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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000
Combined Rate and Power Adaptation in DS/CDMA
Communications over Nakagami Fading Channels
Sang Wu Kim, Senior Member, IEEE, and Ye Hoon Lee, Student Member, IEEE
Abstract—We consider combined rate and power adaptations
in direct-sequence code-division multiple-access communications,
where the transmission power and the data rate are adapted relative to channel variations. We discuss the power gain that the
combined adaptations provide over power adaptation. Then, we
consider an integrated voice and data transmission system that offers a constant bit rate voice service, using power adaptation and
a variable bit rate data service with rate adaptation. We present
an expression for the required average transmission power of each
traffic type having different quality-of-service specifications and
discuss the capacity gain over power adaptation for voice and data.
Index Terms—Combined rate
DS/CDMA, Nakagami fading.
and
power
adaptation,
I. INTRODUCTION
T
HE RADIO link for either a portable or a vehicular unit
can be characterized by a time-varying multipath fading,
which causes the link quality to vary with time. When the transmitter is provided with channel fading information, the transmission schemes can be adapted to it, allowing the channel to
be used more efficiently. In general, the transmitter may adapt
its data rate and transmission power. Adaptive variation of transmission power was considered in [1], following adaptive variation of data rate [2], constellation size [3], and adaptive coding
scheme [4], all for narrow-band systems. For code-division multiple-access (CDMA) cellular systems (IS-95), power adaptation is employed to maintain the received power of each mobile at a desired level [5]. Adaptive code rate and processing
gain control in cellular direct-sequence/CDMA (DS/CDMA)
systems is considered in [6]. The optimization of powers, and
both powers and rates in achieving a given quality-of-service
(QoS) requirement for multimedia CDMA systems, is considered in [7] and [8], respectively. In [8], the optimization is performed with a maximum transmission power and a minimum
rate requirement. In [9], a combined power/rate control scheme
is considered that limits the increase in power by some fixed
value and gets the extra gain required by reducing the rate.
In this paper, we consider the average data rate that meets
adequate QoS requirements, subject to an average transmission
power constraint and a maximum transmission power limit. We
propose two combined rate and power adaptation schemes that
Paper approved by A. Goldsmith, the Editor for Wireless Communication of
the IEEE Communications Society. Manuscript received June 1, 1998; revised
February 15, 1999. This work was supported by the Korea Science and Engineering Foundation (KOSEF), Korea.
The authors are with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea (e-mail:
swkim@san.kaist.ac.kr).
Publisher Item Identifier S 0090-6778(00)00515-8.
limit the transmission power when the channel gain is low. We
derive the average data rate as a function of average transmission
power and then derive the power gain that proposed adaptation
schemes provide over power adaptation. We find that the power
gain is more significant for channels with faster decaying multipath intensity profiles or weaker line-of-sight components and
for transmitters with lower peak-to-average power ratios. The
power gain implies a power reduction at the transmitter, which
translates into a reduction of interference to other users, leading
to a capacity increase.
Then, we consider an integrated voice and data transmission
system which offers a constant bit rate (CBR) voice service
using power adaptation and a variable bit rate (VBR) data service, such as e-mail and file transfer, using rate adaptation. The
motivation for applying rate adaptation to the data traffic is that
the rate adaptation provides a power gain over the power adaptation, while still maintaining both the same average data rate (or
throughput) and bit-error rate (BER). We present a closed-form
expression for the required average transmission power for each
traffic type having different QoS specifications and then discuss
the capacity gain over the power adaptation for voice and data.
The remainder of this paper is organized as follows. In Section II, we describe the system model and analyze the average
data rate in general. In Section III, we propose two combined
rate and power adaptation schemes and investigate the power
gain that they provide over power adaptation. In Section IV, we
analyze the performance of an integrated voice and data transmission system that employs power adaptation for voice and rate
adaptation for data. In Section V, conclusions are made.
II. SYSTEM MODEL AND ANALYSIS
We assume that the channel is frequency-selective with respect to the spreading bandwidth. Also, the channel variation,
due to multipath fading, is slow relative to the bit duration. We
further assume that the multipath fading is characterized by the
Nakagami- probability density function (pdf). We look only at
a single cell system. The implications of a multiple cell system
can be accounted for by the out-of-cell interference coefficient
users in the system, and each
[5]. We assume that there are
nonreference-user signal is misaligned relative to the reference
, which is uniformly
signal by an amount
distributed over a bit interval.
The Nakagami- distribution spans a range of fading envi, which
ronments from one-sided Gaussian fading (
). It is
corresponds to worst case fading) to nonfading (
corresponds to Rayleigh fading, and the
well known that
Rician and lognormal distributions can be closely approximated
0090–6778/00$10.00 © 2000 IEEE
KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS
by the Nakagami distribution with
. The Nakagamifading model fits experimental data from a variety of fading environments, including urban and indoor multipath propagation
[10].
The bit energy-to-equivalent noise spectral density ratio
at the -finger RAKE receiver output for user is given
by
163
where
(10)
can be expressed by
(1)
(11)
where
(2)
is the pdf of and
is the characteristic funcwhere
. However, since
is a convex function, a
tion of
lower bound on the average data rate can be obtained by using
Jensen’s inequality [12]
(12)
is the channel power gain due to multipath fading for user
on the th path,
is the transmission power for user ,
is
is the chip time, and
is the
the bit duration for user ,
one-sided power spectral density of the background noise. We
are independently, identically distributed
assume that
random variables with
(3)
where reflects the rate at which decay occurs. The pdf of
is given by [11]
(4)
(13)
We will see later that the lower bound is very close to the exact
value.
It should be noted that the instantaneous data rate
should not exceed the chip rate
, in order to keep
, i.e.,
the bandwidth constant. Therefore, when
should be
is
limited by . However, since the probability of
negligibly small for parameter values of practical interests, (9)
yields the actual average data rate.
where
III. COMBINED RATE AND POWER ADAPTATION
(5)
(6)
and
(7)
It follows from (1) that in order to maintain an adequate trans[bits/s] and the transmission quality, the data rate
mission power of user should be given by
The major disadvantage of power adaptation is that much of
the transmission power is used in compensation for deep fades in
order to maintain a CBR. This translates into large interference
to other users, leading to a capacity reduction. This problem can
be solved by limiting the transmission power when the channel
gain is low, if the users can tolerate some delay in their transmission. In this section, we consider two combined rate and power
adaptation schemes that reduce the average transmission power,
while still maintaining the same average data rate and BER.
We assume that transmitters are subject to a maximum trans. A full compensation of fading can
mission power limit of
or
be attained by power adaptation if
(14)
(8)
(15)
is the value required for adequate performance
where
is the chip rate. Typiof the modem and decoder and
depends on its implementation, use of error corcally,
recting coding, channel impairments, such as fading, and error
is given by
rate requirements. Then, the average data rate
is the target received signal power that meets
requirement. In the first scheme, the data rate is
and the transmission power is adjusted
fixed when
is equal to a desired value
. When
,
such that
is fixed at
, and the data
the transmission power
can be attained. This will
rate is adapted such that
be called power and rate adaptation. The truncated power
adaptation in [13] and the power adaptation are special cases
and
(or
), respectively. In the
of
second scheme, the data transmission is suspended when
where
(9)
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000
. Otherwise, the data rate is adapted with a fixed
. This will be called truncated
transmission power
rate adaptation. The rate adaptation is a special case of
(or
). Note that both schemes save power by limiting
.
the transmission power when
1) Power and Rate Adaptation: When the power and rate
is given by
adaptation is employed,
(16)
and the average transmission power
given by
at the mobile unit is
(17)
Let
(18)
(19)
Fig. 1. The average data rate R versus S =N with power and rate
5M; L = 3; m = 1; (E =N ) = 7 (dB),
adaptation; R
= 0:5; = 1; = 0:3; S = S
.
=
(20)
(21)
and
(22)
(23)
The average data rate
can be obtained by combining (9),
can be obtained by
(11), (16), and (27). A lower bound on
combining (12), (16), and (17) as shown in (28), at the bottom
of the page. Fig. 1 indicates that the lower bound is virtually
identical to the exact value.
makes
, for
Since the power adaptation
all , it follows from (9) and the fact that
that the (average) data rate
is given by
where
(24)
Then, the pdf of
is given by
(29)
with power adaptation. Comparison of (28) and (29) indicates
that the power and rate adaptation provides a power gain
(25)
(26)
and
are the unit step function and the Dirac delta
where
function, respectively, and the characteristic function of
is given by
(30)
(27)
over the power adaptation.
2) Truncated Rate Adaptation: When the truncated rate
and
adaptation is employed,
(28)
KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS
165
missions are required, then
. Another definition of
an outage event is discussed in [14], where the outage event is
defined as the signal-to-noise ratio going below a threshold and
staying longer than a minimum duration. The notion of minimum duration outage will lead to a different performance measure.
Comparison of (29) and (34) indicates that the truncated rate
adaptation provides a power gain
(36)
(37)
Fig. 2.
The average data rate R versus S =N with truncated rate adaptation;
= 3; m = 1; (E =N ) = 7 (dB), = 0:5; = 1; =
R = 5M; L
0 :3 .
function
of
. The pdf
are given by
and the characteristic
(31)
(32)
and
(33)
can be obtained by comrespectively. The average data rate
can be obtained
bining (9), (11), and (33). A lower bound on
from (12)
(34)
Fig. 2 shows that the lower bound is also virtually identical to
the exact value.
, the
Since no data is transmitted (i.e., no service) if
is given by
outage probability
(35)
represents the fraction of time during which no data transmission occurs. For example, when 99% of the time data trans-
over the power adaptation. The power adaptation and the rate
) of the power and rate adapadaptation are special cases (
tation and the truncated rate adaptation, respectively. So the difand
, when
, is the power gain
ference between
that the rate adaptation provides over the power adaptation. An
intuitive explanation for this power gain is that the power adaptation uses a lot of the transmission power in compensating for
deep fades in order to maintain a CBR. However, the rate adaptation uses a constant power and compensates for deep fades
by reducing the rate rather than using a large power. Thus, rate
adaptation saves power during bad channels and may use power
more effectively for better channels. However, rate adaptation
experiences a time delay when the channel gain is low. The
relative benefits of rate and power adaptations can be utilized
in multimedia communications, where users can tolerate some
delay in their transmission.
and
versus . We
Fig. 3 is a plot of power gains
find that the power gain is more significant for channels with a
faster decaying multipath intensity profile (larger ) or weaker
line-of-sight component (smaller ). We also find that
is higher than
. The higher gain is attained at a cost of a
and
wider range of rate variations. Also, the power gains
increase as
increases. This indicates that traffic which
tolerates a longer delay requires less transmission power.
IV. INTEGRATED VOICE AND DATA TRANSMISSION
We have seen previously that rate adaptation requires less
transmission power than power adaptation in maintaining a
given average data rate and a given BER requirement. Since
data traffic can tolerate a larger delay, a VBR service can be
provided to data users with a significant advantage in saving
transmission power and also producing less interference to
other users. In this section, we consider an integrated voice and
data DS/CDMA system that offers a CBR voice service using
power adaptation and a VBR data service, such as e-mail and
file transfer using rate adaptation.
users transmitting voice traffic
We assume that there are
bits/s with an average transmission power
at a fixed rate of
and
users transmitting data traffic at an average rate
bits/s with fixed transmission power
. Let
and
of
be the transmission powers of voice user
and data user
, respectively, with
and
, and
and
are the channel gains of voice user and
where
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000
TABLE I
REQUIRED AVERAGE TRANSMISSION
POWER FOR VOICE AND DATA USERS: m = 1; L = 3; = 0:5; R =
(kb/s), R = 32 (kb/s), R = 5M; = 6 (dB), = 10 (dB),
8
= 3=8; = 1
and
Fig. 3.
Power gains G
and G
versus ; = 1; L = 3; S = S
.
(42)
data user , respectively. Note that there are two indices, one
corresponding to the information types (superscripts), and the
other corresponding to the user numbers (subscripts).
Then, the bit energy-to-equivalent noise spectral density ratio
for voice user 1 and data user 1 are, respectively, given
by
. The validity of the apwhere
proximation is justified later by a Monte Carlo simulation. For
and
, where
and
are
and average data rate for data traffic, respecthe desired
tively, it follows from (42) that
(43)
(38)
and
, where
Similarly, for
and
are the desired
and data rate for voice traffic,
respectively, it follows from (41) that
(44)
(39)
is the bit duration for voice and
is the bit duration
where
and
, and
is
for data, namely
the voice activity factor of user . Since power adaptation is
for some
applied to voice traffic such that
, we obtain
desired received power
(40)
where we assumed that voice activity factors are the same for
all users, namely . If we approximate the interference by the
data traffic by its mean value, then we get
(41)
Therefore, it follows from (43) and (44) and the relationships
and
that the
required average transmission powers for voice and data users
are approximately given by
(45)
(46)
. Table I presents the rewhere we assumed that
quired average transmission powers for each type of traffic. It
should be noted that the number of data users has a signifiand
. This is because the
cant influence on
requirements for the data
average data rate and the
traffic are much higher than for voice traffic.
KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS
167
V. CONCLUSIONS
Fig. 4. The maximum number of voice and data users in an integrated voice
1; = 0:5; L = 3; S =N = 65 (dB),
and data system;
S =N = 60 (dB), R = 8 (kb/s), R = 32 (kb/s), = 6 (dB),
= 10 (dB), = 3=8; R = 5M .
m=
The maximum number of voice and data users,
can be obtained from (43) and (44) as
and
,
We have considered combined rate and power adaptations in
CDMA communication systems, where the transmission power
and the data rate are jointly adapted relative to channel variations. First, we considered the power and rate adaptation scheme
which performs the rate adaptation when the transmission power
required to meet a target QoS exceeds the maximum transmisand adapts otherwise the transmission power limit of
sion power to ensure a fixed-rate transmission. Then, we considered a truncated rate adaptation scheme that suspends transmitting data when the channel gain is below a threshold and
then otherwise adapts the rate with a constant power. We derived the average data rate as a function of the average transmission power and the power gain that the combined adaptation
schemes provide over the power adaptation scheme. The power
gains are found to be more significant for channels with a faster
decaying multipath intensity profile and weaker line-of-sight
components. The power gain translates into a reduction interference to other users, therefore leading to a capacity increase,
and prolongs battery life at the transmitter.
Next, we considered an integrated voice and data transmission system which offers a CBR voice service using power
adaptation and a VBR data service using rate adaptation. We
presented an expression for the required average transmission
power for each type of traffic having different quality of service
specifications and then discussed the capacity gain over the
power adaptation for voice and data.
REFERENCES
(47)
in
When voice and data are both power adapted, then
, where
(41) and (42) is equal to a desired received power
. Following the same procedure
in obtaining (47), the maximum number of voice and data users,
and
, with power adaptation are given by
(48)
Fig. 4 is a plot of the maximum number of voice and data
users in an integrated voice and data transmission system. Fig.
4 shows that the estimate on the maximum number of users by
(47) and (48) is very close to the Monte Carlo simulation result.
For comparison purposes, we also plotted the maximum number
of users when voice and data users are both power adapted. As
expected, the proposed scheme provides a higher capacity than
the power adaptation for voice and data, while still maintaining
the same average data rates and BER requirements.
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000
San Wu Kim (SM’98) received the Ph.D. degree
in electrical engineering from the University of
Michigan, Ann Arbor, in 1987.
Since 1987, he has been with the Korea Advanced
Institute of Science and Technology (KAIST),
Taejon, Korea, where he is currently a Professor
of Electrical Engineering. His research interests
include spread-spectrum communications, wireless
communications, and error correction coding. From
1996 to 1997, he was a Visiting Associate Professor
at the California Institute of Technology, Pasadena.
Ye Hoon Lee (S’99) was born in Taegu, Korea,
in 1968. He received the B.S. and M.S. degrees in
electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Taejon,
Korea, in 1990 and 1992, respectively. Currently,
he is working toward the Ph.D. degree in electrical
engineering at KAIST. His research interests include
spread-spectrum techniques in wireless mobile
communications and error control coding.