Centralized Radio Resource Allocation for OFDMA ... - Semantic Scholar

2 downloads 0 Views 187KB Size Report
carriers and the relative transmission format on the basis of the experimented link ... radio resource allocator for the multi-cell scenario of an. OFDMA cellular ...
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

Centralized Radio Resource Allocation for OFDMA Cellular Systems Andrea Abrardo, Alessandro Alessio, Paolo Detti

Marco Moretti

Dipartimento di Ingegneria dell’Informazione Universit`a di Siena E-mail: {Abrardo,Alessio,Detti}@dii.unisi.it

Dipartimento di Ingegneria dell’Informazione, Universit`a di Pisa E-mail: [email protected]

Abstract— Efficient resource allocation in cellular OFDMA systems envisages the assignment of the number of subcarriers and the relative transmission format on the basis of the experimented link quality. In this way, a higher number of sub-carriers with low per-carrier bit rates should be assigned to users at cell border. This strategy has already proved its efficiency in the single-cell scenario, while no study has been provided in the multi-cell scenario with reuse factor equal to one, i.e., in presence of severe interference conditions. In this paper we propose an optimum centralized radio resource allocator for the multi-cell scenario of an OFDMA cellular system which allows to highly outperform iterative decentralized allocation strategies based on local optimization criteria. The proposed scheme is characterized by huge implementation complexity, and, hence, it can be hardly implemented in the real world. However, it can help the system designer in catching the essence of interference limitations in OFDMA cellular systems, thus allowing the elaboration of efficient heuristic decentralized approaches. As an example, we prove that the sub-carrier transmission format adaptation is not useful in a multi-cell scenario. This is because users at cell border tends to consume the most of the resources (i.e., they are assigned the most of sub-carriers), thus producing interference for the neighbor cells over a large set of sub-carriers. Hence, since in this case neighbor cells are forced to use those (few) sub-carriers which experiment low interference, the diversity gain tends to be missed.

I. I NTRODUCTION The main challenge of future evolution wireless networks is that of meeting the ”anywhere and anytime” concept, so that future wireless systems are expected to converge into an heterogeneous all-IP architecture with the same performance and the same quality of service (QoS) of wired networks [1]. To achieve such a far-reaching goal, it is well known [2] that wireless systems should exploit multi-user diversity in order to share the radio resources among users with good channel conditions only. However, the decision about which terminal is allowed to transmit is a difficult task on account of mutual interactions among mobile users due to radio interference (i.e., the user which experiments the best channel condition could be also a high interfering user). Moreover, such

an approach leads to a solution where the users with best channel quality are allowed to use the most of the available resources. To cope with the case of unequal fading statistics or average Signal to Noise Ratios (SNRs), it has been then proposed to exploit fairness-aware criteria, which offer a compromise between cell throughput and equity between the users [3], [4], [5], [6]. Together with the diffusion of the multi-user diversity concept, wireless systems have been evolved in the last years toward the possibility of providing each user with the highest level of single user diversity. As an example, multipath and space diversity is obtained in WCDMA for 3G systems, frequency diversity is obtained in OFDM and OFDMA for IEEE 802.16 WiMax, while multiple-input multipleoutput (MIMO) transmission schemes, which benefit form space diversity, are recommended for long term evolution wireless systems. A very interesting scenario, where the concept of multi-user and single-user diversities are strictly connected is represented by OFDMA transmission systems. Such a radio technology has been proposed for the implementation of WiMax networks, and is one of the most promising techniques for next generation of wireless systems. For fixed or portable applications where the radio channels are slowly varying, an intrinsic advantage of OFDMA over other multiple access methods is its capability to exploit the multi-user diversity embedded in diverse frequency-selective channels [7], [8], [9]. Assigning the available sub carriers to the active users in an adaptive manner is a viable method to achieve multi-user diversity: propagation channels are independent for each user and thus the sub carriers that are in a deep fade for one user may be good ones for another. Several papers have recently focused on the problem of optimum channel allocation of OFDMA cellular systems, and some of them have also considered the joint scheduling-allocation problem [10], [11]. In this case, higher level requirements are given to the resource allocator in the form of minimum and maximum bit rate so that layer one has the flexibility of allocating more resources to good users, while layer

1-4244-0353-7/07/$25.00 ©2007 IEEE

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

2 has to dynamically upset its requirements so that long term fairness can be guaranteed. All the studies have so far concentrated on the single cell scenario. In this paper we propose a centralized optimization method for sub-carriers allocation in the downlink of an OFDMA multi-cell scenario. Performance of the proposed allocation strategy are given in terms of requested power for a given system throughput, and comparisons with a decentralized approach, where allocation is performed by each base station separately, are given as well. The paper is organized as follows. Section 2 describes the system model. Section 3 introduces the Single-cell scenario, i.e., a scenario where no extra cell interference is present, and proposes an optimization approach which is based on network flow formulation. Section 4 proposes a centralized optimization approach for the multi-cell scenario. Section 5 describes a possible decentralized allocation strategy for the multi-cell scenario. In this case, each base station performs the single-cell allocation algorithm based on network flow and tries to iteratively converge to a solution taking into account at each iteration the measured extracell interference. Section 6 shows the results obtained for the centralized and the decentralized allocation strategies. Finally, Section 7 provides conclusive remarks. II. S YSTEM MODEL We consider the downlink of an OFDMA system: the overall frequency bandwidth is divided into m subcarriers. The propagation channel is frequency selective and quasi static, i.e. it does not vary within a block of transmission. Moreover, the coherence bandwidth of the channel is larger than the bandwidth spanned by each subcarrier. In the centralized approach we also assume that there is a central controller that possesses perfect channel state information (CSI) relative to all users. Finally, we assume that every base station (BS) employs a control channel to communicate to the receiving terminals the set of sub-carriers assigned to each user so that each receiver is able to recover its serial data-stream. The problem of channel allocation is formulated so as to minimize the overall power consumed by the system, given a certain constraint on the rate of each user. Physical layer performance depends on the chosen coding scheme and modulation format, while in general traffic requests from the scheduler are in terms of informative bit rates. Therefore, to keep the discussion general and avoid the specific details of practical implementations we use Shannon capacity as a measure of the transmission rate achievable by a certain user on a particular channel. To further simplify the resource allocation algorithm, we follow the approach of [12] and [13] and we impose that each user adopts just one transmission format on

all assigned sub-carriers. In particular, we use the subcarrier allocation algorithm presented in [13] based on vector form Newtons method to decide the number of subcarriers and the format to assign to each user. Although suboptimal, the choice of using only one transmission format for each user is justified by the great reduction in complexity and the only marginal performance loss. The major drawback is that users are not able to adapt their transmissions to the quality of the assigned channels and thus can not fully exploit the channel frequency diversity. This loss is partially compensated by the exploitation of the multi-user diversity. As a consequence of resource allocation, the mean value of the gains of the assigned channels is larger than in the case of channel-independent allocation, and the standard deviation is much smaller. The larger the number of users, the larger is the set of channels over which to perform the allocation and the larger is the multi-user diversity gain. Thus, link adaptation becomes progressively a less effective measure. III. S INGLE - CELL SCENARIO The problem in the single-cell scenario is formally described in the following. We are given a set of subcarriers M = {1, . . . , m}, a set of users U = {1, . . . , n} in the cell. Transmission requirements for a given user i set the corresponding rate Ri . Due to interference phenomena, users cannot share sub-carriers. Given a certain Signal-to-Interference Ratio (SIR), the ideal rate achievable on a channel that spans a bandwidth B is R = Bη, where η = log2 (1 + SIR) is the channel spectral efficiency in bit/s/Hz. Depending on the users rate requirements and on channel condition, the BS sets for each user a target spectral efficiency. The spectral efficiency ηi for user i is set so that the rate constraint Ri can be converted into an integer number of sub-carriers ri = Ri /ηi . In particular, setting the spectral efficiency ηi is tantamount to set the target SIRi for user i: SIRi = 2ηi − 1. If sub-carrier j is assigned to user i, it requires a transmission power pi (j) equal to pi (j) = SIRi

BN0 Gi (j)

(1)

where SIRi is the Signal-to-Interference Ratio of user i to achieve target spectral efficiency ηi , Gi (j) is the channel gain of user i on sub-carrier j and N0 is the power spectral density of the zero-mean thermal noise. A feasible radio resource allocation consists in assigning sub-carriers to users in such a way that 1) for each user i, ri sub-carriers are assigned to it, 2) each sub-carrier j can be assigned to at most a user. The problem, that we call single-cell radio resource allocation problem (SCRRAP), can be formulated as follows:

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

Definition 1: – Given a set M of sub-carriers, a set of users U = {1, . . . , n}, transmission requirements ri for each user i ∈ U , the single-cell radio resource allocation problem is the problem of finding a feasible radio resource allocation that minimizes the total transmission power. A. A network flow formulation for SCRRAP SCRRAP can be formulated as a min cost flow problem by introducing a direct graph G = (V, E) with m + n + 2 nodes and m + n + mn edges. In Particular, the node set is V = {s ∪ t ∪ VM ∪ VU }, where s and t are a source and a sink node, respectively, VM is a set of m nodes, one for each sub-carrier, and VU is a set of n nodes, one for each user. The edge set E can be partitioned into three sets, namely, Es−M , EM −U and EU −t . The set Es−M contains m direct edges, connecting node s with nodes in VM . The set EM −U contains mn direct edges, connecting a node in VM with a node in VU . Edges in the set EU −t connect each node in VU with node t. We associate to edges in E the following capacities and costs. Edges (s, j) ∈ Es−M cost have cost 0, and a minimum and a maximum capacity equal to 0 and 1, respectively. Edges (j, i) ∈ EM −U are edges with a minimum and a maximum capacity equal to 0 and 1, respectively, and a cost equal to pi (j) (see relation (1)). Finally, Edges (i, t) ∈ EU −t have cost 0, and a minimum and a maximum capacity equal to ri and Ri , respectively (i.e., the minimum and the maximum number of sub-carriers that must be assigned to user i). In Figure 1, the graph for solving SCRRAP is presented.

Fig. 1.

The graph formulation of SCRRAP.

It is easy to see that a flow of minimum cost on graph G corresponds to an optimal solution of SCRRAP. IV. M ULTI - CELL SCENARIO In this section, the Multi-cell scenario is addressed, and the problem of channel allocation in OFDMA cellular systems for downlink transmissions is considered. In particular, we address the problem of allocating sub-carriers among users, in such a way that users transmission requirements, in terms of transmission quality and throughput,

are satisfied. The objective to be minimized is the overall transmission power. The problem in the multi-cell scenario is formally described in the following. We are given a set of subcarriers M = {1, . . . , m}, a set of cells {1, . . . , K}, and for each cell k a set of users Uk = {1, . . . , nk }. Let K  U = Uk be the set of all users in the system. For k=1

each user i, we denote by b(i) the cell of user i. Hence, b(i) = k for all i ∈ Uk . Having set for each user a certain target spectral efficiency, transmission requirements for a given user i correspond to a certain number of sub-carriers ri . In general, users belonging to different cells can share the same sub-carrier (while interference phenomena do not allow to users in the same cell to transmit on the same sub-carrier). However, the power to transmit on a given sub-carrier increases as the number of users transmitting on that sub-carrier increases. More precisely, let S(j) be the set of users (belonging to different cells) which are assigned the same sub-carrier j. Hence, the transmission powers requested by users in S(j) on sub-carrier j are linked by the following relations. SIRi = 

Gi (j)pi (j) h∈S(j),h=i

b(h)

Gi

(j)ph (j) + BN0

(2)

where SIRi is the target Signal-to-Interference Ratio corresponding to the spectral efficiency ηi of user i, Gi (j) is the channel gain of user i on sub-carrier j, Gki (j) is the channel gain between user i and the base station of cell k = b(i) on sub-carrier j. Values Gki (j) are a measure of the interference between user i and users of other cells transmitting on the same sub-carrier j. In Equation (2), we refer to the  b(h) term h∈S(j),h=i (Gi (j))ph (j) as to interference term. Thus, being SIRi the target SIR corresponding to the spectral efficiency ηi , we use (2) to determine the power pi (j)  b(h) (j)ph (j) + BN0 h∈S(j),h=i Gi (3) pi (j) = SIRi Gi (j) Note that, power pi (j) increases as the interference term increases, moreover, the interference term depends on the set of users, other than i, which are assigned the same subcarrier. Note also that, system (2) could not have a feasible solution. On the other hand, if only user i is assigned subcarrier j (i.e., if the interference term is 0), by (2) is power i BN0 pi (j) = SIR Gi (j) . A feasible radio resource allocation consists in assigning sub-carriers to users in such a way that a) for each user i, ri sub-carriers are assigned to it, b) users in the

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

same cell are not assigned to the same sub-carriers, c) given the sub-carrier j and the set S(j), the system (2) has a feasible solution. The problem, that we call multicell radio resource allocation problem (MCRRAP), can be formulated as follows Definition 2: – Given a set M of sub-carriers, K cells, a K  Uk , transmission requirements ri for set of users U = k=1

each user i ∈ U , the multi-cell radio resource allocation problem is the problem of finding a feasible radio resource allocation that minimizes the total transmission power. In the following, an Integer Linear Programming (ILP) formulation for MCRRAP is presented. Let xij be a binary variable equal to 1 if user i is assigned subcarrier j (and 0 otherwise), and let pi (j) be a positive real variable denoting the transmission power allocated for user i on sub-carrier j. The MCRRAP is formulated at the bottom of this page. The objective function accounts for the overall transmission power. In Constraints (4) and (5), Q is a suitable large positive number. Constraints (4) are logic constraints, forcing power pi (j) to be 0 if sub-carrier j is not assigned to user i. In according with Equations (2), Constraints (5) state that if user i is assigned sub-carrier j (i.e., xij = 1) power pi (j) cannot SIRi (



G

b(h)

(j)ph (j)+N0 )

h∈U, b(h)=b(i) i be smaller than . On Gi (j) the other hand, if xij = 0, the right term of (5) is a large negative number, and Constraints (5) are always satisfied. Constraints (6) state that at most a user per cell can be assigned to a given sub-carrier. Constraint (7) requires that ri sub-carriers are assigned to each user i. Finally, Constraints (8) are redundant, but improve the solution of the linear programming relaxation. They state that if user i is assigned sub-carrier j power pi (j) cannot be

min



smaller than than the right-hand-side term. In Section VI, we test the above ILP formulation on randomly generated MCRRAP problems. V. A DECENTRALIZED ALGORITHM FOR MCRRAP This section targets the MCCRAP following an approach based on a decentralized strategy. This approach, although suboptimal, it is attractive for practical implementation. It has the advantage of reducing: a) the overall complexity of the allocation and b) the amount of information that needs to be exchanged on the network between the different cells and the central controller. A distributed resource management (RRM) leads to the implementation of an iterative allocation procedure: sequentially, each cell solves its resource allocation as a SCRRAP. Just as in the centralized approach, inter-cell interference is explicitly taken into account to compute the resources’ costs using (3). One by one the cells in the system allocate all their users on the given bandwidth. When a given user is allocated on a certain resource it interferes with all (if any) users allocated on the same frequency band in other cells. As a consequence, a variation in the allocation in one cell perturbs the optimal allocation of all neighboring cells. At each iteration the resources cost need to be updated and the allocation procedure requires a certain number of iterations before reaching a steady-state. This resembles power control in interference-limited networks, where altering the power of one user affects all other users. The difference is that this can be seen as a vector power control problem: each user has now an entire set of optimization variables, i.e. the transmitted powers on each sub-carrier. The convergence of this decentralized algorithm is not guaranteed: it depends on the overall

pi (j)

i,j

Gi (j)pi (j) −

 h, b(h)=b(i)

pi (j) ≤ Q xij b(h) SIRi Gi (j)ph (j)



xij ≤ 1

∀i, j ≥ SIRi N0 (1 − Q(1 − xij ))

(4) ∀i, j

(5)

∀k, j

(6)

∀i

(7)

i∈Uk



xij = ri

j

SIRi N0 xij ∀i, j Gi (j) ∀i, j pi (j) ≥ 0 xij ∈ {0, 1} ∀i, j

pi (j) ≥

(8) (9) (10)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

We tested the centralized ILP approach and the distributed heuristic algorithm presented in Section V on randomly generated problems. We assume to have m = 8 sub-carriers which span a 5 MHz bandwidth, i.e., the bandwidth per single carrier is B = 625 kHz. We also assume a fixed throughput per cell equal to Rtot bit/sec and that such a per-cell throughput is evenly shared among U users in the cell, which are uniformly distributed in a hexagonal cell with radius R = 500 meter. There are K = 7 cells and the number of users per cell is U = 4. Under the hypothesis that each user requires the same amount of traffic, each user has a throughput of Rtot /4 bit/sec. 28

19%

Total power [dbW]

41%

57% 88%

20

99% 100%

99% 100%

16 100% 100% 12 10

Centralized Distributed 12.5 R

tot

15 [Mb/s]

17.5

2% 3% 10% 24 42% 96%

80%

93%

84%

20 98% 100% 16

VI. N UMERICAL RESULTS

24

28

Total power [dbW]

traffic load of the system. As long as the load does not exceed a certain threshold, the amount of interference the cells generate is under control and LP approach of the SCRRAP is able to exploit channel and multiuser diversity to the degree of allowing a frequency-reuse distance equal to one. When the traffic load exceed the given threshold the proposed scheme is no longer able to cope with the amount of interference and the allocation does not converge to a steady-state and the transmitted power grows unbounded.

Distributed Centralized 12 10

12.5 R

tot

Fig. 3.

15 [Mb/s]

17.5

20

Power versus per-cell throughput with sub-carrier allocation.

In the second case, we adopt the sub-carrier allocation algorithm described in [13], so that each user, depending on its position in the cell, is assigned a different transmission format ηi and, consequently, a different number of subRtot . By assigning a higher number of subcarriers ri = 4η iB carriers to those users that experiment high path loss values (i.e., users at the cell border), the algorithm presented in [13] is supposed to achieve better performance than just assigning the same amount of resources to all users regardless of their channels. The results relative to this second case are shown in Fig. 3. Figs. 2 and 3 show the requested global power 7  k=1 i∈Uk p(i) expressed in dbW, as a function of the per-cell throughput Rtot . The percentages shown on the performance curves indicate the percentage of instances when the proposed algorithms achieve convergence with a total transmitted power per-cell lower than a maximum value Pc . This means that a feasible solution must fulfill:  p(i) ≤ Pc (4) i∈Uk

20

Fig. 2. Power versus per-cell throughput without sub-carrier allocation.

We consider two different scenarios.In the first case we assume that all users adopt the same transmission format, i.e., it ηi = η for all users on all sub-carriers. Since the rate per sub-carrier is Bη, the condition to achieve the Rtot . Note that, in this case, requested Rtot is that η = 8×B each user is assigned a fixed number of sub-carriers ri = 2. The results relative to this first case are shown in Fig. 2.

for k = 1 . . . , 7. In Figs. 3 and 4 we have set Pc = 100 W, i.e., the requested global power is always lower than 700 W or, equivalently, 28.5 dbW. A percentage value below 100 indicates that there are some user and traffic configurations that lead to unfeasible solution for the MCRRAP, that is to maximum power per-cell exceeding Pmax . As expected, the higher the overall throughput Rtot , the larger is the interference the cells generate and the higher is the probability that it does not exist a feasible solution. In both the considered scenarios the centralized approach clearly outperform the distributed heuristic, both in terms of consumed power and of percentage of times a feasible

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

solution is found. The proposed centralized resource allocation strategy is characterized by huge implementation complexity, and, hence, it can be hardly implemented in the real world. To be specific, while the distributed heuristic achieves a convergence point (in the positive case convergence is achieved) in few simulations seconds, the centralized approach requires several hundreds of seconds to come out with the optimum solution. However, despite its implementation complexity, it is very useful for its ability of catching the essence of interference limitations in OFDMA cellular systems. Moreover, it can provide a useful performance bound to which efficient heuristic decentralized approaches can be compared. This issue will be investigated in a subsequent work by the same authors. It is worth noting that the sub-carrier allocation algorithm described in [13] leads to a performance degradation for both the centralized and the distributed heuristic cases. This is because users at cell border tends to consume the most of the resources (i.e., they are assigned the most of sub-carriers), thus producing interference over the neighbor cells over a large set of sub-carriers. Hence, since in this case neighbor cells are forced to use those (few) sub-carriers which experiment low interference, the diversity gain tends to be missed. This effect has not been foreseen in previous works dealing with a single-cell environment, and is one of the most interesting results of this study. R EFERENCES [1] P. Agrawal, T. Zhang, C. J. Sreenan, and J.-C. Chen, ”All-IP wireless networks,” Journal on Selected Areas in Communications, vol. 2, no. 4, pp. 613-616, May 2004. [2] V. Tsibonis, L. Georgiadis, L. Tassiulas, ”Exploiting Wireless Channel State Information for Throughput Maximization,” Proc. IEEE INFOCOM ’03, April, 2003. [3] T. Nandagopal, T. Kim, X. Gao, and V. Bharghavan, ”Achieving mac layer fairness in wireless packet networks,” Proceedings of MOBICOM, pages 87-98, Boston, MA, August 2000. [4] M. Neely, E. Modiano, and C. Li, ”Fairness and optimal stochastic control for heterogeneous networks,” Proceedings of INFOCOM, Miami, Florida, March 2005. [5] S. Sarkar and L. Tassiulas, ”End-to-end bandwidth guarantees through fair local spectrum share in wireless ad-hoc networks,” IEEE Transactions on Automatic Control, September 2005. [6] L. Tassiulas and A. Ephremidis, ”Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks,” IEEE Transactions on Automatic Control, 37(12):1936-1948, Dec 1992. [7] D. Tse, ”End-to-end bandwidth guarantees through fair local spectrum share in wireless ad-hoc networks,” Proceedings of International symposium on Information, Ulm Germany,June 1997, p. 27. [8] R. Knopp and P. A. Humblet, ”Information capacity and power control in single-cell multiuser communications,” Proc. IEEE Int. Conf. Comm. 1995, Seattle, WA, June 1995, pp. 331-335. [9] G. J. Pottie, ”System design choices in personal communications,” IEEE Personal Communication, vol. 2, no. 5, Oct. 1995, pp. 50 -67.

[10] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, ”Multiuser OFDM with adaptive sub-carrier, bit, and power allocation,” IEEE J. Select. Areas Commun., Vol. 17, No. 10, pp. 1747-1758, Oct. 1999. [11] Y. Zhang and K. Letaief, ”Energy-efficient MAC-PHY resource management with guaranted QoS in wireless OFDM networks,” Proc. IEEE ICC 2005, Seoul, Korea 2005. [12] D. Kivanc, G. Li, and H. Liu, Computationally efficient bandwidth allocation and power control for OFDMA, IEEE Trans. Wireless Commun., vol. 2, no. 6, pp. 1150-1158, November 2003. [13] I. Kim, I. Park, and Y. Lee, Use of linear programming for dynamic sub-carrier and bit allocation in multiuser OFDM, IEEE Trans.Vehic. Technol., vol. 55, no. 4, pp. 1195-1207, July 2006.