set of subcarriers that perform better for a user if they are part of the super group instead of the regular group. Similarly, the network can find another set which provides a better gain for the same user if that set is allocated to a sector within the regular group instead of the super group. Thus, the dynamic subcarrier partitioning according to long term channel state can improve the overall system performance. The proposed DSA scheme overcomes both of the shortcomings of the static FFR system. The objective of this research is to improve the long-term system data rate of a downlink OFDMA multicell network by intelligently distributing and allocating subcarriers first among geographical locations of cells and later, within a cell, among users. We assume that the cell power is equally distributed among the subcarriers. For this purpose, we propose a dynamic FFR cell architecture where subcarriers are dynamically partitioned among geographical locations by RNC DSA. The BS schedules those subcarriers to the users opportunistically.

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The combined solution is based on the cross layer technique of channel-aware allocation and scheduling of resources. The rest of the paper is organized as follows. Section II provides details of the system and channel models. Section III formulates the combined DSA problem in the multicell FFR OFDMA networks. Section IV presents the proposed solution scheme and Section V discusses its numerical results. The paper concludes in Section VI. II. S YSTEM A RCHITECTURE AND M ODEL A. Dynamic Fractional Frequency Reused Cell Architecture Unlike the static FFR, where users and subcarriers are partitioned into two groups namely super and regular groups, the proposed dynamic FFR only partitions subcarriers into physical groups. Among users, there are no rigid boundaries between super and regular groups. Both user groups cover the whole cell surface. Therefore, all users of a cell are virtual members of both groups. Their physical membership or otherwise in a particular group or both groups is determined by the scheduling algorithm at the BS and it can change from one scheduling slot to another. Fig. 1(b) shows the cell partitioning and the frequency band allocation of the proposed FFR architecture. We see from this figure that the super group (that is, the circle) covers the whole cell and the subcarriers allocated to it can be assigned to any user in the cell. The regular group also covers the whole cell surface, and as an example, it is further partitioned into 3 sectors. The subcarriers assigned to a sector are available for scheduling to the inner and the cell edge users falling within the boundaries of the sector. The subcarriers are distributed between the groups and the sectors belonging to the regular group by the proposed RNC DSA algorithm. The subcarriers assigned to the super and the sectors within the regular groups are orthogonal. The distribution of subcarriers to a geographical region is performed dynamically considering their average channel states. Furthermore, the distribution decisions are made so that the system performance increases and the performance requirements of the users belonging to the respective region are satisfied. By allowing overlap between super and regular group users, the trunking efficiency of the scheduling algorithm operating at the BS level also increases. In this paper, we consider 7 and 19-cell grids with 3 sectors per cell3 (see, Fig. 2). B. System Model We consider K-cell OFDMA cellular network where service area consists of all K cells. A central radio network controller (RNC) manages the K BSs. Furthermore, we assume that there are adjacent grids to the service area having identical structure; therefore, every cell in the service area have K − 1 adjacent cells. Let Υk denote the set of and |Υk | = Mk be the number of K k. The total number of users are Mc = Kusers in a cell M and k k=1 k=1 Υk is the set of all users in the network. 3 The choice of 7 and 19-cell grids and 3 sectors per cell is due to the fact that these cell models are commonly used in the literature. We want to emphasize that our proposed solution is capable of handling any cell model.

In the proposed dynamic FFR architecture, super and regular groups cover the whole cell area. The regular group divides the cell area into sectors. Assume that each cell is partitioned into L sectors where l identifies a particular sector. Further assume, that Υlk denote the set of users and |Υlk | = Mkl is the number L of users in a sector l of a cell k. Thus, Υk = l=1 Υlk and L  l Mk = l=1 Mkl . Furthermore, M l = K k=1 Mk represents th the total number of users in the l sector of all cells. Let N be the number of subcarriers available, and Csup and Creg be the set of subcarriers assigned to the super and regular groups, respectively. The regular group subcarriers are l further divided into sectors. Let Creg be the set of subcarriers L l . The intraallocated to a sector l where Creg = l=1Creg cell interference is zero which means Csup Creg = {} and L l l Creg = {}. Further assume, Qsup and Qlreg be the set of interferers for a user in the super group and a sector l of the regular group, respectively. For a 19-cell grid, there are 18 and 7 interferers experienced by the super and regular group users, respectively. For example in Fig. 2(b), the set of interferers for a user in sector A of cell 1 includes all the adjacent cells in the super group and cells numbered {5, 6, 13, 14, 15, 16, 17} in the regular group setting.

C. Channel and Data Rate Models The channel gain for a user i on a subcarrier j from the serving BS k is given by, Gi,j,k = 10−

Γi,k (r) 10

× Si,k × ζi,j ,

(1)

where Γi,k (r), Si,k and ζi,j are path loss at distance r, shadowing and fading coefficient, respectively. See [14] for modeling details. The corresponding SINR is given as, SIN Ri,j =

Gi,j,k P |Q| N0 f + q=1 Gi,j,q P

(2)

where N0 is the noise power spectral density, f is the subcarrier spacing, P is the power per subcarrier, Q is the set of interferers which is Q = Qsup for the super group and Q = Qlreg for the regular group sector l. Employing continuous rate adaptation, the SINR is mapped to data rate as follows: Ri,j = f log2 (1 + λSIN Ri,j )

(3)

where, λ is a constant related to the target bit error rate (BER) −1.5 as λ = ln(5BER) [15] , f is the subcarrier spacing and Ri,j is the achievable data rate by the ith user and j th subcarrier pair. In the following, a subcarrier j which falls within the regular reg group will have Ri,j achievable data rate for user i. Similarly, sup Ri,j identifies the achievable data rate of subcarrier j in the super group. Furthermore, RNC algorithm employs average sup reg sup reg , Ri,j ) whereas the BS uses instantaneous (Ri,j,t , Ri,j,t (Ri,j ) values of these achievable rates.

ALI and LEUNG: DYNAMIC FREQUENCY ALLOCATION IN FRACTIONAL FREQUENCY REUSED OFDMA NETWORKS

Fig. 2.

Fractional Frequency Reused based cell models (a) 7-cell grid (b) 19-cell grid. N 

III. P ROBLEM F ORMULATION In this section we formulate the dynamic subcarrier assignment problem for the downlink of OFDMA multicell networks. The formulated problem is a representation of the joint RNC and BS DSA objectives. The DSA objective is to maximize the system data rate while satisfying individual users lower data rate requirements. Additionally, problem satisfies some other constraints related to subcarrier assignments like a subcarrier could be assigned to only one user in a cell, that is, no intra-cell interference is allowed, and the available subcarriers are reused in all cells of the network. sup Let xsup i,j be the binary decision variable, that is, xi,j ∈ {0, 1}. When this variable is 1, it signals that the subcarrier j is assigned to the user i and belongs to the super group of sup subcarriers. When its complement xi,j = 1, it signals that the subcarrier j is assigned to the user i and it falls in the regular group of subcarriers. Thesuper and regular group subcarriers are orthogonal, i.e., Csup Creg = {}. The joint DSA solves the following binary integer program for every scheduling time slot t:

max sup xi,j

s.t.

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Mc N   j=1 i=1



sup xsup i,j Ri,j,t +

Mc N  

reg xsup i,j Ri,j,t ,

xsup i,j ∈ {0, 1}, k = 1 · · · K, j = 1 · · · N,

i∈Υk Mc  i=1 Mc  i=1

(4a)

j=1 i=1

(4b)

xsup i,j ∈ {0, K}, j = 1 · · · N,

(4c)

xsup i,j ∈ {0, K}, j = 1 · · · N,

(4d)

sup sup req xsup i,j Ri,j,t + xi,j Ri,j,t ≥ Ci , i = 1 · · · Mc . (4e)

j=1

where Ci be the lower bounds on data rates for user i. The objective function (4a) maximizes the weighted sum of the instantaneous achievable data rates for all users and sup sup all subcarriers in the network. The weights, xi,j and xi,j , are binary decision variables and represent the allocation of subcarriers to the users. The constraint (4b) enforces that a subcarrier can be assigned to only one user in a cell, and constraint (4c) satisfies that if a subcarrier j is assigned to the super group in one cell then this subcarrier should be reused in all the cells. Likewise, (4d) adds similar reuse constraints for the regular group subcarriers. The constraint (4e) enforces that the subcarriers assigned to a user results in equal or more data rate than the lower bound for the user. IV. P ROPOSED S OLUTION Due to the complexity of the multicell FFR DSA, we decompose the joint problem into two parts. The first part is solved by a central location, like RNC, which computes the membership of subcarriers in the super group or a sector within the regular group. For decision making, RNC DSA requires average achievable rates information for all user subcarrier pairs in the super and regular group settings. Thus, there are 2 × N × Mc values needed for every execution of the RNC DSA which is after every super-frame. The second part operates at the BS level and allocates subcarriers to the users. The BS DSA requires instantaneous data rate information for all user subcarrier pairs. Unlike RNC, BS only needs these values for the group that subcarrier belongs to. Thus, if a subcarrier has been assigned to the super group then BS only needs the super group values for the subcarrier. Likewise, if another subcarrier is assigned to

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a sector of the regular group then BS needs rate information for the regular group for that subcarrier. In several standards developed for wireless communication, the user equipment has the capability of estimating instantaneous SINR for all subcarriers [3], [16], [17]. The BS can map SINR to data rates, use them in the BS DSA and maintain time averages of achievable rates for every user subcarrier pair. These time averages can be sent to the RNC to be used by the RNC DSA. The only additional requirement that the proposed solution places on existing standards is that averages are found for the super and regular group settings. Therefore, if a subcarrier is assigned to the super (regular) group then the BS already has its time average for this group. However, RNC also needs its average estimate for regular (super) group settings. This additional requirement could be met by assigning this subcarrier to regular (super) group for short period of time between two super-frames, transmitting a training sequence and estimating its average. Having identical structure and subcarrier distribution in all the cells of the grid, this additional requirement can be met by transmitting in parallel on all the subcarriers in all cells. In the following sub-sections, we present the proposed solution to solve these problems.

A. RNC DSA Algorithm The RNC algorithm distributes the available subcarriers among the geographical regions within a cell. In the proposed dynamic FFR architecture, the geographical regions include, super group and all sectors of the regular group. The distribution of the subcarriers to the geographical regions is replicated for all the cells in the grid. The algorithm employs greedy approach where the assignments are made so that they result in the increased system throughput for the whole grid. Furthermore, the algorithm considers the minimum data rate requirements of users so that the assigned subcarriers are able to satisfy the load in their respective geographical regions. Therefore, algorithm has a sense of fairness while distributing resources at the RNC level. The RNC algorithm pseudocode is presented in Fig. 3 where i, j, l and k are iterators for users, subcarriers, sectors and cells, respectively. In the following discussion, reference to step number is to the line numbers given in Fig. 3. The algorithm requires, as input, average achievable rates for all users on all subcarriers in the super and regular sup reg , Ri,j , and the minimum data rate group settings, that is, Ri,j requirements Ci for all users.  sup = As an output, algorithm returns binary vector X reg {xsup = {xl,reg |l = j |j = 1 · · · N }, and a binary matrix X j sup 1 · · · L, j = 1 · · · N }. A value of 1 for xj signals that the subcarrier j is assigned to the super group, whereas a value of 1 for xl,reg means that the subcarrier j is assigned to the j regular group sector l. Because a subcarrier can be assigned to only one geographical region within a cell, the algorithm sets thesevariables such that Lthe lconditions listed in Section II-B, = {}, are satisfied. Thus, the Csup Creg = {} and l Creg resulting output values have the following relations,



xl,reg ∈ {0, 1} j

and

  xsup = ∨ xl,reg , j j

l

where operator ∨ is logical OR operator applied on the j th column of Xreg . From the above relation, it is clear that  sup can be uniquely determined. once Xreg is known then X Therefore, the RNC algorithm determines Xreg during its  sup in step main loop (steps 1 to 10), and later computes X 11. During initialization phase, algorithm assigns zeros to all entries of Xreg . This assignment signals that no subcarrier is assigned to any sector of the regular group and all subcarriers are allocated to the super group. Initialization phase of the algorithm declares some variables and computes utility values of the subcarriers. The variable g l is the assigned rate of a sector. Its value is updated after assigning each subcarrier in the main loop (steps 5 and 7). The utility values, Wjsup and Wjl,reg , measure the utility of a generic subcarrier j assigned to the super group or lth sector of the regular group, respectively. These values are found assuming that the subcarrier is time multiplexed between all the users in the region and summed for all the cells in the grid. The Ujl,reg variables hold fractional utility gain if subcarrier j is removed from the super group and assigned to sector l of the regular group. A negative value of Ujl,reg for all l means that the allocation of the subcarrier to any sector of the regular group lowers the system data rate. In this case, algorithm assigns it to the super group (step 5). Because of the overlap of users, the assigned subcarrier is available to the users of all sectors in the regular group. Consequently, the assignment to the super group increases the assigned data rates of all regular group sectors. The algorithm incorporates this fact in step 5 when it updates g l by a fraction of Wjsup assuming time multiplexing of the subcarrier by the respective users. The main part of the RNC algorithm consists of a loop that iterates on the subcarriers. As stated earlier, during initialization phase, the algorithm assigns all subcarriers to the super group. In the main  loop, it iterates on subcarriers, in the descending order of Ujl ,reg , and attempts to assign the subcarrier to a sector in the regular group which increases the most system data rate. If the algorithm finds such a sector, then it assigns the subcarrier to it and increases the assigned rate for the sector and updates the corresponding output variable (steps 6 and 7). Otherwise, the algorithm leaves the xl,reg j subcarrier to the super group (step 5). So far our description has only reported the greedy aspects of the proposed algorithm. The fairness measure is added in step 2 and 3 by a simple condition. Here, during every iteration, the algorithm first looks for the sectors which are lacking in radio resources such that their assigned data rates are less than their required load. If algorithm finds such sectors, then it considers only those sectors in the subsequent assignment steps during the iteration. If algorithm does not find any sectors, it means all sectors have sufficient radio resources to satisfy their required load, then it behaves as greedy algorithm and considers all sectors in the subsequent allocation steps. Consequently, when all sectors are considered

ALI and LEUNG: DYNAMIC FREQUENCY ALLOCATION IN FRACTIONAL FREQUENCY REUSED OFDMA NETWORKS

Algorithm RNC DSA sup reg Inputs: Ri,j , Ri,j , Ci i = 1 · · · Mc , j = 1 · · · N sup Outputs: xj , xl,reg , j = 1 · · · N, l = 1 · · · L j l = 0, g = 0, j = 1 · · · N, l = 1 · · · L Initialization: xl,reg j   reg sup Ri,j K K i∈Υl i∈Υk Ri,j sup l,reg k = Wj = k=1 , ∀j and W , j k=1 Mk Ml k

l,reg sup Wj −Wj   l,reg max Wj l

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∀j, l

, l = 1 · · · L, j = 1 · · · N Ujl,reg = K  l ∀l //rate requirements per sector C = k=1 i∈Υl Ci , k Z = {1, · · · , N }, L = {1, · · · , L} //sets of subcarriers and sectors, respectively 1. FOR j=1 : N do //channel iteration  2. Find set of sectors, L , that satisfy C l − g l > 0, l ∈ L   3. IF L == {} THEN L = L ENDIF 

(Ujl Find sector subcarrier pair (l∗ , j ∗ ) that satisfies max 

4.



l

,reg

l ,j

),





l ∈L , j∈Z

M 5. IF Ujl∗ ,reg < 0 THEN g l = g l + Wjsup , l∈L ∗ Mc l∗ ,reg ∗ =1 //assign j subcarrier to l∗ sector 6. ELSE xj ∗ l∗ ,reg l∗ l∗ 7. g = g + Wj ∗ //update assigned rate for l∗ sector 8. ENDIF 9. Remove j ∗ from Z 10. End FOR   , j = 1 · · · N, ∀ l = ∨ xl,reg 11. xsup j j

Fig. 3.

Pseudocode for RNC DSA algorithm.

then the one that increases the most system data rate will be assigned the subcarrier. The time complexity of the RNC DSA algorithm is linear as it consists of only one main loop that iterates N times. The initialization stage has complexity of O(L × N ) where L being the number of sectors in a cell which is generally a very small value. The whole algorithm does not need any sorting operation. B. BS DSA Algorithm

i∈Υk

The RNC algorithm forwards the subcarrier assignments  sup and Xreg to every BS where a copy of the BS DSA runs. X The BS DSA employs the minimum performance guarantee (MPG) opportunistic scheduling rule of [18]. In order to describe MPG for the proposed system, we define RiT (x) as the average data rate of user i up to time T where x represents the decisions made by the BS scheduler . For the system under consideration, RiT (x) is estimated as: ⎧ ⎫⎤ ⎡ |Creg | sup | T ⎨|C ⎬   1 sup sup reg reg ⎦ Ri,j,t xi,j,t + Ri,j x RiT (x) = ⎣  ,t i,j  ,t ⎭ ⎩ T  t=1

j=1

j =1

(5) reg and x are binary integer variables which where xsup  i,j,t i,j ,t signal the corresponding allocation decisions of the scheduler  at a time slot t. Additionally, R(x) = i|Υk | E (Ri (x)) is the average cell data rate where T →∞

The MPG problem can be written as x

s.t.

E (Ri (x)) ≥ Ci .

th

Similarly, for the l sector subcarrier assignments in the  l regular group, that is j ∈ Creg , the BS DSA finds the user i∗ that fulfills the following expression reg i∗ = arg max βi∗ Ri,j  . ,t

(8)

i∈Υlk

The true controlling parameters βi∗ in the above solutions are chosen such that βi∗ ≥ 1 for all i, E (Ri (x)) ≥ Ci for all i, and if E (Ri (x)) > Ci then βi∗ = 1. Furthermore, employing stochastic approximation techniques , the true values of βi can be estimated in real time as follows,     βit+1 = max βit −  E (Ri (x)) − Ci , 1 , (9) where  is a small positive real number that acts as a step size for learning the true value of βi . V. N UMERICAL R ESULTS AND D ISCUSSION

E (Ri (x))  lim sup RiT (x).

max R(x),

The solution to the above problem is found by multiplying the instantaneous achievable rates of all users for all subcarriers by user specific control variables and then for every subcarrier, finding a user which has the maximum product [18]. This generic solution can be easily transformed for the BS DSA problem. For the assignment of the super group subcarriers, j ∈ Csup , the algorithm finds the user i∗ that satisfies the following expression at every scheduling slot t. sup (7) i∗ = arg max βi∗ Ri,j,t

(6)

We compare the proposed DSA algorithm with the full frequency reuse with full interference (FFFI), conventional sectored, and static FFR allocations. All the four schemes considered have a frequency reuse factor of 1. The simulation

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TABLE I S IMULATION PARAMETERS

7

11

x 10

Comparison of proposed scheme with conventional schemes (grid size = 7) Proposed Scheme FFFI Conventional Sectored Reuse Static FFR

10

: : : : : : : : : : : : : : : : : Min. rate requirement : Target BER :  (9) :

Values 5 Mhz 2 Ghz 300 15 Khz -174 dBm/Hz 3-sectored hexagonal 19 cells 1000 to 5000 m Jakes Model 43 dBm ITU Vehicular, 30 km/h 2 ms 5 slots 64 frames Uniformly distributed 15 to 20 per cell Uniformly distributed on cell surface magnitude: 50m to radius,& angle: 0 to 2π Uniformly distributed 0 to 512 Kbps 10−6 0.02

9 System throughput (bps)

Parameters Channel bandwidth Carrier frequency Number of subcarriers f N0 Grid layout Cell radius Fast fading BS Transmit power Channel model Slot duration Frame length Super-frame length Number of users Location of users

8 7 6 5 4 3 2 1

2

3 Cell Radius (km)

5

(a) 8

1.6

x 10

Comparison of proposed scheme with conventional schemes (grid size = 19) Proposed Scheme FFFI Conventional Sectored Reuse Static FFR

System throughput (bps)

1.4

parameters are given in Table I. The simulation employs realistic models commonly used in the literature. The algorithms differ in terms of the RNC DSA. For FFFI, all the subcarriers are available for allocation to all the BSs in the grid with full inter-cell interference without any sectoring. For the conventional sector allocation, RNC randomly selects a subset of the subcarriers for a sector. This subset is repeated in the same sector of all the cells. The size of the subset is proportional to the number of users in the sector, i.e., equal Ml to N Mkk  for l = 1 · · · L − 1, and for the Lth sector it is L−1 Ml N − l=1 N Mkk . The static FFR scheme divides users according to a distance threshold from the serving BS. The users within 70 percent of the cell radius are considered members of the super group. The remaining users are members of the regular group which is divided in 3 sectors. At the RNC level, the subcarriers are randomly allocated to these regions and the number of subcarriers are proportional to the number of users in the region [14]. The BS part of all the four allocation schemes is based on the MPG opportunistic scheduling [18]. The simulation runs for 64 sec, i.e., 100 super-frames. The channel undergoes fast fading according to the Jakes model. The number of users in each cell, the cell dimensions, and the BS locations remain the same for the 100 super-frames whereas user locations vary according to the random walk mobility model [19]. Fig. 4(a) and (b) compares the system throughput, which is the aggregate throughput received by all the users in all the cells, achieved by the proposed, conventional sector, FFFI and static FFR allocations for 7 and 19 cell grids, respectively. The comparison is performed as a function of the cell radius. The aggregate throughput is found by summing data rates of all users and then averaging it for 100 super-frames. The proposed DSA scheme performs better than the other three schemes. The reason for this performance improvement is that the RNC DSA intelligently distributes subcarriers into geographical regions so that there is reduced interference and increased trunking gain that improves the system throughput. For small to mid cell sizes, proposed algorithm significantly outperforms other three schemes because, for such cell structures, there is increased interference from the adjacent cells. Therefore, intelligently allocating subcarriers makes significant positive

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effect on the system performance. The increase in cell radius reduces the interference from neighbors and the cell capacity. This reduction is due to the increased path loss. For such situations, all four schemes achieve comparable performance. For example as shown in Fig. 4(a), for grid size 7 and cell radius 3 km or higher, proposed DSA is only marginally better than the other three schemes. Because there is little or no interference; therefore, RNC DSA cannot benefit significantly from the subcarrier allocation. The grid size 19 comparison also shows the same trends (see Fig. 4(b) ), except that because of large number of interferers, the proposed scheme is able to achieve significantly higher performance for moderate size cells in comparison to other schemes. For example, for cell size of 3000 m, proposed scheme showed 21 percent improvement than the FFFI. In general, FFFI experiences more interference than the conventional sector scheme; therefore, proposed scheme has larger gains against it. Likewise, for 19 cells grid, the FFFI has lower performance than the conventional sector allocation because of the increased interference in the grid whereas, for 7 cell grid, it has higher performance than the sectored allocation. The static FFR shows significant improvements over FFFI scheme for grid size 19. This result is in line with the results of [14]. However, in comparison to the proposed scheme and the traditional sectored allocation, static FFR performs badly due to the reduced trunking.

ALI and LEUNG: DYNAMIC FREQUENCY ALLOCATION IN FRACTIONAL FREQUENCY REUSED OFDMA NETWORKS

CDF of achieved data rates and lower bounds (grid size=7) 9 Proposed Scheme FFFI Conventional Sectored Reuse Static FFR Lower Bounds

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Fig. 5 compares the cumulative distribution functions (CDF) of the achieved rates of users and their minimum data rates requirements for 7 cell grid size. This figure shows that all four schemes have been able to comply with the minimum performance requirements. This compliance is due to the BS scheduling algorithm which is MPG opportunistic scheduling. Among the four DSA schemes considered, the proposed scheme is able to provide increased data rates. A group of users in the proposed scheme is able to have very high data rates. This behavior is in line with the objectives of the proposed DSA as the RNC DSA is a greedy algorithm. As long as minimum requirements are satisfied, the algorithm allocates resources to the geographical locations (that is, set of users present in those locations) in greedy fashion. Therefore, a set of users have increased data rates. Similar behavior is also observed for 19 cell grid size. Fig. 6 shows the network throughput comparison as a function of time for a cell radius of 2000 m and grid of 19 cells. The plot shows the total network throughput which is the sum of data rates of all the users in the grid as a function of simulation time. The proposed scheme achieves higher network throughput in comparison to the other three schemes. The increase is because of the way RNC DSA distributes subcarriers among geographical locations and the increased trunking advantage of the proposed BS DSA. In comparison to the FFFI allocation, the proposed scheme achieves an

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average gain of 64 percent. Whereas, in comparison to the conventional sectored allocation, the proposed scheme reports an average gain of 31 percent. The gain is higher against the FFFI allocation because FFFI experiences lower data rates due to higher interference from 18 interferers than conventional sectored allocation. The proposed scheme is also able to outperform the static FFR allocation. For the above experiment, we compare the performance of the cell edge users in Fig. 7(a). In this comparison, the cell edge users are those users which are at a distance of 1400 m or higher from the serving BS. The static FFR is able to report the highest data rates for the cell edge users followed by the FFFI and the sectored allocation. These three schemes are able to report better results than the proposed scheme. The static FFR is designed for the improvements of the cell edge users. The sectored allocation is able to show this performance because every sector gets subcarriers proportional to the number of users in that sector. In comparison to the other three schemes, the proposed scheme is a greedy allocation strategy which attempts to satisfy the lower bounds. Once those lower bounds are satisfied, the scheme mostly allocates its resources to the group of users that can provide the maximum gain to the performance. Because cell edge users generally have weaker channels, the proposed solution allocates any additional subcarriers, those left over after satisfying the minimum performance requirements, to

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the users with stronger channels. Hence, the proposed scheme reports reduced throughput for the edge users. However, it is important to mention that the proposed scheme is able to satisfy the minimum requirements of all cell edge users as shown in Fig. 7(b) where CDF of achieved data rates of cell edge users and their requirements are shown. Therefore, the proposed scheme is not in violation of any design objectives. The problems of low data rates for edge users in comparison to those in the center of the cell can be solved by increasing the minimum requirements of such users or by placing upper bounds on the maximum data rate that inner cell users can achieve by employing algorithms proposed in [20] and [21]. VI. C ONCLUSION In this paper, we have presented a novel dynamic channel allocation and opportunistic scheduling scheme for the multicell OFDMA networks. The scheme proposes a new dynamic fractional frequency reused system architecture where a cell surface is virtually partitioned into two regions. Both of these regions cover the whole cell surface. The first region is called super group, and the user-subcarrier pairs in this group experience interference from all the neighboring cells in the grid. The second region is called the regular group which is physically partitioned into sectors. The user-subcarrier pairs for this group experience reduced interference. The system architecture supports full frequency reuse. By covering whole cell surface, both groups include all the cell users which results in increased trunking gain. The proposed DSA scheme makes best use of the FFR architecture and consists of two algorithms. The first algorithm runs at the RNC and allocates subcarriers to the groups so that the system performance is increased while satisfying the sum of the minimum performance requirements of those groups. The second algorithm runs at every BS where opportunistic scheduling decisions are made and subcarriers are assigned to the users. The dynamic system architecture, the intelligent distribution of subcarriers to groups by the RNC, and the opportunistic scheduling at the BS level helps the proposed scheme to perform significantly better than the conventional allocation schemes. Simulation results compare the performance of the proposed scheme against traditional allocation schemes. For small to medium cell and large grid sizes, the proposed scheme outperforms the traditional schemes. R EFERENCES [1] G. Li and H. Liu, “Downlink radio resource allocation for multi-cell OFDMA system," IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3451-3459, Dec. 2006. [2] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas," IEEE Trans. Inform. Theory, vol. 48, no. 6, pp. 1277-1294, June 2002. [3] “IEEE standard for local and metropolitan area networks part 16: Air interface for fixed and mobile broadband wireless access systems," IEEE, Tech. Rep. 802.16, Oct. 2004. [4] “IEEE standard for local and metropolitan area networks part 16 and amendment 2," IEEE, Tech. Rep. 802.16e, Feb. 2006. [5] “Evolved universal terrestrial radio access (E-UTRA); physical channels and modulation, (release 8)," 3GPP, Tech. Rep. TS 36.211, Mar. 2008. [Online]. Available: http://www.3gpp.org/ftp/Specs/html-info/36211.htm [6] G. Song and Y. G. Li, “Cross-layer optimization for OFDM wireless networks—part I: theoretical framework," IEEE Trans. Wireless Commun., vol. 4, no. 2, pp. 614-624, Mar. 2005.

[7] J. Jang and K. B. Lee, “Transmit power adaptation for multiuser OFDM systems," IEEE J. Select. Areas Commun., vol. 21, no. 2, pp. 171-178, Feb. 2003. [8] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit and power allocation," IEEE J. Select. Areas Commun., vol. 17, no. 10, pp. 174–1758, Oct. 1999. [9] “Evolved universal terrestrial radio access (E-UTRA) and evolved universal terrestrial radio access network (E-UTRAN); overall description; stage 2 (Release 8)," 3GPP, Tech. Rep. Ts 36.300, 2008. [Online]. Available: http://www.3gpp.org/ftp/Specs/html-info/36300.htm [10] “Physical layer aspects for Evolved UTRA, (release 7)," 3GPP, Tech. Rep. TR 25.814, Oct. 2007. [Online]. Available: http://www.3gpp.org/ftp/Specs/html-info/25814.htm [11] Huawei, “Soft frequency reuse scheme for UTRAN LTE," 3GPP TSGRAN WG1 Contribution, Tech. Rep. R1-050507, May 2005. [Online]. Available: www.3gpp.org/ftp/tsg_ran/wg1_rl1/TSGR1_41/Docs/R1050507.zip [12] M. Sternad, T. Ottosson, A. Ahlen, and A. Svensson, “Attaining both coverage and high spectral efficiency with adaptive OFDM downlinks," in Proc. IEEE VTC, vol. 4, Oct. 2003, pp. 2486-2490. [13] “Downlink inter-cell interference co-ordination/avoidance evaluation of frequency reuse," 3GPP TSG-RAN WG1 Contribution, Tech. Rep. R1-061374, May 2006. [Online]. Available: http://www.3gpp.org/ftp/tsg_ran/WG1_RL1/TSGR1_45/Docs/R1061374.zip [14] X. Z. Haipend LEI, Lei ZHANG and D. Yang, “A novel multi-cell OFDMA system structure using fractional frequency reuse," in IEEE PIMRC, Sept. 2007, pp. 1-5. [15] X. Qiu and K. Chawla, “On the performance of adaptive modulation in cellular systems," IEEE Trans. Commun., vol. 47, no. 6, pp. 884-895, June 1999. [16] “Radio resource control (RRC); protocol specification, (release 8)," 3GPP, Tech. Rep. Ts 25.331, Apr. 2008. [Online]. Available: http://www.3gpp.org/ftp/Specs/html-info/25331.htm [17] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, and A. Viterbi, “CDMA/HDR: a bandwidth-efficient high-speed wireless data service for nomadic users," IEEE Commun. Mag., vol. 38, no. 7, pp. 70-77, July 2000. [18] X. Liu, E. K. P. Chong, and N. B. Shroff, “A framework for opportunistic scheduling in wireless networks," Computer Networks, vol. 41, no. 4, pp. 451-474, Mar. 2003. [19] T. Camp, J. Boleng, and V. Davies, “A survey of mobility models for ad hoc network research," Wireless Communication and Mobile Computing (WCMC), Special issue on Mobile Ad Hoc Networking, vol. 2, no. 5, pp. 483-502, 2002. [20] S. H. Ali, K.-D. Lee, and V. C. M. Leung, “Throughput constrained opportunistic scheduling in cellular data networks," accepted for publication in IEEE Trans. Veh. Technol., Apr. 2008. [21] M. Andrews, L. Qian, and A. Stolyar, “Optimal utility based multi-user throughput allocation subject to throughput constraints," in Proc. IEEE INFOCOM, vol. 4, Mar. 2005, pp. 2415-2424. Syed Hussain Ali (S’05-M’09) received the bachelor’s degree from Nadirshaw Edulji Dinshaw (NED) University of Engineering and Technology, Karachi, Pakistan in 1993, and the master’s degree from King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia in 1998, both in computer engineering. He received the Ph.D. degree in Electrical and Computer Engineering from University of British Columbia, Vancouver, Canada in 2008. From 1993 to 1996, he worked on several communication and networking projects in Pakistan. From 1999 to 2003, he served as a Lecturer and Network Engineer at KFUPM where he received several service awards for his performance. He is a recipient of a UBC graduate fellowship and a Josephine T. Berthier fellowship. His current research interests include cross-layer design and resource allocation strategies for wireless networks.

ALI and LEUNG: DYNAMIC FREQUENCY ALLOCATION IN FRACTIONAL FREQUENCY REUSED OFDMA NETWORKS

Victor C. M. Leung (S’75-M’89-SM’97-F’03) received the B.A.Sc. (Hons.) degree in electrical engineering from the University of British Columbia (U.B.C.) in 1977, and was awarded the APEBC Gold Medal as the head of the graduating class in the Faculty of Applied Science. He attended graduate school at U.B.C. on a Natural Sciences and Engineering Research Council Postgraduate Scholarship and completed the Ph.D. degree in electrical engineering in 1981. From 1981 to 1987, Dr. Leung was a Senior Member of Technical Staff at Microtel Pacific Research Ltd. (later renamed MPR Teltech Ltd.), specializing in the planning, design and analysis of satellite communication systems. He also held a part-time position as Visiting Assistant Professor at Simon Fraser University in 1986 and 1987. In 1988, he was a Lecturer in the Department of Electronics at the Chinese University of Hong Kong. He returned to U.B.C. as a faculty member in 1989, where he is currently a Professor and the inaugural holder of the TELUS Mobility Industrial Research Chair in Advanced Telecommunications Engineering in the Department of Electrical and Computer Engineering. He is a member of the Institute for Computing, Information and Cognitive Systems at U.B.C. He also holds Guest/Adjunct Professor appointments at Jilin University and Beijing Jiaotong University, China. Dr. Leung has authored/co-authored more than 400 journal/conference papers and book chapters. His research interests are in the areas of architectural and protocol design and performance analysis

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for computer and telecommunication networks, with a current focus on wireless networks and mobile systems. Dr. Leung is a registered member of the Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), Canada. He is a Fellow of IEEE, a Fellow of the Engineering Institute of Canada, a Fellow of the Canadian Academy of Engineering, and a voting member of ACM. He is a Distinguished Lecturer of the IEEE Communications Society. He serves on the editorial boards of IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS, IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY, IEEE T RANSACTIONS ON C OMPUTERS , C OMPUTER C OMMUNICATIONS, the I NTERNATIONAL J OURNAL OF S ENSOR N ETWORKS , the I NTERNA TIONAL J OURNAL OF W IRELESS C OMMUNICATIONS AND N ETWORKING , and the I NTERNATIONAL J OURNAL OF C OMMUNICATION N ETWORKS AND D ISTRIBUTED S YSTEMS . He has guest-edited several special journal issues, and served on the technical program committee of numerous international conferences. He is the General Co-chair of the 2009 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing in Vancouver, BC. He was TPC chair of the wireless networks and cognitive radio track of IEEE VTC-fall 2008 in Calgary, AB. He was the General Chair of QShine 2007 in Vancouver, BC, and Symposium Chair for Next Generation Mobile Networks in IWCMC’08, IWCMC’07 and IWCMC’06. He was a General Co-chair of ACM MSWiM’05 in Montreal, Canada, and a TPC Vice-chair of IEEE WCNC’05 in New Orleans, USA.