04698555

Step Size Optimization for Fixed Step Closed Loop

Power Control on WCDMA High Altitude Platforms

(HAPs) Channel

Iskandar†, A. Kurniawan

†, E.B. Sitanggang

†, and S. Shimamoto

††

†School of Electrical Engineering and Informatics, Bandung Institute of Technology

Jalan Ganesha no. 10 Bandung 40132, INDONESIA ††

Global Information and Telecommunication Studies of Waseda University, JAPAN

E-mail: [email protected]

AbstractThis paper evaluates fixed step algorithm of closed

loop power control and investigates an optimum step size for

WCDMA communication employing high altitude platforms

(HAPs). In CDMA, power control must be used to overcome

near-far effect, shadowing and multipath fading. Users who are

distributed within HAPs coverage will have different channel

characteristic depending on their elevation angle. Therefore,

parameter of power control algorithm should be designed to

comply with the channel characteristic. Step size is one

parameter in fixed step closed loop power control that will be

investigated in this paper. Considering the measured HAPs

channel characteristic, this paper investigates an optimum step

size that will resulting a minimum power control error (PCE).

Computer simulation shows that optimum step size depends on

user’s elevation angle. The higher the elevation angles the

smaller the optimum step size of the power control.

Keywords− HAPs; Fixed step, step size, closed loop; power

control; WCDMA; SIR.

I. INTRODUCTION

High altitude platforms (HAPs) or known as a

stratospheric platform (SPF) has attracted much attention in

recent year. This novel infrastructure is proposed to provide a

robust and reliable wireless delivery method with high

capacity services and performed as a complementary wireless

system to the traditional terrestrial and satellite systems [1]-

[5]. HAPs is able to exploit much the advantages and at the

same time overcome the drawback of the traditional systems

in terms of propagation delay and path loss suffered by

satellite system or a huge number of base station required by

the terrestrial system.

Next generation mobile service is one application that is

proposed in HAPs communication. This service basically will

employ CDMA technology. In CDMA, power control must

be used to overcome many problems such as near-far effect,

shadowing and multipath problem. Open loop power control

can effectively overcome near-far effect and shadowing.

However, multipath fading still degrades the performance

significantly, so that closed loop power control needs to be

employed to achieve an acceptable error rate at the receiver.

In closed loop power control, fading characteristic of the

uplink channel must be estimated and then fed back to mobile

user via the downlink channel so that mobile user can adjust

the necessary transmit power [6]. There are two types of

closed loop power control in general, those are fixed step and

variable step closed loop power control. The performance of

both types is depending on many parameters such as signal to

interference ratio (SIR) estimation method, step size, Doppler

frequency, feedback delay, etc. To limit the scope of this

work, we focus our research on the optimization of the step

size of the power control for each users who are located on

HAPs coverage at different elevation angle. We used our

proposed SIR estimation method in power control algorithm

[7] and defined Doppler frequency based on user’s speed and

elevation angle.

The channel characteristic of HAPs communication is

well known to follow Ricean fading distribution due to the

presence of line of sight signal. In this case, multipath fading

behavior is represented by K factor which is defined as ratio

between line of sight power and multipath scattered power.

We have experimentally investigated for HAPs channel that

the value of K is governed by user elevation angle, α [8]. The

higher the elevation angle the bigger the value of K. This K

factor value indicates the fading rate and fading depth. The

smaller the value of K will result fading rate more rapid and

fading depth more deep. To overcome such problems power

control is required. In this work, an optimum step size in

fixed step close loop power control will be investigated at

different user’s elevation angle.

The remaining part of this paper is outlined as follows.

Section 2 presents channel model and characteristic in a

HAPs system. Section 3 reviews in detail a concept of fixed

step power control. Simulation model of fixed step power

control is explained in Section 4. Section 5 shows simulation

result and finally concluding remark is drawn in Section 6.

II. HAPS CHANNEL MODEL AND CHARACTERISTIC

Ricean fading is a general case of a fading channel model

that there are two components of signal arrive at the receiver.

First component arrive at receiver through line of sight (LOS)

path and second component come from multipath scattered

signal. In case of no LOS component, the channel

characteristic is represented by Rayleigh channel distribution.

In HAPs communication channel, it is possible to have both

components because HAPs is highly positioned above the

ground. Therefore, channel characteristic in HAPs system can

be represented by Ricean distribution which the probability

density function of the signal envelope is expressed as

,0,2

exp)(202

22

2≥+= S

SAI

ASSSP

σσσ (1)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.978-1-4244-2324-8/08/$25.00 © 2008 IEEE. 1

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 00

5

1 0

1 5

2 0

2 5

E l e v a t i o n a n g l e [ d e g ]

K f

acto

r [

dB

]

F re q u e n c y 1 . 2 G H zF re q u e n c y 2 . 4 G H z

Fig. 1 The measured K factor in HAPs channel.

where S denotes the envelope of the received signal, σ 2 is the variance or average power of the multipath components, Arepresents the amplitude of the LOS path or dominant signal

and I0(.) is the zeroth order modified Bessel function of the first kind. The composite received signal envelope at the

receiver can be described by the probability density function

(PDF) of Ricean distribution as a function of K.

{ }++−+=][

][)1(exp

][

)1()(

2

22

2 SE

SEKSK

SE

SKSp

+][

)1(2

20SE

KKSIx , (2)

where ][SE and 2/)2(][ 222 σ+= ASE are the first and

second moment of measured data, respectively, and 22 2/ σAK = . The first and second moment can be obtained

from original Rice distribution expressed as follow.

++Γ= −K

nFe

nSE

Knn;1;1

2)1

2()2(][

11

2/2σ , (3)

n is the order of the moment. By using the confluent

hypergeometric function definition, we can solve (3) to obtain

++−+

Γ=22

)1(2

exp1

)2/3(

][

][10

2

KIK

KIKx

K

KSE

SE . (4)

Using the aforementioned method above of K estimation,

we have experimentally investigated the parameter of Ricean

channel for the case of HAPs in term of K factor as a function

of elevation angle from 100 to 900 in a step of 100 as depicted

in Fig. 2 [8]. Here we use the measurement result of K at

frequency 2.4 GHz in order to approach spectrum allocation

for next generation mobile based on HAPs [9]. This

estimation of Ricean fading characteristic will therefore be

used to evaluate an optimum step size of the fixed step closed

loop power control over HAPs channel. The fading rate and

depth are simulated based on the value of K and user’s speed

so that the performance of fixed step power control for each

elevation angle can be evaluated.

III. FIXED STEP POWER CONTROL IN HAPS SYSTEM

It is well-known that open loop power control algorithm

has been successfully implemented to overcome the near-far

and shadowing problem. However, multipath fading such as

experienced in HAPs channel can not be solved by this

algorithm because signal variation is faster than power

updating rate of this algorithm. Closed loop algorithm is

therefore developed to overcome such problem. In closed

loop power control, channel condition is estimated with the

result that power updating rate must be much faster than

fading rate. For that purpose, channel estimation must be

done quickly and precisely. One method which is used in

closed loop power control to estimate channel condition is

based on SIR estimation. Power control based on SIR

estimation exhibits better performance than that based on

signal strength [6].

In HAPs communications, one spotbeam or cell on the

ground is realized by the spotbeam antenna array refer to as a

base station in terrestrial system. However, here all base

stations will be realized by multi spotbeam antenna array and

those are located on the same location at the bottom of HAPs.

This situation is prone to interference between spotbeam

unless spotbeam antenna is designed to have sidelobe gain

very much smaller than mainlobe gain. Antenna pattern in

HAPs communications should follow an ITU

recommendation expressed in the following formula [9].

( )

≤≤−≤≤−≤≤

≤≤−

=

00

00

00

002

9037,2.38

3787.5),(log6095.55

87.553.4,8.9

53.40,57.1/38.34

)(

θθθθ

θθ

θ

for

for

for

for

G (5)

where )(θG is the antenna gain in (dBi) of the spotbeam with

boresight angle θ . In case the spotbeam antenna radiation

pattern is not perfectly designed, guard frequency among

spotbeams must be allocated to minimize interference level

and hence more bandwidth is required. This situation encourages us to select power control algorithm which is able

to conserve bandwidth utilization.

Fixed step power control is one algorithm that capable to minimize the signaling bandwidth compared with variable step that consumes more signaling bandwidth [10]. Moreover, fixed step algorithm performs much simpler than variable step whereas the performance of both algorithms is comparable. In the fixed-step algorithm, power control command (PCC) contains only a single bit and therefore can be considered as the PCM scheme with mode q=1. The PCC bit can be expressed as

[ ]≥−−<−+

=−= =0)(,1

0)(,1)(

Die

DieDiesignbitPCC

iq(6)

The above equation can be interpreted as follows. If the estimated SIR is less than the target SIR, the PCC bit -1 is

sent to the mobile to increase its transmit power by p dB. On

the opposite, if estimated SIR is higher than the target SIR,

the PCC bit +1 is sent to the mobile to decrease its transmit


Fig. 2 SIR based power control mechanism [7].

power by p dB. This means that step size algorithm requires

only one bit PCC in assigning mobile users to increase or

decrease their transmit power. Another reason to use the fixed step size algorithm in HAPs system is that it can reduce peak

transmit power during deep fades. In a variable-step

algorithm, the peak transmit power is high to compensate for

deep fades, and therefore may decrease the capacity due to

excessive interference to other users.In Fig. 2 SIR based power control mechanism using an

auxiliary spreading sequence is shown [7]. The auxiliary

spreading sequence is a spreading sequence that is reserved

for estimating the interference and is not assigned to any user

in the system. By using the auxiliary spreading sequence, the

multiaccess interference can be estimated after despreading (at symbol level) and thus reduces the complexity. It is

important to note that all users can use the same auxiliary

spreading sequence for estimating the multiple access

interference, so that the spreading sequence is not wasted.

In HAPs communications, interference will come from all

users at its serving beam and users from adjacent beam. Every user will give different interference effect based on its

position to the center of interfered beam which determined by

the angle (θo,ij) and distance (r0,ij) as described in Fig. 3. It is important to note that all interfering users considered in the

simulation follow an antenna pattern which is expressed in (5).

Considering the formula, we found only the first tier of

interfering cell has significant effect and therefore we only consider the first tier cell and assume that the interference

from tiers further away is negligible.

Assuming WCDMA system in HAPS communication is

employing QPSK modulation, one symbol can carry 2

information bit. The transmitted baseband signal of the kth

user can therefore be expressed as

)(2)( tscbAtxkkkkk

= , (7)

where 2Ak is the transmitted power of in-phase (bk) and

quadrature (ck) component and sk(t) is the chip waveform of

the kth user, respectively. Total received signal at the base station from all K users can be expressed as

Fig 3. HAPS interference geometry.

( )=

+=K

k

kkkkkkktntscbAtGtr

1

)()(2)()()( σβψ (8)

where G( k) is normalized antenna gain, k(t) is the fading

channel coefficient which is found for HAPs channel

depending on K as in Fig. 1. n(t) denotes the additive white

Gaussian noise (AWGN) with unit power spectral density and

k is the standard deviation of the AWGN experienced by the kth user. The SIR for kth user can be expressed as follows

≠

+=

kj

kjjjj

kkk

k

nnAtG

nAtn

))()(()()(

)()()(

22

2

σββψ

ββγ (9)

The parameter of k(t) and j(t) are calculated based on two

parameters, those are the measured K factor and user’s speed.

In order to evaluate an optimum step size of the power control, we perform simulation using fixed step size and

measure power control error (PCE) which is defined as the

standard deviation of the power-controlled SIR. Then we

repeat the simulations using different step sizes. The power

control error is plotted as a function of step size to find the

optimum step size, which is one that produces the minimum PCE. First we must define the variance of the power-

controlled SIR as follows

[ ] [ ]=

−=tN

i

test

t

esti

N 1

2)(

1var γγγ (10)

where Nt is the number of samples, est(i) is the power-controlled SIR in decibel estimated at the ith slot, and t is the

SIR target in decibel. Therefore we can define the PCE for

each value of step size p as

[ ] [ ]est

pPCE γσ γ var==∆ (11)

reference HAPs

reference cell jth

interfering cell

Ith

user

BS0 BSj

20 km

θ0,ij θij

P0,ijP ij

r0,ij rij


Fig. 4 Simulated Doppler frequency in a HAPs channel.

IV. SIMULATION MODEL

The simulation model is described simply in Fig. 2. As

mentioned before, in the model, fixed step closed loop power

control is based on SIR estimation using auxiliary spreading

sequence proposed in [7]. Error estimation produced by the

difference between estimated SIR and the target SIR is

quantized using a binary representation and then transmitted via PCC bit to the mobile stations. On the receiving of a PCC

bit, mobile stations increase or decrease their transmit power

on the basis of fixed value. In order to evaluate the

performance of fixed step power control in mitigating HAPs

channel fading, parameters such as step size of the prower control, users elevation angle, feedback delay, Doppler

frequency, and SIR estimation error are considered in this

paper.

We assume only one spotbeam served by HAPs with the

minimum elevation angle of 100. The number of user is 10

users. Frequency of 2.4 GHz is used so that we can use HAPs channel characteristic presented in Section 2 to calculate the

performance of fixed step power control. Additionally, close

to this frequency, ITU has allocated the spectrum for the next

generation services served by HAPs. HAPs channel fading is

generated using a “modified” Jack’s method to include LOS

component. The purpose is to obtain Ricean fading channel as commonly suggested in HAPs communication. Vehicle’s

speed and elevation angle refer to K factor value as shown in

Fig. 2 are parameters that affect the Doppler frequency. The

simulated Doppler frequency as a function of elevation angle

experienced by the users in HAPs communication can be

shown in Fig. 4. The lower the elevation angle the higher the Doppler spread. We can see in high elevation angle, for

example close to 900, the Doppler frequency almost zero even

vehicle’s speed is very high. It means users in high elevation

angle who even travel very fast will experience almost no

Doppler effect. An example of simulated Ricean HAPs channel fading is

illustrated in Fig. 5 for different elevation angle when user

velocity is assumed constant at 50 km/h. We can see from the

figure that fading rate and fading depth in 100 elevation angle

(K = 1.4 dB) is higher than that in 800 elevation angle (K =

12.2 dB). We can also see, that fading depth for 100 elevation

Fig. 5 Signal strength in Rician HAPs channel fading

with user speed of 40 km/h.

TABLE I. SIMULATION PARAMETERS

Parameters Notation and Value

Platform height h = 20 km

Frequency f = 2.4 GHz

Number of User N = 10

Vehicle’s speed vmobile = 10, 40, and 80 km/h

Modulation QPSK

Symbol Rate Rs = 60 ksps

Symbol duration T = 16,7 s

Number of symbol B = 40 symbol/time slot

Chip Rate Rc = 3,84 Mcps

Power control rate fp = 1.5 kbps

Processing Gain M = 64

Step Size p = 0.5, 1, 2 dan 3 dB

angle and user speed of 40 km/h, can be more than 40 dB.

Elevation angle in this case is a parameter that is directly

represented by measured K factor. We generate other Ricean

HAPs channel for different elevation angle and different user

speed to evaluate the performance of fixed step closed loop power control algorithm. The greater detail of simulation

parameter used in this paper is described in Table I.

V. SIMULATION RESULTS

Simulation shows that an optimum step size is depending on user’s elevation angle and speed. We perform simulation

for three different user’s speed to find an optimum step size at

each elevation angle. Figs. 6 show PCE at each elevation in

three different user speeds. It is shown that user with low

speed (Fig. 6 (a)) needs smaller step size than that user with

higher speed (Figs. 6 (b) and (c). Moreover user with high elevation angle needs smaller step size compared with user

with low elevation angle. An optimum value of the step size

for each elevation angle is the one that produces the smallest

value of the PCE. An average value of the optimum step size

at each elevation angle is obtained by averaging PCE for three

different user’s speed and the result is presented in Table 2. We found from simulated step size obtained for a case of

HAPs channel is smaller than that for a case of terrestrial

system with rayleigh fading channel model [6]. Therefore,


(a)

(b)

WCDMA performance in HAPs communication is expected

to perform much better than that in terrestrial system.

VI. CONCLUSIONS

Evaluation of optimum step size in fixed step closed loop

power control for HAPs communication has been proposed in

this paper. Simulation result shows that there are two major

parameters that contribute significantly to the optimum step size of the power control. Those are user’s elevation angle

and user’s speed because these parameters directly affect the

signal characteristic of HAPs channel. For a fixed user’s

speed, we found an optimum step size in HAPs

communication is decreased when user’s elevation angle is increased. On the other hand when elevation angle is fixed,

we found an optimum step size is decreased if user’s speed is

low.

REFERENCES

[1] G.M. Djuknic, J. Freidenfelds, and Y. Okunev, “Establishing wireless communications services via high altitude aeronautical platforms: A

concept whose time has come?,” IEEE Commun. Mag., vol. 35, no. 9,

pp. 128-135, Sept. 1997. [2] Y. Hase, R. Miura, and S. Ohmori, “A novel broadband all-wireless

access network using stratospheric platforms,” in Proc. 48th IEEE VTC

Spring, vol. 2, May 1998, pp. 1191-1194.

(c)

Fig. 6 PCE estimation for each elevation angle with user’s speed,

(a) 10 km/h; (b) 40 km/h; (c) 80 km/h.

TABLE II AN OPTIMUM VALUE OF STEP SIZE

Elevation Angle [deg] Step Size [dB]

10 2.1

20 2.0

30 1.9

40 1.8

50 1.3

60 1.3

70 0.6

80 0.3

90 0.1

[3] S. Ohmori, Y. Yamao, and N. Nakajima, “The future generations of mobile communications based on broadband access technologies,”

IEEE Commun. Mag., vol. 38, no. 12, pp. 134-142, Dec. 2000.

[4] J. Thornton, D. Grace, C. Spillard, T. Konefal, and T.C. Tozer, “Broadband communications from a high altitude platform: The

European Helinet Programme,” IEE Elec. and Commun. Eng. J., vol.

13, no. 3, pp. 138-144, June 2001. [5] S. Karapantazis and F.N. Pavlido, “Broadband communications via

high altitude platforms: a survey,” IEEE J. on Commun. Surveys and

Tutorials, vol. 7, issue 1, pp. 2-31, 2005. [6] A. Kurniawan, Predictive Power Control in CDMA System, PhD

dissertation, Institute for Telecommunication Research, The University

of South Australia, Februari 2003. [7] A. Kurniawan, “SIR estimation in CDMA systems using auxiliary

spreading sequence,” Magazine of Electrical Engineering, Institut

Teknologi Bandung (Indonesian: Majalah Ilmiah Teknik Elektro), vol. 5,

no. 2, pp. 9-18, August 1999.

[8] Iskandar and S. Shimamoto, “Channel characterization and performance evaluation of mobile communication employing

stratospheric platform,” IEICE Transactions on Communications, vol.

E89-B, no.3, pp. 937-944, March 2006. [9] "Minimum performance characteristics and operational conditions for

high altitude platform stations providing IMT-2000 in the bands 1885-

1980 MHz, 2010-2025 MHz, and 2110-2170 MHz in the Regs. 1 & 3 and 1885-1980 MHz and 2110-2160 MHz in Reg. 2," ITU-R M. 1456,

2000. [10] A. Kurniawan, “Effect of feedback delay on fixed step and variable

step power control algorithms in CDMA systems,” in Proceedings of

International Conference on Communication Systems (ICCS) 2002, November 2002, CD-ROM 3P-02-04.


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