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Distributed Adaptive Subchannel and Power Allocation for Downlink OFDMA with Inter-Cell Interference Coordination Haichao Zhang and Qinghai Yang

Feifei Gao

Kyung Sup Kwak

State Key Laboratory on ISN, School of Telecommunications Engineering, Xidian University, China Email: [email protected]

School of Engineering and Science Jacobs University Bremen Campus Ring 1, Bremen, Germany Email: [email protected]

UWB-ITRC, Inha University, #253 Yonghyun-dong, Nam-gu, Incheon, 402-751, Korea Email: [email protected]

Abstract— In this paper, we propose a distributed adaptive interference coordination algorithm for a practical orthogonal frequency division multiple access (OFDMA)-based mobile cellular systems. The designed algorithm can achieve an efficient frequency reuse for any user distribution and traffic load. Since no a priori frequency planning is required, the minimal coordination between base stations is also achieved. Moreover, the proposed algorithm can adapt to different network interference conditions and is power-saving in some degree. We also develop a way to decompose a multi-cell optimization problem into distributed single-cell optimization problems, which greatly reduces the computational complexity.

I. I NTRODUCTION Frequency reuse factor in an orthogonal frequency multiple access (OFDMA) cellular systems can be chosen as large as one to maximize spectral efficiency [1]. However, when it comes to a multi-cell environment, heavy inter-cell interferences (ICI) from adjacent cells significantly degrade the system performance and, especially, cell edge user performance [2]. As a consequence, inter-cell interference coordination (ICIC) schemes have been proposed to mitigate ICI of celledge users and to balance the communication quality for both cell-edge and cell-interior users in [3]– [8]. In order to protect the weak users from ICI, literatures [3]– [7] investigated the fractional frequency reuse (FFR) interference coordination scheme with multiple frequency reuse factors in the same cellular system. Although FFR is simple and is capable of eliminating frequency collisions, it suffers from the poor spectrum efficiency. The soft frequency reuse (SFR) scheme was introduced in [8] to improve the spectrum efficiency. Usually, SFR is effective in static scenarios when the traffic across the whole network is evenly distributed. However, in realistic cellular scenarios wherein the user distribution and traffic load exhibit significant variations versus time, the This research was supported in part by the Fundamental Research Funds for the Central Universities, NSF China (60832001), the 111 Project (B08038), China, National Key Project (2009ZX03003-003-01, 2009ZX03003-006-03) and the MKE, Korea, under the ITRC program supervised by the NIPA (NIPA2010-C1090-1011-0007).

SFR scheme could not provide satisfactory performance any more. In this paper, we propose an distributed and adaptive interference coordination scheme to achieve efficient frequency reuse and to improve power efficiency for any user distributions and traffic load conditions. By combining conventional SFR with the adaptive frequency and power resource allocation algorithm, we design an adaptive frequency reuse partitioning system. The proposed scheme only requires minimal coordination between base stations and does not need a priori frequency planning. By user grouping, we can efficiently decompose the multi-cell resource-allocation optimization problem into distributed single-cell optimization problems. In this way, the complexity of optimal resource allocation is significantly reduced, which makes our algorithm suitable for practical applications. II. S YSTEM M ODEL We consider a down-link OFDMA multi-cell system with N hexagonal grid cells and one base station (BS) at the center of each cell. Each BS is equipped with one omnidirectional antenna and has a maximum total transmit power constraint Pmax . In each of these cells, there are K single-antenna users whose indices k belong to GK = {1, 2, ..., K}. We further denote the index sets of cell-interior and cell-edge user groups as GKI and GKE , respectively, with GKI ∪ GKE = GK and GKI ∩ GKE = ∅. The cardinalities of the sets are K = |GK |, KI = |GKI | and KE = |GKE | with K = KI + KE . We assume the total system bandwidth is W and each cell has T sub-carriers. Since adjacent sub-carriers have the similar fading characteristics [9], we consider a group of consecutive sub-carriers as the smallest scheduling unit for resource allocation and then name one group as one sub-channel. Generally, grouping subcarriers can reduce the system overhead, e.g., the number of feedback and required control signaling. Let each sub-channel occupy a bandwidth B. The total number of sub-channels is W/B and the sub-channel index is denoted as j, where j ∈ J = {1, 2, . . . , W/B}.

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(i)

where m ∈ CN , Pj is the transmit power allocated on the j-th sub-channel of the i-th cell, and N0 is the power spectral density of the additive white Gaussian noise (AWGN). The instantaneous information rate for the k-th user on the j-th sub-channel in the n-th cell is then given by:

A

(n)

B

Seven-cell system and frequency planning for SFR with q = 1/3.

Within a cell, different users transmit through different subchannels and no intra-cell interference exists. In the paper, we consider that ICI in a cell comes only from the neighboring cells where frequency reuse happened. The sub-channels available for assignment in the cell-interior and cell-edge user (n) (n) groups of cell n are chosen from the sets JI and JE , (n) ⊆ J, respectively, where n ∈ CN = {1, 2, ..., N }, JI (n) (n) (n) JE ⊆ J, with JI and JE being chosen based on the frequency reuse partitioning scheme. The SFR partitioning scheme will be considered in the paper. As illustrated in Fig. 1, the SFR scheme reserves a fraction of the total system bandwidth for the cell-edge users, whose bandwidth is denoted as WE = qW , q ≤ 1. Neighboring cells coordinate to ensure that their cell-edge bands are orthogonal (n) (m) of each other, i.e., JE ∩ JE = ∅, ∀n = m. The cell-interior users will then transmit over the remaining sub-channels, which occupies a bandwidth WI = (1 − q)W . Note that the adjacent cell-interior bands may not be orthogonal, i.e., (n) (m) = ∅, ∀n = m. Without loss of generality, JI ∩ JI (n) we assume JI = {qW/B + 1, qW/B + 2, ..., W/B} and (n) JE = {1, 2, ..., qW/B}. Unlike the traditional frequency reuse approach, the total usable bandwidth per-cell in our scheme is still W . The radio propagation can be modeled by two factors, distance dependent attenuation (path loss) and the shadowing. Hence, the link propagation model can be described as: Pr = Ptx AGP S

(1)

where Ptx and Pr stand for the transmit and receive power, respectively, A is the overall antenna gains, S is the shadowing gain, and GP is the path gain for a particular BS-User link that is a function of the distance R from the user to the BS. From equation (1), the instantaneous received signal-tointerference noise ratio (SINR) over the j-th sub-channel of the k-th user in the n-th cell can be computed as: (n) SINRj,k

(n)

=

(3)

III. P ROBLEM S TATEMENT

C Fig. 1.

(n)

Rj,k = B log2 (1 + SINRj,k )

(n)

(n)

(n)

Pj Aj,k GP (Rj,k )Sj,k

m∈CN ,m=n

(m)

Pj

(m)

(m)

(m)

Aj,k GP (Rj,k )Sj,k + N0 B (2)

To simplify the cell-planning, most static interference coordination schemes discard the traffic inhomogeneity and the varying distribution of user groups within a cell. However, such an approach leads to significant performance degradation in data throughput. On the other hand, adaptive and dynamic interference coordination can efficiently allocate system resource to minimize ICI and to enhance the system throughput. Hence, the adaptive and dynamic approach will be adopt in this paper. To guarantee the quality of service (QoS) for most cell-edge users and the fairness between the two user groups, we set a minimum target rate RE−M in for all cell-edge users as well as a minimum target rate RI−M in for all cell-interior users. The system then allocates power and sub-channel resources to cell-edge active users to satisfy their basic QoS demands. The remaining resources are then used to maximize the throughput of the cell-interior user group. We can formulate this multi-cell optimization problem as follows:

Pmulti

⎧ (n) ⎪ RI,k max ⎪ (n) (n) (n) ⎪ ⎪ n∈C k∈G {J },{J },{p } N KI j I,k E,k ⎪ ⎪ ⎪ (n) ⎪ ⎪ s.t. R ≥ R E−M in , k ∈ GKE , n ∈ CN ⎪ ⎨ E,k(n) pj ≤ Pmax , n ∈ CN : j∈J ⎪ ⎪ ⎪ (n) ⎪ ⎪ RI,k ≥ RI−M in , k ∈ GKI , n ∈ CN ⎪ ⎪ ⎪ (n) (n) ⎪ ⎪ JI,k + JE,k ≤ W/B ⎩ k∈GKI

(n)

k∈GKE

where pj is the transmit power over the j-th sub-channel, (n) (n) RI,k and RE,k are the instantaneous throughput of the kth cell-interior and the k-th cell-edge users in the n-th cell, respectively. The objective function in Pmulti represents the (n) sum-rate of all cell-interior users in the system, JI,k and (n) JE,k are the instantaneous number of sub-channels used by the k-th cell-interior and the k-th cell-edge users in the nth cell, respectively. Here we set RI−M in ≥ 2RE−M in for the purpose of balancing the communication quality of two different users groups. Even in the single-cell case and ignoring inter-cell interference ,the joint optimal sub-channel and power allocation problem has been shown to be NP hard, which makes it computationally expensive to solve the Pmulti directly. In order to cope with such difficulties, in the following, we propose a new approach to decouple the multi-cell joint optimal allocation problem into several subproblems.

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IV. A DAPTIVE AND D ISTRIBUTED I NTERFERENCE C OORDINATION S CHEME In this section, a heuristic and suboptimal algorithm is developed to solve Pmulti in a distributed manner. Each cell only provide the local sub-channel and power allocation with minimal information exchange between coordinated cells. Firstly, users are categorized into cell-interior and cell-edge groups based on their locations. We compute the maximum power can be assigned over cell-interior and cell-edge subchannels via the mechanism called compensated power control method (CPCM) that is described as follows: 1) The system decides the number of cell-edge active users (n) (n) KE and the number of cell-interior active users KI within the n-th cell through certain detection. (n) 2) Denoting the number of active users as K (n) = KE + (n) KI , the number of sub-channels allocated to the celledge user group in the n-th cell can be expressed as: (n)

=

β

=

NE

L · β , (n) KE /K (n) , 1 3,

(n)

KE /K (n) ≤ else,

1 3

(4)

where L is the number of sub-channels in a cell, and · denotes maximum integer that is smaller than the inside argument. The number of available cell-interior (n) (n) sub-channels can be described as: NI = L − NE . Moreover, β should not be larger than 1/3 to guarantee that the adjacent cells can allocate non-overlapping frequency bands for their cell-edge traffic. 3) We then compute the maximum total available power (n) for cell-interior sub-channels PI (max) and cell-edge (n) sub-channels PE (max) from: (n)

(n)

PI (max)/PE (max)

(n) PI (max)

+

(n) PE (max)

(n)

(n)

= NE /NI

(5)

= Pmax .

(6)

4) For easier implementation, we set the same powers for all cell-interior sub-channels and the same power for all cell-edge sub-channels. The maximum power over each cell-interior sub-channel and each cell-edge sub-channel can be respectively computed as: (n)

(n)

(n)

(n)

pJ,I (max)

= PI (max)/NI ,

pJ,E (max)

= PE (max)/NE .

(7)

The above maximized power will be assigned over all cellinterior sub-channels, i.e., pJ,I = pJ,I (max). The average transmit power on each sub-channel can be denoted as PAV = Pmax /(W/B). Following CPCM, we obtain KE /KI , KE /K ≤ 13 pJ,I = aPAV , a = (8) 1 2 , else and, pJ,E (max) = PAV /a.

(9)

Based on the above described user group partitioning scheme, we can decouple Pmulti into two subproblems with respect to cell-interior and cell-edge user groups, respectively.

A. Subproblem for Cell-Edge User Group We first assign equal power pJ,E to each cell-edge subchannels and then minimize the usage of sub-channels within a minimum rate constraint RE−M in . Let us represent this optimization problem as Pmin . Clearly, the feasibility of Pmin depends on the target rate RE−M in and the initial power allocation. Generally, one can increase pJ,E to check the feasibility of Pmin as long as pJ,E ≤ PAV /a is satisfied. For simplicity, we consider a homogeneous user distribution over all cells.1 The details of our algorithm for cell-edge user group are presented as follows: Minimization of the Number of Sub-Channels 1) Set pJ,E = δ×PAV (0 ≤ δ < 1) as an initial power level (here δ should be set at a reasonable level to guarantee the computational efficiency); 2) Update pJ,E = pJ,E + step p, assign pJ,E ≤ PAV /a power on each sub-channel of the cell-edge user group (step p is a positive power step-length value); 3) Solve the minimization problem of the sum sub-channels number ⎧ (n) (n) ⎨ min WE = JE,k .B (n) (n) k∈GKE {JE,k } Pmin : ⎩ (n) s.t. RE,k ≥ RE−M in , k ∈ GKE , n ∈ CN (n)

4) Make a comparison of 1/3 and KE /K (n) , if W/3 ≥ (n) (n) KE /K (n) , β = KE /K (n) ; else β = 1/3; Then, use (n) WE to perform some judgments and selections. (n) 5) If WE > βW , then go to step 2); If pJ,E > PAV /a, break(out of the cycle). BS then temporarily rejects the user who occupies the largest amount of sub-channels to access the system and then go to step 1). Otherwise, we (n) (n) (n) (m) can determine JI and JE , given that JE ∩JE = ∅, (n) (n) ∀n = m, and WI = W − WE . In such a case, the parameter q associated with the SFR partitioning scheme is given by:2 (n)

q = WE /W.

(10)

From the above algorithm we can derive the total transmit power allocated to the cell-edge users group in the n-th cell as (n) (n) (11) PE = WE pJ,E /B B. Subproblem for Cell-Interior User Group In this case, BS allocates the residual power and subchannels among the cell-interior users. Initially equal power pJ,I = aPAV is allocated to each cell-interior sub-channel. Under this uniform power allocation, we maximize the sum rate for the cell-interior users subject to the ergodic restrictive condition that the rate for every cell-interior should be no less than RI−M in . 1 It can be easily extended to the case when sub-channels are allocated in a selective manner. 2 In inhomogeneous user distribution, it shows different value of q for each cell.

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Algorithm of Sum Rate Maximization 1) Allocate equal power over all cell-interior sub-channels, such that pJ,I = aPAV . 2) Solve the sub-channel allocation problem ⎧ (n) ⎪ max ⎪ ⎪ {J (n) } k∈G RI,k ⎪ KI ⎨ I,k (n) (n) : Pmax s.t. R ≥ RI−M in , k ∈ GKI , n ∈ CN ⎪ I,k (n) ⎪ (n) ⎪ ⎪ JI,k .B ≤ WI , n ∈ CN ⎩ k∈GKI

An difficulty for the above algorithms is to set a relatively reasonable RI−M in . If RI−M in is set too small, then most users can achieve the rate target with very few resources, and all the remaining resources will be allocated to the user that has the best channel conditions, giving this particular user very large instantaneous information rate compared to others. Such an unfairness should be avoided in a practical system. On the other hand, if we set RI−M in too large, many cellinterior users with the relatively poor channel conditions will be suspended because of resource-limitation. C. Fair Algorithm for Sum Rate Maximization of Cell- Interior User Group From the previous discussion, we know that the above sum rate maximization algorithm can hardly maintain the fairness among vast majority of the cell-interior users. Therefore, we shall modify the above constrained maximization problem by considering the tradeoff between fairness and efficiency of resources allocation. Namely, under the limitation of total available bandwidth, we guarantee each cell-interior active user can achieve an equal minimum information rate RI−M in , but at any circumstance this minimum information rate can not be less than 2RE−M in . In other words, RI−M in changes with different locations of cell-interior active users and becomes fixed for a certain user distribution. Thus, the algorithm can adapt to the changes of user distribution and various network interference conditions in different user grouping cycle, by which means the fairness among all users can be guaranteed. Algorithm for Fairness 1) Let pJ,I = aPAV . Depending on the number of cellinterior active users, set an initial value for the uniform minimum information rate limit RI−M in . (This value should be large enough and unattainable for the majority of users). 2) For RI−M in = RI−M in + stepR (setpR is a negative step-length value), we solve the following bandwidth minimization problem. ⎧ (n) (n) ⎨ min WI,Z = JI,k .B (n) (n) k∈G {J } KI Pmin : I,k ⎩ (n) s.t RI,k ≥ RI−M in , k ∈ GKI , n ∈ CN If RI−M in < 2RE−M in , break (Out of the cycle), goto step 3); else, goto step 4). 3) BS rejects those active users that have most harsh channel conditions, then goto Step 1).

(n)

(n)

(n)

(n)

4) If WI,Z > WI , goto step 2); else if WI,Z ≤ WI , (n) (n) then allocate (WI −WI,Z )/B remaining sub-channels uniformly to users with the best channel condition, such that both the resource allocation efficiency and the overall throughput of the active cell-interior users can be improved. The overall throughput is (n) (n) RI,k (12) RI = k∈GKI

Remark 1: In contrast to non-fairness algorithm (in subsection B), the algorithm here sacrifices the total throughput to offer a throughput-fairness trade-off for cell-interior user group. Moreover, the fairness algorithm also allows cellinterior users to make full use of the available cell-interior subchannels and is also power-saving. The down-link co-channel interference from the serving BS to the users in adjacent cells is also reduced. V. S IMULATIONS A ND R ESULTS A NALYSIS A. Simulation Models and Parameters To evaluate the proposed adaptive and distributed SFR (ADSFR) ICIC schemes, we focus on a multi-cell OFDMA downlink system with 7-cell hexagonal layout with omnidirectional antennas at the center of each cell, and each cell has the same number of uniformly distributed users. The FFT size is taken as T = 512 and the total bandwidth W is 10M Hz. We assume each cell has 40 active users and each user has unlimited traffic to transmit on the down-link (full load). The distance between adjacent base stations is 1732 m and the distance threshold Dth is 660 m, where the cell-interior and cell-edge users are classified based on their distances from the serving BS, i.e., if Dk is the distance of user k from serving BS and Dk ≤ Dth , then user k belongs to the cell-interior user group.3 B. Simulation Results and Discussions In Fig. 2 and Fig. 3, we compare the performance of Reuse 1, conventional SFR, and AD-SFR, including the algorithm for fairness. Reuse 1 scheme is the universal frequency reuse scheme and consider that all users are allocated with equal power and bandwidth irrespective of their categories (cell-edge or cell-interior users). For the conventional SFR scheme, we fixed a priori q = 1/3 with the power ratio equal to 1/4. AD-SFR-1 refers to the proposed sum rate maximization algorithm with unfairness while AD-SFR-2 is the one with fairness. For capacity estimation, a fully loaded network is assumed. As no wrap-around method is deployed, only users at the center site are incorporated for the evaluation. The average overall cell throughput, average cell-edge user throughput and average transmit powers on each sub-carrier are obtained from 500 different user location scenarios. In Fig. 2(a) to Fig.2(b), we observe that our proposed schemes can provide better performance in terms of average 3 By varying Dth, it is expected that performance gaps between different reuse schemes will be different since the ratio of the cell-interior to cell-edge users depend on this distance threshold

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Overall Throughput (Mbits/s)

0.6 0.5 0.4 0.3 0.2 0.1 0

60 40 20

Reus1 SFR ADSFR1 ADSFR2 (a) Cell edge user Throughput Comparison

10 8 6 4 2 0

80

Ruse1 SFR ADSFR1 ADSFR2 (c) Spectrum Efficiency Comparison

Energy Efficiency (Kbit/s/mW)

Spectrum Efficiency (bit/s/Hz)

Cell edge user Throughput (Mbits/s)


0

Reuse1 SFR ADSFR1 ADSFR2 (b) Overall Throughput Comparison

4 3 2 1 0

Reuse1 SFR ADSFR1 ADSFR2 (d) Energy Efficiency Comparison

Fig. 3. Comparison of average transmit powers over each subcarrier for Dth=660m, RE−M in =0.6(Mbit/s) Fig. 2. (a) Comparison of average throughput of cell-edge users for Dth=660m, RE−M in =0.6(Mbit/s); (b) Comparison of overall average cell throughput for Dth=660, RE−M in =0.6; (c) Comparison of overall frequency efficiency for Dth=660 , RE−M in =0.6; (d) Comparison of average energy efficiency for Dth=660, RE−M in = 0.6

cell-edge user throughput, average cell throughput, and the bandwidth efficiency. AD-SFR-1 algorithm not only provides a higher average throughput but also gives a better protection on the cell-edge users by maintaining a minimum rate requirement. The AD-SFR-2 algorithm provide a tradeoff between efficiency and fairness for cell-interior users, which results in a sacrifice on the average cell throughput compared with AD-SFR-1 method. However, the performance is still better than than that of the conventional SFR. Fig. 2(a) also shows AD-SFR-2 algorithm has the same average cell-edge user throughput as AD-SFR-1 algorithm. Because each of the Reuse 1, SFR, AD-SFR-1 and AD-SFR-2 schemes allows to use the whole system frequency bandwidth W , the evaluation of the corresponding frequency efficiency depends on the comparison of overall average cell throughput. As shown in Fig. 2(c), AD-SFR-1 and AD-SFR-2 schemes yield higher frequency efficiency than SFR, and the frequency efficiency of AD-SFR-1 is even better than that of Reuse 1. In Fig. 2(d) and Fig. 3, we observe that both AD-SFR schemes are power-saving ICIC methods compared with the Reuse 1 and SFR approaches. From previous statement of CPCM in section IV, we know the power control method for AD-SFR-1 and AD-SFR-2 are the same. Hence in Fig.3, we use AD-SFR to present both of them. Although the average transmit powers on the cell-edge sub-channels of AD-SFR scheme are larger than that of the Reuse 1 scheme, the whole transmit power declines contrarily. This is because that in the AD-SFR scheme the average transmit power on the cellinterior sub-channels is much smaller than that of Reuse 1 scheme, and the total number of cell-interior sub-channels are 2/3 at most.

VI. C ONCLUSION In this paper, we developed an adaptive scheme, i.e., ADSFR, for distributed multi-cell interference coordination. The proposed scheme not only achieves an efficient frequency reuse for various user distribution and traffic load, but also decreases the overall power consumption of the system. By dividing users into cell-interior and cell-edge groups, we could decomposed a multi-cell optimization problem into several single cell resource allocation problems, which greatly reduces the computation complexity. Simulation results demonstrated the superior performance of our proposed algorithm to conventional frequency reuse schemes. R EFERENCES [1] Y. J. Choi, C. S. Kim, S. Bahk. ”Flexible Design of Frequency Reuse Factor in OFDMA Cellular Networks.” IEEE Inter-national Conference on Communications, Vol. 4, pp. 1784-1788. June 2006. [2] LG Electronics, Interference mitigation in evolved UTRA / UTRAN[S]. in 3GPP R1-050833, TSG RAN WG1#42, London, UK, Sept. 2005. [3] S. E. Elayoubi, O. B. Haddada, and B. Fourestie, Performance evaluation of frequency planning schemes in OFDMA-based networks, IEEE Trans. Wireless Commun., vol. 7, no. 5, pp. 1623-1633, May 2008. [4] R. Giuliano, C. Monti, and P. Loreti, WIMAX fractional frequency reuse for rural environments, IEEE Wireless Commun. Mag., vol. 15, no. 3, pp. 60-65, Jun. 2008. [5] Y. Xiang, J. Luo, C. Hartmann, ”Inter-cell Interference Mitigation through Flexible Resource Reuse in OFDMA based Communication Networks,” In Proc. 13th European Wireless Conference EW2007, Paris, France, April 2007. [6] G. Li and H. Liu, ”Downlink radio resource allocation for multi-cell OFDMA system,” IEEE Trans.Wireless Com., vol. 5, no. 12, pp. 34513459, Dec.2006. [7] Ericsson, Downlink inter-cell interference coordination/avoidance Evaluation of frequency reuse, in 3GPP R1-061374, TSG RAN WG1 Meeting 45, Shanghai, CHINA, May 2006. [8] Huawei, ”Soft frequency reuse scheme for UTRAN LTE,” in 3GPP R1050507, TSG RAN WG1 Meeting 41, Athens, GREECE, May 2005. [9] Q. Wang, D. Xu, J. Xu, ”A grouped and proportional-fair subcarrier allocation scheme for multiuser OFDM systems,” in proc. of 25th IEEE International IPCCC, pp.97-101, April 2006.

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