self-organizing power control

7/29/2019 Self-Organizing Power Control

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Self-Organizing Fractional Power Control for

Interference Coordination in OFDMA Networks

Richard Combes,Zwi Altman and Eitan Altman

France Telecom Research and Development

38/40 rue du General Leclerc,92794 Issy-les-Moulineaux

Email:{richard.combes,zwi.altman}@orange-ftgroup.comINRIA Sophia Antipolis

06902 Sophia Antipolis, France

Email:[email protected]

AbstractThis paper shows a Self-organizing networks (SON)algorithm for interference coordination in downlink OrthogonalFrequency-Division Multiple Access (OFDMA) networks. A dis-tributed algorithm is introduced with a proof of convergence fora static user population. The algorithm uses closed-form formulasfor the transmit powers update, and is therefore computationally

light. The proposed algorithm is applied to a 39 cells dynamicnetwork simulator with an File Transfer Protocol (FTP) service,showing significant performance gains over a Reuse 1. TheQuality of Service (QoS) of cell-edge users improves withoutdegrading the QoS of other users. The trade-off between BlockCall Rate (BCR), which is the proportion of users rejectedby admission control, and cell-edge user throughput is shown,and a simple method for the network operator to manage it isprovided.1

Index TermsWireless networks, Self-Optimizing Networks,OFDMA Networks, Interference Coordination, DistributedPower Control

I. INTRODUCTION

In multiuser communication networks, interference man-agement is often a central issue for increasing the system

performance and has been the subject of much research in both

wired and wireless networks. Different techniques have been

suggested: optimization of a static power allocation ([1], [2]),

dynamic power control ([3]), inter-cell scheduling ([4], [5]),

load balancing ([6]) and dynamic beam-forming ([7]) to name

but a few. Interference is particularly harmful for cell-edge

users i.e users with low Signal to Interference plus Noise Ratio

(SINR) and can cause considerable degradation of experienced

QoS. Strict requirements for cell-edge user throughput have

been defined by [8].

Two issues have not, to our knowledge, been addressed by

previous work: the first is the fact that interference coordi-

nation can possibly increase the BCR of some Base Station

(BS) and how to control it, and the second is how to find

closed-form formulas for the power update, so that the power

control algorithm is computationally light. We address both

these problems in this paper, and show that the signaling load

of the algorithm is minimal.

1This work has been partially supported by the Agence Nationale de laRecherche within the project ANR-09-VERS0: ECOSCELLS.

The first contribution of this paper is a distributed dynamic

interference coordination algorithm for downlink OFDMA net-

works which uses information available from neighboring cells

through the X2 interface (a link between neighboring BSs).

The BSs update their transmit powers every 1s using closed-

form formulas which incorporate the effects of fast-fadingand opportunistic scheduling. The computing power required

is hence minimal. The second contribution of this paper is

to show the trade-off between cell-edge user throughput and

BCR, and to provide the network operator with a simple

way to manage this trade-off by adjusting a parameter of our

algorithm.

This paper is organized as follows: Section II states the

dynamic power control problem in an OFDMA network and

gives a general distributed algorithm to solve it. Section III

describes the system model of a downlink OFDMA network

we are considering, and provides the closed-form formulas that

are necessary for the power control algorithm. An analysis

of the signaling load of the algorithm is given. In SectionIV we simulate the proposed algorithm in a 39 BSs dynamicnetwork simulator, and demonstrate the important resulting

gains. A method for managing the trade-off between cell-edge

user throughput and BCR is also given. Section V concludes

the paper.

I I . PROBLEM STATEMENT AND PROPOSED ALGORITHM

A. Optimization Problem

We consider a downlink OFDMA network and an FTP

service with NBS BS. The bandwidth allocated to each cell

is divided into Np Physical Resource Block (PRB). For more

generality, PRBs are grouped in Nb sub-bands, and the powertransmitted by a BS on two PRBs of the same sub-band is the

same. We introduce the following quantities: P(b)s is the power

emitted by BS s on a PRB of band b, Pmax the maximum

transmit power on a PRB, and Us is the utility observed by s,

to be defined in the next section. The total network utility is

then U =

1sNBSUs. For a given distribution of users in

the network, the BSs have to solve the optimization problem

described in (1), where gl , 1 l Nl are convex functionswhich represents constraints and will be addressed later. We

978-1-61284-231-8/11/$26.00 2011 IEEE

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings


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assume that we do not control the scheduling strategy.

maximize U (1)

subject to 0 P(b)s Pmax , 1 s NBS , 1 b Nb

and gl((P(b)s )1bNb) 0 , 1 s NBS , 1 l Nl

Let us denote by P the subset of (R)NbNBS which satisfiesthe constraints in (1), and Ps the subset ofRNb which satisfiesthe constraints relative to BS s. It is noted that P = P1 ... PNBS is a product of convex sets, hence convex.

B. Requirements on the algorithm

We first impose the choice of a distributed algorithm which

fits the flat architecture of future radio access networks. At

each step of the algorithm, BS s observes its utility Us,

exchanges some information with its neighbors and modifies

its transmit powers (P(b)s )1bNb accordingly. Furthermore,

it is noted that finding the global optimum in (1) is NP-

hard ([9]) in most cases, hence we are simply concerned with

finding a local maximum ofU in a few iterations with minimal

computing effort.

C. Basic Algorithm

We use the approach introduced in [10] for solving a

constrained optimization problem in a distributed fashion. Let

(t) RNbNBS , t N denote the power allocation of thenetwork at time t, and (0) P. We can then apply thefollowing gradient descent algorithm:

(0) P , (t + 1) =

(t) + U((t))+

(2)

where [.]+ denotes the projection on P with respect to theeuclidean norm, and a constant step size. It is noted that the

projection is well defined since P is convex.Furthermore, since P is a product of convex sets, we have

that (2) can be implemented in a distributed way. Let s(t) RNb , t N denote the power allocation of BS s, at time t,we then obtain the following algorithm, for 1 s NBS:

s(0) Ps , s(t + 1) =

s(t) + sU(s(t))+

(3)

where s is the gradient with respect to (P(b)s )1bNb .

Furthermore, [10](Proposition 3.8, Page 219) gives the

following convergence theorem:

Theorem 1. If we assume thatP is a product of convex sets,thatU is bounded below and that U is Lipschitz continuous,

then there exists 0 such that if0 < 0 then (3) convergesto a local maximum of U in P.

III. MULTI-CELL OFDMA SYSTEM MODEL

A. SINR

We consider a multi cell OFDMA network, and an FTP ser-

vice. Users arrive randomly according to a Poisson process of

rate , with a file of a given size, and leave the network when

they have completed the transfer. It is noted that some users

might be rejected because of admission control mechanisms.

Let us consider a user i and a BS s. The signal from s received

by i is proportional to the power emitted by s, and we define

hs,i the proportionality coefficient, which is the product of

path loss and shadowing:

hs,i =A

(ds,i)s,i (4)

where ds,i is the distance between i and s, s,i = 101+220 with

1 and 2 are two independent normally distributed random

variables with mean 0 and variance and A and are twoconstants that depend on the environment.

Let s be the serving BS for user i and Ns the neighboringBSs of s. The mean SINR on a PRB in band b S

(b)s,i is

then calculated by summing the interference from neighboring

cells:

S(b)s,i =

hs,iP(b)s

N20 +

sNshs,iP

(b)s

(5)

with N20 the thermal noise.

B. Proportional Fair (PF) scheduler

We will use the following notations: let r(p)i,tm denote theinstantaneous bitrate of user i at time tm on PRB p, and ri,tmthe average allocated bitrate to user i during [t0, tm]. Let

denote a small constant averaging parameter. We write T(p)tm

=i if user i was scheduled for transmission on PRB p at time

tm. The average bitrate is then calculated by the following

low-pass filter:

ri,tm+1 = (1 )ri,tm +

Npp=1

i,T

(p)tm+1

r(p)i,tm+1

(6)

where is Kroneckers delta.The PF scheduler chooses the user for transmission on PRB

p at time tm+1 according to the following rule:

T(p)tm+1

= arg maxi

r(p)i,tm+1

ri,tm(7)

We denote by ri the limit of ri,tm when tm + , 0+ if it exists. For a proof of convergence of the PF scheduler,the reader can refer to [11], and to [12] for the more general

case of the -fair scheduler.

C. Scheduling gain

We assume a Raleigh fading model: r(p)i,tm

= (S(p)i

(p)i,tm

)

where (p)i,tm

is an exponentially distributed random variable of

mean 1, with (p)i,tm

(p)i,tm

, p = p, (p)i,tm

(p)i,tm

, i = i and

(p)i,tm (p)i,tm

, m = m. is a quality table which links achannel state to the corresponding instantaneous bitrate and is

obtained by link-level simulation.

We first define which associates the SINR of a user on aPRB of band b with his throughput on this band when he is

alone in the cell:

(S(b)s,i ) =

Np

Nb

+0

(xS(b)s,i )e

xdx =Np

NbS(b)s,i

L

1

S(b)s,i

(8)



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with L the Laplace transform of. We can then calculate themean allocated throughput by the Round Robin (RR) scheduler

for user i:

ri,RR =1

Nu(s)

Nbb=1

S(b)s,i

(9)

where Nu(s) is the number of users present in s.

For the PF, the mean throughput can also be calculated inclosed form, see [13]:

ri,PF =

Nbb=1

Nu(s)1k=0

Nu(s) 1

k

(1)k

k + 1

S(b)s,i

k + 1

(10)

One must be careful however, since (10) is only exact when

the mean SINR of a user is the same on all PRBs, that is

S(b)s,i = S

(b)s,i , (b, b

, s , i), and becomes a lower bound forri,PF in other cases. A formal justification for this is given in

[14].

D. Form of utility and gradient calculation

We choose an -fair form of utility ([15]), with R+,

d > 0 a small constant, and f(x) =(x+d)11

1 if = 1and f1(x) = log(x + d) :

Us =

Nu(s)i=1

f(ri) (11)

We can now calculate the gradient of the network utility

with respect to the BSs power levels for both RR and PF

schedulers.

1) RR scheduler: We first consider the derivative with

respect to the BSs own power level:

Us

P(b)s

=1

Nu(s)

Nu(s)i=1

1

(ri,RR + d)

Nbb=1

S(b)s,i

P(b)s,i

S(b)s,i

(12)

Now we consider the neighbors power level, if s1 Ns:

Us

P(b)s1

=1

Nu(s)

Nu(s)i=1

1

(ri,RR + d)Nbb=1

hs1,i(S

(b)s,i )

2

hs,iP(b)s

S(b)s,i

(13)

2) PF scheduler: For a PF scheduler, the same type of

formulas can be obtained:

Us

P(b)s

=

Nu(s)i=1

1

(ri,PF + d)

Nb

b=1

Nu(s)1k=0

Nu(s) 1

k

(1)kS(b)s,i

(k + 1)2P(b)s,i

S(b)s,i

k + 1

(14)

Us

P(b)s1

=

Nu(s)i=1

1

(ri,PF + d)

Nb

b=1

Nu(s)1k=0

Nu(s) 1

k

(1)k+1hs1,i(S(b)s,i )

2

(k + 1)2hs,iP(b)s

S(b)s,i

k + 1

(15)

E. Constraints

We define constraints on the maximal and minimal totaltransmit power: g1((P

(b)s )1bNb) =

NpNb

Nbb=1 P

(b)s Ptot

and g2((P(b)s )1bNb) = Ptot

NpNb

Nbb=1 P

(b)s where Ptot

is the maximum total transmit power and (0, 1] - theminimum proportion of total transmit power. It is noted that

those functions are linear hence convex.

The constraint on the minimal transmit power has two

interests: first, it prevents a numerical instability near 0 when > 0, since the utility gradient becomes very large if a BStransmits a total power of zero. The second interest is that

for close to 0, the unconstrained algorithm could result incertain BSs transmitting very low power, causing a dramatic

increase in their load and BCR.

It is noted that fixing a value of is akin to giving alower bound on the worst-case BCR. The justification is the

following: consider the case in which BS s transmits a total

power of Ptot, and all its neighbors transmit at full power.

Then the BCR observed in BS s in this situation is an upper

bound for the BCR that could be observed in other situations

in BS s. Therefore, taking the maximum of this value on all

BSs gives an upper bound for the BCR observable on the

network.

Furthermore, increasing reduces the size of the constraints

set, reducing the maximum possible gains achievable by a

power control algorithm. This is why controls a trade-off

between BCR and Inter-Cell Interference Coordination (ICIC)

gains.

F. Implementation and signaling load

Every 1s, BS s calculates and forwards UsP

(b)s1

, 1 b Nb

to s1 if s1 is a neighbor of s. Hence, assuming Nb = 3 bands,6 neighbors for each BS and that each derivative is stored asa 32-bits floating point number, the signaling load is of 576

bits/s per station, which is extremely small compared with the

expected capacity available on the X2 interface. Furthermore

the delay requirement of 1s is also easily satisfied, as a delaybetween 20ms and 50ms is expected on the X2 interface.

IV. SIMULATION

A. Network Simulator

The algorithm is implemented in a large scale network

simulator with 39 BSs. The throughput allocated by thescheduler is calculated in closed-form using equations (9) and

(10). Every 1s, the transmit power of each BS is adjustedaccording to the power control algorithm described above. The

algorithm has been simulated for Nb = 3. Three algorithmsare compared, using the following nomenclature:

Reuse 1 where all stations transmit at full power



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Soft Reuse which is a static power allocation described

in [16]

FFR which is the proposed dynamic algorithm

We choose = 2 since it implies maximizing the harmonicthroughput of BSs, which is a natural metric of capacity for

elastic traffic (see for example [17]) and gives good practical

results.

Because of the finite size of the network, we only calculatethe Key Performance Indicators (KPIs) on the subset of inner

BSs to minimize truncation effects, and the transient period

at the beginning of the simulation is not counted to calculate

KPIs. Simulation parameters are described in Table I.

Simulator parameters

Spatial resolution 25m 25mTotal simulated area 8km 8kmTime resolution 1sSimulation time 3000sUser speed 5km/hFile size 10MbytesNumber of sub-bands 3Number of PRBs 9Size of a PRB 180kHzNumber of stations 39Cell layout 13 eNBs 3 sectors 5% 2Maximum BS transmit power 30WService Type FTPScheduler Type Proportional FairThermal noise 174dBm/HzPath loss 128 + 37.6log10(d) dB, d in kmShadowing standard deviation 6dB

TABLE IMODEL PARAMETERS

B. Simulation results

All results are given for = 2, unless specified. Figures1, 2 and 3 compare the BCR, mean file transfer time and

mean network throughput respectively for the three scenarios,

and we can see a clear improvement for the three KPIs.

The most notable is the BCR improvement from 5.5% to2.3% in high traffic, demonstrating that the proposed algorithmeffectively reduces congestion in the network. Figure 4 shows

the cumulative distribution function (c.d.f) of the file transfer

time in the network for = 9, and we can see that all users

benefit from the reduced congestion, the ones benefitting themost being cell-edge users, namely users with long transfer

times. Figure 5 shows the power allocated to each band

through time by the algorithm. Figure 6 shows the BCR and

the proportion of users whose File Transfer Time (FTT) is

longer than 10s as a function of , for = 0. It illustrates thetrade-off between the FTT reduction and increase in BCR.

Is allows the network operator to set the parameter in

order to enforce some policy, for example to obtain the best

performance while keeping the BCR under a certain threshold.

9 9.5 10 10.5 11 11.5 120

1

2

3

4

5

6

Arrival Rate (mobiles/s)

BlockCa

llRate(%)

Reuse 1

Soft ReuseFFR

Fig. 1. BCR of the network, = 2

9 9.5 10 10.5 11 11.5 1210

12

14

16

18

20

22


Meantransfertime(s)

Reuse 1

Soft Reuse

FFR

Fig. 2. Mean FTT in the network, = 2

9 9.5 10 10.5 11 11.5 120.95

1

1.05

1.1

1.15

1.2

1.25x 10

5


Meannetwork

throughput(kbps)

Reuse 1Soft ReuseFFR

Fig. 3. Mean network throughput, = 2



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0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Filetransfertimec.d.f

Reuse 1

Soft Reuse

FFR

Fig. 4. c.d.f of FTT of all users in the network, = 2

0 200 400 600 800 1000

0

0.5

1

1.5

2

2.5

3

3.5

4

Time (s)

BSpower(W)

Band 1

Band 2Band 3

Fig. 5. Transmit power of a BS, = 2

10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

45

Gamma(%)

BCR

andFTT(%)

BCR

FTT > 10

target BCR

Fig. 6. Trade-off between FTT and BCR for = 0

V. CONCLUSION

This work has presented a distributed SON algorithm for

interference coordination in OFDMA networks. The algorithm

uses information available from neighboring cells and closed

form formulas, making it both computationally light and

suitable for practical implementation. It has been applied

to a large-scale network simulator, showing important gains

over a full power allocation, for cell-edge users, while notdegrading other KPIs. The trade-off between gains for cell-

edge users and increase in the BCR has been shown, and a

straightforward method for the network operator to manage it

has been provided.

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