Soft Handover Overhead Reduction by RAKE Reception With Finger Reassignment

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 2, FEBRUARY 2008 213

Soft Handover Overhead Reduction byRAKE Reception with Finger Reassignment

Seyeong Choi, Member, IEEE, Mohamed-Slim Alouini, Senior Member, IEEE,Khalid A. Qaraqe, Senior Member, IEEE, and Hong-Chuan Yang, Senior Member, IEEE

Abstract— We propose and analyze in this paper a new fingerassignment technique that is applicable for RAKE receivers whenthey operate in the soft handover (SHO) region. This schemeemploys a new version of generalized selection combining (GSC).More specifically, in the SHO region, the receiver uses by defaultonly the strongest paths from the serving base station (BS)and only when the combined signal-to-noise ratio (SNR) fallsbelow a certain pre-determined threshold, the receiver uses moreresolvable paths from the target BS to improve the performance.Hence, relying on some recent results on order statistics weattack the statistics of two correlated GSC stages and providethe approximate but accurate closed-form expressions for thestatistics of the output SNR. By investigating the tradeoff amongthe error performance, the path estimation load, and the SHOoverhead, we show through numerical examples that the newscheme offers commensurate performance in comparison withmore complicated GSC-based diversity systems while requiringa smaller estimation load and SHO overhead.

Index Terms— Fading channels, diversity techniques, RAKEreceiver, generalized selection combining (GSC), performanceanalysis.

I. INTRODUCTION

IN wideband code division multiple access (WCDMA)systems and ultra wideband (UWB) systems, the diversity

branches correspond to the different resolvable multi-pathsand RAKE reception, with several baseband correlators calledfingers, is used to combine these paths in order to increase theoverall signal-to-noise ratio (SNR) and to lower the probabilityof deep fades [1, Section 9.5.1]. If there are j resolvablepaths, the optimal number of fingers is j, but due to receivercomplexity and processing power constraints (especially formobile units), we assume that i (≤ j) fingers are employedby the RAKE receiver. Usually, the mobile unit receiver islimited to 3 fingers while the base station (BS) receiver can use4 or 5 fingers depending on the equipment manufacturer [2].Note that in the handover (HO) region the number of available

Paper approved by R. Schober, the Editor for Modulation and Signal Designof the IEEE Communications Society. Manuscript received June 1, 2006;revised October 11, 2006. This paper is an extended version of work thatwas presented at the 10th IEEE International Conference on CommunicationSystems 2006 (ICCS’2006), Singapore, Nov. 2006. This work was supportedin part by the Qatar Foundation for Education, Science, and CommunityDevelopment, Qatar, in part by Qatar Telecom (Qtel), Qatar, and in part bya startup fund from the University of Victoria and a Discovery Grant fromNSERC, Canada.

S. Choi, M.-S. Alouini, and K. A. Qaraqe are with the Department ofElectrical Engineering, Texas A&M University at Qatar, Education City,Doha, Qatar (e-mail: {seyeong.choi, alouini, khalid.qaraqe}@qatar.tamu.edu).

H.-C. Yang is with the Department of Electrical and Computer Engineering,University of Victoria, BC, V8W 3P6, Canada. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCOMM.2008.060340.

resolvable paths can be quite high since they can come fromthe serving BS as well as the target BS. Hence, it is naturalto consider how to judiciously select a subset of paths forRAKE reception in the soft HO (SHO) region in order forthe receivers to achieve the required performance while (i)maintaining a low complexity and low processing powerconsumption and (ii) using a minimal amount of additionalnetwork resources.

Many newly proposed low complexity combining ap-proaches can be used for our problem of interest (i.e., combin-ing in the SHO region) [3]–[12]. Among them is generalizedselection combining (GSC) [3]–[6] which is a generalizationof selection combining (SC) and which chooses a fixednumber of paths with the largest instantaneous SNR fromall available diversity paths and then combines them as perthe rules of maximal ratio combining (MRC). As a power-saving implementation of GSC, minimum selection GSC(MS-GSC) [7]–[9], minimum estimation and combining GSC(MEC-GSC) [10], and output-threshold GSC (OT-GSC) [11],[12] were recently proposed. While these combining schemescan be applicable for our problem of interest, the way theyoperate does not make them distinguish the resolvable pathscoming from the serving and the target BS. As such, if theyare used without any modification or adaptation to the SHO,they end up using continuously the hardware/transmissionresources of the serving and the target BS and result thereforein a considerable increase in overhead on the network (knownas SHO overhead [13, Section 9.3.1.4]).

In this paper, we propose and study a new fingerreassignment-based scheme that is specifically applicable forRAKE reception in the SHO region. With this scheme, weassume that the Lc out of total L resolvable paths fromthe serving BS are by default assigned to the RAKE fingersof the mobile unit in the SHO region following Lc/L-GSCtype of combining. Only when the output SNR falls below apredetermined fixed SNR threshold (known also as a targetSNR), the receiver asks for the additional resources from thetarget BS. More specifically, the receiver scans the additionalLa resolvable paths from the target BS and selects againthe strongest Lc paths but now among the L + La availablepaths (i.e., the receiver uses Lc/(L + La)-GSC). Unlike MS-GSC and OT-GSC, our proposed scheme always uses a fixednumber of fingers, i.e., Lc, but as we will show in theperformance results section, it can reduce the unnecessarypath estimations and the SHO overhead compared to theconventional GSC.

0090-6778/08$25.00 c© 2008 IEEE

Authorized licensed use limited to: Texas A M University. Downloaded on January 26, 2010 at 05:59 from IEEE Xplore. Restrictions apply.

214 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 2, FEBRUARY 2008

The main contribution of this paper is to derive the statisticsof the receiver output SNR for our newly proposed scheme,including its probability density function (PDF), cumulativedistribution function (CDF), and moment generating function(MGF). We provide not only the analytical framework thatleads to exact but complicated expressions but also an al-ternative approximate approach which yield relatively simpleexpressions that come close to the exact solutions. Theseresults are then used (i) to analyze the performance in termsof the average probability of error and (ii) to investigate thetradeoff between complexity and performance. Some selectednumerical results show that in poor channel conditions ourscheme can essentially give the same performance as the GSCscheme while it offers in good channel conditions a smallerpath estimation load and considerable reduction in the SHOoverhead. To simplify our analysis and make it tractable, weassume that the receiver operates over a “perfect” uniformpropagation delay profile provided by a multi-path searcher ina way that the multi-path components are correctly assignedto the RAKE fingers.

The remaining of this paper is organized as follows. InSection II, we present the system and channel model underconsideration as well as the mode of operation of the proposedscheme. Based on this mode of operation, we derive the ex-pressions for the statistics of the combined SNR in Section III.These results are next applied to the performance analysis ofthe proposed system in Section IV. This section also illustratesthe tradeoff of complexity versus performance by comparingthe number of path estimations and the SHO overhead ofour proposed systems to that of conventional GSC and MRC.Finally, Section V provides some concluding remarks.

II. FINGER REASSIGNMENT-BASED RAKE COMBINING

A. System and Channel Model

We consider a multi-cell CDMA system with universalfrequency reuse. Each cell uses different sets of spreadingcodes to control the intercell interference. We focus on thereceiver operation when the mobile unit is moving from thecoverage area of its serving BS to that of a target BS. Weassume that the mobile unit is equipped with an Lc fingerRAKE receiver and is capable of despreading signals fromdifferent BSs using different fingers, and thus facilitatingSHO. The RAKE receiver also implements a GSC-based pathselection mechanism to select the Lc best paths for RAKEcombining among all the resolvable paths.

Note that in the SHO region the mobile unit is of roughlythe same long distance from the serving and the target BSs. Wefurther assume that the average signal strength on a path fromboth BSs is the same. As such, we assume that the receivedsignals on all the resolvable paths from the serving and thetarget BSs experience independent and identically distributed(i.i.d.) Rayleigh fading1. Let γi denote the instantaneousreceived SNR of the ith resolved path. Then, γi follows thesame exponential distribution, with common PDF and CDF

1In [14], more practical channel environments, such as non-identical/correlated fading channels and outdated channel estimation,are considered.

given as [1, Eq. (6.5)]

fγi(x) =

1γ

exp(−x

γ

), x ≥ 0 (1)

and

Fγi(x) = 1 − exp

(−x

γ

), x ≥ 0, (2)

respectively, where γ is the common average faded SNR.

B. Mode of Operation

We assume without loss of generality that in the SHOregion, the mobile unit resolves L multi-paths from the servingBS and La additional paths from the target BS. As the mobileunit enters the SHO region, the RAKE receiver relies at firston the L resolvable paths gathered from the serving BS andas such starts with Lc/L-GSC. If we let Γi:j be the sum ofthe i largest SNRs among j ones, i.e., Γi:j =

∑ik=1 γk:j

where γk:j is the kth order statistics (see [5] for terminology),then the total received SNR after GSC is given by ΓLc:L. Atthe beginning of every time slot, the receiver compares thereceived SNR, ΓLc:L, with a certain target SNR, denoted byγT . If ΓLc:L is greater than or equal to γT , a one-way SHO2

is used and no finger reassignment is needed. On the otherhand, whenever ΓLc:L falls below γT , a two-way SHO3 isattempted. In this case, the RAKE reassigns its Lc fingers tothe Lc strongest paths among the L + La available resolvablepaths (i.e., the RAKE receiver uses Lc/(L + La)-GSC). Nowthe total received SNR is given by ΓLc:L+La

.Based on the above mode of operation, we can see that the

final combined SNR, denoted by γt, is mathematically givenby

γt =

{ΓLc:L+La

, 0 ≤ ΓLc:L < γT ;ΓLc:L, ΓLc:L ≥ γT .

(3)

III. STATISTICS OF THE COMBINED SNR

Although the mode of operation in (3) describes a schemethat essentially switches between Lc/L-GSC and Lc/(L +La)-GSC depending on the channel conditions, we can notobtain the statistics of γt directly from the statistics of theoutput SNR with conventional GSC. Hence, in this section,we rely on some recent results on order statistics [8], [12] toderive the statistics of the combined SNR, γt.

A. CDF

From (3), the CDF of γt, Fγt(x), can be written as

Fγt(x) = Pr [γt < x]

= Pr [γT ≤ ΓLc:L < x]+ Pr [ΓLc:L+La

< x,ΓLc:L < γT ] . (4)

Since it is clear that ΓLc:L ≤ ΓLc:L+La, we can rewrite

Pr [ΓLc:L+La< x,ΓLc:L < γT ] in (4) as shown in (5). Sub-

stituting (5) into (4), we can express the CDF of γt, Fγt(x),

as shown in (6). To obtain a closed-form expression for

2One-way SHO refers to the scenario in which the mobile unit is connectedonly to the serving BS while being in the SHO region.

3Two-way SHO refers to the scenario in which the mobile unit is connectedto the serving and the target BSs while being in the SHO region.


CHOI et al.: SOFT HANDOVER OVERHEAD REDUCTION BY RAKE RECEPTION WITH FINGER REASSIGNMENT 215

Pr [ΓLc:L+La< x,ΓLc:L < γT ] =

⎧⎪⎨⎪⎩

Pr [ΓLc:L+La< x] , 0 ≤ x < γT ;

Pr[ΓLc:L+La< γT ]

+ Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ] , x ≥ γT

(5)

Fγt(x) =

⎧⎪⎨⎪⎩

Pr [ΓLc:L+La< x] , 0 ≤ x < γT ;

Pr [γT ≤ ΓLc:L < x] + Pr[ΓLc:L+La< γT ]

+ Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ] , x ≥ γT

(6)

Fγt(x), we just need to find a closed-form expression of

the joint probability, Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ], in

(6). This joint probability can be calculated as

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ]

= Pr[ΓLc:L < γT ] Pr [γT ≤ ΓLc:L+La< x|ΓLc:L < γT ]

= Pr[ΓLc:L < γT ]∫ x

γT

fΓLc:L+La |ΓLc:L<γT(y0)dy0. (7)

By recursively performing the following integration

fΓLc:L+2|ΓLc:L<γT(y0)

=∫ ∞

0

fΓLc:L+2,ΓLc:L+1(y0, y1)fΓLc:L+1|ΓLc:L<γT(y1)dy1,

(8)

we can express the conditional PDF in (7), for the generalvalue of La (≥ 2), as shown in (9). Even though the jointPDFs and the conditional PDF in (9) are available in closed-form using some results that will be shown in what follows,the resulting expressions are complicated and quite tediousto obtain. Here, we rather use in what follows another ap-proximate approach which leads to results that are very closeto the exact solutions as we will demonstrate it by computersimulations in Section IV.

Going back to Eq. (7) and based on thederivation in the Appendix, we can show thatPr [γT ≤ ΓLc:L+La

< x,ΓLc:L < γT ] can be expressedapproximately as shown in (10). Substitution (10) into (6)gives the CDF of γt, Fγt

(x), as shown in (11), where

J (x) = Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 < γT ] . (12)

Although (11) looks more complicate than (6), it actuallyleads to the desired final result, as we show in what follows.Since for i.i.d. Rayleigh fading channels, all probabilities,Pr[·], in (11) can be easily obtained by using the well-knownCDF of the GSC output SNR [15, Eq. (9.440)], we justneed to derive a closed-form expression for J (x) in (12).This joint probability can be expressed as shown in (13).Since all branch SNRs are i.i.d. random variables, γL+La

is independent of both ΓLc−1:L+La−1 and γLc:L+La−1. Assuch, we can compute the joint probability in (13) by usingthe joint PDF of ΓLc−1:L+La−1 and γLc:L+La−1, denoted byfγLc:L+La−1,ΓLc−1:L+La−1(y, z), and the single-branch CDF ofγL+La

, FγL+La(·), given in (2), as shown in (14). For i.i.d.

Rayleigh fading channels, it has been shown in [8, Eq. (9)]that the joint PDF in (14) is given by (15). After substitution(15) into (14) and integrations, we can obtain the closed-formexpression for J (x) as shown in (16), where

(A

a1,a2,··· ,an

)

is the multinomial coefficient, defined as(

Aa1,a2,··· ,an

)=

A!a1!a2!···an! , A =

∑nw=1 aw. Hence, we can obtain the closed-

form expression for the CDF of γt by substituting (16) in(11).

B. PDF

Differentiation of (11) gives the PDF of γt, fγt(x), as

shown in (17), which leads to (18). For i.i.d. Rayleigh fadingchannels, fΓi:j (x) and FΓi:j (x) are the well-known PDF andCDF of i/j-GSC output SNR which can be found in [15, Eqs.(9.433)(9.440)], respectively.

C. MGF

Substituting (18) into (17) leads to the desired closed-formexpression for the PDF of the proposed scheme. With this PDFin hand, the MGF of γt, Mγt

(s) =∫∞0

esxfγt(x)dx, can be

obtained in closed-form after lengthy and tedious calculationsas

Mγt(s) = A(Lc : L + La, 0, s) + A(Lc : L, γT , s)

− 1 − B(Lc : L, γT )1 − B(Lc : L + La − 1, γT )

× (A(Lc : L + Lc, γT , s) − C(γT , s)) , (19)

which leads to (20), (21), and (22), and where Γ[·, ·] andγ[·, ·] are the upper and lower incomplete gamma functions,respectively, defined as [16, Eq. (8.350)]

Γ[α, β] =∫ ∞

β

e−ttα−1dt, γ[α, β] =∫ β

0

e−ttα−1dt.

(23)

IV. PERFORMANCE RESULTS

In this section, we apply the closed-form results fromthe previous section for the performance analysis of ourproposed combining scheme over Rayleigh fading channels.More specifically, we first examine its average bit error rate(BER) by using the well-known MGF-based approach [15,Sec. 9.2.3]. We then look into the average number of pathestimations and the SHO overhead it requires.

A. Average BER Comparison with MRC and GSC

First, we consider the relationship between the number ofresolvable paths from the serving BS and the average BERperformance. In Fig. 1, the average BER of binary phaseshift keying (BPSK) versus the average SNR per path, γ,of the proposed scheme for various values of L over i.i.d.



fΓLc:L+La |ΓLc:L<γT(y0) (9)

=∫ ∞

0

· · ·∫ ∞

0︸︷︷︸La−1 folds

L+La−1∏j=L+1

fΓLc:j+1,ΓLc:j (yL+La−j−1, yL+La−j)fΓLc:L+1|ΓLc:L<γT(yLa−1)dy1 · · · dyLa−1

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ] = Pr [γT ≤ ΓLc:L+La

< x] − 1 − Pr[ΓLc:L < γT ]1 − Pr[ΓLc:L+La−1 < γT ]

× (Pr [γT ≤ ΓLc:L+La< x] − Pr [γT ≤ ΓLc:L+La

< x,ΓLc:L+La−1 < γT ]) (10)

Fγt(x) =

⎧⎪⎨⎪⎩

Pr [ΓLc:L+La< x] , 0 ≤ x < γT ;

Pr [γT ≤ ΓLc:L < x] + Pr[ΓLc:L+La< γT ] + Pr[γT ≤ ΓLc:L+La

< x]− 1−Pr[ΓLc:L<γT ]

1−Pr[ΓLc:L+La−1<γT ] (Pr[γT ≤ ΓLc:L+La< x] − J (x)) , x ≥ γT

(11)

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 < γT ] = Pr [γT ≤ ΓLc−1:L+La−1 + γL+La

< x,ΓLc−1:L+La−1 + γLc:L+La−1 < γT ](13)

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 < γT ] (14)

=∫ γT

Lc

0

∫ γT −y

(Lc−1)y

fγLc:L+La−1,ΓLc−1:L+La−1(y, z)(FγL+La(x − z) − FγL+La

(γT − z))dzdy

fγLc:L+La−1,ΓLc−1:L+La−1(y, z) (15)

=L+La−Lc−1∑

t=0

(−1)t(L + La − 1)!(z − (Lc − 1)y)Lc−2

(L + La − Lc − 1 − t)!(Lc − 1)!(Lc − 2)!t!γLce−

z+(t+1)yγ , y ≥ 0, z ≥ (Lc − 1)y

J (x) =(e−

γTγ − e−

xγ

)(γT

γ

)Lc L+La−Lc−1∑t=0

Lc−1∑u=0

(−1)t+u(

L+La−1Lc,L+La−Lc−t−1,t

)(Lc − u − 1)! ((t + 1)γT /(γLc))

u+1

×[1 − e−

(t+1)γTγLc

u∑v=0

((t + 1)γT

γLc

)v

/v!

](16)

fγt(x) =

⎧⎨⎩fΓLc:L+La

(x), 0 ≤ x < γT ;

fΓLc:L(x) + fΓLc:L+La(x) − 1−FΓLc:L (γT )

1−FΓLc:L+La−1 (γT )

(fΓLc:L+La

(x) − I(x)), x ≥ γT

(17)

I(x) =d

dxJ (x) =

1γ

e−xγ

(γT

γ


Lc−1∑u=0

(−1)t+u(


)(Lc − u − 1)! ((t + 1)γT /(γLc))

u+1

×[1 − e−

(t+1)γTγLc

u∑v=0

((t + 1)γT

γLc

)v

/v!

](18)

A(i : j, k, s) =∫ ∞

k

esxfΓi:j (x)dx =(

j

i

)[Γ [i, (1 − sγ)k/γ](i − 1)!(1 − sγ)i

+j−i∑l=1

(−1)i+l−1

(j − i

l

)(i

l

)i

×(

ek(s− 1γ − l

iγ )

1 + i(1 − sγ)/l+

i−2∑m=0

(l

i(sγ − 1)

)m+1 Γ [m + 1, (1 − sγ)k/γ]m!

)](20)



B(i : j, k) = FΓi:j (k) =∫ k

0

fΓi:j (x)dx =(

j

i

)[γ [i, k/γ](i − 1)!

+j−i∑l=1

(−1)i+l−1

(j − i

l

)(i

l

)i

×(

1 − e−(1+ li ) k

γ

(1 + i/l)−

i−2∑m=0

(−1)m

(l

i

)m+1γ [m + 1, k/γ]

m!

)](21)

C(k, s) =∫ ∞

k

esxI(x)dx =ek(s− 1

γ )

1 − sγ

(γT

γ


Lc−1∑u=0

(−1)t+u(


)(Lc − u − 1)! ((t + 1)γT /(γLc))

u+1

×[1 − e−

(t+1)γTγLc

u∑v=0

((t + 1)γT

γLc

)v

/v!

](22)

−10 −5 0 5 10 1510

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Average SNR per Path [dB]

Ave

rage

BER

Lc−fold MRC (Lc/3−GSC)

Lc/(3+La)−GSC

Lc/(4+La)−GSC

Lc/(5+La)−GSC

Proposed Scheme (L=3)Proposed Scheme (L=4)Proposed Scheme (L=5)Simulation Results

Fig. 1. Average BER of BPSK versus the average SNR per path, γ, withMRC, GSC, and the proposed scheme for various values of L over i.i.d.Rayleigh fading channels when Lc = 3, La = 2, and γT = 5 dB.

Rayleigh fading channels is plotted. For comparison purpose,we also plot the average BER of BPSK with Lc-MRC andLc/(L + La)-GSC. In this graph, we set Lc = 3, La = 2,and γT = 5 dB. The simulation result for the case of L = 4shows that our alternative simple approach is indeed a goodapproximation4. It is clear from this figure that our proposedscheme always outperforms MRC. Also it is very interestingto note that when the channel condition is poor, i.e, γ isrelatively small compared to γT , our scheme has the sameerror performance as GSC. This behavior can be explainedas follows. When γ is small compared to γT , our proposedscheme acts most of the times as Lc/(L + La)-GSC sinceLc/L-GSC output SNR has a high chance of not exceedingthe required target SNR. On the other hand, in good channelconditions, our scheme shows a higher error probability. Thisis because when γ becomes larger, the combined SNR ofLc/L-GSC has a higher chance to exceed the target SNR, γT ,and as such does not need to rely on the additional resolvable

4We note that all other numerical evaluations obtained from the analyticalresults derived in this paper have been also compared by Monte Carlosimulations of the system under consideration in order to justify our approach.

−10 −5 0 5 10 15 2010

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100


Ave

rage

BER

Lc−fold MRC

Lc/L−GSC

Lc/(L+1)−GSC

Lc/(L+2)−GSC

Lc/(L+3)−GSC

Proposed Scheme (La=1)



Fig. 2. Average BER of BPSK versus the average SNR per path, γ, withMRC, GSC, and the proposed scheme for various values of La over i.i.d.Rayleigh fading channels when L = 4, Lc = 3, and γT = 5 dB.

paths from the target BS. Hence, we can conclude that ourproposed combiner relies on the additional resources providedby the target BS only in poor channel conditions. For a betterunderstanding of our scheme, we study when L is fixed andLa is variable in what follows.

Fig. 2 shows the average BER of BPSK with MRC, GSC,and the proposed combining scheme versus the average SNRper path, γ, for various values of La over i.i.d. Rayleigh fadingchannels when L = 4, Lc = 3, and γT = 5 dB. Similar trendsto those observed in Fig. 1 can also be seen in this figure, butsince L is fixed, as one expects intuitively, all the curves ofour proposed scheme are converging to the case of Lc/4-GSCin the higher average SNR region.

We now study the average BER dependence on the thresh-old SNR, γT . Fig. 3 represents the average BER of BPSKversus the average SNR per path, γ, with MRC, GSC, and theproposed scheme for various values of γT over i.i.d. Rayleighfading channels when L = 4, Lc = 3, and La = 2. Fromthis figure, it is clear that the higher the threshold, the betterthe performance, as one expects. However, high thresholdsincrease the path estimation load. We examine in what follows



−10 −5 0 5 10 15 2010

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100


Ave

rage

BER

Lc−fold MRC

Lc/L−GSC

Lc/(L+L a)−GSC

Proposed Scheme ( γT=0 dB)



Fig. 3. Average BER of BPSK versus the average SNR per path, γ, withMRC, GSC, and the proposed scheme for various values of γT over i.i.d.Rayleigh fading channels when L = 4, Lc = 3, and La = 2.

this issue in details.

B. Average Number of Path Estimations

With the proposed scheme, the RAKE receiver estimatesL paths in the case of ΓLc:L ≥ γT or L + La in the caseof ΓLc:L < γT . Hence, we can easily quantify the averagenumber of path estimations, denoted by NE , as

NE = L·Pr [ΓLc:L ≥ γT ]+(L+La)·Pr [ΓLc:L < γT ] , (24)

which reduces to

NE = L + La · FΓLc:L(γT ), (25)

where FΓLc:L(γT ) can be calculated from (21) for i.i.d.Rayleigh fading channels. Note that Lc-MRC and Lc/(L +La)-GSC always require Lc and L + La estimations, respec-tively. Fig. 4 shows the average number of path estimationsversus the output threshold, γT , with MRC, GSC, and theproposed scheme for various values of La over i.i.d. Rayleighfading channels when L = 4, Lc = 3, and γ = 0 dB.For a better illustration of the tradeoff between complexityand performance, Fig. 5 shows the average BER of BPSKversus the output threshold, γT , with MRC, GSC, and theproposed scheme. As we can see, the error rate of the proposedscheme decreases to that of Lc/(L+La)-GSC when the outputthreshold increases. Considering Figs. 4 and 5 together, weobserve that the proposed scheme can save a certain amountof estimation load with a slight performance loss compared toGSC if the required threshold is 2 to 6 dB above γ for ourchosen set of parameters.

C. SHO Overhead

In this section, we investigate the probability of the SHOattempt and the SHO overhead. In our proposed scheme,the SHO is attempted whenever ΓLc:L is below γT . Hence,the probability of the SHO attempt is same as the outage

−6 −4 −2 0 2 4 6 8 10 12 142.5

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Output Threshold, γT [dB]

Ave

rage

Num

ber o

f Pat

h Es

timat

ion

Lc −fold MRC

Lc /(L+La )−GSC

Proposed Scheme

La

=1

La

=2

La

=3

Fig. 4. Average number of path estimations versus the output threshold, γT ,with MRC, GSC, and the proposed scheme for various values of La overi.i.d. Rayleigh fading channels when L = 4, Lc = 3, and γ = 0 dB.

−6 −4 −2 0 2 4 6 8 10 12 1410

−3

10−2

Output Threshold, γT

[dB]

Ave

rage

BER

Lc−fold MRC

Lc/(L+L a)−GSC

Proposed Scheme

La=1

La=2

La=3

Fig. 5. Average BER of BPSK versus the output threshold, γT , with MRC,GSC, and the proposed scheme for various values of La over i.i.d. Rayleighfading channels with L = 4, Lc = 3, and γ = 0 dB.

probability of Lc/L-GSC evaluated at γT , i.e., FΓLc:L(γT ).The SHO overhead, denoted by β, is commonly used toquantify the SHO activity in a network and is defined as [13,Eq. (9.2)]

β =N∑

n=1

nPn − 1, (26)

where N is the number of active BSs and Pn is the averageprobability that the mobile unit uses n-way SHO.

1) La < Lc: Based on the mode of operation in SectionII-B, P1 and P2 can be defined as

P1 = Pr [ΓLc:L ≥ γT ] + Pr [ΓLc:L < γT , γLc:L ≥ γ1:La] ,(27)



−6 −4 −2 0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Output Threshold, γT

[dB]

SHO

Ove

rhea

d (β

)

Lc/(L+L a)−GSC

Proposed Scheme

La=1

La=2

La=3

Fig. 6. SHO overhead versus the output threshold, γT , with GSC and theproposed scheme for various values of La over i.i.d. Rayleigh fading channelswith L = 4, Lc = 3, and γ = 0 dB.

andP2 = 1 − P1, (28)

where γLc:L is the Lcth strongest path among L ones fromthe serving BS and γ1:La

is the strongest path among La onesfrom the target BS. Substituting (27) and (28) into (26), wecan express the SHO overhead, β, as

β = P1 + 2P2 − 1 (29)

= FΓLc:L(γT ) Pr [γLc:L < γ1:La|ΓLc:L < γT ] .

Since γ1:Lais independent to γLc:L and ΓLc:L,

we can calculate the conditional probability,Pr [γLc:L < γ1:La

|ΓLc:L < γT ], as

Pr [γLc:L < γ1:La|ΓLc:L < γT ]

=∫ ∞

0

FγLc:L|ΓLc:L<γT(x)fγ1:La

(x)dx. (30)

The conditional CDF in (30) can be written as shown in (31),where fγLc:L,ΓLc−1:L(y, z) can be obtained from (15). Aftersuccessive substitutions from (31) to (29), we can express theSHO overhead, β, as shown in (32). Finally, integrating (32),we can obtain the exact closed-from expression for the SHOoverhead, β [17].

2) La ≥ Lc: In this case, we need to consider the proba-bility that a call is completely handed over to the target BS.Hence, the joint probability, Pr[ΓLc:L < γT , γ1:L ≤ γLc:La

],should be added to P1 in (27) where γ1:L is the strongestpath among L ones from the serving BS and γLc:La

is theLcth strongest path among La ones from the target BS. Thisjoint probability is given by the analytical expression shownin (33), where fγ1:L,γ2:L,γ3:L,··· ,γLc:L(· · · ) is the joint PDF ofthe first Lc order statistics out of L ones [15, Eq. (9.420)].Unfortunately, it seems difficult to obtain a simple close-formexpression for this nested Lc + 1 multi-fold integral.

Fig. 6 shows the SHO overhead versus the output threshold,γT , with GSC and the proposed scheme for various values of

La over i.i.d. Rayleigh fading channels when L = 4, Lc = 3,and γ = 0 dB. The SHO overhead of Lc/(L + La)-GSC isplotted by calculating P1 and P2 as

P1 =

{Pr [γLc:L ≥ γ1:La

] , La < Lc;Pr [γLc:L ≥ γ1:La

] + Pr[γ1:L ≤ γLc:La], La ≥ Lc,

(34)and

P2 = 1 − P1. (35)

It is clear from this figure that we have a higher chance touse 2-way SHO, as the number of additional paths from thetarget BS increases. Note that our proposed scheme acts asLc/(L + La)-GSC when the output threshold is very high.Hence, we can observe that the SHO overhead of the proposedscheme converges to that of GSC as γT increases. From thisfigure together with Fig. 5, we can see the SHO overheadreduction of our proposed scheme. For example, if the requiredthreshold is 6 dB above γ, our scheme shows for La = 2around 0.55 SHO overhead while maintaining the same errorrate as GSC which requires 0.8 SHO overhead.

V. CONCLUSION

In this paper, we proposed a new finger assignment schemefor RAKE receivers in the SHO region. In this scheme, thereceiver checks the GSC output SNR from the serving BSagainst a certain pre-determined output threshold. If the outputSNR is below this threshold, the receiver performs a fingerreassignment after using GSC on the paths coming from theserving BS and the target BS. We derived the statistics of theoutput SNR of the proposed scheme in accurate approximateclosed-form, based on which we carried out the performanceanalysis of the resulting systems. We showed through nu-merical examples that the new scheme offers commensurateperformance in comparison with more complicated GSC-based diversity systems while requiring a smaller estimationload and SHO overhead.

APPENDIX

DERIVATION OF EQ. (10)

The joint probability Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ]

in (7) can be written as

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ]

= Pr[ΓLc:L < γT ] Pr [γT ≤ ΓLc:L+La< x|ΓLc:L < γT ] .

(36)

For simplicity, if we define the events A, B, and C as

A = γT ≤ ΓLc:L+La< x, (37)

B = ΓLc:L < γT , (38)

C = ΓLc:L+La−1 < γT , (39)

then (36) can be rewritten as (40), where C is the complemen-tary set of event C, i.e., C = ΓLc:L+La−1 ≥ γT . Since eventB includes event C, we have Pr[A|B,C] = Pr[A|C]. Notealso that when event B and event C happened, ΓLc:L andΓLc:L+La−1 are sums of different set of exponential randomvariables. Based on the memoryless property of exponentialrandom variables and noting that given that C happened after



FγLc:L|ΓLc:L<γT(x) =

Pr [γLc:L < x,ΓLc:L < γT ]Pr [ΓLc:L < γT ]

=Pr [γLc:L < x,ΓLc−1:L + γLc:L < γT ]

Pr [ΓLc:L < γT ](31)

=1

FΓLc:L(γT )

{∫ x

0

∫ γT −y

(Lc−1)yfγLc:L,ΓLc−1:L(y, z)dzdy, 0 ≤ x < γT

Lc;∫ γT /Lc

0

∫ γT −y

(Lc−1)yfγLc:L,ΓLc−1:L(y, z)dzdy, x ≥ γT

Lc

β =∫ γT

Lc

0

(fγ1:La

(x)∫ x

0

∫ γT −y

(Lc−1)y

fγLc:L,ΓLc−1:L(y, z)dzdy

)dx (32)

+[1 − Fγ1:La

(γT

Lc

)]∫ γTLc

0

∫ γT −y

(Lc−1)y

fγLc:L,ΓLc−1:L(y, z)dzdy

Pr[ΓLc:L < γT , γ1:L ≤ γLc:La] = (33)∫ ∞

0

∫ min[γT ,γLc:La ]

0

∫ min[γT −γ1:L,γ1:L]

0

∫ min[γT −γ1:L−γ2:L,γ2:L]

0

· · ·∫ min[γT −�Lc−1

j=1 γj:L,γLc−1:L]

0

fγLc:La(γLc:La

)fγ1:L,γ2:L,γ3:L,··· ,γLc:L(γ1:L, γ2:L, γ3:L, · · · , γLc:L)dγ1:Ldγ2:Ldγ3:L · · · dγLc:LdγLc:La

Pr [A,B] = Pr [B] Pr [A|B] (40)

= Pr [B](Pr [A|B,C] Pr [C|B] + Pr

[A|B,C

]Pr[C|B])

B, B may have little effect on A since a path reassignmenthappened, we have Pr[A|B,C] ≈ Pr[A|C]. Therefore, we canexpress (40) as shown in (41). Hence, the joint probability in(36) can now be written as shown in (42). Using the followingrelationships

Pr[ΓLc:L < γT |ΓLc:L+La−1 < γT ] = 1, (43)

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 ≥ γT ]

= Pr [γT ≤ ΓLc:L+La< x]

− Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 < γT ] , (44)

and

Pr[ΓLc:L < γT |ΓLc:L+La−1 ≥ γT ]

= 1 − 1 − Pr[ΓLc:L < γT ]1 − Pr[ΓLc:L+La−1 < γT ]

, (45)

we finally arrive at the desired result given in (10).

REFERENCES

[1] G. L. Stuber, Principles of Mobile Communication, 2nd ed. Norwell,MA: Kluwer Academic Publishers, 2001.

[2] [Online]. Available: http://www.cdmaonline.com/interactive/workshops/terms1/1035.htm

[3] T. Eng, N. Kong, and L. B. Milstein, “Comparison of diversity combin-ing techniques for Rayleigh-fading channels,” IEEE Trans. Commun.,vol. 44, no. 9, pp. 1117–1129, Sept. 1996.

[4] M. Z. Win and J. H. Winters, “Analysis of hybrid selection/maximal-ratio combining in Rayleigh fading,” IEEE Trans. Commun., vol. 47,no. 12, pp. 1773–1776, Dec. 1999.

[5] M.-S. Alouini and M. K. Simon, “An MGF-based performance analysisof generalized selection combining over Rayleigh fading channels,”IEEE Trans. Commun., vol. 48, no. 3, pp. 401–415, Mar. 2000.

[6] Y. Ma and C. C. Chai, “Unified error probability analysis for generalizedselection combining in Nakagami fading channels,” IEEE J. Select.Areas Commun., vol. 18, no. 11, pp. 2198–2210, Nov. 2000.

[7] S. W. Kim, D. S. Ha, and J. H. Reed, “Minimum selection GSC andadaptive low-power RAKE combining scheme,” in Proc. IEEE Int.Symp. on Circuit and Systems (ISCAS’03), May 2003.

[8] H.-C. Yang, “Exact performance analysis of minimum-selection general-ized selection combining (GSC),” in Proc. IEEE Int. Conf. on Commun.(ICC’05), May 2005.

[9] R. K. Mallik, P. Gupta, and Q. T. Zhang, “Minimum selection GSC inindependent Rayleigh fading,” IEEE Trans. Veh. Technol., vol. 54, no. 3,pp. 1013–1021, May 2005.

[10] M.-S. Alouini and H.-C. Yang, “Minimum estimation and combininggeneralized selection combining (MEC-GSC),” in Proc. IEEE Int. Symp.on Information Theory (ISIT’05), Sept. 2005.

[11] H.-C. Yang and M.-S. Alouini, “MRC and GSC diversity combiningwith an output theshold,” IEEE Trans. Veh. Technol., vol. 54, no. 3, pp.1081–1090, May 2005.

[12] L. Yang and H.-C. Yang, “Performance analysis of output-threshold gen-eralized selection combining (OT-GSC) over Rayleigh fading channels,”in Proc. IEEE Wireless Commun. & Networking Conf. (WCNC’06), Apr.2006.

[13] H. Holma and A. Toskala, WCDMA for UMTS, revised ed. New York,NY: John Wiley & Sons, 2001.

[14] S. Choi, M.-S. Alouini, K. A. Qaraqe, H.-C. Yang, and Y.-C. Ko, “Apractical study of adaptive finger reassignment and replacement in thesoft handover region,” in Proc. IEEE Int. Symp. on Signal Processingand its Applications (ISSPA’07), Feb. 2007

[15] M. K. Simon and M.-S. Alouini, Digital Communication over FadingChannels, 2nd ed. New York, NY: John Wiley & Sons, 2005.

[16] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, andProducts, Corrected and Enlarged ed. San Diego, CA: Academic, 1994.

[17] S. Choi, “Design and performance evaluation of rake finger managementschemes in the soft handover region,” Texas A&M University, tech. rep.for Ph.D. dissertation.



Pr [A,B] = Pr [B](Pr [A|C] Pr [C|B] + Pr

[A|C]Pr

[C|B])

= Pr [B]

(Pr [A,C]Pr [C]

Pr [B|C]Pr [C]Pr [B]

+Pr[A,C

]Pr[C] Pr

[B|C] Pr

[C]

Pr [B]

)(41)

= Pr [A,C] Pr [B|C] + Pr[A,C

]Pr[B|C]

Pr [γT ≤ ΓLc:L+La< x,ΓLc:L < γT ] (42)

= Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 < γT ] Pr[ΓLc:L < γT |ΓLc:L+La−1 < γT ]

+ Pr [γT ≤ ΓLc:L+La< x,ΓLc:L+La−1 ≥ γT ] Pr[ΓLc:L < γT |ΓLc:L+La−1 ≥ γT ]

Seyeong Choi (S’03, M’08) was born in Seoul,Korea. He received his B.S. and M.S. degrees fromHanyang University, Seoul, Korea, in 1996 and1998, respectively, and Ph.D. degree in Electricaland Computer Engineering from the Texas A&MUniversity, College Station, TX, in 2007. From1998 through 2001 he worked as a researcher atLGTeleCom’s Network R&D Center, Seoul, Ko-rea, operating the CDMA mobile communicationnetworks. His research interests include wirelesscommunications, MIMO fading channels, diversity

techniques, and system performance evaluation.

Mohamed-Slim Alouini (S’94, M’98, SM’03) wasborn in Tunis, Tunisia. He received the Ph.D. degreein Electrical Engineering from the California Insti-tute of Technology (Caltech), Pasadena, CA, USA,in 1998. He was an Associate Professor with thedepartment of Electrical and Computer Engineer-ing of the University of Minnesota, Minneapolis,MN, USA. Since July 2006, he has been withthe Electrical Engineering program of Texas A&MUniversity at Qatar, Education City, Doha, Qatar.His current research interests include the design and

performance analysis of wireless communication systems.

Khalid A. Qaraqe (M’97, SM’00) was born inBethlehem. Dr. Qaraqe received the B.S. degree inEE from the University of Technology, Baghdadin 1986, with honors, he received the M.S. degreein EE from the University of Jordan, Jordan, in1989, and he earned his Ph.D. degree in EE fromTexas A&M University, College Station, TX, in1997. From 1989 to 2004 Dr. Qaraqe has held avariety positions in many companies and he has over12 years of experience in the telecommunicationindustry. Dr. Qaraqe has worked for Qualcomm,

Enad Design Systems, Cadence Design Systems/Tality Corporation, STC,SBC and Ericsson. He has worked on numerous GSM, CDMA, WCDMAprojects and he has experience in product development, design, deployments,testing, and integration. Dr. Qaraqe joined the department of ElectricalEngineering of Texas A&M University at Qatar, in July 2004, where heis now a visiting associate professor. Dr. Qaraqe research interests includeperformance analysis of the 3G UMTS wireless communication, WCDMAestimation theories, Fading channels, Frequency hopping, and STTD diversity.

Hong-Chuan Yang (S’00, M’03, SM’07) was bornin Liaoning, China. He received the Ph.D. degreein Electrical Engineering from the University ofMinnesota, MN, USA in 2003. Dr. Yang is now anassistant professor of the Electrical and ComputerEngineering Department of the University of Victo-ria, Victoria, B.C., Canada. His research focuses ondifferent aspects of wireless and mobile communica-tions, with special emphasis on diversity techniques,cross-layer design, energy-efficient communications,and system performance evaluation. Dr. Yang is a

recipient of the Doctoral Dissertation Fellowship (DDF) Award from thegraduate school of the University of Minnesota for the 2002-2003 academicyear.


Soft Handover Overhead Reduction by RAKE Reception With Finger Reassignment

Documents

Transcript of Soft Handover Overhead Reduction by RAKE Reception With Finger Reassignment