centralized vs distributed resource allocation

7/29/2019 Centralized vs Distributed Resource Allocation

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Centralized vs Distributed Resource Allocation in

Multi-Cell OFDMA Systems

Sergio CicaloENDIF at University of Ferrara, Italy

Email: [email protected]

Velio TralliENDIF at University of Ferrara, Italy


Ana I. Perez-NeiraTechnical University of Catalonia (UPC) and

Tech. Center of Catalonia (CTTC), Spain


AbstractRadio Resource Management with Inter-cell Inter-ference Coordination (ICIC), is a key issue under investigationfor next generation wireless systems such as Long Term Evolu-tion (LTE). Although centralized resource allocation (RA) andcollaborative processing can optimally perform ICIC, the overallrequired complexity suggests the consideration of distributedtechniques. In this paper we propose and compare a centralizedRA strategy aimed at maximizing the sum-rate of a multi-cellclustered system in presence of power and fairness constraints, anda distributed RA strategy where inter-cell interference is partiallycoordinated through power planning schemes with preassignedpower (an example is fractional frequency reuse). The distributedRA strategy reduces both signaling and feedback requirements,preserves intra-cell fairness and jointly works with a load bal-ancing algorithm to support inter-cell fairness. We show in theresults that the distributed RA with aggressive frequency reuseis able to approach the performance of the centralized RA whenthe number of users is large, while preserving the same level offairness.

I. INTRODUCTION

The 3rd Generation Partnership Project (3GPP) Long Term

Evolution (LTE) [1] is expected to assure high data rates and

quality of service (QoS) support by exploiting the degrees

of freedom offered by the Orthogonal Frequency Division

Multiple Access (OFDMA). OFDMA provides a high spectral

efficiency and a very flexible access by exploiting the multi-

user diversity. Radio Resource Allocation (RA) in the downlink

of OFDMA systems has been studied extensively for the single-

cell case [2]-[5]. However, to address realistic scenarios, a

multi-cell environment has to be considered. In this case,

LTE specifications suggest aggressive frequency reuse and

distributed low-complexity implementations [1]. Nevertheless,

if the frequency resource is fully reused in every cell of the

network and no inter-eNodeB (eNB) cooperation/coordination

is supported, the cell throughput will be reduced in the attempt

of serving the users at the cell edge, due to inter-cell interfe-

rence (ICI). Radio resource management with ICI coordination

is a key issue under investigation by LTE research community.

ICI coordination can be achieved through the implementation

of different degrees of network coordination and complexity.

High complexity MIMO network approach [6] requires the

availability of user data to be transmitted at all the eNBs, as

well as collaborative processing based on dirty-paper coding

and suitable precoding. A first step toward complexity reduction

is to keep network coordination to only perform RA. In a

centralized RA, a control unit collects all the channel state

information (CSI) of every user in the system and allocates

the available Physical Resources Block (PRB) of each eNB

trying to maximize the capacity according to fairness and

power constraints. Without an efficient and fast infrastructure,

centralized scheduling is an hard task due to the stringent time

required to exchange the inter-cell scheduling information and

the large feedback required by the User Equipments (UEs) to

send all the CSI. Some strategies to reduce this complexity

are under study for LTE-advanced [7] where joint transmission

coordinated multi-point (JT-COMP) is proposed [8].However, distributed RA at each eNB is suggested for low-

complexity multi-cell radio design. In distributed RA each

eNB allocates resources to its users only, and UEs feed back

a partial CSI. ICI can be partially avoided by means of an

off-line coordinated resource control among the cells in a

cluster. Examples are given by Fractional Frequency Reuse

(FFR) and Soft Frequency Reuse(SFR) [9][10], power planning

techniques [11][12], load balancing (LB) [13], or by partial

coordination as in [14] where only cell-edge users send CSI of

interfering links. The lack of full coordination in RA simplifies

the implementation at the expense of some capacity degradation

with respect to centralized RA.

Few contributions until now, e.g. [14],[15], are addressing

RA in multicell OFDMA systems. In this paper we first

introduce a centralized RA algorithm aimed at maximizing the

sum-rate of a multi-cell clustered system in presence of rate and

power contraints. The algorithm is obtained from an ergodic

optimization framework extending the work in [5]. A stochastic

approximation is applied to derive on-line implementation.

After, we reformulate the algorithm to consider the constraints

of a distributed RA based on power planning schemes with

pre-assigned powers. The distributed RA algorithm preserves

intra-cell fairness, but requires a LB algorithm to ensure inter-

cell fairness. All the algorithms support PRB-based allocation

typical of LTE systems.By comparing centralized and distributed schemes, this work

shows that distributed schemes with aggressive reuse manage to

approach the capacity of a centralized system when the number

of users is large. However, a fractional reuse beetwen 2/3 and

4/5 helps to reduce the gap. This work is organized as follows.

In sect. II we introduce the OFDMA multi-cell system model,

whereas in sect. III we present formulation and algorithms

for centralized RA. The distributed RA and its algorithmic

solution is shown in sect. IV. In sect. V the FFR schemes with

978-1-4244-8331-0/11/$26.00 2011 IEEE


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preassigned power for distributed RA are presented. Finally,

results are discussed in sect. VI.

I I . SYSTEM MODEL

We consider a a cluster of Q cells with a total of K UEs orusers and a multicarrier transmission system with M availablesubcarriers divided in G groups Gg, g = 1, . . . , G, of N =

12adjacent subcarriers. The piece of frame composed of

Nallocable subcarrier and one slot is defined as PRB, which isthe elementary resource unit for RA. Each cell is served by one

eNB. In this paper, only the basic configuration where eNBs and

UEs are equipped with one antenna is investigated. However,

methods and algorithms developed here can also be extended

to multi-antenna configurations.

We use the discrete variable or index ug,q K0 ={0, 1, . . ,K} to indicate the user (i.e. 0 means no user) thatis scheduled to use cell q on PRB g. Note that only one useror none can be scheduled for each PRB and each cell. The

whole set of these variables is the matrix U KGQ0 , whereasthe whole set of powers assigned for transmission is the matrix

P R+,MQ

{0}. It is implicitly assumed that if ug,q = 0then pm,q = 0, m Gg that also means that P has an implicitdependence on U and viceversa as shown afterwards.

Network coordination is only exploited to perform RA, i.e.

no cooperative processing is implemented. The signal carrying

the payload for each user is scheduled to be transmitted by only

one eNB. The signals coming from other eNB are considered

as inter-cell interference. We define the Signal-to-Interference

plus Noise Ratio (SINR) of user k at frequency m, when thesignal is coming from cell q, as

k,m,q(pm) =pm,qck,m,q

1 +Q

s=1,s=q pm,sck,m,s(1)

where pm = [pm,1, . . . , pm,Q] and ck,m,q = |h(m)k,q |

2/2n, being

2n the noise power and |h(m)k,q |

2 the channel power gain between

eNB q and UE k on subcarrier m that includes the contributionof path-loss, shadowing and fast fading.

III. CENTRALIZED RA

We consider here a centralized architecture where a control

unit collects all the CSI of every user in the system and allocates

the resource units of the cluster trying to maximize the capacity

according to fairness and power constraints.

Following the approach in [2], we consider the framework of

ergodic sum-rate maximization for continuous (capacity based)

rates extended to the multi-cell case. The problem can be

formulated as

maxU,P

Kk=1

Rk(U,P)

s.t. Pq(U,P) Pq, q

Rk(U,P) k

Ks=1

Rs(U,P), k

(2)

where

Rk(U,P) = E[Rk(U,P)]

=

Gg=1

mGg

Qq=1

E[ug,qk C(k,m,q(pm))]

(3)

is the average rate per unit bandwidth provided to user k and

Pq(U,P) =

Mm=1

E[pm,q] (4)

is the total average power spent by cell q to serve the allocatedusers. Finally, uk is the Kroneckers delta

1 and C(x) =log2(1 + x).

The first constraint refers to the total average power used

by q-th eNB, which must be less than or equal to a maximumamount Pq. Let us note that this constraint allows instantaneouspower levels to exceed the average power when necessary. The

second constraint determines the share of throughput finally

achieved by each user. Therefore = [1, . . . , K]T defines

the required QoS by each user and must satisfy the conditionKk=1 k = 1.

A. Solutions for the allocation problem

Here, we follow the approach presented in [5] for a single-

cell multi-antenna system, which is based on a dual op-

timization framework that utilizes the Lagrangian function

L(U,P,,), where the dual variables = [1,...,Q]T, =

[1, . . . , K]T relax the cost function. The dual problem be-

comes

min,

g(,)

s.t. > 0, 0, (1 T) = 0(5)

where the third constraint on holds if sum-rate is not

diverging to infinity and g(,) = maxU,P L(U,P,,) isthe dual objective.

Although the system utility in (2) is non-concave, for ergodic

optimization it is proved that duality gap is zero if the cumula-

tive density function (CDF) of channel gains is continuous,

which happens in classical Rayleigh and Ricean scenarios.

However, it is not possible to guarantee the dual problem is

differentiable. Hence, an iterative subgradient method which

updates the Q + K solutions , of the dual problem (5)at each iteration can be applied. Nevertheless, in the practical

applications, the adaptive implementation is suggested, where

the iterations are performed along time and the evaluation of

the average power and rate in the subgradients can be done

through a stochastic approximation, as outlined in [2], [5].

In order to derive the dual objective g(,) given ,the expression of the Lagrangian function can be suitably

manipulated as in [5], leading to:

g(,) =

Qq=1

qPq + ME

max

ug,pm,mGgM(ug,P)

(6)

1uk

= 1 if u = k , 0 otherwise


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where ug = [ug,1, . . . , ug,Q] and

M(ug,P) =Q

q=1,ug,q=0

mGg

ug,qC(ug,q ,m,q(pm)) qpm,q

(7)

The optimal solutions for the evaluation of the dual objec-

tive, given ,, denoted as U

= [u

1,...,uG]T

, P

=[p1,...,p

M]

T, becomes:

ug = arg maxug

M(ug) (8)

with

M(ug) = maxpm,mGg

M(ug,P) (9)

and pm is the argument that finally leads to M(ug).

It should be noted that user allocation in (8) represents a

discrete optimization problem which requires in general an

exhaustive search in the space of all possible vectors ug.

This huge search space can eventually be reduced by using

suboptimal heuristic algorithms as in [5]. However, for each

element of this search space the power allocation solution,i.e. (9), has to be computed. This non-convex problem can be

solved by using successive convex approximation methods as

in [16]. A suboptimal solution is obtained by simplifying power

allocation with the water-filling solution evaluated by assuming

constant uniform power for the interfering cells, i.e.

pm,q =

ug,qq ln2

V

ug,q ,m,q(Vm)

+(10)

where the components of Vm are vm,q = V ug,q0 . The power

V is a parameter which estimates the power of interfering cellsin each subcarrier.

Even though the power allocation algorithm based on (10), aswell as the update of variables in the adaptive implementa-

tion, can be distributed on each base station, user allocation

algorithm as in (8) requires a centralized controller which

determines, for all sub-carriers, the vectors ug and sends them

to eNB through signaling. Therefore, each eNB has to forward

the received CSIs of each UE to the centralized controller and

to receive back the allocation informations before trasmitting,

resulting in a high blackhaul signaling. Besides, the signaling

interface in realistic systems, i.e. LTE X2 interface, has not a

negligible latency, resulting in an additional delay on the CSIs

report, that should be taken into account, especially in very fast

fading environments. Thus, in a realistic network, centralized

resource allocation is practically difficult to be realized. Inthe next section we provide a distributed solution and analyze

techniques to mitigate the inter-cell interference.

IV. DISTRIBUTED RA

In distributed RA each eNB allocates resources to its users

only without any knowledge of the allocation process at the

other eNBs, meaning without knowledge of the actual ICI. Only

partial ICI information is available at each eNB, which essen-

tially consists of a power mask Vm = [Vm,1, . . . , V m,Q],

m = 1, . . . , M , used to limit the power allocated by eacheNB q on each subcarrier m. The effects of ICI can be furthermitigated by means of an off-line coordinated resource control

among the cells in a cluster, which is the subject of next Section.

To formulate the distributed RA problem, let us first define

K(q), with cardinality K(q), as the set of users served by the q-

th eNB, where K(1)

. . .

K(Q) = {0} and

Q

q=1K(q) = K.

In the distributed setting, only the lower-bound of the SINR

which depends on the power mask Vm, m = 1, . . . , M isknown at the eNB, i.e. k,m,q(pm) pm,qk,m,q where

k,m,q =ck,m,q

1 +Q

s=1,s=q Vm,sck,m,s(11)

is the normalized SNIR lower-bound. The UE can measure

k,m,q and send it through a feedback channel to its eNB only.The average rate per unit bandwidth that can be provided to

user k in cell q, without incurring in outages, is given by

Rk(U,P) =Gg=1

mGg

E[ug,qk C(pm,qk,m,q)], k K

q (12)

We can then write the distributed problem as a maximizationproblem for each cell q = 1, . . . , Q :

maxU,P

kKq

Rk(U,P),

s.t. Pq(U,P) Pq,

Rk(U,P) ksKq

Rs(U,P), k Kq

pm,q Vm,q, m

(13)

where now there is a restriction on the set of allocation

variables U, i.e. ug,q Kq, and k must satisfy the constraint

kKq k = 1, q. In this way each cell tries to maximize itssum-rate, taking care of intra-cell fairness only.

A solution for the RA problem can derived for each cell

q by following the same approach of Sec.III through dualoptimization and adaptive algorithms. The set of dual variables

to be updated is still the same, but now the constraints on

change as (T)(q) =

kKq kk = 1. The allocationproblem, due to cell decoupling, is now simpler than before,

because it avoids the non-convex multi-cell power allocation,

and requires, for each cell q and PRB g, the maximization ofthe following metric

M(q)(ug,q ,P) =

mGg

ug,qC(pm,qug,q ,m,q) qpm,q

(14)leading to the optimal solution

pm,q = min

Vm,q,

ug,q

q ln 2

1

ug,q ,m,q

+(15)

ug,q = arg maxug,q

M(q)(ug,q ,P) (16)

The main drawback of this solution is the fact that the

fairness of rate allocation is confined within each cell, whereas


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global fairness depends on load and channel conditions on each

cell. The fairness issue can be partially solved with an off-line

algorithm that balances the eNBs load, as contemplated by LTE

[1]. Although LB is not within the scope of our paper, we will

evaluate the performance of distributed RA when a simple LB

algorithm, is running, which is reported in the Appendix for

the sake of completeness.

A. PRB based power/rate allocationIn order to decrease feedback complexity, in a realistic LTE

scenario also rate and power are allocated per PRB, as channel

state feedback is reduced to no more than one value per PRB. In

this case, the Exponential Effective SNIR Mapping (EESM)[18]

is used to evaluate the SNIR of each PRB, by taking into

account that power mask is constant inside each PRB, i.e.

Vm = Vg, m Gg, Vg = [Vg,1, . . . , V g,Q]. The EESMfor user k, PRB g, cell q is defined as

(eff)k,g,q = log

1

N

mGg

e(Vg,qk,m,q

(min)k,g,q

)

+

(min)k,g,q

(17)

where (min)k,g,q = Vg,q minmGg k,m,q and the parameter isused to tune the approximation. Here, with respect to [18], the

term (min)k,g,q is introduced as an offset that keeps the range of

exponential function limited. The effective instantaneous rate

for user k using PRB g in cell q, when a power pg,q is allocatedfor transmission, becomes

r(eff)k,g,q = N C

pg,q

(eff)k,g,q

Vg,q

(18)

Parameter in (17) has to be designed to keep the probabilityP(rk,g,q r

(eff)k,g,q), where rk,g,q = mGg

C(pg,qk,m,q),below a given threshold to prevent outage events.

In distributed RA using EESM feedback for each PRB, the

equations (12), (14) and (15) change by replacing k,m,q with

(eff)k,g,q/Vg,q and by setting pm,q = pg,q , Vm,q = Vg,q , m Gg.

V. POWER PLANNING FOR IC I COORDINATION

Generally, in distributed RA each eNB allocates resources

without complete knowledge of ICI. However, when the max-

imum value of the transmitted power is predefined and known

to all the eNB, partial information on ICI is available, which

enables some kinds of ICI coordination. Since the loss of

performance is usually due to the unlucky UEs close to the

cell border which drain radio resources in the attempt to obtain

the same capacity of the lucky UEs closer to the eNB, ICI

coordination techniques can be used to reduce interference in

resource units assigned to unlucky users.

In this work we denote in general as power planning

techniques those technique aimed at determining the set of

values Vg, g = 1, . . . , G that allow the best distribution of ICIacross resource units as function of system and load conditions.

Within this framework, the simplest techniques that consider

an offline static design of maximum power values are FFR and

Fig. 1. An example of FFR based power planning for a cluster of Q = 3cells with overall reuse factor 2/3

Subband 1 2 3 4 5 Overall Reuse Factor

Reuse 1/3 1/3 1/3 1/3 1/3 1/3

Reuse 1/3 1/3 2/3 2/3 2/3 8/15

Reuse 1/3 2/3 2/3 2/3 1 2/3

Reuse 2/3 2/3 2/3 1 1 4/5

Reuse 1 1 1 1 1 1/1

TABLE I

FREQUENCY PARTITIONING FOR DIFFERENT FFR SCHEMES WITH Q = 3

SFR. In this paper we consider FFR techniques to be combined

with distributed RA. Improvements might come from more

sophisticated power planning techniques which optimize all the

values ofVg with a limited set of constraints, but this calls for

further investigation.

When FFR is applied, Vg is one of the elements of a finite

set V; we assume that if the vector V is an element of V, thenall the vectors obtained as cyclic shifts ofV are elements of

V. All the available PRBs are partitioned in G/Q subbands of

Q PRBs. Inside each subband the Q shifts of the same powervector V V are assigned to the Q PRBs. If G/Q is notinteger we may apply the partitioning and assignment of power

vectors to a pool of GQ PRBs over Q slots. If one or moreof the elements of power vector V V are zero, we say thatthe resource unit or PRB is working with power vector V has

a reuse factor smaller than 1. This means that for one cell the

PRB has a reduced ICI, because one or more of the other cells

are not allowed to transmit in the PRB.

As an example for Q = 3 we consider the following elementsof V:

V13

= [V(0)13

, V(1)13

, V(2)13

] = [, 0, 0]

V23 = [V(0)

23 , V

(1)

23 , V

(2)

23 ] = [

3

2V,3

2V, 0] V1

1= [V

(0)11

, V(1)11

, V(2)11

] = [V , V , V ]

and we also assume that Pq = P , q and V = P /G. Theparameter allows a simple off-line optimization of powerlevels. Note that in the power vector V1

3the non zero elements

is infinity, because there is no need to limit the power when all

the other cells are not allowed to use the PRB. The assignment

of these vectors to subbands and PRBs is illustrated in Fig.1

with reference to a system with overall reuse factor 2/3. The just


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System model

U se r d is tr ibu ti on U ni fo rm , i n ave ra ge 5 , 1 0, 1 5, 2 0 pe r s ec to r

Cell layout Single Hexagonal Cluster, with 3 sectors

Inter-eNB distance 520 m

Channel model

Path Loss 40 + 15.2log(d), d = distance in meter

Doppler Bandwidth 6Hz

Shadowing model Log-normal with 6dB standard deviation

Fast Fading 3GPP Pedestrian model

Delay spread 2.3 sPHY model

System Bandwidth 3 MHz

Subcarrier spacing 15 KHz

Number of allocable subcarriers 180

N um be r o f c ar rie r p er P RB 1 5

Frame duration 10 ms

Slot duration 0.5 ms

DL slots per frame 8 (TDD - Configuration 1 [1])

OFDM symbols per slot 7

CSI update 5 ms

Average Maximum eNB Power 1 W

Noise Power Density 2 1020 W/Hz

TABLE IISIMULATION MODEL

introduced concept allow us to define other FFR schemes. Wesummarize in table I the most relevant used to obtain numerical

results.

VI . NUMERICAL RESULTS

The performance evaluation is carried out through Monte-

Carlo simulations according to models and assumptions sum-

marized in Tab. II, also following the guidelines for LTE in

[1][17]. In the evaluation of assigned rates an SNR gap of 3dB

is taken into account. We consider a downlink scenario with a

cluster ofQ = 3 cells, where the centralized and distributed RAtechniques described in the paper are evaluated and compared.

We denote with S1 the distributed system where the power andthe user rates are evaluated per subcarriers (sect. IV), whereas

S2 indicates the distributed system with per-PRB power and

rate allocation based on the EESM metrics (subsect. IV-A). The

fairness in rate allocation is evaluated through the well-known

Jain Index [19] J =(K

k=1 xk)2

K

Kk=1 x

2k

where xk is modified to take

account of inter-class fairness, i.e. xk =Rkk

. However, without

loosing generality, we presents here the results for one class,

i.e. k =1K

, k in centralized RA and k =1

K(q), k Kq in

distributed RA.

Fig. 2 provides a comparison of the different RA tech-

niques proposed in the paper by showing the capacity loss

of distributed RA with various FFR schemes with respect to

centralized RA for different number of UEs in the cluster. The

LB algorithm is implemented for the distributed RA. All the RA

schemes allocate rates with a Jains index ranging from 0.97

with K=15 user to nearly 1. We note that the capacity loss

decreases when the number of users increases, emphasizing

that multiuser diversity significantly help distributed RA. We

also note that FFR schemes with reuse factor of 4/5 reduce the

capacity gap with respect to full-reuse RA, and a loss of some

percent units is due to to per-PRB allocation. Optimal reuse

Fig. 2. Capacity loss of distributed RA with respect to centralized RA

K q without LB with LBLq J R[kbps] Lq J R[kbps]

151 1.371 2.7562 1.773 0.845 5402 3.054 0.971 49693 4.188 2.441

301 6.178 5.1062 4.341 0.941 6532 4.341 0.990 66213 3.046 4.344

451 3.131 7.6282 8.498 0.944 8103 6.933 0.998 7398

3 7.226 7.226

601 5.811 8.9652 7.068 0.968 9636 8.601 0.999 95013 12.582 9.122

TABLE IIILOAD METRIC, JAI NS INDEX AND SUM-RATE IN EACH CELL (Q = 3 ) OF

THE CLUSTER FOR DIFFERENT VALUES OF K AND FULL-REUSEDISTRIBUTED RA IN A SINGLE SIMULATION SCENARIO

factor moves towards 1 as the number of users get large. In

all the investigated cases the capacity loss is between 5% and

30%. In the centralized RA investigated here power allocation

is evaluated with suboptimal solution (10). However, it hasbeen checked that optimal power allocation provides a limited

capacity gain around 7% for K = 30 users, at the expense ofmore complexity.

Table III collects results illustrating the impact of LB tech-

niques to ensure fairness in distributed RA. The table shows

the sum-rate and Jains index of the whole system, with and

without LB, as well as the load metric (see Appendix) in each

cell. Without LB a larger sum-rate is achieved at the expense of

fairness among users. It is also interesting to note that in case

of spatially uniform distribution of user, LB looses relevance

when the number of users get large.

Next table, Tab. IV shows the trade-off between allocated

sum-rate and outage rate as function of parameter in theEESM metric. According to these results we set = 410 for

all simulations in order to keep P(rk,g,q r(eff)k,g,q) below 1%.

Finally, in Fig. 3 we investigate the sensitivity of achieved

sum-rate to the choice of parameter , which selects the valuesin the power vectors used in distributed RA with K = 30 users.It is shown that the maximum capacity is obtained with = 1,which is the value used in all simulations. This result does not

change for different values of K.


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350 395 400 405 410 420 450Sum-rate [Kbps] 6402 6433 6440 6442 6444 6449 6466

Outage Prob. % 0.00 0.34 0.51 0.72 0.96 1.56 3.96

TABLE IVSUM -RATE AND OUTAGE PROBABILITY P(rk,g,q r

(eff)k,g,q

) VS EESMPARAMETER . DISTRIBUTED RA WITH FULL-REUSE AND K = 30

Fig. 3. Sum-rate vs parameter in S2 systems with K = 30 UEs

VII. CONCLUSIONS

In this work we have introduced and compared centralized

and distributed RA schemes which try to maximize sum-rate

whilst supporting with fairness different UEs in a multi-cell

cluster. Distributed RA aims at reducing the stringent time

requirement to exchange information and the high feedback

complexity of centralized RA. Partial interference coordination

is obtained through power planning techniques, like FFR. The

results for a three-cell cluster have shown that a distributed

system with high frequency reuse and large number of users

manages to approach the benchmark of centralized RA without

fairness degradation. However, few percent of capacity loss are

introduced by PRB-based allocation typical of LTE systems.

APPENDIX: A GREEDY LB ALGORITHM

The algorithm considers for each cell q of the cluster thefollowing load metric:

Lq =kKq

lk,q =kKq

kK(q)

C(SI Rk,q)(19)

where SI Rk,q is the signal-to-interference ratio of user k withrespect to cell q evaluated by taking only into account distance-based attenuation. The load metric lk,q estimates the amountsof resource units needed by user k, if served by cell q, to

achieve the required portion k of the sum-rate. After the initialassignment of each users to the cell providing the maximum

SI Rk,q , the LB algorithm works as follows:1. min = argminqLq, max = argmaxqLq2. = Lmax Lmin3. Dk = lk,min lk,max, k K

max

4. u = argminkKmax,Dk0

Dk

5. Lmax = Lmax lu,max, Lmin = Lmin + lu,min6. min = argminqLq, max = argmaxqLq

7. if Lmax Lmin > stop8. Kmax = Kmax {u}, Kmin = Kmin {u}9. go to step 2

ACKNOWLEDGMENT

This work was supported by the European Commission

under Network of Excellence NEWCOM++ (G.A. 216715) and

OPTIMIX project (G.A. 214625)

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centralized vs distributed resource allocation

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