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step sizeTRANSCRIPT
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
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. 2
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
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. 3
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,
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. 4
(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.
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(c)
Fig. 6 PCE estimation for each elevation angle with user’s speed,
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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
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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. 5