Reduced feedback links for power minimization indistributed multicell OFDMA networksBerna Ozbek

CEDRIC/LAETITIACNAM, Paris, France

Email: berna.ozbek@cnam.fr

Didier Le RuyetCEDRIC/LAETITIACNAM, Paris, France

Email: didier.le ruyet@cnam.fr

Mylene PischellaCEDRIC/LAETITIACNAM, Paris, France

Email: mylene.pischella@cnam.fr

Abstract—In the next generation of multicell networks, adap-tive resource allocation techniques will play an important role toimprove both quality of service and spectral efficiency. In orderto employ distributed power allocation for multicell OrthogonalFrequency-Division Multiple Access (OFDMA) networks, thechannel state information (CSI) belonging to all users is requiredto share among base stations. However, the amount of feedbackincreases with the number of users, base stations and subcarriers.Therefore, it is important to perform a selection at the userside for multicell networks. In this paper, we propose reducedfeedback links by choosing the users based on their approximatesignal to interference noise ratio (SINR). The performance ofthe reduced feedback links are illustrated in multicell OFDMAsystems.

I. INTRODUCTION

The increasing demand for wireless multimedia has led tocoordinated multicell transmission which can increase datarate and reduces outage in cellular systems by mitigatingintercell interference (ICI). In coordinated multicell Orthogo-nal Frequency Division Multiple Access (OFDMA) networks,the optimal resource allocation (RA) requires to solve theproblem of both the power and subcarrier allocation jointly inall considered cells, taking into account interactions betweenusers of different cells via the multicell interference. RA canbe performed to maximize the sum or weighted sum rateor to minimize the power consumption. No exact solutionsexist for these problems. Throughout this paper, the powerminimization problem to satisfy the users’ data rate constraintsis considered for multicell networks.

In [1], an overall transmitted power has been minimizedunder each users maximal power and minimal rate constraintsusing a distributed noncooperative game approach for multi-cell OFDM networks. In [2], an algorithm performing RAvia two phases has been presented: First, the users whosepower should be zero are identified for each subcarrier withthe assumption of uniform power allocation. Then, an iterativedistributed algorithm called Dual Asynchronous DistributedPricing (DADP) [3] has been applied for the remaining usersunder high signal to interference noise ratio (SINR) assump-tion. Some margin-adaptive joint RA algorithms have beenproposed for the downlink of multicell OFDMA systems in[4] [5] by optimizing each subcarrier individually. In [6], afterthe subcarrier assignment, the determination of power levelfor each user in each cell has been performed via an iterative

allocation algorithm.Base station (BS) cooperation entails sharing control sig-

nals, transmit data, channel state information (CSI) and/or pre-coders via wired backhaul links to establish coordinated trans-mission. In practice, however, the backhaul will be bandwidth-limited due to the prohibitive costs involved in establishinghigh-capacity links. Therefore, the amount of informationexchanged among BSs should be restricted, which in turndetermines the level of cooperation and the performance gains.In order to reduce the backhaul load, partial cooperativestrategies have been considered where the BSs share only theusers’ CSIs [7]. Adaptive limited feedback schemes selectingthe transmission strategy depending on power level at cell-edge and the users’ locations are presented for single carriermultiantenna multicell networks in [8].

The existing RA algorithms have assumed that the quantizedCSI belonging to serving and interfering BSs of all users isavailable at all BSs, which causes a high feedback load anda sophisticated resource allocation algorithm at the BSs. Thereduced feedback links for multicell OFDMA systems have notbeen considered in the literature so far. Therefore, we proposea reduced rate user selection based on SINR to feed back CSIbelonging to serving and interfering BSs for multicell OFDMAnetworks while satisfying users’ data rate constraints.

This paper is organized as follows. In Section II, the systemmodel for multicell OFDMA networks is described includingRA problem. In Section III, we propose reduced feedbacklinks for multicell OFDMA networks. In Section IV, wepresent joint user scheduling and power allocation algorithmincluding distributed solutions for 2-cells and 3-cells networks.In Section V and VI, the performance results are illustratedand the concluding remarks are drawn respectively.

II. SYSTEM MODEL

We consider a downlink cellular OFDMA system withone transmit and one receive antenna, composed of U basestations, each of which has K users as shown in Figure 1.Using OFDMA system with N subcarriers, BS u serves agroup of users for cell u assuming that the number of usersat each cell is smaller than N .

The channel power gain of subcarrier n from BS v to auser k in cell u is denoted by Gv,u,k,n which includes pathloss and multipath effect of the wireless channels. Note that

IEEE ICC 2012 - Wireless Communications Symposium

978-1-4577-2053-6/12/$31.00 ©2012 IEEE 3884

BS u

Gw,u

BS w

BSv

Gu,u

Gv,u

Fig. 1. A multiuser multicell network.

if u �= v, Gv,u,k,n represents the power gain of the cochannelinterfering link from BS v to the user k, otherwise (u = v)it denotes the power gain of the communication channel from(serving) BS u to the user k for subcarrier n. It is assumed thatthe wireless channel between each BS-user pair remains staticover a sufficiently long duration, so that RA can be carriedout for that duration.

The power-allocation related notations are defined in thefollowing. Pmax

u denotes the total available power at BS u,and Pu,n represents the allocated power to subcarrier n byBS u. {Pu,n}

Uu=1 is stacked into a U × 1 vector Pn =

[P1,n, P2,n, ..., PU,n] and then [Pn]Nn=1 is stacked into a U×N

matrix P, satisfying [P]u,n = Pu,n, where [P]u,n representsthe entry at the uth row and the nth column of P.

The subcarrier-allocation related notations are defined inthe following. A binary variable Au,k,n, which indicatesthat subcarrier n is allocated to user k in cell u ifAu,k,n = 1. {Au,k,n}

Nn=1 is stacked into the vector Au,k =

[Au,k,1, Au,k,2, ..., Au,k,N ]T , and then Au,k is stacked to

a matrix Ak column by column. Finally, a matrix A =[A1, ...,AU ] indicates how subcarriers are allocated to allusers for all cells.

The margin adaptive resource allocation problem is definedas:

minA,P

U∑u=1

K∑k=1

N∑n=1

Au,k,nPu,n (1)

subject to

Ru,k ≥ Rttu,k, ∀k, ∀u (C1)

N∑n=1

Pu,n ≤ Pmaxu , ∀u (C2)

(2)

Pu,n ≥ 0, ∀u, ∀n (C3)K∑

k=1

Au,k,n ≤ 1, ∀u, ∀n (C4)

Au,k,n ∈ {0, 1}, ∀k, ∀u, ∀n (C5)

(C1) is the target rate of each user at each cell, (C2) is the sumpower constraint per BS with (C3), (C4) is the orthogonalityconstraint for OFDMA subcarrier allocation with (C5).

The optimization variables are the set of subcarriers A andthe set of power values P per BS and per subcarrier.

The user rate (b/s) is calculated as,

Ru,k =

N∑n=1

Au,k,nRu,k,n(Pn) (3)

where Ru,k,n is the rate of subcarrier n when allocated to userk in cell u and is calculated by:

Ru,k,n(Pn) =B

Nlog2(1 + γu,k,n(Pn)) (4)

where B is the total bandwidth.The SINR, γu,k,n(Pn)), is determined by,

γu,k,n(Pn) =Pu,nGu,u,k,n

σ2n +∑U

v=1,v �=u Pv,nGv,u,k,n

(5)

where σ2n =N0BN

is the noise power per subcarrier and N0 isthe power noise density.

III. THE PROPOSED REDUCED FEEDBACK LINK

For single cell OFDMA systems, in order to reduce thefeedback load, the clustering structure where adjacent subcar-riers are grouped and only the CSI related to the strongest Sclusters in terms of channel gain for each user are fed backto the transmitter, has been presented in [9]. In this paper,we perform clustering for multicell networks by consideringthe criterion based on approximated SINR values instead ofchannel gain only.

A. The proposed clustering for multicell OFDMA

Firstly, the subcarriers are grouped into clusters where thecorrelation is high among the adjacent subcarriers. Then, onlyone value for each cluster is sufficient to represent it. Inmulticell networks, in order to determine the representativevalue of each cluster, we distinguish the channel coefficientsbelonging to serving BS and interfering BSs. For the servingBS, the CSI value belonging to the subcarrier of minimumchannel gain is chosen as,

¯Gu,u,k,q = Gu,u,k,x, u = 1, 2, ..., U. (6)

where

x = (q − 1)NQ + arg min1≤i≤NQ

{Gu,u,k,(q−1)NQ+i}, ∀q

with NQ = N/Q is the number of subcarriers in one clusterand Q is the number of clusters in a OFDM symbol.

3885

For interfering BSs, the CSI value belonging to the subcar-rier of maximum channel gain is selected as,

Gv,u,k,q = Gv,u,k,y, v, u = 1, 2, ..., U v �= u. (7)

where

y = (q − 1)NQ + arg max1≤j≤NQ

{Gv,u,k,(q−1)NQ+j}, ∀q

Then, by assuming full and equal power transmission fromrespectively all BSs and all clusters, the approximate SINRvalue of each user at each cluster in multicell network iscalculated as:

γu,k,q =(Pmax

u /Q) ¯Gu,u,k,q

(σ2/Q) + (Pmaxu /Q)

∑Uv=1,v �=u Gv,u,k,q

(8)

=Pmaxu

¯Gu,u,k,q

σ2 + Pmaxu

∑Uv=1,v �=u Gv,u,k,q

where σ2 = N0B is the noise power.The reason of selecting minimum channel gain for serving

BS and maximum channel gain for interfering BSs is to avoidoutage by calculating the lowest approximate SINR value foreach cluster.

B. Clustered S-Best criterion at fixed feedback rate

For this criterion, each user at each cell constructs indepen-dently a set Su,k composed of the strongest S clusters basedon γu,k,q values. Then, the CSIs of serving and interferingBSs of Su,k are fed back and shared among BSs.

Let Tu,q be the set of users that are fed back their CSIassociated to the cluster q at cell u as,

Tu,q = {k ∈ {1, 2, . . . ,K} : q ∈ Su,k} (9)

The S parameter is once fixed to satisfy all users’ rate con-straints as a function of K and Rtt

u,k such that S = f(K,Rttu,k).

Total feedback load is proportional to KS at each cell.

IV. THE DISTRIBUTED RESOURCE ALLOCATION FOR

POWER MINIMIZATION

In order to illustrate the performance of the proposedreduced feedback links for multicell networks, we examinethe optimal solution for U = 2 and U = 3 cells in distributedmanner by considering the clustered structure and selected userset which are introduced in previous section.

In order to solve this optimization problem in a distributedmanner, the power values are calculated for any combinationof the allocation of users to each cluster at each cell. Then,the user pair which requires the minimum sum power [10]satisfying the constraints is selected in each BS separately.

A. The distributed solution for U=2

A simple scenario with only 2 cells is considered with twofollowing assumptions. Assumption 1 is that the users’ targetrates are the same by having the same SINR value, γtt, percluster. Assumption 2 is that the channel gain of ¯G1,1,k1,q,G1,2,k1,q, ¯G2,2,k2,q and G2,1,k2,q for k1 ∈ T1,q and k2 ∈ T2,q

for each cluster is perfectly known at BS1 and BS2.

Then, the optimization problem can be simplified as:

min

K∑k=1

Q∑q=1

(A1,k,qP1,q +A2,k,qP2,q) (10)

All constraints remain the same except the first constraint (C1)which can be simplified to

Q∑q=1

Au,k,q ≥ Qtt

where Qtt = RttQB log

2(1+Γγtt) with Γ is a constant gap that is

chosen depending on the required bit error rate (BER).The joint user scheduling and power minimization:• For q = 1 to Q:

– Step 1: For BS1, the required power for each userpair is calculated:∗ For any (k1,k2) where k1 ∈ T1,q and k2 ∈ T2,q ,

the power can be determined as:

P k1,k2

1,q =a1 + a2b121 − b12b21

P k1,k2

2,q =a2 + a1b211 − b21b12

where

au =σ2qγ

tt

¯Gu,u,ku,q

, u = 1, 2

b12 =G1,2,k1,qγ

tt

¯G1,1,k1,q

b21 =¯G2,1,k2,qγ

tt

G2,2,k2,q

where σ2q = σ2/Q.∗ End.

– Step 2: Choose the feasible power pairs(P k1,k2

1,q , P k1,k2

2,q ) that satisfy the power constraintsin (C2) and (C3) and the conditions of b12 < 1 andb21 < 1.

– Step 3: Among the feasible powers pairs, the userpair that requires the minimum total transmittedpower is selected as following:

(k∗1 , k∗2) = argmin(P k1,k2

1,q + P k1,k2

2,q )

– Step 4: At BS1, the user k∗1 is scheduled asA1,k∗

1,q = 1 and its power is assigned as P1,q =

Pk∗

1,k∗

2

1,q .– Step 5: Check that the user k∗1 satisfies the rate

constraint in (C1). If so, remove this user from theset T1,q, ∀q. Moreover, this user does not continueto feed back any information in the OFDM frame.

• End.The same algorithm is performed at BS2 separately and the

user is scheduled and the power is assigned as P2,q = Pk∗

1,k∗

2

2,q

and A2,k∗

2,q = 1.

3886

B. The distributed solution for U=3

We extend the same solution to U = 3 cells with Assump-tion 1 and Assumption 2 by considering 3 BSs in the network.

In order to obtain feasible power values, we firstly selectthe users which fulfill the following condition [6]:

γtarget

Eu,k,q

< 1 ku ∈ Tu,q, ∀u, ∀q (11)

where

Eu,k,q =¯Gu,u,k,q

U∑v=1,v �=u

Gv,u,k,q

(12)

Then, we perform joint user scheduling and power allo-cation algorithm by taking into account these users k′u ∈T′u,q, ∀u, ∀q.The joint user scheduling and power minimization:• For q = 1 to Q:

– For BS1, the required power for each user pair iscalculated:∗ For any (k′1, k′2, k′3) where k′1 ∈ T

′1,q , k′2 ∈ T

′2,q,

k′3 ∈ T′3,q , the power can be determined by:

P = B−1

A

where

P = [Pk′

1,k′

2,k′

3

1,q Pk′

1,k′

2,k′

3

2,q Pk′

1,k′

2,k′

3

3,q ]T

andA = [a1 a2 a3]

T

B =

⎡⎣

1 −b12 −b13−b21 1 −b23−b31 −b32 1

⎤⎦

with

au =σ2qγ

tt

¯Gu,u,k′

u,q

, u = 1, 2, 3

b1v =Gv,1,k′

1,qγ

tt

¯G1,1,k′

1,q

, v = 2, 3

b2w =Gw,2,k′

2,qγ

tt

¯G2,2,k′

2,q

, w = 1;w = 3

b3y =Gy,3,k′

3,qγ

tt

¯G3,3,k′

3,q

, y = 1, 2

∗ End.– Considering the constraints of (C2) and (C3), the

feasible power levels at each BS for each pair ofusers is calculated and then, Step 2 to Step 5 de-scribed in the previous algorithm are performed toschedule the user for BS1.

• End.The same algorithm is performed at BS2 and BS3 sepa-

rately and the user is scheduled and the power is assignedas P2,q = P

k∗

1,k∗

2,k∗

3

2,q , A2,k∗

2,q = 1 at the BS2 and P3,q =

Pk∗

1,k∗

2,k∗

3

3,q , A3,k∗

3,q = 1 at the BS3.

V. PERFORMANCE RESULTS

We obtain the performance results to illustrate the benefitsof the reduced feedback links in multicell OFDMA networksfor U = 2 and U = 3 using the parameters listed in Table I. Itis assumed that the users are uniformly distributed in multicellnetwork. The target SINR values are chosen as γtt = 7.45dBand γtt = 4.65dB [11].

TABLE ITHE SIMULATION PARAMETERS

Parameter ValueCell radius 500m

BS Transmit Power 43.10dBmNoise Power density −174dBm/Hz

Path Loss Lp 128.1 + 37.6 log10(d)dBChannel Model 3GPP, TU

FFT size 512Subcarriers per cluster 12

Number of clusters 40Bandwidth 5MHz

Carrier frequency 2.6GHzBandwidth per subcarrier 15kHz

Feedback time 1msFrame Duration 10ms

In Figure 2, the percentage of satisfied users according tothe number of feedback clusters is demonstrated based on theproposed SINR criterion for distributed solution when U = 2.Based on user satisfaction criterion, the minimum number ofrequired clusters, S, is listed in Table II for different rate’constraints for U = 2 and U = 3. As seen in the Table II,when the number of users in the cell increases, the requirednumber of feedback clusters also increases to satisfy all users’constraints for higher target data rates and/or higher numberof interfering BSs.

As shown in Figure 3, the reduction on the feedback loadcompared to the full feedback is much higher when the numberof the users is increased in the multicell networks. It is notedthat the feedback load is averaged by taking into account theframe structure, which indicates that the feedback load is alsochanging in one frame since the satisfied users do not continueto feed back any information to the BSs.

TABLE IITHE NUMBER OF REQUIRED FEEDBACK CLUSTERS

K 4 8 12 16 20 Case

S 3 3 3 6 12 Rtt = 1M, γtt = 7.45dB, U = 2S 2 2 2 2 2 Rtt = 0.4M, γtt = 4.65dB, U = 2S 5 5 5 7 11 Rtt = 0.4M, γtt = 4.65dB, U = 3

According to the minimum number of required feedbackclusters in Table II, the total transmitted power that achieves99% of users’ rate satisfaction is drawn in Figure 4. The per-formance results indicate that the feedback load is significantlyreduced while achieving almost the same average transmittedpower compared to full feedback scheme. When the numberof users are increased in the multicell network, the maximum

3887

1 3 5 7 9 110

10

20

30

40

50

60

70

80

90

100

The number of feedback clusters,S

The

per

cent

age

of s

atis

fied

user

s

K=4K=8K=12K=16K=20

Fig. 2. The percentage of satisfied users in each cell vs. the number offeedback clusters for Rtt = 1MB/s with γtt = 7.45dB, U = 2.

4 8 12 16 200

10

20

30

40

50

60

70

80

The number of user,K

The

feed

back

load

rat

e pe

r ce

ll

Reduced, U=2Reduced, U=3Full

Fig. 3. The feedback load vs. the number of users in the cell for Rtt =0.5MB/s with γtt = 4.65dB.

difference on the power level between the reduced and fullfeedback is only 1dBm which occurs at higher target datarates.

VI. CONCLUSION

In this paper, we have examined the reduced feedback linksfor cooperative multicell OFDMA networks. The clustered S-best criterion has been proposed based on approximate SINRvalues. It has been shown that the feedback load is reduced upto 75% for 3cell networks when the number of users increasesin the cell. The proposed reduced feedback links have alsoflexible structure by changing the number of clusters in timeby satisfying users’ rate constraints. As a result, the proposedreduced feedback link achieves the same performance than

4 6 8 10 12 14 16 18 2029

30

31

32

33

34

35

36

37

38

39

The number of user,K

The

ave

rage

tran

smitt

ed p

ower

, PT, d

Bm

RB,Rtt=1M,U=2

FB,Rtt=1M,U=2

RB,Rtt=0.5M,U=2

FB,Rtt=0.5M,U=2

RB,Rtt=0.5M,U=3

FB,Rtt=0.5M,U=3

Fig. 4. The transmitted power vs. the number of users at different targetrates.

full feedback in terms of user satisfaction ratio and powerminimization while reducing the feedback load significantly.

ACKNOWLEDGMENT

This research was supported by a Marie Curie Intra Euro-pean Fellowship within the 7th European Community Frame-work Programme as a part of INTERCELL project with thecontract number PIEF-GA-2009-255128.

REFERENCES

[1] Z. Han, Z. Ji, and K. J. R. Liu, Power Minimization for Multi-CellOFDM Networks Using Distributed Non-cooperative Game Approach,IEEE Globecom 2004, pp.3742-3747.

[2] M. Pischella, J-C. Belfiore, Weigthed sum throughput maximization inmulti-cell OFDMA networks, IEEE Transactions on Vehicular Technol-ogy, vol. 59, no. 2, pp.896-905, Feb. 2010.

[3] J. Huang, R. Berry, and M. L. Honig, Distributed interference compen-sation for wireless networks, IEEE J. Sel. Areas Commun., vol. 24, no.5, pp. 1074-1084, May 2006.

[4] S. Pietrzyk and G. J. M. Janssen, Radio resource allocation for cellularnetworks based on OFDMA with QoS guarantees,in Proc. IEEE GlobalTelecommunications Conf., Nov. 2004, pp.2694-2699.

[5] A. Abrardo, A. Alessio, P. Detti, and M. Moretti, Centralized radioresource allocation for OFDMA cellular systems,in Proc. IEEE Int. Conf.Communications, Jun. 2007, pp.5738-5743.

[6] M. Pischella and J.-C. Belfiore,Distributed resource allocation for rateconstrained users in multi-cell OFDMA networks, IEEE CommunicationsLetters, vol. 12, pp:250-252, April 2008.

[7] F. Boccardi and H. Huang, Limited downlink network coordination incellular networks, Proc. of the IEEE Int. Symp. on Personal Indoor andMobile Radio Comm. (PIMRC), Athens, Greece, Sept. 2007.

[8] J. Zhang and J. G. Andrews, Adaptive Spatial Intercell InterferenceCancellation in Multicell Wireless Network, IEEE Journal on SelectedAreas in Communications, vol:28, no:9, pp:1455-1468, Dec. 2010.

[9] P. Svedman, S. K. Wilson, L. J. Cimini and B. Ottersten, OpportunisticBeamforming and Scheduling for OFDMA systems, IEEE Trans. onCommunications, vol. 55, pp.941-952, May 2007.

[10] G. J. Foschini and Z. Miljanic, A simple distributed autonomous powercontrol algorithm and its convergence, IEEE Trans. Veh. Technol., vol.42, pp. 641-646, Nov. 1993.

[11] A. Goldsmith, S. Chua, Adaptive coded modulation for fading channels,IEEE Trans. Commun., vol. 46, no.5, pp. 595-602, 1998.

3888