Rake recei ver

MRC

Li nk gai nPower cont rol

Sl ow f adi ng

channel

p∆±

Tp

Integrator

user1 user1

userNuserN

Base stat i on

Mobi l e t ermi nal

Channel

par ameters (dB)

Transmi t t ed

power (dB)

++

Figure 1. System model

Predictive Linear Quadratic Power Control Algorithm

in WCDMA Wireless Cellular Networks

Liu Jiabin

Department of Communications Engineering

Beijing Institute of Petrochemical Technology

Beijing 102617, PRC

liujiabin@bipt.edu.cn

Abstract—Combining the approaches of optimal control theory

and linear prediction technique, the user’s transmitting powers

are minimized and the system capacity is maximized with the

quality of services (QoS) being satisfied simultaneously for all

mobile terminals. A linear quadratic form of power control

problem in wideband code division multiple access (WCDMA)

systems is established and the fading channel path-gain is

predicted. Simulation results show graphically that the proposed

predictive linear quadratic power control (PLQ-PC) algorithm

converges faster no less than 7 percents and makes the system

support about 1.2 times users compared with those obtained by

auto-tuning fuzzy power control (ATF-PC) and signal-

interference ratio based power control (SIR-PC) algorithms, respectively.

Keywords-prediction; linear quadratic; power control; optimal

control

I. INTRODUCTION

In recent years, many studies have been published concerning power control design for wideband code division multiple access (WCDMA) wireless cellular networks.

A series of traditional distributed power control algorithms for cellular radio networks have been classified and compared in [1]. The stable conditions and the convergent regions of those algorithms are given and computer simulations are implemented under following three situations: fixed base stations, dynamic assign base station, and macro-diversity. Mandhare and Ghrayeb [2] presented a SIR-based power control (SIR-PC) algorithm and examined the algorithm for time varying multi-path Rayleigh fading environment. It is demonstrated that SIR-PC achieves better convergence and works well for different mobile speeds with a continuously changing channel. Ming, Huei, Huang, and Chyuan [3] proposed an auto-tuning fuzzy power control (ATF-PC) architecture for the multi-rate WCDMA. The performance of ATF-PC and the conventional selective power control (S-PC) method were evaluated by computer simulations. According to the simulation results, the ATF-PC architecture has a smaller outage probability and a higher average transmission rate than that of the conventional S-PC method in a wireless fading channel. Osery and Abdallah [4] introduced the concept of state space into power control design and proposed a linear quadratic power control (LQ-PC) algorithm in CDMA cellular

systems. The simulation results have shown LQ-PC’s higher efficiency and faster convergence.

In this study, a predictive linear quadratic power control (PLQ-PC) algorithm is proposed. It is an extension of schemes proposed by [4] and can be used in WCDMA multimedia environment. We compare the performances of PLQ-PC with that of SIR-PC and ATF-PC, and show that PLQ-PC outperforms SIR-PC and ATF-PC in terms of convergence speed and the number of users accommodated by the system.

II. MODELS USED BY PLQ-PC ALGORITHM

A. System Model

The system model used by PLQ-PC is shown in Fig.1. The upper part denotes base station (BS) and the lower part denotes mobile terminals.

BS receives the signal transmitted by dedicated user i,estimates link gain by channel predictor, gets the power control decision-making bit by PLQ-PC algorithm and dispatches it to the user. The user adjusts its transmitting

power up or down a step size ∆p according to the power control bit.

For a measure of quality of service requirements in the system, we define the average signal interference plus noise power ratio (SINR) at the receiver of BS b in a power control period Tp as

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 1

(m-1)Tm(m-2)Tm (m-1/2)Tm mTm (m+1/2)Tm(m+1)Tm

12 −m

biG m

biG2 12 +m

biG

Tm

Figure 2. Predictive model (Tm=Tp)

i

ibi

N

in

bnrbn

ibi

N

in

bnr

rii

I

PG

PG

PG

P

P

=

+=

+=

≠≠ηη

γ

, (1)

where N is the number of users, Pri the average power in duration of Tp, Pi the transmitted power (assume constant in Tp)constrained by Pimax, b the thermo-noise power,

b

N

in

bnni GPI η+≡≠

the total received power at BS b. Gbi

denotes the link gain from user i to BS b, which is our predictive object.

The overall system performance is expressed by average dropping probability

==

N

i

oio PN

P1

1. (2)

Where )(obPr 0iioiP γγ <≡ is the dropping probability of

user i and 0iγ is the target SINR of user i set by system.

B. Predictive Model

Assume predictive period is Tm. The previous M Gbi (from k

biG tomk

biG−+1

) are adopted to predict linearly the next Gbi

(1+k

biG ) in power control period Tp. We have

=

−++ =M

m

mk

bim

k

bi GG1

11 α , (3)

where M is the predictive orders, αm is predictive coefficient and can be calculated by Levison-Durbin algorithm[5], the superscript k denotes iterative indexes.

It is propitious to reduce the predictive error by setting Tm=Tp and by being overlapped 50 percents for each other [6, 7]

as shown in Fig.2. The current control period starts at mTm, so 121 ++ = m

bi

k

bi GG .

C. Linear quadratic model

In optimal control theory, problems concerned in practice are often transformed into linear quadratic forms and then are worked out the optimal control trajectory with the optimal control linear quadratic algorithm. The power control design in WCDMA system is also without exception.

From (1), the SINR of user i at BS b in the kth power control period is

)(

)()(

kI

kPk

i

rii =γ , (4)

and then the SINR of user i at BS b in the k+1th power control period is

( )

)()(

)(

)(

)(

)(

)(

)()(1

kuk

kI

kv

kI

kP

kI

kvkPk

ii

i

i

i

ri

i

iri

i

+=

+=+

=+

γ

γ, (5)

where vi(k) is a control variable brought to bear and

)(/)()( kIkvku iii ≡ the quantity of SINR to be changed.

The purpose of our power control design is to make

0)( ii k γγ → .

To transform our power control design into a linear

quadratic form, we define 0)()( iii kke γγ −≡ and its

integrated form )()()1( kekk iii +≡+ ξξ . Let

=)(

)()(

ke

kkX

i

iξ and )()( kukU i= .

After some derivations, we have

)()()1( kUBkXAkX ⋅+⋅=+ , (6)

where

=10

11A and =

1

0B .

The performance index is defined by the linear quadratic form shown as below

[ ]−

=∞→⋅⋅+⋅⋅=

1

0

)()()()(limK

k

TT

KkURkUkXQkXJ , (7)

where Q is a semi-positive symmetrical matrix to be chosen and denotes the error of control; R is a positive symmetrical matrix to be chosen and presents the cost of control. The purpose of optimal control is to minimize J by finding control sequence U(k).

Equations (6) and (7) are the linear quadratic form of our power control design in WCDMA systems. It can be proved that the linear system described by (6) is controllable [8]. So we

have 0ii γγ → without doubt as ∞→k .

III. PLQ-PC ALGORITHM

Firstly, according to optimal control theory [8], we can find control sequence of U(k) by iterative method. Secondly, we figure out X(k+1) using (6). And finally, we determine the

optimal transmitting power )1( +kPi based on the definition

of )1( +kei as

( ) ( )[ ] ( )⋅++=+ +1

0

max

1,min1

k

bi

iii

iiG

kIkePkP

γ. (8)

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 2

8 9 10 11 12 13 14 15 16 17 186

6.5

7

7.5

8

8.5

9

Number of voice users

Iter

atio

n in

dex,

k

SIR-PC

ATF-PCPLQ-PC

Figure 3. Iteration index versus the nuber of voice users under the

system dropping probability Po=1%

15 16 17 18 19 20 21 22 23 24 25

3

4

5

6

7

8

9

Number of voice users

Sys

tem

dro

ppin

g pr

obab

ility

, P

o (%

)

SIR-PC

ATF-PCPLQ-PC

Figure 4. System dropping propability versus the number of voice users

To determine )1( +kPi , it is prerequisite to predict the

link gain 1+k

biG according to (3). It is noted that U(k) can be

calculated and saved off-line and that predictive algorithm (3)

of1+k

biG can be implemented on a special integrated circuit.

So the speed of our proposed PLQ-PC scheme can be very fast.

IV. SIMULATION RESULTS

We study a multimedia system that offers two services (voice and data) and present comparison results for SIR-PC algorithm, ATF-PC algorithm, and the proposed PLQ-PC algorithm interms of convergence speed and the number of users accommodated by the system. The system considered in this study is same as that of the uplink model of FDD WCDMA. The channel model is considered to be a frequency selective Rayleigh fading channel with 4 paths. The fading channel is assumed to be changing per frame. The background noise is modeled as additive white gaussian noise (AWGN)

with power ηb=10-12 watts. The maximun transmitting power of

mobile terminals is constrained by Pmax=500 mW. The target SINRs are fixed to -19dB for voice service and -11dB for data service, respectively. The number of data service users is fixed to 8. Closed loop power control environment as shown in Fig. 1 is been simulated. Because the mobile terminals are assumed to be mobile with a velocity of less than 40 Km/hr for all the simulation results, the predictive orders can be set to M=8 [6].

Fig. 3 shows the convergence performance comparison among the three algorithms. Po of 0.01 is set while simulation and 5 of data users are assumed to access the system resources simultaneously with 4 diversity paths. It can be observed that the ATF-PC algorithm has better convergence as compared to SIR-PC algorithm. But the proposed PLQ-PC algorithm has better convergence speed (above 7%) compared to the other tow algorithms. Faster convergence means less time to achieve the desired value and thus there is a system performance improvement.

Fig. 4 presents the system dropping probability Po for different number of voice users. It can be seen that the proposed ATF-PC algorithm makes the system accommodate about 1.2 times users over the algorithms under comparison at given Po.

V. CONCLUSIONS

In this paper, we present a distributed power control algorithm. The proposed algorithm is a linear quadratic algorithm which uses linear predictive technology to adapt power update step size for faster convergence. We demonstrate that the proposed algorithm converges faster compared to the other two algorithms. We consider the users to be mobile during the simulation to simulate the real time scenario. The algorithms are also examined for the system dropping probability Po versus different number of voice users and the proposed algorithm is found to perform better also on the system capacities. The work can be extended by considering the effects of soft handover during power control loop.

REFERENCES

[1] J. D. Herdtner and E. K. .P. Chong, “Analysis of a class of distributed asynchronous power control algorithms for cellular wireless systems,”

IEEE Trans. JSAC, vol.18, March 2000, pp. 436-446.

[2] G. P. Mandhare and A. Ghrayeb, “A distributed SIR-based power

control algorithm for WCDMA systems,” Proceedings of VTC Fall 2006. IEEE, Hyatt Regency Montreal, Montreal, QC, Canada, vol.1,

Sep. 2006, pp.1-5.

[3] W. J. Ming, J. C. Huei, P. C. Huang, and C. C. Chyuan, “Auto-tuning fuzzy power control for multi-rate WCDMA systems,” Proceedings of

ICICIC 2007. IEEE, Kumamoto, Japan, vol.1, Sep. 2007, pp. 338-341.

[4] A. E. Osery and C. Abdallah, “Distributed power control in CDMA cellular systems,” IEEE Trans. Antennas and Propagation Mag., vol.42,

April 2000, pp. 152-159.

[5] S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1995.

[6] F. C. M. Lau and W. M. Tam, “Novel SIR-estimation-based power

control in a CDMA mobile radio system under multipath environment ,” IEEE Trans. Veh. Technol., vol.50, Jan. 2001, pp. 314-320.

[7] V. Wieser and V. Psenak, “Mobile radio channel state prediction for

power control in WCDMA mobile network” Proceedings of 17th International Conference 2007. IEEE, Brno, Czechoslovakia, vol.1,

April 2007, pp.1-4.

[8] B. D. O. Anderson and J. B. Moore. Optimal Control Linear Quadratic

Methods. Englewood Cliffs, NJ Prentice-Hall, 1990.

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