Joiunt Determilnat'ion of Power andl Decod'ing Order for

Successive Inter- and Intra-Cell Interference Cancellation

Hye Won Chung, Sang-Woon Jeon, Do-Hyung Park, and Sae-Young ChungSchool of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea

E-mail: {hwisland, swjeon, dohyungpack}jkaist.ac.kr, sychung ee.kaist.ac.kr

Abstract- The performance of multiple access systemsmainly depends on the management of interference arisingfrom both intra-cell and inter-cell transmission. Successiveinterference cancellation (SIC) is a promising approach tomanage interference in both the practical and infoirmationtheoretic senses. Because the messages of the cell boundaryusers are likely to be decoded not only at the serving basestation but also at an adjacent base station, it is possible tosubtract inter-cell interference of the cell boundary users beforeSIC of the intra-cell users. This is the motivation of our work.In this paper, we first decode the messages of the adjacentcell boundary users and subtract them, and then perform SICwithin the serving users. It shows better performance comparedto the conventional schemes with the SIC within the servingusers only.

J. INTRODUCTION

In the cellular systems, the transmit power control hasbeen an essential technique, i.e., code division multipleaccess (CDMA) systems, since interference from other usersdegrades the system performance. In order to support dataservices such as a file or image download, current cellularsystems allocate more resources for the downlink trafficthan for the uplink traffic. Due to the increasing downlinktraffic, most of the previous works of the power controland rate allocation has been concentrated, on the downfinkeinvironments [1], [2]. More recently, Ihowever, the demaind ofthe uplink traffic also increases proportional to the downfinktraffic. Due to the dynamic downlink resource allocation,more channel feedbacks or control messages are needed.Furthermore, some applications such as a file or image up-load require large amount of uplink resources. Based on thisconsideration, some works [3], [4], [5] related to the uplinkpower control and rate allocation have been performed.

In direct sequence CDMA systems, multiple-access inter-ference (MAI) causes performance loss due to the nonorthog-onality of spreading codes. Successive interference cancel-lation (SIC) is one of the promising methods as a practicalapproach toward multiuser detection (MUD) The iterativepower controls for SIC are proposed in [6], [7] and the effectof a channel estimation error is considered in [8] Powercontrols based on the multirate direct sequence CDMAsystems are considered under non fading and fading channelsin [9].

It is known that, for a given transmit power constraint, SICcombined with the minimum mean square error (MMSE)detection can achieve the sum-rate capacity [10]. In this

0 /0 Users at BSA0 Users at BSB

Fig. 1. Two adjacent cells with overlap region.

paper, we consider the scheme which performs SIC notonly within the intra-cell users but also within the inter-cell users who are at cell boundaries. By employing partialSIC of the inter-cell users, it is possible to improve systemperformances.

II. SYSTEM MODEL

We consider an uplink multi-cell cellular system in whichthere exists intra-cell and, inter-cell interference. In cellularsystems, coverages of each cell are overlapped, with theadjacent cells since it is impossible to make a beam tothe perfect hexagonal shape. The messages of cell-boundaryusers, which are located in the shaded region in Fig. 1, arelikely to be decoded from both base stations since the cell-boundary users are usually supported with a low rate, andtheir channel gain to the serving base station (BS) is similarto the channel gain to the adjacent BS.

In this paper, we simplify the multi-cell system to an onedimensional network and consider only one adjacent BS asshown in Fig. 2. Two BSs are separated by distance 2Rand the coverage of each cell is up to (1 + a)R, whereai denotes the overlap factor BSA denotes the serving BSfor users served bmy it and BB denotes the adjacent BSwhose serving users cause inter-cell interference to BSA.There are N number of users in BSA and the users are

uniformly distributed in (1 a)R region. It is assumedthat BSB has the mirror users corresponding to the servingusers in BSA, which means that the mirror user locates with(2R- r) distance apart from the origin when the servinguser is located at r. This assumption is reasonable if thereexists many users in each cell and only a small fraction ofinterference caused by the adjacent cell's users is canceled.

Let r denotes the distance from the origin to the kth

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"s"s ~~~~~~~~~~~~~~~~~~~~~~~I

I

I I ttf

In this paper, we consider the following problem of findingthe transmission power and the decoding order for inter-cell and intra-cell interference cancellation that minimizesthe total power consumption:

w;w;U.

N

f (PH' H) mmZinp,,rimP7k (5)

subject toi-4 RR

Users at BSA

(1± a)R T Users at BSB

Fig. 2. One-dimensional distribution of users between two base stations.

serving user. The channel gain of the k h serving user isgiven by

gk1

SINR r(k) y>7 Vk C [1?N]SINRO(fk) > T, Vk c [1,M]

P7(k) <mPmax,7(k), VkeE [1 N]where P = [P,(),, *, PW(N)]T is the transmit power vector,Pmax = [Pmnax,Tr(1) FPmax,ar(N)l ;is the maximum trans-mit power vector, and M is equal to the cardinality of Hl°.

(1)

w:here 3 is the path loss exponent. The channel gain of thek" mirror user is given by

gk (2R r-)3 (2)

When SIC is employed for inter-cell and, intra-cell inter-ference cancellation, the reverse link signal-to-interference-plus-noise ratio (SINR) of the -F(k)th serving user can berepresented as

III. POWER ALLOCATION FOR INTRA- AND INTER-CELLCANCELLATION

A. Decoding Order and Corresponding Power Assignment

First, let us assume that we do not employ inter-cellinterference cancellation. Then, the inter-cell interference Ieis given by NI ggPj. From (3) and (6), the transmit powerof each user should satisfy the following equation:

AGP > B

SINR T(k) =Po(k)+P (k)

N0+Ie j=k+l PT()pT(u)

where G is a diagonal matrix with the 1il diagonal elementof g(j) and B [-[yNo, .. . , yNO]T. A is given by (12).

Vk C [I, N] (3) By assuming perfect power control, i.e., SINR,(k) = afor all k C [1, N], we can find the minimum transmissionDower vector which satisfies (9) with eaualitv. Therefore.

where II = {7r(1), , -F(N)} is the ordered set that ind.icatesthe decoding order of the serving users. P,(k) is the transmitpower of the -F(k)th serving user and V0 is the noisevariance. If we cancel inter-cell interference up to NI mirrorusers, the inter-cell interference 'e is given by E¶ i plPj-

j=1 g,, (j)P,(j), where H°0 {= (1), ,z0(M)} is theordered set that indicates the decoding order of the mirrorusers. Since the channel gain and, interferer distributionbetween the serving user and BSA is symmetric with thatbetween the corresponding mirror user and BSB, the trans-mit power Pi of the ith serving user is equal to Pi° for alli C [1, N], where P0 is the transmit power of the ith mirroruser. It is assumed that the message of the T(k)t user canbe decoded if SINR,(k) > y, where y denotes the targetSINR valu.e.

In order to decode Al mirror users, the additional con-straints such as SINR° (k) > 3y should be satisfied for allk C [1, M]. The SINR of the o(k)th mirror user is givenby

SINRO K7r - (k)

N

rV (k) PT (k)hr Z oi

7 S11Mokp-90 0V ,k 1, NI] ()I

the transmit power of the 7r(k)th user is obtained as

P1T(k)

Lemma 1 In order to minimize the total power consu:mp-tion by using intra-cell interference cancellation, the servingusers should be decoded in the order of their channel gain.

Proof: Let's consider the serving user a1 and a2 whosechannel gains satisfy the relationship > p02 Supposethe 1 l's message is decoded and canceled at the1k h orderand next the U2 s message is decoded. The assigned powerfor each user is given by

P01

PU

gul (1+KJN0N

( 1-- )k 1( I7tl +( 1' 2 )I +7 91g 1+ gu2

I _I)k X

9 2 1 +Y Y1+y/,I '+-11

2

ISBN 978-89-5519-131-8 93560

w;w;U.eD

(6)(7)(8)

(9)

1 ( 1 )k- I x9(k)~ 1-Y/

2()(I10)

(1 1)

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-7(1 + 99r

1

97r(

97r(97r(2)

7r(2)

I) Y(1 + 97r (N -

(1 9yS

I 9~~~~~~7r(N -

1 9=(Nry( 9 7o(N-)9-,T(NN-19N

IIT

7r N -I

)

)7(1+ 97r(N) )7r(N)

r(N)

(12)

(Pul + u2)- (Pu

(1 )k-

1 Y LC - (1

(13)c _ D/( 1 )k-1I{2

where c is a constant that is not changed according tothe decoding order of user u1 and u2. If the message ofthe serving user a2 is canceled before decoding the servinguser al s message, the assigned power for each user, whichare denoted as Pu' and 2 respectively, are obtained bychanging the variable u1 to U2 and U2 to Ul in (11). Thedifference of the sum power between two strategies is givenby (13).From (1) and (2), we can derive that if gu, > 9u21 then

1 < go Therefore, (13) has a negative value. This means

that the sum power, which is calculated by assunming that theuser ul's message is canceled, before u.ser a2's message, issmaller than that of being calculated by assuming the reverse

decoding order. In conclusion, in order to minimize the totalpower consumption the serving users should be decoded inthe order of their channel gain.

Ifwe perform SIC for intra-cell interference in the order oftheir channel gain, the assigned power for each user is givenby (10) with fl such that g (1) > 9PT(2) > (.).> 97r(N)-

Next, let's consider inter-cell interference cancellation. Ifwe assume that lkl mirror u.sers are canceled, g.,U) = O

for wF(j) C Ho in (10). Therefore, the required, power foreach user decreases as M increases. However, the additionalconstraints, which is given by (4) and (7), should be satisfiedto employ inter-cell interference cancellation. Even thoughthe decoding order of the mirror users does not affect the

SINR values of the serving users the SINR values of themirror users in (4) depend on Ho.

Let's consider two mirror users v, and v2 whose channelgains satisfy the relationship, go > go Suppose that P,(k)is the transmit power that satisfies SINR(k)= for allk C [1, N] with inter-cell interference cancellation of v1 andv2 mirror users. Since gog, it is reasonable to cancel

the message of v, mirror user first, and then decode thatof the v2 mirror user to make 1v2l > I2 under the given

{P7(,kk C [IYN}. 'v and 1v2 are the total interference

-yNo I I I

gul~~9u1++79uJu

{ -L)L-,,g2 I(+ 7gul ]

when BSA decodes the v, and, V2 mirror users' message,respectively. With this ordering, the SINR values for mirrorusers are balanced, so that it is more likely to satisfy theSINR constraints in (7). Therefore, I° should be ordered tomeet the condition, 9° >) g9°° (2) > ... > 97((M)

In conclusion, the ord.ered. set and, Ho should satisfy9PT(1) > 91 (2) > p..> 9,(N) and goo(,) > 9 2) > * >9gr(M)' respectively. Since the serving users and its mirrorusers are located symmetrically, 7T0(k) is equal to (N + 1-

7r(k)) for all k C [1, M]. Applying this relationship to (10),the transmit power of -r(k)t" user can be represented as

PT(k)I (1 1 k -1

9,(k) ±1+

-yNo) (14)( 1 +-y I N -a yN-MA (__ g)1 M

The SINR condition for the M mirror users can also besimplified by applying 7w(k) = N + 1 -7r(k) to (4) and, (7),

SINR° (k)9"r(k) P7r(k)

1i PiV +F-I p

Vke[N+1 VtMNJ (15)

B. Efficient Power Allocation for Saving Total Power Con-sumption

In this section, we propose a suboptimal algorithm to findthe maximum number of mirror users which are canceled

before intra-cell interference. The corresponding power al-location is also be determined. The ordered set HI, which issuggested in the previous section, is used in the following

Lemma 2. Since gr( ) > 97(2) > > 97r(N) in H1,o > go >o... > go Therefore we will97(N) ' 7(N-1) ' - 7(i)- 1leeoe ew

cancel inter-cell users in the descending order from r(N)to F(N + V-tM), where is the number of inter ce'll users

which are canceled.

There exists an upper bound for t, denoted by tupper.

Mupp, is the number of the mirror users whose channel

ISBN 978-89-5519-131-8 93560

1

-7 1)7r(1)

9 -T97r(1)

jP.j=l

A

zf)JJ1ij=l

-7(i + 9 7r (N) )

Pu2)

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20 1.4N No Inter-Cell SIC

1.3 1.4 1.5 1.6~~~~Z 1.2 . ..

M,

. Inter-Cell SICpppr u~15M1.~~~~~~10~ ~ ~ ~

~0.6

0.4

0.2

0 01.3 1.4 1.5 1.6 1.3 1.4 1.5 1.6

Overlap factor, cx Overlap factor, cx

Fig. 4. The effec of ov~xerlap factor in the reduction ratio 4f transmit pow erper user.

8

MN. 6

= 5

P |: 3

~2I

'u 0.8

- 0.6._

= 0.4

o= 0.2

_ No Inter-Cell SIC= Inter-Cell SIC

Fig. 3. Flow chart for determining the maximum value of M. 0.4 0.6 0.8Loading factor

0.4 0.6 0.8Loading factor

gain meets the condition 9w',(k) > 9T(k) For all k C [N +1I-M, ], in order to be SINRT(k) SINR, (k) = itis necessary to satisfy 9w(k) > 9f(k)

Lemma 2: If SINR in (15) is larger than y assumingMo + 1 mirror users were canceled, i.e., M Mo + 1, with{p( 0+1) k C [1, N]}, then the target SINR is also satisfied,for tehe case assuming NO mirror users were canceled, i.e.,

M NMo, with {P(<)), [1,NI}. P(<) denotes theassigned power of the 7r(k)t 1 serving user assuming Mmirror users were canceled.

Proof: From (14), PY) = pP( for all k C[1, N], where p(O < p < 1) does not depend on k. By sub-stituting P(m/ ') and P Mf)) in (15), and, using P(M7/))PPjo), we can get SINRO(vIo+1) < SINRo(Mo) for all

7(k 7 ~~~~(k) Tr(k)

k C [N + -Mo,N]. SINRJ(km) is the SINR of the7r(k)t 1 mirror user, assuming M mirror users were canceled.Therefore, if SINR° mo+') > -y Vk C [N + 1 (MN

1),N, then SINR(Mj) > Vyk C UN + -Mo N]. Inconclusion, if it is possible to employ SIC for (Mo + 1)mirror users then it is also possible to employ SIC formirror users.

Based on Lemma 2 a suboptimal algorithm to determineNIma, is proposed in Fig. 3, where Nmax, denotes the num-

ber of the mirror users that can be decoded and subtractedat the serving BS.

It is assumed that the total number of users assigned, toeach BS is N. In Step 1, the initial value of M is set tozero. In Step 2, it is assumed that one more mirror user can

be decoded and subtracted The value of M is checked in

Fig. 5. The effect of loading factor in the reduction ratio of transmit power

per user.

Step 3, whether it exceeds the upper bound for M, denotedby MNupp,r, or not. If M < Mupper, the simulation proceedsto Step 4, but if this condition is not satisfied, MImax equalsMNupper. In Step 4, P,(k) is determined, by using (14) withthe assumed. value of NI. In Step 5, with given {fP((), k C[1, N]}, SINR for the mirror users are checked whether allthese values satisfy the target y, or not. If the condition issatisfied, simulation goes back to Step 2 to increase the valueof M, and to check whether or not these M mirror users can

be canceled, and decoded at the serving BS. If the conditionin Step 5 is not satisfied, the simulation is finished and M,ma,is set as (M- 1).

IV. SIMULATION RESULTS

In this section, computer simulation results are given toverify the effectiveness of inter-cell interference cancellationin the reduction of transmit power per user In order to verifythe effectiveness of inter-cell SIC scheme, the followingsimulations show the reduction ratio of transmit power

per user between the schemes with and without inter-cellSIC. Moreover, the reduction ratio of power is compared

according to different overlap factors and loading factors.The maximum number N of users in each cell the

maximum number M,,,,, of inter-cell users which can bedecoded and canceled, and the upper bound Mupper for Mare compared with respect to different overlap factor a whenonly intra-cell SIC is employed, in the left graph of Fig. 4.

ISBN 978-89-5519-131-8 93560

Mmax =M-1

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As two adjacent cells are more overlapped, the maximumnumber of users, which meet the target SINR and powerconstraints, decreases. It is because the effect of inter-cell interference increases with overlap factor a. However,the ratio of MIfax,, to N increases as two cells are moreoverlapped. Therefore, by employin'g inter-cell SIC scheme,the reduction ratio of power consumption per user increaseswith overlap factor a as shown in the right graph of Fig. 4.

Next, with fixed overlap factor a = 1.5, the effect ofloading factor on the number N of users in each cell andthe maximum number Mil of canceled inter-cell usersare analyzed in the left graph of Fig. 5. Mmax is slightlyincreased with the loading factor. The power saving ratio isalmost same for the loading factors from 0.4 to 1 as shownin the right graph of Fig. 5.

[7] J. Andrews, A. Agrawal, T. Meng, and J. Cioffi, "A simple It-erative Power Control for Successive Interference Cancellation,"IEEE Int. Symp. Spread Spectrum Techniques and Applications,vol. 3, pp. 761-765, 2002.

[8] A. Agrawal, J. G. Andrews, J. M. Cioffi and T. Meng, "IterativePower Control for Imperfect Successive Interference Cancella-tion." IEEE Trcans. Wirelss Communicaltion, vol. 4, Issue 3, pp.

878-884, May 2005.[9] H. Li, H. V Poor, "Power Allocation, Decoding Order

and Spectral Efficiency of Successive Interference CancellationBased Multirate DS-CDMA Systems," IEEE Conf Globecom,pp. 774-778, June 2004.

[10] S. Shamai and S. Verdu, "The impact of frequency-flat fadingon the spectral efficiency of CDMA," IEEE Trans. Inform.Theory, vol 47, pp. 1302-1327, Mar. 2001.

V. CONCLUSIONS

A new inter- and intra-cell SIC scheme, which reducestotal transmit power compared to the general intra-cell SICscheme, is proposed. Power and decoding order for inter- andintra-cell users are jointly determined in order to minimizetotal power consumption. A suboptimal algorithm to find themaximum number of inter-cell users, which can be decodedand canceled at the serving base station, is suggested. Byusing this algorithm, we show that the proposed SIC schemeimproves system perforimance.

ACKNOWLEDGEMENT

This work was supported by the center for BroadbandOFDM Mobile Access (BrOMA) at POSTECH through theITRC program of the Korean MIC, supervised by IITA.(IITA-2006-C1090-0603-0037) and by the Basic ResearchProgram of the Korea Science & Engineering Foundation(RO1 -2006-000-11112-0).

REFERENCES[1] P. Bender et al, "CDMA/HDR A Bandwidth Efficient High

Speed Wireless Data Service for Nomadic Users" IEEE Com-munications Magazine, 2000.

[2] D. M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, R.ViJayakumar, and P. Whiting, "CDMA Data QoS Schedulingon the Forward Link with Variable Channel Conditions," BellLabs Technical Memo Ao. 10009626-000404-O5TA, 2000.

[3] F. Berggren and S. L. Kim, "Energy-Efficient Control ofRate and Power in DS-CDMA Systems," JEEE Transactionson Wireless Communication vol 3 NO 3 pp. 725-733 May2004.

[4] K. Kumaran and L. Qian, "Uplink Scheduling in CDMAPacket Data Systems," JEEEL nfocom, vol. 1, pp 292 300, Mar2004.

[5] H. Nie, P. T. Mathiopoulos and G. K. Karagiannidis, "Re-verse Link Capacity Analysis of Cellular CDMA Systems withControlled Power Disparities and Successive Interference Can-cellation" IEEE Tiransactions on Wireless Communication, vol.5 NO.9 pp. 292-300 pp. 2447-2457 Sep 2006.

[6] F. Berggren and S. Ben Slimane, "Power Allocation for aSimple Successive Interference Cancellation Scheme in a Multi-Rate DS-CDMA System." IEEE Int. Conf Communication, vol.1, pp. 351-355 Apr 2002.

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