Practical Evaluation of Power Control Performance for Multipath Mitigation in Wireless Mobile Communication
Adit Kurniawan
School of Electrical Engineering and Informatics ITB, Bandung, Indonesia
Abstract: In this paper, practical evaluation of power control technique to combat multipath fading in wireless mobile communications is performed using computer simulation. We consider two types of power control algorithm in Code Division Multiple Access (CDMA) system in this paper, namely fixed-step and variable step algorithms. Practical aspects of power control investigated in this paper are focused on the effect of power update step size, fading rates, and feedback transmission error on the power control performance. The results show that the fixed-step power control algorithm exhibits only a slightly lower performance than that of the variable step algorithm, and therefore is more desirable in practice to minimize the signaling bandwidth. The effect of fading rates on power control performance also shows that variable step algorithm outperforms the fixed step algorithm during high fading rates but gives a comparable performance when fading rates are low. Finally when feedback information is subject to transmission errors, the performance of variable-step algorithm degrades more significantly because it is more sensitive to command error than that of fixed-step algorithm.
Keywords: Fixed step; multipath fading; power control; variable step.
1. Introduction
The most serious problem in mobile wireless communication systems is the signal distortion due to multipath fading channels. When a moving terminal, e.g. a mobile user transmits information to a base station, the signal received at the base station will experience severe fluctuations as well as possible intersymbol interference due to multipath propagation experienced by a moving vehicle. To overcome the problem of intersymbol interference due to frequency selective fading condition when transmitting high speed data, several techniques have been developed using orthogonal frequency division modulation or multicarrier communication schemes [1]-[2]. The effect of severe signal fluctuation, however, remains to be overcome despite the fact that multicarrier techniques can mitigate the frequency selectivity of wireless channel. The signal-to-noise ratio SNR in a flat or Rayleigh fading channel varies according to the channels’ response, and in CDMA systems the required SNR, or more precisely called the signal-to-interference ratio, SIR, to achieve a certain level of BER depends on its distribution as a result of fading channel [3]. To keep the SIR nearly constant at the desired level, power control can be used [4]. There are two types of power control algorithms:
open-loop and closed-loop power control algorithms. The open-loop power control is designed to overcome the near-far problem, while the closed-loop power control aims at reducing the effect of Rayleigh fading. In this paper, we focus on the evaluation of closed loop power control, particularly the effect of mobility rate of the user and also the effect of power update step size on practical situation of power control algorithm.
Received: December 27th, 2011. Accepted: October 4th, 2012
The rest of the paper is organized as follows. Section II presents the wireless channel as well as the CDMA signal and mathematical models. Section III describes power control algorithm, Section IV provides computer simulation and numerical results. Finally, Section V concludes the paper.
2. Wireless Channel and CDMA Signal Models A. Wireless Channel Model
In a mobile communication system, a signal transmitted through a wireless channel will undergo a complicated propagation process that involves diffraction, multiple reflections, and scattering mechanisms. In most cases, a line-of-sight path (LOS) between the mobile and the basestation is hardly in existence due to a very dense propagation environment between the mobile and the basestation.
Figure 1 shows the near-far distance problem and also describes the signal fluctuation due to multipath fading. To overcome the near-far problem, an open-loop power control can be used [5]. The open-loop power control is designed to ensure that the received powers from all users are equal in average at the basestation. In the open-loop algorithm, the mobile user can compute the required transmit power by using an estimate from the downlink signal (no feedback information is needed). This is because the large-scale propagation loss is reciprocal between uplink and downlink channels [6].
Figure 1. Channel Modelling in Wireless Mobile Communications
In contrast to the large-scale propagation loss, the small-scale propagation loss is uncorrelated between uplink and downlink. A mathematical model to describe the received multipath signal can be determined as follows. Let the transmitted signal be x(t) which can be expressed as
(b) Mu ltipath fading
Location 2
Location 1
2
Pt1
Pr1
Pr2
Pt2
d1
d2
Receive
transmit
Base Station
User
(a) Near ‐far distance
x ( t
where s(t) c is the sp signal r(t)
) r ( t
where Cl
fD = v/λ is to the mo random v frequency from the l delay τl is perfect, so B. CDMA In CD (user’s co transmitte spreading orthogona property.
In this for simpl However, crosscorre recovered a factor eq Proble communi mechanis basestatio channel fr downlink the spread
) ( ) = s t e
) is the comple peed of light, a
) as the superpo
1
)
L l
C
=
= ∑
is the fraction s the maximum obile velocity v variables indica y shift due to D
lth path. In this s not taken int o the effect of A Signal and M DMA systems
ode). The spre er and the rece g sequence wi
al (with zero A simple exam
F s example, onl
icity. In a mu , the correlatin elation betwee d symbol can a qual to the num ems arise wh cations system ms and Dopp on to a mobile from a mobile u k channels exhi
d signals for a
) 2
( f t
j π c
, ex baseband si and λ is the wav
osition of L mu
)
(
ll
s t − τ
of the lth path m Doppler spre vector, v. From ating signal lev Doppler freque research we c to account. Th Doppler shift i Mathematical M
the users spre eading sequenc
iver. The data ith the receiv crosscorrelati mple of a single
Figure 2. A ba ly one user is t ltiuser CDMA ng receiver can en different us attain the proce mber of spread hen the chan m where the c
ler effects. In user is called user to a basest ibit different be all users are tra
gnal with band velength of the ultipath compo
[(
2 fc fD
e
j π +of the incomi ead, and ψl is th m (2), we can s vel and phase ency, and τl re onsider the cha he carrier frequ is negligible.
Models ead the data sy
ce consists of can be recove ved signal. Th
ion), or rando e user CDMA
aseband single u transmitting da A system, more n still recover er’s code is su essing gain afte ing code for ea nnel is not p
channel is tim a wireless sy the downlink tation is called ehaviours to a ansmitted sync
dwidth W, fc = e radio frequen onents can be e
)
cos l c
D ψ t− f τ
ing signal amp he direction of see that the m fluctuation, fD
epresents the ti annel is freque uency demodu
ymbol by their a sequence of red at the rece he spreading om sequences system is show
user CDMA sy ata through a p e than one use the transmitte ufficiently low er decorrelation ach data symbo perfect such me varying du ystem, the com or forward lin d the uplink or multiuser CDM chronously by
= c/λ is the carr ncy (RF) signal expressed as
l]
,
plitude, τl is the f the lth scatter
agnitude and p
D cos ψl repres ime delay of s ency flat, so the ulation is also
r unique sprea f chips that is
iver by correla sequences can s with low cr wn in Figure 2.
ystem
perfect channel er transmit ont ed symbols pro w. As shown in n operation at t ol.
as in a wi ue to multipat mmunication ch
nk, while the c r reverse link. T
MA system. In the basestation
(1) rier frequency, l. The received
(2)
e lth path delay, er with respect phase of r(t) is sent the carrier signal received e effect of path assumed to be
ading sequence known to the ating the user’s n be mutually rosscorrelation .
l without noise to the channel ovided that the
n Figure 2 the the receiver by ireless mobile th propagation hannel from a communication The uplink and n the downlink, n because they , d
, t s r d h e
e e s y n
e . e e y e n a n d , y
originate channel, orthogona spreading CDMA ch
The m ck(m). By kth user a and (Q) d At a m received employed becomes componen pointed o different which can level than In the because th are not us different different levels at power lev [9]. Figur At the signal wi spreading from the correlatin from othe will suffe in the upl considera
from the same experience th al spreading se g sequence can hannel model w
message bk(n) g y considering a and ck(m) = ck(I
designate the in mobile station, signal with th d in the downli the dominant nt, a distant u out that these d cells are not m n be done at t n those located e uplink, synch
he users transm sed in the upli
mobile users propagation pa the basesation vels in the rev re 4 ilustrates th e basestation, t
ith the kth us g sequences of other K-1 use ng receiver may
er users with h er from the inte
link is indispe able channel-ca
e location (bas he same propa equences can b n be maintained with K users fo
Figure 3. CD generated by th a QPSK modul
(I)(m) + j ck(Q)
(m nphase and qua
the kth mobile he kth spreadin ink, there is no interference co user will suffer distant users w
mutually ortho the basestation
nearby the bas hronous transm mit from differ ink because the
are also subj ath losses and n. Due to non erse link, mult he uplink CDM he kth user rec ser spreading f different user
ers. If the rece y not be able t higher power le erference gene ensable to keep
apacity improv
sestation). The agation path l be used in the d, and coheren or the downlink
DMA downlink he kth user is lation, bk(n) = m) is the kth us adrature compo
e user recovers ng sequence. S o multi access omponent. Wh r due to large will suffer from ogonal. In this n by letting the
sestation.
mission from d rent locations.
eir orthogonali ject to differe independent f n-orthogonal s tiple access in MA channels in
covers the tran sequence. Du rs, the kth user eived power le to detect the w evels. Clearly,
rated by strong p the interferen
ement.
ese signals will loss, and fade downlink beca nt detection can k is shown in F
k channel mod spread by the bk(I)
(n) + j bk(Q
ser spreading s onent, respectiv s the transmitt Since orthogon
interference ( hen thermal no e propagation m other cells’ in
s case, downli e distant user t different users Therefore, orth ity cannot be m ent propagatio fading that lead spreading sequ nterference bec
n a wireless com nsmitted symbo
ue to non-zero r will observe evels at the ba weak user’s sig if a user is rec ger users’ sign nce acceptable
l go into the s e simultaneou ause the orthog n be performed Figure 3.
del.
kth user sprea
Q)(n) is the nth sequence. The vely.
ed symbol by nal spreading MAI) and ther oise is the majo
path loss. Als nterference bec ink power con to operate at a s is very diffic hogonal spread maintained [7]
on mechanisms d to unequal r uence and une
omes a seriou mmunication s ol by correlatin o crosscorrela
multiple acce asestation are gnal due to hig ceived with a w nals. Therefore e to all users a
same multipath sly. Therefore gonality of the d. A simplified
ading sequence symbol of the superscript (I) correlating the sequences are rmal noise n(t) or interference so it has to be cause users in ntrol is needed a higher power cult to achieve ding sequences ]. Signals from s, resulting in received power equal received s problem [8]- system.
ng the received ations between ss interference not equal, the gh interference weak power, it power control and to obtain a h e e d
e e ) e e ) e e n d r e s m n r d - d n e e e t l a
If pow will be a Therefore show that all users perfect po
Figur In a D chips (spr sequence follows. C Figure 5.
jbk(Q)
(n) i
…, M}. It ck(I)
(M)} a
wer control is able to commu e, this will obv
t the system ca are received w ower control sc
e 5. CDMA sig DS-CDMA sys
reading sequen of length M. W Consider a CD
In a CDMA s spread by th t is important and ck(Q)
={ck( bk( Q )( n ) bk( I )( n )
c a r r i e π / 2 I
Q
Figure 4. C not performed unicate with t viously decreas apacity of a mu with equal lev cheme.
gnal model wit stem the spread
nce) per symb We will conside MA transmissi
system, the n e kth user’s sp to realise that
Q)(1), ck(Q)
(2),
W a s h a f i l t ck( I )( m )
ck( Q )( m )
W a v e s h a p i n g f i l t e r s
c e r
H ( f )
H ( f )
CDMA uplink d, only users a the basestation se the capacity ultiuser CDMA vel [10]-[12], w
th QPSK modu d spectrum wa bol M, the chi er each of thes ion system wit nth transmitted preading seque
the user’s spre
…, ck(Q)
(M)}
H ( f )
c a r r a v e
a p in g t e r s
H ( f ) π
ck( Q )( m ) ck( I )( m )
+ ( a )
( b )
channel model associated with n without bei y of the CDMA A system is opt
which is only
ulation: (a) mod aveform is cha ip waveforms,
e parameters in th a QPSK mod symbol of th ence ck(m) = ck
eading sequenc are known to
Q r i e r
/ 2
+
∑ m yk( m ) I
l.
h the highest r ng jammed b A system. In fa timum when th achievable by
dulator; (b) dem aracterized by
and the type n the CDMA s dulation schem he kth user bk(
k(I)
(m) + jck(Q)
(m ces ck(I)
={ck(I)
( the receiver. T
A W G N
D e c i s i o n yk( n )
eceived power y other users act it is easy to he signals from y an ideal and
modulator.
the number of s of spreading signal model as me described in
(n) = bk(I)
(n) + m), m ∈ {1, 2, (1), ck(I)
(2), …, The number of r . o m d
f g s n + , , f
chips per symbol M is called the processing gain or spreading factor of a DS-CDMA system. It reflects the ratio of the signal bandwidth after spreading to that of the unspread data symbol.
A PN spreading sequence can be used to approximate the random spreading sequence and can be easily generated using a feedback shift register, and thus has widespread applications.
Although a rectangular chip waveform can be easily generated, it has a considerable frequency spectral component beyond the spectral null at 1/Tc, where Tc is the chip period. Therefore, a smooth chip waveform such as a sync chip waveform is usually used for the sake of spectral efficiency. Since the uplink is considered in this study, a random spreading sequence is assumed and will be used for simulations. The correlation property of a random spreading sequence can be expressed as follows
⎪⎩
⎪⎨
⎧
≠
=
= =
∑
=
= k j
j m k
cj k m M c M m E kj
for 0
0 and for
) 1
*( ) ( 1 )] 1
(
[
τ
τ
ρ
. (3)Here, τ is the chip asynchronism in a multiple of chip period, cj*
is the complex conjugate of cj, and M is the number of chips (spreading sequence) per symbol or the spreading factor. In (3.1), m is the chip index in every symbol period. The second moment of the crosscorrelation function of a random sequence with rectangular chip waveform can be expressed as [87].
⎪⎩
⎪⎨
⎧
≠
≠
=
≠
=
=
=
0 , for
3 / 1
0 , for
/ 1
0 , for
1 )]
2( [
τ τ τ τ
ρ
j k M
j k M
j k
E kj . (4)
For the real systems using PN spreading sequence, the synchronous correlation property of a PN spreading sequence can be expressed as
⎪⎩
⎪⎨
⎧
≠
−
= =
∑
==
k jM
j k m
c m c M
m
j k kj
M
for1 for 1
) ( ) ( 1
1
*ρ
. (5)We can see that the crosscorrelation of PN spreading sequence differs only by -1 from that of the pure random sequence. In the simulations, we normalise the amplitude of the quadrature spreading sequence, so that the magnitude of its complex form is unity and can be expressed as
) ( 2 ) 1 ( 2 ) 1
( m c
( )m j c
( )m
c
k=
kI+
kQ . (6)The superscripts (I) and (Q) in Figure 5 represent, respectively, the in-phase and the quadrature components of the QPSK modulation. In a QPSK modulation scheme, the transmitted symbols sequence bk(n) from the kth user can be expressed as
} ..., , 2 , 1 { , ) ( )
(n A nej n B
bk = k
θ
kn ∈. (7)
Here Ak(n) is the scale factor of symbol amplitude, θkn ∈{± π/4, ± 3π/4} is the modulation phase, and B is the number of the transmitted symbols. If Ak(n) = 1 (the transmission power is normalised to unity), the spread sequence of the transmitted symbol expressed in a chip index m can be written as
Δp Tp
Integrator
Step size +
+
+ _ +
γt -
γest
PCC bit error
e(i) PCC bits
MAI and AWGN
Mobile station
DTp Loop delay
Uplink channelβ(t) Downlink channel
Basestation
} ..., , 2 , 1 { ), 2 (
) 1 2 (
) 1
( m b
( )m j b
( )m m MB
b
k=
kI+
kQ∈
, (8)where bk(I)
(m), bk(Q)
(m) ∈{+1,-1}. The spread sequence is modulated by a carrier and then filtered before transmission through the channel. For SIR estimation purposes, we assume perfect carrier modulation/demodulation and filtering, so that we can simplify the model by only considering the signal at the baseband level. In a fading channel situation, the received baseband signal from all K users at demodulator can be expressed as
) ( )
( )
(t t b c nt
r k k k k
k
σ
β
+=
∑
(9)Here βk(t) is the fading channel coefficient and n(t) is the additive white Gaussian noise (AWGN) with unit power spectral density (σk is the standard deviation of the AWGN, experienced by the kth user.
After carrier demodulation and filtering in a QPSK CDMA scheme, the received baseband signal is despread by the conjugate of the kth user’s spreading sequence ck*
and then integrated over one symbol period (over M chips) to obtain the decision variable, yk(n). For a slow fading channel (βk(t) is constant over one symbol period), the SIR of the kth user computed during one symbol period can be expressed as follows
∑
≠+
=
k j
k j
j k k k
n n
M A
n n A
2 2
2
) (
| ) ( 1 |
| ) ( ) |
(
σ β
γ β . (10)
The factor 1/M (crosscorrelation between spreading sequences) in the denominator of (10) is the result of despreading user j by the kth user’s spreading sequence. The first term of the denominator represents the multi access interference from the other K-1 users due to non-zero crosscorrelations between users’ spreading sequences, and the second term represents the thermal noise. In the following sections, we will use the SIR as the control parameter of the CDMA power control algorithm.
3. CDMA Power Control Algorithms
For power control based on SIR, the mechanism of uplink power control algorithm is shown in Figure 6.
Figure 6. Power Control Model of Uplink Wireless Channel
The power control algorithm proceeds as follows. First, the SIR for each user, γest is estimated at the basestation for the ith time slot. Then the estimated SIR γest(i) is compared with the target SIR γt to produce the error signal e(i). The error signal e(i) is then quantised using a binary representation, so it can be transmitted via the downlink channel to the mobile station.
The quantised form of error signal is called the power control command (PCC) bits, which can be implemented using a pulse code modulation (PCM) realisation of mode q, where q is the number of PCC bits required in each power control interval.
The PCC bits are transmitted to a mobile station via the downlink channel. However, the PCC bits are subject to high bit error rates because they are not coded or interleaved in order to minimise signalling bandwidth on the downlink channel and to avoid the corresponding delays due to the interleaving [13]-[14]. The feedback loop delay, however, is unavoidable for at least one measurement interval. Therefore, transmission of the PCC bits on the downlink channel suffers from two major impairments: PCC bit errors and feedback delay. The PCC bits error is represented as a multiplicative disturbance on the PCC bits, while feedback delay is represented by a delay operator of DTp, which represents a multiple integer D of power control interval Tp. After the PCC bits are received by a mobile station, the mobile station computes
⎪⎪
⎪⎪
⎪⎪
⎩
⎪⎪
⎪⎪
⎪⎪
⎨
⎧
−
≥
−
−
−
<
≤
−
−
−
<
≤
−
+
−
<
≤ +
−
−
+
−
<
−
=
−
−
−
−
−
−
−
−
−
−
−
2 / 1 2 index ),
1 2 (
2 / 1 2 index 2 / 3 2 ),
2 2 (
. .
. .
2 / 1 index 2 / 1 ,
0
. .
. .
2 / 3 2 index 2 / 1 2 ,
2 2
2 / 1 2 index ,
1 2
) (
1 1
1 1
1
1 1
1
1 1
q q
q q
q
q q
q
q q
Dq
i
e (11)
where index is the difference between the estimated SIR (γest) and the desired SIR (γt). The difference between the estimated and the desired SIR is quantified to yield e(i-D)q, which is sent to the mobile to adjust the mobile’s transmit power by Δp. e(i-D)q dB. The loop delay DTp
accounts for the delays due to SIR estimation process and transmission time of the PCC bit on the forward link expressed as a multiple, D, of the time slot unit, Tp. In the absence of PCC bit errors, the transmit power at the next interval is
p(i+1) = p(i) - Δp . e(i-D)q, (12)
where e(i-D)q is expressed in (1). For the fixed step algorithm (q=1) the PCC bit can be expressed as
⎩⎨
⎧
≥
<
−
= +
−
= =
0 D) - (i 1 -
0 ) ( ] 1 ) ( [ bit
PCC 1
e D i D e
i e
sign q , (13)
where e(i-D) is the power control error at the (i-D)th power control interval designating DTp
loop delay from the ith control interval. In this work, the power control performance is evaluated when the PCC bits received by a mobile are subjerct to transmission error due to the impairment of the downlink (feedback) channel. If the PCC bits are received in error, a mobile will experience incorrect power adjustments. If the downlink channel error has a BER of Ppcc, the probability that the mobile transmit power will be reduced is
P’d[γest] = (1- Ppcc) Pd[γest] + PpccPu[γes], (14)
and the probability that the mobile transmit power will be increased is
P’u [γest] = (1-P’d[γest] ) = (1-Ppcc) – (1-2Ppcc) Pd[γest], (15) where Pd[γest] = P[γest > γt] and Pu[γest] = P[γest < γt], γest is the estimated SIR to which the power
control algorithm is based on, and γt is the target SIR level.
4. Computer Simulation and Numerical Results A. Simulation Procedure
In the simulation, a single-cell CDMA system with the number of users K = 10 is considered. To reflect a practical situation, all users are considered in motion with different vehicle’s speeds and thus have different maximum Doppler spreads. We model this situation by varying the users’ vehicle speeds from 10 to 100 km/h at 10 km/h interval (i.e., the speed of the kth user is vk = 10 k km/h for k = 1, 2 , …, 10. Carrier frequency fc = 1.8 GHz is used, so that the corresponding maximum Doppler spreads, fD for the users are approximately ranging from 17 to 170 Hz at 17 Hz interval. The DS-CDMA processing gain is M = 64 and the modulation scheme is QPSK with a data rate Rb = 120 kbps (symbol rate Rs = 60 ksps in QPSK scheme).
The power-update rate of 1.5 kHz is considered, which corresponds to the power control interval Tp = 0.667 ms [16].
SIR estimation/measurement is performed in every time slot that corresponds to one power control interval Tp = 0.667 ms. All data symbols in the time slot are utilised by SIR estimator to estimate the SIR. The chip rate Rc = 3.84 Mcps as given in the 3G specification for uplink data channel [14] is assumed in the simulation, resulting in each time slot to contain 2560 chips.
Therefore, 40 binary symbols per time slot are available for SIR estimation. Feedback delay is assumed to be one measurement interval (D=1) in that the mobile user can adjust its transmit power as soon as the measurement of each time slot (equal to Tp) is completed. The simulation parameters is summarized in Table 1.
Table 1. Simulation parameters
Parameter Notation and value
Number of users K = 10 Carrier frequency fc = 1.8 GHz
Vehicle’s speed vk = 10.k km/h, k = 1, 2, …, K Maximum Doppler spread fD = 1.67 vk Hz
Processing gain M = 64
Chip rate Rc = 3.84 Mcps
Power control interval Tp = 0.667 ms Data rate Rb = 120 kbps Power update step size Δp = 1 dB
A Gaussian distribution of the feedback channel error is assumed. To model the downlink transmission error, a Gaussian distributed random number consisting of {+1, -1} is generated according to the BER of PCC bits required for simulation. Then they are multiplied with the actual PCC bits generated by the power control algorithm. Performance evaluation is performed for both fixed-step and variable-step algorithms when the transmission of the PCC bits is subject to error with BER = 0.001, 0.01, and 0.1. The simulation is conducted for fDTp = 0.01, and the performance is evaluated in terms of bit error rate (BER) as a function of bit energy-to-interference power density ratio (Eb/I0)..
B. Numerical Results
In this section, the BER performance of a fixed-step and a variable-step algorithm are compared. The variable-step algorithm is implemented using a PCM realisation described in
[15] with modes q = 2, 3, and 4. In the variable-step algorithm with mode q = 4, the quantised error signal can be derived from (11) as follows
(16) where the index is defined as e(i-D)/Δp. It is clear from (16) that the required number of bits for PCC is 4 for each power control interval. The mapping of PCC bits is shown in Table II.
The first bit of the PCC bits sequence represents the sign of the command, i.e. 0 represents the positive sign and 1 represents the negative sign. The remaining bits represent the value of step size in a multiple of Δp for the mobile to increase or decrease its transmit power. The first four rows in Table 4.3 reflect the instructions to decrease the mobile transmit power, the fifth line indicates the instruction for the mobile to keep the same transmit power as in the previous interval, and the last four lines are instructions to increase the transmit power. The mobile will change its transmit power with variable step sizes of Δp.e(i-D)q=4 as expressed in (4). For PCM realization with modes q = 2 and q = 3, the mapping technique is the same with that shown in (3) and Table 1, with the index quantity of error signal e(i-D) /Δp are mapped to integer numbers of between –2 and 2 for q =2 and between –3 and 3 for q = 3. Therefore, the number of PCC bits required for PCM realization of modes q = 2 and q = 3 are 2 and 3 bits, respectively.
To see the effect of fading rates, we introduce the parameter fDTp, which is defined as the ratio of the fading rate to the power-updating rate. Since the power-updating rate is standardised at 1.5 kHz, the parameter fDTp will only depend on the fading rate fD, which is directly proportional to the vehicle’s speed. For 1.8 GHz carrier frequency, the vehicles’ speed of 10, 30, and 60 km/h correspond, respectively, to the maximum Doppler spread of 16.7, 50, and 100 Hz. With a power control interval of Tp = 0.667 ms (standardized power-updating rate is 1.5 kHz for 3G system) and for a mobile travelling at 10 km/h, the parameter fDTp equals 0.01, which means that the mobile transmit power is updated 100 times faster than the fading rate. For mobile speeds of 30 and 60 km/h, the parameter fDTp are 0.033 and 0.067, which correspond to the transmit power updating rates of 30 and 15 times faster than the fading rates, respectively. In the fixed step power control algorithm (q = 1), only the sign of the error signal e(i-D) is needed by the mobile to either increase or decrease its power by a fixed step size. In the fixed step size algorithm the algorithm is now simplified as follows. If the estimated SIR, γest(i) is less than the target SIR, γt, the PCC bit -1 is sent to the mobile to increase its transmit power by Δp dB. While if γest is higher than γt, the PCC bit +1 is sent to the mobile to decrease its transmit power by Δp dB. Note that with one PCC bit, the power control algorithm will still increase or decrease the mobile transmit power by Δp even when the target SIR has been achieved.
⎪⎪
⎪⎪
⎪⎪
⎩
⎪⎪
⎪⎪
⎪⎪
⎨
⎧
≥
−
<
≤
−
<
≤
−
<
≤
−
<
≤
−
−
<
≤
−
−
<
≤
−
−
<
≤
−
−
<
=
− =
5 . 3 index ,
4
5 . 3 index 5 . 2 , 3
5 . 2 index 5 . 1 , 2
5 . 1 index 5 . 0 , 1
5 . 0 index 5 . 0 , 0
5 . 0 index 5 . 1 , 1
5 . 1 index 5 . 2 , 2
5 . 2 index 5 . 3 , 3
5 . 3 index ,
4
) (i Dq 4 e
Table 2. PCC bits with PCM realisation (q = 4).
e(i-D)q = 4 PCC bits
4 3 2 1 0 -1 -2 -3 -4
0100 0011 0010 0001 0000 or 1000
1001 1010 1011 1100
To see the effect of different modes of variable-step algorithm, the BER performance is evaluated for the same channel condition with the parameter fDTp = 0.01. The BER performance is shown in Figure 7. The top curve is the BER for fading channel without power control, while the bottom curve is the BER for AWGN channel (perfectly power-controlled)
Figure 7. BER performance of power control with PCM realisation (fDTp = 0.01).
We can see in Figure 7 that variable-step power control algorithm outperforms the fixed- step algorithm. This is because with variable-step algorithm, power control can track the fading slope more quickly by using a higher step size and can reduce the oscillation when the target SIR has been achieved by using a smaller step size. Note that the performance improvement by using a higher mode (higher number of PCC bits) is obtained at the expense of a higher signaling bandwidth on the downlink channel. This is not desirable because the downlink channel capacity in third generation systems is crucial for internet downlink traffic, and thus needs to be preserved. Moreover, as we can see from Figure 7, the performance improvement at a voice quality BER of 10-3 is not significant when the quantisation mode is increased from q
= 1 (fixed step size with 1 PCC bit) to q = 4 (variable step size with 4 PCC bits). Yet the required signaling bandwidth for power control updates is four times higher. This result can answer the question why most practical power control schemes rely on a fixed-step algorithm, because the gains offered by the variable-step algorithm over the fixed-step algorithm may not be justified.
To evaluate the effect of fading rates on the power control performance, we perform simulations using a fixed step algorithm and variable step algorithm with mode q = 4. The simulation results are presented in Figure 8 (a) and (b), respectively. From Figure 8 (a) we can see that the fixed step power control is less effective at higher fading rates with fDTp greater
0 2 4 6 8 10 12 14 16 18 20
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Bit error rate, BER
Eb/Io (dB) Fading channel
Fixed step (q=1) Variable step (q=2) Variable step (q=3) Variable step (q=4) AWGN channel
than 0.033. However it works effectively at slow fading channel, as it is shown by the BER performance at fDTp = 0.01. Similar behaviour is obtained with variable-step algorithm, i.e the
0 2 4 6 8 10 12 14 16 18 20
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Bit error rate, BER
Eb/Io (dB) Fading channel
fDT
p = 0.067 fDT
p = 0.033 fDTp = 0.01 AWGN channel
a. Fixed-step algorithm (q=1)
0 2 4 6 8 10 12 14 16 18 20
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Bit error rate, BER
Eb/Io (dB) Fading channel
fDTp = 0.067 fDT
p = 0.033 fDT
p = 0.01 AWGN channel
Variable-step algorithm (q=4)
Figure 8. BER performance of power control for different fading rates
performance improves with decreasing values of the parameter fDTp as we can see in Figure 8 (b). For the same value of fDTp, the variable step algorithm has a better performance than the fixed step size algorithm as has previously explained.
The limited performance of fixed-step algorithm to combat higher fading rates is due to the fact that the algorithm is too late to follow the channel variations. In a higher fading rate, the fading factor changes dramatically, while the fixed-step power control can follow the channel variation step by step.
We then evaluate the performance degradation of fixed-step and variable-step algorithms when the transmission of the command bits is subject to error with BER = 0.001, 0.01, and 0.1. A Gaussian distribution of the feedback channel BER is assumed. The simulation results are shown in Figure 9.
(a) fixed-step algorithm (q=1)
(b) variable-step algorithm (q=4).
Figure 9. Effect of command bit errors on power control performance (fDTp = 0.01) From Figure 9, we can see that the variable-step algorithm is more sensitive to the feedback error than the fixed-step algorithm, as its performance degrades more significantly when the BER on feedback channel increases. This is because if the command bits are in error, the variable-step algorithm will result in larger power command errors than the fixed-step algorithm. In the fixed-step algorithm if the command bit is wrong, the resulting power control command error is limited by the fixed step size, which is usually preset at 1 or 2 dB. Therefore, the fixed step size algorithm is more robust than the variable step size when the feedback channel is subject to high bit error rates.
5. Conclusion
We have evaluated, by computer simulation, the effect of step size. Evaluation is conducted by using a fixed step size algorithm with 1 PCC bit and also by using a variable step size of 2, 3, and 4 PCC bits. The results show that the fixed step algorithm exhibits only slightly lower performance compared to that of variable step size algorithms. Therefore, fixed-step power control algorithm is more desirable than the variable-step algorithm in order to minimise the signalling bandwidth.
0 2 4 6 8 10 12 14 16 18 20
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Bit error rate, BER
Eb/Io (dB) Fading channel
Command BER = 0.1 Command BER = 0.01 Command BER = 0.001 Command BER = 0 AWGN channel
0 2 4 6 8 10 12 14 16 18 20
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Bit error rate, BER
Eb/Io (dB) Fading channel
Com m and BER = 0.1 Com m and BER = 0.01 Com m and BER = 0.001 Com m and BER = 0 AW GN channel
We have also shown that, in order for the power control to be effective, the power-updating rates must be much higher than the fading rates. We can see that the fixed step power control algorithm is less effective at higher fading rates with fDTp greater than 0.033. However it works effectively at slow fading channel, as it is shown by the BER performance at fDTp = 0.01.
Similar behaviour is obtained with variable-step algorithm, i.e the performance improves with decreasing values of the parameter fDTp. However for a slow fading rate, both algorithms exhibit a comparable performance.
We have also shown that the variable step algorithm is more sensitive to feedback-channel error than the fixed-step algorithm. Fixed-step algorithm is preferable for implementation in the real systems. The variable step algorithm can be advantageous when imperfections of the real system can all be overcome, and the bandwidth of feedback channel is not a constraint.
Therefore this experimental approach of CDMA power control can be used to design and optimized the system parameters. This approach is also important to evaluate the performance of CDMA power control in a practical or real implementation.
Acknowledgment
This research is supported by the ITB Research and Innovation Grant 2011. The authors thank ITB for their financial support.
References
[1] C. So-In, R. Jain, A.K. Tamimi, “Scheduling in IEEE 802.16e Mobile WiMAX Networks: Key Issues and a Survey”, IEEE Journal on Selected Areas in Communications, vol. 27, No. 2, Februari 2009.
[2] R. Prasad, OFDM for Wireless Communications. Norwood, MA, USA: Artech House, 2004.
[3] L. Song, N. B. Mandayam, and Z. Gajic, “Analysis of an Up/Down Power Control Algorithm for the CDMA Reverse Link Under Fading,” IEEE Journal on Selected Areas in Communications, vol. 19, No. 2, Feb. 2001, pp. 277-285.
[4] R. B. Kerr, “On Signal and Noise Level Estimation in a Coherent PCM Channel,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-2, pp. 450-454, July 1966.
[5] S. L. Su, and S. S. Shieh, “Reverse-link power control strategies for CDMA cellular network,” in Proceedings IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, vol. 2, September 1995, pp. 461-465
[6] K. S. Gilhousen, I. M. Jacobs, R. Padovani, A. J. Viterbi, L. A. Weaver, Jr., and C. E.
Wheatley III, “On the capacity of a cellular CDMA system,” IEEE Transactions on Vehicular Technology, vol. 40, no. 2, pp. 303-312, May 1991.
[7] A. J. Viterbi, A. M. Viterbi, and E. Zehavi, “Performance of power-controlled wideband terrestrial digital communication,” IEEE Transactions on Vehicular Technology, vol. 41, no. 4, pp. 559-569, April 1993.
[8] F. Simpson and J. M. Holtzman, “Direct sequence CDMA power control, interleaving, and coding,” IEEE Journal on Selected Areas in Communications, vol. 11, no. 7, pp.
1085-1095, September 1993.
[9] S. Ariyavisitakul and L. F. Chang, “Signal and interference statistics of a CDMA system with feedback power control,” IEEE Transactions on Communications, vol. 41, no. 11, pp. 1626-1633, November 1993.
[10] S. Ariyavisitakul, “Signal and interference statistics of a CDMA system with feedback power control – part II,” IEEE Transactions on Communications, vol. 42. No. 2/3/4, pp.
597-605, February/March/April 1994
[11] J. M. A. Tanskanen, J. Mattila, M. Hall, T. Korhonen, and S. J. Ovaska, “Predictive closed loop power control for mobile CDMA systems,” in Proceedings IEEE Vehicular Technology Conference, vol. 2, May 1997, pp. 934-938.
[12] K. S Whe Vehi [13] A. J
terre no. 4 [14] F. S
and 1085 [15] C. J
reali Tran [16] “Phy Thir Octo
S. Gilhousen, I eatley III, “On icular Technol J. Viterbi, A. M
estrial digital c 4, pp. 559-569 Simpson and J.
coding,” IEEE 5-1095, Septem . Chung, J. H.
ization for th nsactions on V ysical Channel rd Generation P
ober 1999.
A. K Insti Ph.D the Mr.
Engi His Cellu
I. M. Jacobs, R n the capacity logy, vol. 40, n M. Viterbi, and communication , April 1993.
. M. Holtzman E Journal on mber 1993.
Lee, and F. C he uplink of Vehicular Techn ls and Mapping Partnership Pr
Kurniawan re itute of Techno D in Telecomm University o Kurniawan is ineering and I research inter ular Communi
R. Padovani, A y of a cellular no. 2, pp. 303-3 d E. Zehavi, “P n,” IEEE Trans n, “Direct sequ Selected Area C. Ren, “Design
a DS-CDMA nology, vol. 45 g of Transport roject (3GPP)
eceived B.Eng.
oogy, Indones munication Eng
f South Aus currently Asso Informatics, Ba rest covers A
cations, and CD
A. J. Viterbi, L r CDMA syste 312, May 1991 Performance of
sactions on Ve uence CDMA as in Commun n of power con A cellular mo , no. 3, pp. 522 Channels onto Technical Spe
. in Electrical sia in 1986. H
gineering from tralia, respect ociate Professo andung Istitute Antenna and W DMA Wireles
L. A. Weaver, em,” IEEE Tr
.
f power-contro ehicular Techn
power control nications, vol.
ntrol mechanis obile radio sy 2-530, August o Physical Cha ecification TS 2
Engineering f e then receive m The RMIT U
tively in 199 or at the Schoo e of Technolo Wave Propaga s Communicat
Jr., and C. E ransactions on olled wideband ology, vol. 41, l, interleaving, 11, no. 7, pp sms with PCM
ystem,” IEEE 1996.
annels (FDD),”
25.211, v2.5.0,
from Bandung ed M.Eng. and University, and 96 and 2003 ol of Electrical ogy, Indonesia ation, Wireless
tions.
. n d , , . M E
” ,
g d d
. l . s
