Joint Downlink Power Control and Multicode Receivers for Downlink Transmissions in High Speed UMTS

Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2006, Article ID 79148, Pages 1–10DOI 10.1155/WCN/2006/79148

Joint Downlink Power Control and Multicode Receiversfor Downlink Transmissions in High Speed UMTS

Bessem Sayadi, Stefan Ataman, and Inbar Fijalkow

ETIS/ENSEA, University of Clergy-Pontoise/CNRS, 6 Avenue du Ponceau, 95014 Clergy-Pontoise, France

Received 30 September 2005; Revised 28 February 2006; Accepted 19 May 2006

We propose to combine the gains of a downlink power control and a joint multicode detection, for an HSDPA link. We proposean iterative algorithm that controls both the transmitted code powers and the joint multicode receiver filter coefficients for thehigh-speed multicode user. At each iteration, the receiver filter coefficients of the multicode user are first updated (in order toreduce the intercode interferences) and then the transmitted code powers are updated, too. In this way, each spreading code ofthe multicode scheme creates the minimum possible interference to others while satisfying the quality of service requirement. Themain goals of the proposed algorithm are on one hand to decrease intercode interference and on the other hand to increase thesystem capacity. Analysis for the rake receiver, joint multicode zero forcing (ZF) receiver, and joint multicode MMSE receiver ispresented. Simulation is used to show the convergence of the proposed algorithm to a fixed point power vector where the multicodeuser satisfies its signal-to-interference ratio (SIR) target on each code. The results show the convergence behavior for the differentreceivers as the number of codes increases. A significant gain in transmitted base station power is obtained.

Copyright © 2006 Bessem Sayadi et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

As wireless access to the internet rapidly expands, the needfor supporting multirate services (voice, data, multimedia,etc.) over limited spectrum increases. CDMA technologiesare being considered for third-generation wireless networks,UMTS. There are hence two channelization schemes forachieving multirate transmissions. The first, known as thevariable spreading factor scheme, achieves variable-data ratetransmission by assigning the radio link a single variable-length random spreading sequence. However, short codes,when subjected to a large delay-spread multipath channelloose their orthogonality and lead to a significant intersym-bol interference (ISI). To circumvent this limitation, we con-sider the second option called multicode transmission. Thehigh-rate data stream is split into several lower rate data sub-streams [1]. Each substream is spread by a specific spreadingsequence and all the substreams are then transmitted syn-chronously as virtual users. A future transmission mode suchas the high-speed downlink packet access (HSDPA [2]) willmake wide use of multicode to considerably increase the datarate in the downlink with a peak-data rate in the range of 10–14 Mbit/s. All the spreading sequences are orthogonal to eachother to avoid signal interference between parallel channel

codes in a synchronous multipath free channel. However,multipath propagation partially destroys the orthogonality ofthe multicode transmission and leads to a significant self in-tercode interference which increases with the number of par-allel codes for a multicode scheme. Therefore, the quality ofthe downlink under frequency selective fading environmentsis interference limited. In this paper, we consider a single cellenvironment where one or more users employ a multicodedownlink transmission.

In order to improve the quality of the downlink whichis typically defined in terms of the signal-to-interference ra-tio (SIR), a joint multicode reception was recently proposedin [3] with the assumption that the different codes have afixed transmitting power. Based on a description of the signalreceived over fading code-division multiple-access channel,where many different data rates are considered, it is shownin [3] that the problem of recovering the multicode user canbe expressed as a multiuser interference cancelation problem,where each channel code represents a virtual user.

Independently in literature, power control is proposed,classically for the link between the multiusers and the basestation (BS), to overcome the near-far problem, to maintainthe mobile station power consumption, and to reduce thecochannel interference. The power control approach assumes

2 EURASIP Journal on Wireless Communications and Networking

that a fixed receiver, usually the conventional (single user)receiver, is being used. It optimizes the communication be-tween the mobiles and the BS by controlling the transmittedpowers of the different users [4, 5].

Given the importance of power control, an extensive re-search is focused on this subject. In [6], two optimizationcriteria are considered in a single-cell case: minimizing totaltransmitted power and maximizing throughput. In [7], theoptimum power vector is given and also statistics on the re-ceived power are considered. A statistical approach of the op-timum power solution is developed in [8]. The existence (orfeasibility) of this optimal power allocation is also consideredin [7, 9]. A distributed and iterative power control algorithmwhere each user’s power converges to the minimum powerneeded to meet its quality of service (QoS) specification isproposed in [10]. A joint optimization of both receiver filtersand user transmit powers has been considered in [11] to findthe jointly optimum powers and linear MMSE (minimummean square error) filter coefficients. A similar approach isproposed in reference [12] where the authors employ a suc-cessive interference cancelation scheme. Recently, a unifiedapproach of the uplink power control that is applicable toa large family of multiuser receivers is proposed in [13, 14],based on the large system results published in [15].

Based on the fact that for a fixed base station assignmentthe feasibilities of uplink and downlink are equivalent (see[16] for more details), the authors in [16] present a jointpower control and base station assignment for the downlink.Many others researchers are interested on the study of thedownlink power control such as [17–19]. In [17], the authorsstudied the joint optimal power control and beamformingin wireless networks. In [18], the authors studied the down-link power control allocation for multiclass wireless systems.However, in the case of HSDPA system, the way the base sta-tion (BS) must allocate the power on the different codes inthe case of multicode transmission is still an open issue. Itis indeed desirable for the BS not to use more transmissionpower than what it needs to. This paper proposes a possibleway to solve this problem.

In order to achieve this goal, we propose in this paperto combine the downlink power control approach and thejoint multicode detection, presented in [3], for the multi-code user. We propose an algorithm which controls boththe transmitted code powers at the BS and the joint mul-ticode receiver filters implemented in the mobile. The re-sulted algorithm adapts the transmitted code’s powers tak-ing into account a multicode reception strategy at the mo-bile which aims to reduce the intercode interference. Math-ematically, the strategy involves two alternate optimizationproblems which are resolved iteratively in the proposed algo-rithm. At each iteration first the receiver filter coefficients ofthe multicode user are updated to reduce the intercode in-terference and then the transmitted code powers are updatedand assigned. So that, each spreading code of the multicodescheme creates the minimum possible interference to otherswhile satisfying the quality of service requirement. This al-gorithm has as main goals to decrease intercode interferenceand to increase the system capacity. Using downlink power

control, the BS output power is adapted to the radio link con-ditions.

The implementation of this approach, in the HSDPAmobile, requires interference measurements for each code.These measurements are envisaged in HSDPA standard [20].We show, using simulations, that the resulting algorithmconverges to a fixed point power vector where the multi-code user satisfies its signal-to-interference ratio (SIR) tar-get on each code. The feasibility of the proposed approachis based on the transmission of the requested code powervia a feedback link in order to update the BS output pow-ers. Such a feedback is considered in the HSDPA standardwhere the mobile transmits the channel quality indicator tothe base station [2]. In this study, we consider the case of thejoint zero forcing and the joint minimum mean square er-ror (MMSE) multicode linear receivers for various scenarioswhere we compare their performance to those obtained byconsidering a bank of rake receivers considered, here, as theconventional power control strategy.

The paper is organized as follows. Section 2 introducesthe proposed linear algebraic model which describes the sig-nal received over time-dispersive fading channel includinga hybrid multicode/variable spreading factor transmissions.Section 3 gives the problem statement. The proposed strat-egy is introduced in Sections 4 and 5, and its performance ina simplified HSDPA environment is assessed by means of nu-merical simulations in Section 6. Finally, Section 7 presentsour conclusions.

Throughout this paper scalars, vectors, and matrices arelower case, lower-case bold and upper-case bold characters,respectively. (·)T , (·)−1 denote transposition and inversion,respectively. Moreover, E(·) denotes the expected value op-erator.

2. SYSTEM MODEL

We assume a multicode CDMA frequency division duplexcellular system. In each cell, K mobile users, each employ-ing a different rate, communicate with a base station. Eachuser receives a frame with a standardized number of chipsdenoted by Nchip. Based on the quality of service required byuser k, the base station assigns Mk spreading codes, the pro-cessing gain is denoted by Gk, at the condition that Nchip =GkN

(k)bit where N (k)

bit is the number of transmitted symbols foruser k. Under the constraint that a constant chip rate, 1/Tc,where Tc denotes the chip period, must be maintained, thesymbol period, denoted here by Ts,k = GkTc, varies with therequested rate by user k. The index s is related to the symbolperiod and the index k is related to the kth user. In order tofacilitate the description, the terminologies defined in Table 1are used in the rest of this paper.

The path-loss attenuation between the BS and the kthuser is denoted by zk. In the no-shadowing scenario, the pathloss (PL) is modeled as a simple distance-dependent loss:

z(PL)k ≈ λd−σ

k (1)

Bessem Sayadi et al. 3

Table 1: Terminology description.

Notation Description

K the number of user

Nchip the number of chips in a one radio block

Gk the spreading factor assigned to the kth user

Mk the number of spreading code assigned to the kth user

N (k)bit

the number of bits or symbols transmitted in a

one radio block

Tc the common chip period

Ts,k the symbol period related to the kth user, 1 ≤ k ≤ K

zk the attenuation due to the path loss and the shadowing

L the number of paths

τi the delay of the ith path

p(k)m the power of the mth code, 1 ≤ m ≤Mk of the kth user

n the symbol index time

b(k) the transmitted symbol vector by the kth user

C(k) the spreading coding matrix related to the kth user

W(k) the code’s power matrix related to the kth user

H(k) the channel matrix related to the kth user

n the noise vector

or, in dB,

z(PL)k [dB] ≈ 10 log10(λ)− 10 · σ · log10

(dk), (2)

where the constants λ usually depend on the frequency used,as well as the height of the base station and the wirelessterminal. The dk is the distance from user k to the base sta-tion. The attenuation coefficient σ is usually between 2 and 6for most indoor and outdoor environments. The model pre-sented in (1) is a general form for the most empirical andsemiempirical path-loss attenuation model. For more details,the reader can refer to [21].

In the shadowing case (SH), the variation due to shadow-ing is added to the path-loss value to obtain the variations.Therefore, the path-loss can be modeled as the product of adistance-dependent path-loss attenuation and a random log-normally distributed shadowing effect [21]:

z(PL,SH)k ≈ λd−σ

k 10ξk/10, ξk ∼ N(0, σ2

ξ

)(3)

or, in dB,

z(PL,SH)k [dB] ≈ 10 log10(λ)− 10 · σ · log10

(dk)

+ ξk, (4)

where N (0, σ2ξ ) is the Gaussian density with mean 0 (in dB)

and variance σ2ξ (in dB). In the rest of the paper, we denote

z(PL,SH)k by zk.

The effect of the downlink multipath channel is repre-sented by a vector with L paths denoted, here, by

h = [α0,α1, . . . ,αL−1]T

(5)

with corresponding delays [τ0, . . . , τL−1]. Therefore, the

channel, corresponding to user k, is described as the follow-ing:

hk = zkh. (6)

The transmit power towards the kth user onmth code will be

denoted by p(k)m . The transmitted signal for the kth user can

be written as

yk(t) =Nbit,k−1∑

n=0

Mk∑

m=1

√p(k)m b(k)

m (n)c(k)m

(t − nTs,k

), (7)

where

c(k)m (t) =

Gk−1∑

q=0

c(k),(q)m ψ

(t − qTc

)(8)

with Gk the spreading factor for the kth user and b(k)m (n) is

the transmitted symbol at time n for the kth user on the

mth channel-code denoted by c(k)m (t) ·ψ is a normalized chip

waveform of duration Tc. The base-band received signal atthe desired user can be written as

r(t)

=K∑

k=1

zk

L−1∑

l=0

αl

Nbit,k−1∑

n=0

Mk∑

m=1

√p(k)m b(k)

m (n)c(k)m

(t−nTs,k−τl

)+n(t),

(9)

where n(t) is a zero-mean additive white Gaussian noise(AWGN) process.

The received signal is time-discretized at the rate of 1/Tc,leading to a chip-rate discrete-time model that can be writtenas

rl = r(lTc)

=K∑

k=1

zk

L−1∑

l=0

αl

Nbit,k−1∑

n=0

Mk∑

m=1

√p(k)m b(k)

m (n)c(k)m

((l−nGk−tl,k

)Tc)

+ n(lTc),

(10)

where tl,k = �τl/Gk� is the time-discretized path delay in sam-ple intervals (chip period).

Throughout the paper, we employ a block model. Theblocks of transmitted symbols for each user, k = 1, . . . ,K , areconcatenated in a vector:

b(k) =[b(k)

1 (0), . . . , b(k)Mk

(0), . . . , b(k)Mk

(N (k)

bit − 1)]T

(11)

containing N (k)bit bits transmitted with the different codes for

a given user, k.The transmission of the data sequence over the CDMA

channel can be expressed by the received sequence r [3]:

r = [r1, . . . , rNchip+L−1]T

=K∑

k=1

C(k)H(k)W(k)b(k) + n,(12)


where H(k)=diag(hk, . . . , hk) is of size (N (k)bit MkL,N (k)

bit Mk) and

W(k) = diag(P(k), P(k), . . . , P(k))

of size N (k)bit Mk where P(k) =

diag(√p(k)

1 ,√p(k)

2 , . . . ,√p(k)Mk

) and diag(X) represents the di-agonal matrix containing only the diagonal elements of thematrix X. The matrix C(k) represents the code matrix of size

((Nchip + L− 1),N (k)bit MkL) built as follows:

C(k) = [vk0,0,0, . . . , vkNbit,k−1,Mk−1,L−1

],

vkn,m,l =[

0TnGk, uk

T

m,l, 0T(Nbit,k−n−1)Gk

]T,

ukm,l =[

0Ttl , ckT

m , 0TL−tl−1

]T,

ckm =[ckm(1), . . . , ckm

(Gk)]T

,

(13)

where n=0, . . . ,Nbit,k−1,m=0, . . . ,Mk−1, and l=0, . . . ,L−1.0n denotes the null vector of size n. The vector n, of length

Nchip + L− 1, represents the channel noise vector with N0 asa power spectral density.

The vector c(k)m =[ckm(1), . . . , ckm(Gk)]T denotes the spread-

ing code vector of length Gk related to the kth user. It isobtained by the discretization at the chip rate of the func-

tion c(k)m (t) given by (8). The index m denotes the index of

the spreading code in the multicode scheme containing Mk

codes.

The model just proposed for a multirate and multicodeDS-CDMA system follows the structural principles of practi-cal downlink UMTS and leads to a convenient algebraic formwhich allows for a powerful receiver design for a multicodemultirate CDMA system.

For the sake of simplicity, the propagation channel is as-sumed to be time invariant during the transmission of Nchip

chips. We also assume that the interferences due to symbolsbefore and afterNchip data block can be completely cancelled.This is possible when those interfering symbols are known bythe receiver via a training sequence. The model presented in(12) can be generalized to incorporate scrambling codes andmultiple antenna transmissions.

3. PROBLEM STATEMENT

Without loss of generality, the user 1 is chosen as the user ofinterest. By denoting A(k) = C(k)H(k), the received signal canbe expressed as

r = A(1)W(1)b(1)︸︷︷︸

desired signal + intercode interference

+K∑

k=2

A(k)W(k)b(k)

︸︷︷︸MAI + ISI

+ n︸︷︷︸noise

,

(14)

where we separate the user of interest’s signal, the multipleaccess interference (MAI), and intersymbol interference (ISI)caused by the other users and the noise. The first term in(14) contains the useful signal and the intercode interferencecaused by the multicode scheme.

Let F denote the joint multicode receiver filter employedby the receiver of user 1, user of interest. From the outputof the joint multicode receiver, y = FTr, the SIR of virtualuser of interest can be written for code m and symbol n asthe following:

SIR(m,n) =pmE

(β(

F, hk, C(k))∣∣b(1)

m (n)∣∣2)

E(∣∣Ω(pm′ �=m

)∣∣2) (15)

form=1, . . . ,M1,m′=1, . . . ,M1, and n=1, . . . ,Nbit,1·Ω(pm′ �=m)is the sum of the intercode interferences, the multiple accessinterference, the intersymbols interference, and the noise.β(F, hk, C(k)) denotes the term depending on the multicodereceiver filter coefficients, the spreading code and the chan-nel coefficients. pm denotes the power assigned to the mthcode. In the sequel, we present the expression of the termsβ(F, hk, C(k)) and Ω(pm′ �=m) in the case of the rake, the zeroforcing, and the MMSE multicode receivers.

The aim of the power control algorithm in CDMA sys-tem is to assign the mobile the minimum power necessary toachieve a certain QoS which is typically defined in terms ofSIR. In this context, the most employed power control algo-rithm was proposed by Foschini and Miljanic in [10] and itis known as distributed power control (DPC). The optimumtransmission power of user k, supposed monocode user, iscomputed iteratively in order to achieve an SIR target de-noted here by SIRtarget.

pk(n + 1) = SIRtarget

SIR(n)pk(n). (16)

When the target SIR is achieved, the power’s updatingstops. This approach assumes a fixed receiver, usually a sin-gle receiver. To overcome this limitation, Ulukus and Yates in[11] proposes to optimize jointly the multiuser receiver andthe user’s power in the uplink. As the main result, it is shownthat the same performance as the DPC algorithm is achievedwith less transmitted power. In continuation of Yates’ ideaof a combined power control and receiver adaptation in aCDMA uplink, we develop, here, a joint power control andmulticode receiver adaptation algorithm suitable for a high-speed UMTS downlink.

So, the problem is to determine the different code pow-ers, pm, and multicode receiver filter coefficients, such thatthe allocated power to the multicode user is minimizedwhile satisfying the quality of service requirement on eachcode, SIRm≥ SIRtarget, where SIRm = En((SIR(m,n))), m =1, . . . ,M1, and SIRtarget is the minimum acceptable level ofSIR for each code. En denotes the expectation over the sym-bol index. Therefore, the problem can be stated mathemati-cally as follows:

minp

M1∑

m=1

pm (17)


constrained to

pm ≥ SIRtarget

E(∣∣Ω

(pm′ �=m

)∣∣2)

E(β(

F, hk, C(k))∣∣b(1)

m (n)∣∣2)

pm ≤ pmax, m = 1, . . . ,M1,

(18)

where pmax denoted the maximum allowed transmitteduser’s power.

The following optimization problem is difficult since theconstraints denominators are also power dependent. The so-lution is to consider a double optimization problem wherean inner optimization is inserted in the constraint set as thefollowing:

minp

M1∑

m=1

pm (19)

constrained to

pm ≥ SIRtarget minF

E(∣∣Ω(pm′ �=m

)∣∣2)

E(β(

F, hk, C(k))∣∣b(1)

m (n)∣∣2) ,

pm ≤ pmax, m = 1, . . . ,M1.

(20)

In [11], the equivalence between the optimization for-mulation given by (17) and the formulation given by (19)is demonstrated.

The second optimization formulation is a two alternateoptimization problem. The first optimization problem in-volved in (19), and called the outer optimization, is definedover the code power. Whereas the second one, called the in-ner optimization, which is involved in (20), assumes a fixedpower vector. It is defined over the filter coefficients of themulticode receiver. In this stage, we optimize the multicodefilter coefficients to maximally suppress the intercode inter-ference. The implementation of these two alternate optimiza-tion problems are realized iteratively in the algorithm de-scribed in the next section.

4. COMBINED DOWNLINK POWER CONTROLAND JOINT MULTICODE RECEIVERS

In this section, we propose to combine the downlink powercontrol and the joint multicode receivers. The objective ofthe algorithm is to achieve an output SIR equal to a targetSIRtarget for each assigned code to the multicode user. To dothis, we exploit the linear relationship between the outputSIR and transmit code power as is seen in (15). The proposedalgorithm is a two-stage algorithm. First, we adjust the filtercoefficients for a fixed code power vector, the inner optimiza-tion. Second, we update the transmitted code powers to meetthe SIR constraints on each code for the chosen filter coeffi-cients using (16). The description of the proposed algorithmis as follows:

The subscript 1 marks out the considered multicode user.If we consider also a maximum transmit power limitation

pmaxm , for m = 1, . . . ,M1, step (3) from the above algorithm is

(1) i = 0, start with initial powers p(1)0 , . . . , p(1)

M1.

(2) Receiver parameter calculation and receiver output SIRcalculation.

(3) Update the code powers using

p(1)m (i + 1) = (SIRtarget /En[SIR(m,n)])p(1)

m (i), for m =1, . . . ,M1.

(4) [W(i + 1)] j, j =√p(1)m (i + 1), with j = m + (n− 1)M1

where m = 1, . . . ,M1 and n = 1, . . . ,Nbit,1.(5) i = i + 1, stop if convergence is reached; otherwise, go to

step (2).

Algorithm 1

modified according to

p(1)m (i + 1) = min

{SIR(1)

target

En[

SIR(m,n)] p(1)

m (i), pmaxm

}

. (21)

The new code power calculated in step (3) are transmittedvia a feedback link to the BS.

In the sequel, we present the SIR derivation in the case ofthe zero forcing and the MMSE multicode joint receivers.

5. JOINT MULTICODE RECEIVER STRUCTURES

In this section, we derive the expression of the output SIR oneach code by considering the joint multicode receivers: ZFand MMSE.

The received signal given by (14) can be written as

r = AWb + n (22)

by denoting n =∑Kk=2 A(k)W(k)b(k) + n.

5.1. Rake receiver

The conventional data estimator consists of a bank of rakereceivers. In this case, the output signal is

yRake = AHr = ΓWb + AH n, (23)

where Γ = AHA.We separate the desired user’s symbols, the intercode in-

terference generated by the multicode transmission and theMAI + ISI + noise generated by the noise and the other users,

yRake = diag{ΓWb}︸︷︷︸desired symbols

+ diag{ΓWb}︸︷︷︸

intercode interference

+ AH n︸︷︷︸MAI + ISI + noise

,

(24)

where diag(X) = X − diag(X) represents a matrix with zerodiagonal elements containing all but the diagonal elementsof X.

The useful signal for the nth transmitted symbol on themth code is given by

E{(

[ΓW] j, jb(1)1 (n)

)2}= ([ΓW] j, j

)2E{∣∣∣b(1)

1 (n)∣∣∣

2}

,

(25)


where [X] j, j denotes the element in the jth row and jth col-umn of the matrix X.

The interference and the noise are given by

I = E{(ΓWb−diag{ΓWb} + AH n

)2}. (26)

We consider in the sequel that E{|b(1)1 (n)|2} = 1.

After developing the term I and taking the jth diagonalelement, the SIR at the output of the rake receiver related tothe nth transmitted symbol on themth code can be expressedas follows by denoting Γ′ = ΓW and Rn = E[nnT] as thecovariance matrix of the MAI, ISI and noise,

SIRRake(m,n) =([Γ′] j, j

)2

[(Γ′)2

]j, j −

[(Γ′) j, j

]2+[Γ′R′nΓ

]j, j

(27)

for j=m+(n−1)M1 wherem=1, . . . ,M1 and n=1, . . . ,Nbit,1.

5.2. Joint multicode zero forcing receiver

In the case of the joint ZF receiver, the output signal is

yZF = Γ−1yRake = Wb + Γ−1AH n. (28)

The joint ZF receiver leading to the estimate of the de-sired symbols, b, is called zero forcing since it tries to forcethe residual intercode interference to zero.

Therefore, the SIR at the output of the joint ZF receiverrelating to the nth transmitted symbol on the mth code canbe expressed as follows:

SIRZF(m,n) = [W]2j, j

[Γ−1AHRnAΓ−H

]j, j

(29)

for j=m+(n−1)M1 wherem=1, . . . ,M1 and n=1, . . . ,Nbit,1.

5.3. Joint multicode MMSE receiver

The joint multicode MMSE linear receiver minimizes theoutput mean squared error

E{∥∥FyRake −Wb

∥∥2}

(30)

with respect to F which yields

F = W2ΓH[ΓW2ΓH + AHRnA

]−1. (31)

Therefore, the output signal from the MMSE receiver yields,by denoting W0 = FΓ,

yMMSE = FyRake= W0Wb + W−10 ΓAH n. (32)

Now, we can separate the desired user’s symbols, the in-tercode interference generated by the multicode transmis-sion and the MAI + ISI + noise generated by the noise and theother users,

yMMSE = diag{

W0Wb}

+ diag{

W0Wb}

+ W0Γ−1AHAH n.

(33)

The SIR at the output of the MMSE receiver relating tothe nth transmitted symbol on themth code can be expressedas follows by denoting W′ = W0W as

SIRMMSE(m,n)

=([W′] j, j

)2

[W′W′H]

j, j −([W′] j, j

)2+[

W−10 ΓAHRnAΓ−1WH

0

]j, j

(34)

for j=m+(n−1)M1 wherem=1, . . . ,M1 and n=1, . . . ,Nbit,1.The proposed approach involves complex matrix in-

verse computations due to the employment of instantaneousMMSE filtering. This drawback can be recovered by replac-ing instantaneous MMSE filtering with adaptive filtering. Asis suggested in [22], the least mean square and the minimumoutput energy algorithms present an ease implementationand analysis. As a future work, we suggest to focus on thecomplexity reduction of the proposed approach.

6. SIMULATION RESULTS

Simulation results analyze the performance of the proposedstrategy considering the joint multicode MMSE and the jointZF receivers, and the performance obtained from the con-ventional power control which assumes a bank of fixed rakereceivers. We compare the different solutions by evaluatingthe total transmit (or mean transmit) power and the SIR (ormean SIR) at the mobile receiver.

Users are placed randomly in a hexagonal cell with ra-dius R = 1000 m around the BS. The path-loss exponent istaken σ = 4 and no shadowing is assumed. We consider a 6-path downlink channel. The target SIR is fixed at SIRtarget = 4(around 6 dB) for all simulations. We consider a number ofK = 20 users, among them we have K ′, K ′ < K multi-code users. The spreading factor for the single-code users isGk = 128 for any k = K ′, . . . ,K . The multicode users hasa spreading gain Gk′ = 64, k′ = 1, . . . ,K ′. We fix the user1 as user of interest. We vary its number of allocated codesbetween M1 = 4 and M1 = 64.

In Figure 1, we plot the mean SIR, (1/M1)∑M1

m=1 SIR(m),versus iteration index in the case of M1 = 4 for the con-ventional power control algorithm (fixed rake receiver) andthe proposed strategy which optimizes the joint MMSE andZF multicode receiver coefficients. We note the one-iterationconvergence of the multicode ZF receiver, the fast conver-gence of the multicode MMSE receiver, and the much slowerconvergence of the rake receiver.

In the case of M1 = 16, the conventional rake receivercannot meet the target SIR anymore, as shown in Figure 2,where we plot the variation of the SIR(m) on each code.However, the multicode receivers (ZF and MMSE) showgood performance. Adding more virtual users brings theconventional receiver to even worse performance as is shownin Figure 3.

For M1 = 64, the different lines for each receiver typecorrespond to the variation of the SIR on each code, SIR(m),versus iteration index.


1412108642

Iteration index

2

2.5

3

3.5

4

4.5

Mea

nSI

R

SIRRake

SIRZF

SIRMMSE

Figure 1: The SIR convergence for the rake, ZF, and MMSE re-ceivers in the case M1 = 4 multicode.

From Figures 2 and 3, we observe the difficulty of theconventional power control to reach the target SIR becauseof the MAI, ISI, and the intercode interferences. In the caseof low load in the cell (few users), the conventional powercontrol reaches the SIR target; see Figure 1. However, in thiscase, our proposed strategy presents a faster convergence.

The variation of the base station transmit power ra-tios pZF/pRake and pMMSE/pRake versus the iteration index isshown in Figure 4 in the case of a number of codes M1 = 16codes of the multicode user. We note a decrease of about 20%of the transmitted BS power.

However, a much significant gain in transmitted BS pow-er is noted in the case of M1 = 64, as we can deduce from theresults of Figure 5. The MMSE shows its optimality with sig-nificantly improved results with respect to the ZF receiver:the MMSE always gains power with respect to the rake re-ceiver (the ratio is smaller than 1) where the ZF increases firstthe required power to achieve the required SIR.

We observe from Figures 4 and 5 that the proposed strat-egy of joint downlink power control and multicode receiversoutperforms the conventional downlink power control interms of total transmitted power of the multicode user.

In all simulations, we note the very fast (1 iteration) convergence of the ZF receiver, the fast convergence of theMMSE receiver, and the much slower convergence of theconventional power control. The fast convergence of the ZFreceiver is easy to explain: since this receiver performs an or-thogonal projection into the subspace formed by the inter-fering signals, the output desired signal does not depend onthe interfering signals’ amplitudes. There is only one updateof (21). In the case of the joint multicode MMSE receiver, ateach iteration the receiver is updated since it depends on thereceived powers of each code. Finally, the rake receiver is a

1412108642

Iteration index

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Ou

tpu

tSI

Ron

each

code

,m=

1...M

1

SIRRake

SIRZF

SIRMMSE


1412108642

Iteration index

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Ou

tpu

tSI

Ron

each

code

,m=

1...M

1

SIRRake

SIRZF

SIRMMSE


fixed receiver that takes into account only the desired signalprocessing the MAI, ISI, and intercode interferences as noise,therefore yielding the worst performance.

The best performance in minimizing transmit powersand maximizing the cell capacity is obtained by the MMSEreceiver. The ZF receiver shows slightly lower performance,in terms of total transmit power, at high-cell loads (case ofM1 = 64, see Figure 5).


1412108642

Iteration index

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Tran

smit

pow

er’s

rati

o

pZF/pRake

pMMSE/pRake

Figure 4: The mean total transmit powers ratio pZF/pRake andpMMSE/pRake versus the iteration index for M1 = 16.

It should be noticed that at very low-cell loads (i.e., fewinterfering single-code users and few codes for the multicodeuser (case of M1 = 4)) the three receivers show similar per-formance, a result that is expected.

After the convergence of the proposed strategy using ajoint multicode MMSE receiver, the codes’ power alloca-tion is shown in Figure 6. As one can notice, it is not thesame power per code. This confirms the interest of thispower allocation-strategy for the downlink of the multicodeuser.

7. CONCLUSION

In this paper, we have analyzed the benefits of combiningthe downlink power control and the joint multicode detec-tion for a multicode user. The proposed algorithm updatesiteratively the transmitted code powers of the multicodeusers and the joint multicode receiver filter coefficients. Wehave used simulations to show the convergence and perfor-mance of the proposed algorithm in a system of practical in-terest. An important gain in transmit power reduction is ob-tained by implementing joint multicode detection. The per-formance of the ZF receiver allows an important reductionin computations (step 4 is avoided). The study of theoreticalconvergence of the proposed algorithm is under investigationbased on the analysis proposed in [23].

In order to overcome the limitation of power control dueto temporal filtering only, a joint power control and beam-forming for wireless network is proposed in [17] where it isshown that a capacity increase is possible if array observa-tions are combined in the MMSE sense. Therefore, as a di-rection for further research, the combination of the three ba-sic interference cancelation approaches (transmit power con-trol, multiuser detection, and beamforming) represents an

1412108642

Iteration index

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Tran

smit

pow

er’s

rati

o

pZF/pRake

pMMSE/pRake

Figure 5: The mean total transmit power ratio pZF/pRake andpMMSE/pRake versus the iteration index for M1 = 64.

3.532.52

Iteration index

71

71.5

72

72.5

73

73.5

74

74.5

75

Pow

erin

dBm

onea

chco

de

Transmit powers on each code, MMSE receiver

Figure 6: The code power allocation in the case of M1 = 10 codesafter convergence.

ambitious challenge to be met by third-generation systemsin order to provide high-capacity flexible services.

REFERENCES

[1] H. Holma and A. Toskala, Eds., WCDMA for UMTS-Radio Ac-cess for Third Generation Mobile Communications, John Wiley& Sons, New York, NY, USA, 2000.

[2] 3GPP TR 25.858 V5.0.0 (2002-03), “High Speed DownlinkPacket Access: Physical layer aspects, (Release 5)”.

[3] B. Sayadi and I. Fijalkow, “Joint detection for multicode trans-mission in downlink high speed UMTS,” in Proceedings of 60thIEEE Vehicular Technology Conference (VTC ’04), vol. 2, pp.837–840, Los Angeles, Calif, USA, September 2004.


[4] M. Saquib, R. D. Yates, and A. Ganti, “Power control for anasynchronous multirate decorrelator,” IEEE Transactions onCommunications, vol. 48, no. 5, pp. 804–812, 2000.

[5] R. D. Yates, “A framework for uplink power control in cellularradio systems,” IEEE Journal on Selected Areas in Communica-tions, vol. 13, no. 7, pp. 1341–1347, 1995.

[6] A. Sampath, P. S. Kumar, and J. M. Holtzman, “Power controland resource management for a multimedia CDMA wirelesssystem,” in Proceedings of 6th IEEE International Symposiumon Personal, Indoor and Mobile Radio Communications, Wire-less: Merging onto the Information Superhighway (PIMRC ’95),vol. 1, pp. 21–25, Toronto, Ontario, Canada, September 1995.

[7] V. V. Veeravalli and A. Sendonaris, “The coverage-capacitytradeoff in cellular CDMA systems,” IEEE Transactions on Ve-hicular Technology, vol. 48, no. 5, pp. 1443–1450, 1999.

[8] L. C. Yun and D. G. Messerschmitt, “Variable quality of servicein CDMA systems by statistical power control,” in Proceedingsof IEEE International Conference on Communications, Gatewayto Globalization, vol. 2, pp. 713–719, Seattle, Wash, USA, June1995.

[9] S. V. Hanly and D.-N. Tse, “Power control and capacityof spread spectrum wireless networks,” Automatica, vol. 35,no. 12, pp. 1987–2012, 1999.

[10] G. J. Foschini and Z. Miljanic, “A simple distributed au-tonomous power control algorithm and its convergence,” IEEETransactions on Vehicular Technology, vol. 42, no. 4, pp. 641–646, 1993.

[11] S. Ulukus and R. D. Yates, “Adaptive power control withMMSE multiuser detectors,” in Proceedings of IEEE Interna-tional Conference on Communications, vol. 1, pp. 361–365,Montreal, Quebec, Canada, June 1997.

[12] J. G. Andrews, A. Agrawal, T. H. Meng, and J. M. Cioffi, “Asimple iterative power control scheme for successive inter-ference cancellation,” in Proceedings of 7th IEEE InternationalSymposium on Spread Spectrum Techniques and Applications,vol. 3, pp. 761–765, Prague, Czech Republic, September 2002.

[13] F. Meshkati, D. Guo, H. V. Poor, S. C. Schwartz, and N. B. Man-dayam, “A unified approach to power control for multiuserdetectors,” in Proceedings of the 2nd International Workshop onSignal Processing for Wireless Communications, King’s College,London, UK, June 2004.

[14] F. Meshkati, H. V. Poor, S. C. Schwartz, and D. Guo, “Aunified power control algorithm for multiuser detectors inlarge systems: convergence and performance,” in Proceedings ofthe 43rd Allerton Conference on Communications, Control andComputing, Urbana-Champaign, Ill, USA, September 2005.

[15] D. Guo and S. Verdu, “Randomly spread CDMA: asymptoticsvia statistical physics,” IEEE Transactions on Information The-ory, vol. 51, no. 6, pp. 1983–2010, 2005.

[16] F. Rashid-Farrokhi, K. J. Ray Liu, and L. Tassiulas, “Downlinkpower control and base station assignment,” IEEE Communi-cations Letters, vol. 1, no. 4, pp. 102–104, 1997.

[17] F. Rashid-Farrokhi, L. Tassiulas, and K. J. Ray Liu, “Joint op-timal power control and beamforming in wireless networksusing antenna arrays,” IEEE Transactions on Communications,vol. 46, no. 10, pp. 1313–1324, 1998.

[18] J.-W. Lee, R. R. Mazumdar, and N. B. Shroff, “Downlink powerallocation for multi-class wireless systems,” IEEE/ACM Trans-actions on Networking, vol. 13, no. 4, pp. 854–867, 2005.

[19] L. Song and J. M. Holtzman, “CDMA dynamic downlinkpower control,” in Proceedings of 48th IEEE Vehicular Technol-ogy Conference (VTC ’98), vol. 2, pp. 1101–1105, Ottawa, On-tario, Canada, May 1998.

[20] 3GPP TS 25.215 V6.3.0 (2005-06), “Physical Layer - Measure-ments (FDD), (Release 6)”.

[21] A. Aguiar and J. Gross, “Wireless channel models,” Tech.Rep. TKN-03-007, Telecommunications Networks Group,Technische Universitat Berlin, Berlin, Germany, April 2003.

[22] C.-L. Wang, M.-H. Li, K.-M. Wu, and K.-L. Hwang, “Adap-tive interference suppression with power control for CDMAsystems,” in Proceedings of IEEE International Symposium onCircuits and Systems (ISCAS ’01), vol. 4, pp. 286–289, Sydney,NSW, Australia, May 2001.

[23] J. Luo, S. Ulukus, and A. Ephremides, “Probability one con-vergence in joint stochastic power control and blind MMSEinterference suppression,” in Proceedings of 37th Conference onInformation Sciences and Systems, The Johns Hopkins Univer-sity, Baltimore, Md, USA, March 2003.

Bessem Sayadi received the B.S. Engineer-ing degree in signal processing from theEcole Superieure des Telecommunicationsde Tunis (Sup’Com Tunis), Tunisia, in 1999,and both the M.Phil. (2000) and the Ph.D.(2003) degrees from the Signals and SystemsLaboratory (LSS) at Supelec, Gif-sur-Yvette,the Paris XI University, Orsay, France. In1999, he joined France Telecom where hewas engaged in research on echo cancelationand adaptive filtering. He has also served as a Teaching Assistant inseveral courses on digital communications, signal processing, andelectronics in the Department of Electronic and Electrical Engi-neering, SUPELEC, ENSEA, and University Parix IX, since Septem-ber 2000. From 2003 to 2005, he was an Associate Researcher inthe Image and Signal Processing Team (ETIS), at ENSEA, Cergy-Pontoise. In 2006, he joined France Telecom as a Research Engineer.His current research interests include Bayesian method, multiuserdetection, video coding, radio resource management, IP-mobility,and cross-layer design.

Stefan Ataman received the B.S. and M.S.degrees from the Polytechnic University ofBucharest, Romania, in 1999 and 2000,respectively, and the Ph.D. degree fromUniversite Paris-Sud, France, in 2004, allin electrical engineering. Currently, heis working as a Research Associate withUniversity Cergy-Pontoise/ETIS laboratory,France. His research interests are in the ar-eas of digital communications and signalprocessing with applications to CDMA wireless communications,power control, and multiuser receivers in CDMA cellular systems.

Inbar Fijalkow received her Engineeringand Ph.D. degrees from Ecole Nation-ale Superieure des Telecommunications(ENST), Paris, France, in 1990 and 1993,respectively. In 1993–1994, she was a Re-search Associate at Cornell University, NY,USA. In 1994, she joined ETIS, UMR 8051(ENSEA - Cergy-Pontoise University -CNRS) in Cergy-Pontoise, France. Since2004, she is the head of ETIS. Her cur-rent research interests are in signal processing applied to dig-ital communications: iterative (turbo) processing (in particularturbo-equalization), analysis of communication systems (including


MIMO, OFDM, CDMA, etc.) and cross-layer optimization. Until2005, she has been Member of the board of the GDR ISIS, which isthe CNRS French national research group on signal, image, andvision processing. She has been an Associate Editor of the IEEETransactions on Signal Processing 2000–2003.

Photograph © Turisme de Barcelona / J. Trullàs

Preliminary call for papers

The 2011 European Signal Processing Conference (EUSIPCO 2011) is thenineteenth in a series of conferences promoted by the European Association forSignal Processing (EURASIP, www.eurasip.org). This year edition will take placein Barcelona, capital city of Catalonia (Spain), and will be jointly organized by theCentre Tecnològic de Telecomunicacions de Catalunya (CTTC) and theUniversitat Politècnica de Catalunya (UPC).EUSIPCO 2011 will focus on key aspects of signal processing theory and

li ti li t d b l A t f b i i ill b b d lit

Organizing Committee

Honorary ChairMiguel A. Lagunas (CTTC)

General ChairAna I. Pérez Neira (UPC)

General Vice ChairCarles Antón Haro (CTTC)

Technical Program ChairXavier Mestre (CTTC)

Technical Program Co Chairsapplications as listed below. Acceptance of submissions will be based on quality,relevance and originality. Accepted papers will be published in the EUSIPCOproceedings and presented during the conference. Paper submissions, proposalsfor tutorials and proposals for special sessions are invited in, but not limited to,the following areas of interest.

Areas of Interest

• Audio and electro acoustics.• Design, implementation, and applications of signal processing systems.

l d l d d

Technical Program Co ChairsJavier Hernando (UPC)Montserrat Pardàs (UPC)

Plenary TalksFerran Marqués (UPC)Yonina Eldar (Technion)

Special SessionsIgnacio Santamaría (Unversidadde Cantabria)Mats Bengtsson (KTH)

FinancesMontserrat Nájar (UPC)• Multimedia signal processing and coding.

• Image and multidimensional signal processing.• Signal detection and estimation.• Sensor array and multi channel signal processing.• Sensor fusion in networked systems.• Signal processing for communications.• Medical imaging and image analysis.• Non stationary, non linear and non Gaussian signal processing.

Submissions

Montserrat Nájar (UPC)

TutorialsDaniel P. Palomar(Hong Kong UST)Beatrice Pesquet Popescu (ENST)

PublicityStephan Pfletschinger (CTTC)Mònica Navarro (CTTC)

PublicationsAntonio Pascual (UPC)Carles Fernández (CTTC)

I d i l Li i & E hibiSubmissions

Procedures to submit a paper and proposals for special sessions and tutorials willbe detailed at www.eusipco2011.org. Submitted papers must be camera ready, nomore than 5 pages long, and conforming to the standard specified on theEUSIPCO 2011 web site. First authors who are registered students can participatein the best student paper competition.

Important Deadlines:

P l f i l i 15 D 2010

Industrial Liaison & ExhibitsAngeliki Alexiou(University of Piraeus)Albert Sitjà (CTTC)

International LiaisonJu Liu (Shandong University China)Jinhong Yuan (UNSW Australia)Tamas Sziranyi (SZTAKI Hungary)Rich Stern (CMU USA)Ricardo L. de Queiroz (UNB Brazil)

Webpage: www.eusipco2011.org

Proposals for special sessions 15 Dec 2010Proposals for tutorials 18 Feb 2011Electronic submission of full papers 21 Feb 2011Notification of acceptance 23 May 2011Submission of camera ready papers 6 Jun 2011

Joint Downlink Power Control and Multicode Receivers for Downlink Transmissions in High Speed UMTS

Documents