Distributed Resource Allocation for Femtocell Interference ... - CiteSeerX

Distributed Resource Allocation for Femtocell Interference Coordination Via Power Minimisation ´ Akos Ladányi∗ , David López-Pérez† , Alpár Jüttner‡ , Xiaoli Chu† and Jie Zhang∗ ∗

University of Bedfordshire, Luton, UK. Email: [email protected] † King’s College London, UK. Email: [email protected] ‡ E¨ otvös Loránd University, Budapest, Hungary. Email: [email protected]

Abstract—This paper proposes a decentralized model for the allocation of modulation and coding schemes, subchannels and transmit power to users in OFDMA femtocell deployments. The proposed model does not rely on any exchanged information between cells, which is especially useful for femtocell networks. Coordination between femtocells is achieved through the intrinsic properties of minimising transmit power independently at each cell, which leads the network to self-organize into an efficient frequency reuse pattern. This paper also provides a two-level decomposition approach for solving this intricate resource assignment problem that is able to find optimal solutions at cell level in reduced periods of time. System-level simulations show a significant performance improvement in terms of user outages and network capacity when using the proposed distributed resource allocation in comparison with scheduling techniques based on uniform power distributions among subcarriers.

I. I NTRODUCTION The next generation of cellular networks will be based on Orthogonal Frequency Division Multiple Access (OFDMA) e.g.,Wireless Interoperability for Microwave Access (WiMAX) and Long Term Evolution (LTE). Furthermore, femtocells are foreseen to play a key role in the deployment of these systems. These small cells are designed for improved indoor coverage and they are served by low-cost low-power user-deployed units that are connected to the operator via a broadband connection. Femtocells will provide many benefits to future systems [1]: it is expected that femtocells will enhance coverage indoors, deliver both higher throughputs and new applications to users, and off-load traffic from existing macrocellular networks [2]. Since femtocells are experiencing the first signs of maturity, with operators already deploying this technology, e.g., AT&T, the mobile industry is looking for new femtocell markets. For example, the femtocell use in businesses and enterprises. Operators see in the self-organizing nature of femtocells a significant advantage over traditional indoor solutions. If an enterprise suffers from a poor coverage and/or capacity, it can be more cost effective to provide the enterprise manager with a number of femtocells and spread them in the offices than conducting network planning tasks with an engineer team. The demand for mobile services is also growing very fast and business applications represent a promising market for both developers and operators. Thus, enterprise femtocells will not only help to enhance the indoor coverage/capacity, This work was supported by the EU FP6 “RANPLAN-HEC” project under the grant number MEST-CT-2005-020958, and also UK EPSRC Grant EP/H020268/1.

but they will also aid operators to introduce their equipment in this attractive office scenario and provide tailored services. Nevertheless, installing femtocells inside enterprise environments, where more than one femtocell may be necessary, and where many guest users may enter the femtocell coverage, leads to major technical challenges never addressed before in residential deployments. For instance, since enterprise users will install their femtocells in challenging random positions, e.g. close to windows or to each other in neighboring offices, the co-tier interference between femtocells will be a problem in very dense deployments [3]. Particularly, in enterprises with more than one femtocell where only light walls with a low electric insulation separate the different office cubicles, co-tier interference will be the main reason of service failure. In order to make the things more difficult, operators cannot handle this interference using a centralized frequency planning since they do not know the exact number and position of enterprise femtocells, and because they may not own the backhaul. As a result, the development of new distributed approaches in order to manage co-tier interference in enterprise scenarios is a technical challenge that needs to be urgently addressed. A. Discussion Using a uniform distribution of power between subcarriers in Adaptive Modulation and Coding (AMC) systems is a common approach in literature. This approach has been shown to perform well in centralized architectures where a radio resource broker is in charge of intelligently telling which subcarriers must be used by each cell. Furthermore, in [4] [5] [6], the authors suggest that the benefits in network performance due to the allocation of different powers to different subcarriers is low in scenarios with a wide range of signal quality users. Therefore, performance optimization solutions based simply on dynamic subcarrier allocations are preferred over complex joint subcarrier/power allocations. However, this paper will show that in distributed systems, where cells make decisions independently from each other, allocating different powers to different Subchannels (SCs) have remarkable Self-Organazing Network (SON) behaviours. B. Contribution This article focuses on the problem of co-tier interference in enterprise femtocell networks, proposing a new model for the assignment of radio resources.

This model is based on a distributed1 architecture where each femtocell optimizes its performance independently from neighboring femtocells avoiding the need for any a priori centralized frequency planning. Therefore, there is no need to exchange information through the backhaul of femtocells, thus avoiding uncontrolled delays and single points of failure. Each femtocell targets at minimizing its radiated power, allocating different powers to different subchannels according to its user channel conditions and throughput requirements. This approach is used due to the good self-organizing features that it will be shown to have. However, the joint assignment of subchannels and power is an intricate optimization problem. This problem becomes even more complex because of the existence of several Modulation and Coding Schemes (MCSs) in LTE and WiMAX standards: Selecting a low power but a highorder MCS increases decoding errors, while selecting a high power but a low-order MCS increases inter-cell interference. Moreover, the use of a lower power requires a larger bandwidth to meet a given user throughput requirement and vice versa. Furthermore, a user assigned to more than one SC must have the same MCS in all of them2 [7] (although the subchannel conditions may be quite distinct). This paper proposes a reduced complexity approach for solving the joint MCS, SC and power assignment problem in short running times that provides a good network performance. II. N ETWORK M ODELING AND N OTATION Let us define an OFDMA femtocell network as a set of: • • • •

femtocells: F = {F1 , ..., Fm , ..., Fn , ..., FF }, users of femtocell Fm : U m = {U1m , ..., Uum , ..., UUmm }, SCs: K = {1, ..., k, ..., K}, MCSs: R = {1, ..., r, ..., R} (Table I).

RAB MCS1 MCS2 MCS3 MCS4 MCS5 MCS6

TABLE I (M ODULATION AND CODING SCHEMES ) Modulation Code Rate SINR Efficiency QPSK 1/2 2.88 dB 1.00 b/s QPSK 3/4 5.74 dB 1.50 b/s 16QAM 1/2 8.79 dB 2.00 b/s 16QAM 3/4 12.22 dB 3.00 b/s 64QAM 1/2 15.88 dB 4.00 b/s 64QAM 3/4 17.50 dB 4.50 b/s

m Pu,k · Γm,u = PM wu,k + σ 2 0

m Pu,k · Γm,u

m =1,m0 6=m

0

Pum0 ,k · Γm0 ,u + σ 2

SRof dm · SYof dm · effr Tsubf rame

(2)

T Pu,r,k = BRu,r,k · (1 − BLER(r, γm,u,k ))

(3)

BRu,r,k = Θ · effr =

where Θ is a fixed parameter that depends on network configuration, being SRof dm and SYof dm the number of data subcarriers (frequency) and symbols (time) per SC, respectively, and Tf rame is the frame duration in time units. In addition, effr is the efficiency (bits / symbol) of the selected MCS r, which are illustrated in the right most column of Table I. BLER (r, γm,u,k ) represents the BLock Error Rate (BLER) suffered by SC k, which is a function of both r and γm,u,k . C. Measurement Report In the proposed scheme, user u feeds back regularly (Tu,mr ) a Measurement Report (MR) M Ru to its serving femtocell Fm to assess user channel conditions. In this following, user MRs indicating the received strength wu,k of the interference suffered by femtocell user u in all SCs K are employed [7]. III. BASIS OF THE P ROPOSED D ISTRIBUTED A LLOCATION The main idea of this algorithm is that each femtocell Fm , using the optimization procedure presented in the next section, updates the MCS, SC and power assignment to its users U m according to the feedback information received from them. This updating event takes place after a random time interval uniformly distributed between 1 and Tm,up time units after the previous update. In this way, the probability of several femtocells updating their allocation simultaneously is reduced, thus mitigating ping-pong effects. The main target of a femtocell here is to allocate radio resources to users while minimizing its total transmitted power. The reasons for it are as follows: 1) Minimizing the transmitted power reduces interference. This is obvious from the Shannon-Hartley theorem [8]: C = B · log2 (1 +

A. Signal Quality Modeling Assuming that all subcarriers within a SC experience the same channel conditions, the Signal to Interference plus Noise Ratio (SINR) γm,u,k of user u in SC k is modeled as follows: γm,u,k =

B. User Capacity Modeling Both the bit rate BRu,r,k and the throughput T Pu,r,k of user u in SC k when utilizing MCS r are modeled as follows:

(1)

m where Pu,k denotes the power applied by femtocell Fm in each one of the subcarriers of SC k, in which user u is allocated, Γm,u is the channel gain between femtocell Fm and user u, wu,k represents the interference suffered by user u in SC k. Finally, σ is the noise density. 1 This architecture is distributed in the sense that there is no centralized radio resource broker that assigns suchannels to cells to mitigate interference. 2 This constraint simplifies the decoding process minimizing signaling and enhances the performance of turbo codes due to the larger length of blocks.

m m Pu,k · Γm,u Pu,k · Γm,u ) → w = − σ2 u,k C wu,k + σ 2 2B − 1 (4)

where C is capacity in bps and B is bandwidth in Hz. 2) A cell that targets at minimizing its transmit power allocates less power to those users that are closer to the base station or have smaller throughput requirements. Like this and according to (4), interference is mitigated. 3) A cell that targets at minimizing its transmit power tends to utilize those SCs that are not being used by its neighboring cells because less power is necessary in less interfered or faded SCs to achieve a targeted SINR. In [9], it is shown that minimizing power consumption leads the network to self-organize into an efficient and stable frequency reuse pattern. Putting together the concepts behind statements 2) and 3), self-organizing behaviors can be derived in distributed systems when each cell targets at minimizing its own radiated power. Imagine a network comprised of 2 subchannels k and k 0 and 2 cells A and B, providing service to 2 different users each.

In each cell, one of the users is close to the cell-centre while the other one is at the cell-edge. - Case A) Cells targeted at minimizing its radiated power: According to statement 2), those users close to the cell-centre will be allocated less power than those at the cell-edge. According to statement 3), when a cell, e.g., A, decides how to assign k and k 0 to its users, it will observe stronger interference in one SC, e.g., k, than in the other one, i.e., k 0 , due to the difference of power applied by cell B when using k and k 0 . Thus, cell A will allocate its cell-edge user to SC k 0 and its cell-centre user to k. Following this scheme, users in the celledge are not much interfered due to the low power applied by the neighboring cell to the corresponding SCs. - Case B) Power uniformly distributed among subcarriers: In this case, both cells will assign the same power to their users independently of their positions and channel conditions. As a result of this, users located in the cell-edge will then suffer from larger interference than in Case A). IV. R ESOURCE A LLOCATION P ROBLEM (RAP) This section defines our model for the MCS, SC and power assignment in each femtocell, i.e., an optimization problem that will be referred to as Resource Allocation Problem (RAP). Note that RAP does not imply communication between cells, and each femtocell tune its resource allocation independently. m First of all, let us indicate that the power Pu,k,r that femtocell Fm has to allocate in each of the subcarriers of SC k in order to achieve the SINR threshold γr of MCS r is: m Pu,k,r = γr ·

wu,k + σ 2 Γm,u

(5)

m Note that the derivation of Pu,k,r is straightforward from (1) and that Fm knows wu,k and Γm,u due to user MRs (Sec. II-C). Here, a thermal noise density of −174 dBm/Hz is assumed to compute the noise density σ. The optimization problem of the joint MCS, SC and power assignment in femtocell Fm can be thus formulated as the following integer linear problem:

at most one user u, and constraints (6c) and (6d) together guarantee that each user is allocated to at most one MCS. Finally, constraint (6e) makes sure that each user u achieves its throughput demand T Pureq , which may differ for each user. One possible approach for solving this problem is to apply standard Integer Linear Programming (ILP) techniques [10]. Let us note that these techniques are able to solve this problem up to optimality, but the running times incurred by ILP solvers are unpredictable (exponential in the worst case), which renders them inappropriate for use in real off-the-shelf Femtocell Access Points (FAPs). V. S UBCHANNEL AND P OWER A LLOCATION S UBPROBLEM (SPAP) This section discusses an important subproblem of RAP referred to as SC and Power Allocation subProblem (SPAP) that happens when the MCS of each user is known a priori. An efficient solution to this subproblem has two important applications: • It can be employed as a sub-routine in order to solve the RAP problem, as it will be presented in Section VI. • It can be utilized as a low latency SC and power allocation scheme, as it will be discussed in Section VII. Assuming that a MCS ru has been already given to user u, i.e. ρu,r ∀u∀r is known and fixed a priori as part of the input, the whole optimization problem transforms to an easier form. Clearly, the used MCS ru determines the number Du of SCs needed for satisfying the throughput requirement T Pureq of user u. Namely, ' & T Pureq T Pureq = (7) Du := PR r=1

Θ · effr · ρu,r

Θ · effru

In addition, let us introduce the binary decision variable φu,k , which indicates whether user u makes use of SC k, i.e. φu,k :=

R X

χu,k,r

(8)

r=1

min χu,k,r

U X K X R X

m Pu,k,r · χu,k,r

(6a)

u=1 k=1 r=1

Substituting them into (6a)-(6g), we obtain the following SC and power allocation problem.

subject to: U R X X

CS = min φu,k

χu,k,r ≤ 1

∀k

(6b)

subject to: X U

u=1 r=1 R X

ρu,r ≤ 1

∀u

(6c)

∀u, k, r

(6d)

r=1

χu,k,r ≤ ρu,r K X R X

U K X X

m Pu,k,r · φu,k u

(6a*)

u=1 k=1

φu,k ≤ 1

∀k

(6b*)

φu,k = Du

∀u

(6e*)

∀u, k

(6g*)

u=1 K X k=1

Θ · effr · χu,k,r ≥ T Pureq

∀u

(6e)

∀u, r ∀u, k, r

(6f) (6g)

k=1 r=1

ρu,r ∈ {0, 1} χu,k,r ∈ {0, 1}

In this case, χu,k,r (6g) is a decision binary variable that is equal to 1 if user u uses MCS r in SC k, or 0 otherwise. Furthermore, ρu,r (6f) is a decision binary variable that is equal to 1 if user u makes use of MCS r, or 0 otherwise. Constraint (6b) makes sure that SC k is only assigned to

φu,k ∈ {0, 1}

Let us note that due to the totally unimodular property [11] of the matrix of constraints φu,k , the minimum of SPAP can always be selected to be integral. Hence, the integrality constraint (6g*) can be replaced by φu,k ≥ 0

∀u, k,

(6g**)

As a result, this formulation is now efficiently solvable by a general purpose Linear Programming (LP) solving package.

A. Solving SPAP Optimally The following observation makes it possible to solve SPAP optimally even more efficiently. Claim 1: Let us define the following network flow problem [12] with vertex set V := U ∪ K ∪ {s, t},

(9a)

being s, t ∈ V the source and the sink of V , respectively. edge set E :={(su) : u ∈ U} ∪ {(uk) : u ∈ U , k ∈ K}∪ {(kt) : k ∈ K},

cap(ab) :=

Db , 1

if a = s, b ∈ U otherwise,

(9c)

and cost function cost(uk) :=

m Pu,k,r , u 0

if u ∈ U, k ∈ K otherwise.

Value 0 dBi Omni 0 dB 0 dB Omni 9 dB 8 90 s uniform 500 kbps full buffer

(9b)

capacity function

TABLE II S YSTEM - LEVEL SIMULATION PARAMETERS Parameter Value Parameter Simulation time 10 min Femto ant. gain Scenario size 90 × 90m Femto ant. pattern # Femtos (F ) 9 UE ant. gain rf 15 m UE body loss Carrier frequency 2.0 GHz UE ant. pattern Channel bandwidth 5 M Hz UE noise figure Tsubf rame 5 ms UE per femto. (U ) Subcarriers 512 µp Subchannels (K) 8 UE distribution DL OFDM symbols 39 T Pureq Femto TX power 20 dBm Traffic model

(9d)

P Then, a minimal cost network flow of value u∈U Du will provide an optimal solution to SPAP. Problem (V) can thus be formulated and efficiently solved as a minimum cost network flow (assignment problem), where users are assigned RBs so as to minimise sum transmit power. In order to solve this problem, the network simplex algorithm [13] implemented in the LEMON library [14] has been utilised for our simulations. VI. S OLVING R ESOURCE A SSIGNMENT P ROBLEM (RAP) In this section, a smart exhaustive search based approach is proposed for solving RAP. This technique is based on the use of a subroutine that is able to efficiently solve SPAP. The key idea behind this technique is that a smart search can be performed over the MCS assignment solution space, where for each MCS solution, the optimal SC and power allocation can then be obtained by solving SPAP (Section V). In order to provide a better description of this technique, we define Sm as the vector of MCSs assigned to users of Fm . For an arbitrary Sm , solving SPAP, the SC and power assignment associated to Sm is derived. Then, the quality of this MCS allocation Sm is evaluated according to CS (6a*), i.e. the cost of the SC and power assignment found by SPAP. Using this cost function, a smart search is performed to find the MCS allocation that yields the lowest transmitted power. Some assignments can be safely excluded from this search: • If an MCS rmax can be found, which is suitable to satisfy the throughput demand T Pureq of user u by using 1 SC, no higher-order MCSs are allocated thereafter to user u. Let us note that allocating a higher-order MCS would unnecessarily increase the required transmission power. • If an MCS allocation Sm is found, which requires more SCs than that are available to satisfy the throughput demand of the users, no other MCS allocation S 0 that can be derived from Sm by lowering the selected MCS of a single user is then tried. The reason behind is that S 0 m would also require more SCs than that are available. This approach solves RAP optimally and sufficiently fast thanks to the limited number of connected users per femtocell and the speed of network simplex schemes for solving SPAP.

VII. R ESOURCE M ANAGEMENT A RCHITECTURE The whole MCS, SC and power allocation problem (RAP) can be solved by around a second. Meanwhile the SC and power allocation subproblem (SPAP) can be computed faster, in less than one millisecond (details are given in Sec. VIII). As a consequence and with regard to the implementation of this approach in real FAPs: • By solving RAP, the MCSs of users can be updated in a second by second basis in order to cope with per cell time fluctuations of traffic load as well as user mobility. For instance, if a new user connects to a given femtocell, this FAP will raise the MCSs of all its connected users in order to free some SCs for this new user connection. • By solving SPAP, the SC and power allocation to users can be updated independently and in a much faster basis than the assignment of MCSs in order to cope with the fast variations of the channel due to interference/fading. This implementation is named as enhanced RAP (eRAP). VIII. S IMULATIONS AND R ESULTS The scenario employed for this experimental evaluation is an enterprise of 90 m × 90 m hosting 9 OFDMA femtocells. It is assumed that macrocells and femtocells are allocated to orthogonal spectrum resources or that there is no macrocell. So, we can focus on the femto tier (no cross-tier interference). Femtocell were uniformly distributed with in the scenario. Path losses were predicted using the ITU-R P.1238 model with its “office” version [15]. Slow fading was considered using a log-normal shadowing with standard deviation of 8 dB. Subframe errors were modelled by BLER look-up-tables [16]. 8 downlink static users attempt to connect to each femtocell (this represents a 100% network traffic load because the simulated network has 5 MHz bandwidth and 8 subchannels). Users are uniformly distributed within the femtocell radius rf . A user holds its connection for a given time dictated by an exponential distribution of mean µp and thereafter disconnects. When a user disconnects a new one appears in a new position. A full buffer model is utilized to simulate the traffic of users, i.e., there is always data available to be transmitted for a user. Furthermore, all users have a throughput demand of 375 kbps. More details about the system-level simulation tool used for this experimental evaluation can be found in Table II and [17]. When using the proposed distributed approach, in each femtocell, the joint MCS, SC and power assignment (RAP), i.e., clever search plus its associated SPAP-based subroutines, is performed at most every 1.0 s. Meanwhile and in a much more frequent basis (Section VII), the SC and power allocation

(SPAP) is run at most every 0.1 s. In both cases, a uniformly distributed timer is used to decide exactly when the femtocells wake up and run RAP or SPAP. Let us also note that in order to mitigate ping-pong effects, only those assignments that are at least 10 % better than the current ones in terms of cost function (6a*) are employed. A. Approaches Used for Comparison 3 different scheduling schemes are used for performance comparison. In all these schemes, femtocells uniformly distribute their power among all subcarriers, in this case, 512. In addition, if more than one SC are allocated to one user, the MCS selected is that allowed by the SC in worse condition. a) Random assignment: SCs are assigned randomly to users without taking into account any kind of information. Therefore, inter-cell interference coordination does not exist. b) Network listening mode (NLM): Each femtocell periodically measures the received strength of the interference in each SC, and subsequently allocates the SCs suffering from the smallest interference to their users. Let us note that the information used for the scheduling is collected at the femtocell location, not at the user positions. c) Interference minimization (IM): Each femtocell periodically performs an optimization process, whose target is to allocate subchannels to users while minimizing the sum of interference suffered by the femtocell. This scheme is assisted by user MRs. Therefore, the information used for the scheduling is obtained at the user locations. A more detailed description of these approaches can be found in [17]. B. Running Time and Solution Quality One way of solving the joint MCS, SC and power allocation problem is to solve formulation (6) directly by an ILP solver. In this way, the optimality of the solution can be guaranteed. To compare the performance of our two-level decomposition approach with that of an ILP3 , we extracted 100 instances from the simulations of the described scenario. It is to be noted that the computer used for this simulation contained an AMD Opteron 275 dual-core processor running at 2,2GHz with 16 GB of RAM. With regard to running times, the average running time of the ILP solver was 8.58 s, but this running time changed quite a lot along the distinct instances, being the maximum 18.47 s. On the contrary, the average running time of network simplex when solving SPAP was around 0.044 ms, whereas that of the exhaustive search when solving RAP was around 0.60 s. These results show that our two-level decomposition approach provides a large running time improvement over ILP solvers. Let us also note that our two-level decomposition approach was able to find the optimal solution in all problem instances (same as ILP solver). C. Transmitted Power and Resulting Interference Figure 1 shows the Cumulative Distribution Function (CDF) of the transmitted power per subcarrier during the simulation. When using the proposed self-organizing approach, the power applied by each cell changes depending on traffic and channel 3 In

this case, the used ILP solver was: IBM ILOG CPLEX (version 9.130).

Fig. 1.

Fig. 2.

CDF of the transmitted power per subcarrier.

CDF of the received interference per subcarrier.

conditions, and is lower than when using uniform distributions (Note that the CDFs of random, NLM and IM are superposed). As a result, interference towards neighboring cells is mitigated. This is corroborated by Figure 2, which illustrates the CDF of the interference suffered per subcarrier during the simulation. Indeed, this interference is the lowest when using our model. Furthermore, in this last figure, it can be easily seen that the three scheduling methods used for performance comparison perform similarly in terms of inter-cell interference avoidance. This is because when cells are fully loaded and the power is uniformly distributed, these schemes measure approximately the same interference in all SCs during their sensing phase. Hence, no scheduling opportunity exists, and the behaviors of these algorithms are similar to that of random assignments. D. Stability of the Proposed Resource Allocation In order to show the stability of the proposed algorithm, Figure 3 illustrates the sum of the radiated power by the femtocells over time. Note that in this experiment, we stop adding users after a certain time, i.e. 70 s. It can be seen that after this time the power allocation of femtocells is constant, meaning that the femtocell network converges to a stable state.

sum radiated power (mW)

eRAP

200

150

100

50

0 00:00

stop admitting users

00:50

Fig. 3.

Fig. 4.

01:40

02:30 time (mm:ss)

03:20

04:10

05:00

Sum of the radiated power.

Power allocation of three neighboring enterprise femtocells.

There are no ping-pong effects in which a femtocell changes its resource allocation continuously in response to the changes made by neighboring femtocells. Figure 4 illustrates the quantity of power allocated by three neighboring cells in each one of the 8 existing subchannels. Figure 4 depicts how interference mitigation is not only achieved due to power reduction, but also because the network settles into an efficient SC reuse pattern when utilizing eRAP. In this figure, it can be observed, as explained in Section III, how cells tend to allocate high power in those subchannels in which the neighboring cells assign low power and vice versa. In other words, there is a coordination between cells in the allocation of resources to their cell-edge and cell-centre users. E. System-level Capacity Performance Table III shows the total number of incurred outages and its percentage with respect to the total number of created users, the average number of users connected per cell and the average enterprise network throughput. Users are dropped (unsatisfied) if they cannot transmit at a throughput larger than their demand T Pureq for a period longer than 9 s. Note that simulations with 6 DL users attempting to connect per femtocell (75 % load) have being performed for performance comparison purposes. TABLE III S IMULATION RESULTS : USER STATUSES Cell load Scheme Rnd NLM IM eRAP

6 users/femto (75 %) Outage Users M bps 76 (18.01 %) 43.94 21.66 68 (16.11 %) 45.76 22.71 29 (6.87 %) 50.58 25.21 1 (0.68 %) 53.93 26.93

8 users/femto Outage 130 (23.94 %) 126 (23.20 %) 97 (17.86 %) 3 (0.56 %)

(100 % load) Users M bps 54.92 27.05 55.37 27.38 60.04 29.77 71.44 35.58

As one can see in Table III, with respect to user outages the proposed self-organizing technique performs the best. Indeed, the improvement in user outages in comparison with the second best scheme is notable (around 17 % improvement).

This is because minimizing the radiated power in each cell, the entire system settles into an stable frequency reuse pattern. Moreover, interference is avoided due to the power reduction. This better interference mitigation is translated into a larger number of active users per cell, and consequently a larger average sum network throughput. Note that when using eRAP, 11.40 users more are connected in average to the network with respect the second best method (around 15 % improvement). In addition, let us note that the performance gain of the proposed self-organizing approach increases when the network load is higher. This is because when the network load is low, both NLM and IM can find subchannels that are not being used by the neighboring cells and thus allocate them to their users. Such scheduling opportunities disappear when the network is fully loaded because of the utilized uniform power distribution. IX. C ONCLUSION We have proposed a self-organized assignment of MCS, SC and power to users for enterprise OFDMA femtocell scenarios. A reduced complexity two-level optimization approach has also been presented to solve the resource allocation problem. We have shown that minimising transmit power independently in each cell allows for an efficient network self-organization, and the coordination of interference in a distributed manner. R EFERENCES [1] J. Zhang and G. de la Roche, Femtocells: Technologies and Deployment. John Wiley and Sons, LTD, January 2010. [2] D. López-Pérez, A. Valcarce, G. de la Roche, and J. Zhang, “OFDMA Femtocells: A Roadmap on Interference Avoidance,” IEEE Communications Magazine, vol. 47, no. 9, pp. 41–48, September 2009. [3] J. Ling, D. Chizhik, and R. Valenzuela, “On Resource Allocation in Desne Femto-deployments,” in IEEE International Conference on Microwaves, Communications, Antennas and Electronics Systems (COMCAS 2009), Tel Aviv, 2009. [4] G. Song and Y. Li, “Cross-layer optimization for OFDM wireless networks-part I: theoretical framework,” IEEE Transactions on Wireless Communications, vol. 4, no. 2, pp. 614–624, 2005. [5] J. Jang and K. B. Lee, “Transmit power adaptation for multiuser OFDM systems,” IEEE Journal on Selected Areas in Communications, vol. 21, no. 2, pp. 171–178, February 2003. [6] S. Hussain and V. C. M. Leung, “Dynamic Frequency Allocation in Freactional Frequency Reuse OFDMA Networks,” IEEE Transactions on Wireless Communications, vol. 8, no. 8, pp. 4286–4295, August 2009. [7] E. Dahlman, S. Parkvall, J. Sköld, and P. Beming, 3G Evolution: HSPA and LTE for Mobile Broadband, 2nd ed. Elsevier, August 2008. [8] C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, pp. 379–423, July 1948. [9] A. Stolyar and H. Viswanathan, “ Self-organizing Dynamic Fractional Frequency Reuse in OFDMA Systems,” in IEEE Conference on Computer Communications (INFOCOM 2008), April 2008, pp. 691–699. [10] Optimization in Operations Research. upper Saddle River, NJ, USA: Prentice Hall, 1998. [11] Séroul R., Programming for Mathematicians. Berlin: Springer-Verlag, p. 162, 2000. [12] R. K. Ahuja and T. L. M. J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. [13] G. B. Dantzig, Linear Programming and Extensions. Princeton University Press, 1963. [14] “Library for Efficient Modeling and Optimization in Networks (LEMON),” http://lemon.cs.elte.hu. [15] S. Saunders, S. Carlaw, A. Giustina, R. R. Bhat, V. S. Rao, and R. Siegberg, Femtocells: Opportunities and Challenges for Business and Technology. John Wiley and Sons, Ltd., 2009. [16] Forsk Atoll-Global RF Planning Solution, http://www.forsk.com. ´ Ladányi, A. Jüttner, and J. Zhang, “OFDMA [17] D. López-Pérez, A. femtocells: A self-organizing approach for frequency assignment,” in IEEE Personal, Indoor and Mobile Radio Communications Symposium (PIMRC), Tokyo, Japan, September 2009.