72 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 1, JANUARY 2004
Adaptive Rate DS-CDMA Systems Using
Variable Spreading Factors
Lie-Liang Yang, Senior Member, IEEE, and Lajos Hanzo, Fellow, IEEE
Abstract—In this contribution, adaptive rate transmissions are
investigated in the context of direct-sequence code-division mul-
tiple-access (DS-CDMA) systems using variable spreading factors
(VSFs). In the context of the recently established family of adap-
tive rate-transmission schemes, the transmission rate is typically
adapted in response to the channel’s fading-induced quality fluc-
tuation. By contrast, in this contribution the transmission rate is
adapted in response to the multiuser interference fluctuations en-
countered. We present the philosophy of the proposed adaptive
rate-transmission scheme and analyze the effective throughput as
well as the achievable bit error rate (BER) performance, when
communicating over additive white Gaussian noise channels. Our
study shows that by employing the proposed VSF-assisted adap-
tive rate-transmission scheme, the effective throughput may be in-
creased by up to 40%, when compared to that of DS-CDMA sys-
tems using constant spreading factors. This increased throughput
is achieved without wasting power, without imposing extra inter-
ference upon other users, and without increasing the BER.
Index Terms—Adaptive rate transmissions, code-division mul-
tiple access (CDMA), Markov chain, matched filter receiver, mul-
tiuser interference, throughput, variable spreading factors (VSFs).
I. INTRODUCTION
D
IRECT-SEQUENCE code-division multiple access (DS-
CDMA) is the prevalent technique in the third-genera-
tion (3G) wireless communications systems [1], [2], because
it is capable of providing numerous advantages as compared
to the other solutions. The capacity of DS-CDMA systems is
limited by both the time-varying characteristics of the wireless
channel and the multiple-access interference (MAI) or multiuser
interference (MUI). The family of efficient techniques designed
for compensating for the time-varying nature of the wireless
channels include the popular RAKE receiver [3], which is con-
trived for achieving frequency diversity. Alternatively, multiple
transmit and/or receiver antennas can be employed for achieving
spatial diversity [4]–[6]. The most efficient technique of com-
bating the MAI is multiuser detection (MUD) [7]. The above
techniques have attracted worldwide attention in recent years.
Another efficient technique of increasing the capacity of
time-varying wireless channels is the employment of adaptive
rate transmissions [8]–[12], in which the transmission rate can
be adaptively adjusted according to the instantaneous channel
Manuscript received July 3, 2002; revised June 13, 2003 and October 17,
2003. This work was supported in the framework of the IST Project IST-2001-
34091 SCOUT, which is supported in part by the European Union.
The authors are with the Department of Electronics and Computer Sci-
ences, University of Southampton, Southampton SO17 1BJ, U.K. (e-mail:
lly@ecs.soton.ac.uk; lh@ecs.soton.ac.uk).
Digital Object Identifier 10.1109/TVT.2003.822027
conditions. The main philosophy behind adaptive rate trans-
missions is the real-time balancing of the link budget through
adaptive variation of the symbol rate, modulation constellation
size and format, spreading factor, coding rate/scheme, etc.,
or in fact any combination of these parameters. However, the
results of [10] and [13] have shown that when a sufficiently
high diversity order is available, regardless of whether this is
due to transmitter or receiver diversity achieved in the time
or frequency domain, the advantages of adaptive rate trans-
missions erode. Hence, in the context of the 3G DS-CDMA
systems using power control, channel fading can be efficiently
mitigated by employing both the RAKE receiver and multiple
transmitter/receiver antennas. In order to combat the MUI in
DS-CDMA systems, as we have mentioned above, the most
efficient approach is to use multiuser detection receivers [7].
The main obstacle of employing DS-CDMA MUD receivers
is, however, the high complexity of the multiuser detection
algorithms. Therefore, the conventional matched-filter-based
receiver remains popular because of its simplicity, despite its
suboptimal performance.
In this contribution, we consider the problem of how the
effective throughput of DS-CDMA systems can be increased
when the conventional matched-filter-based receiver is em-
ployed. Specifically, we consider the uplink transmission of
a single-cell DS-CDMA system, where the number of active
mobile users obeys the Poisson distribution [14] and all the
signals transmitted by the mobile users are power controlled.
Hence, the multiuser interference level can be modeled as a
discrete Markov process [14], which describes the number of
active mobile users. In order to exploit the time-varying nature
of the multiuser interference level, an adaptive rate-transmis-
sion scheme using variable spreading factors (VSFs) [15], [16]
is proposed for increasing the effective throughput. In contrast
to the conventional VSF-assisted adaptive rate-transmission
scheme, where the transmission rate is adapted in response to
the channel-quality fluctuation recorded at the output of the
MUD [17], the transmission rate in the proposed scheme is
adapted in response to the time-varying interference level due
to the MUI, while maintaining the required target BER value.
More explicitly, the mobile users increase their transmission
rate when the number of active interfering users decreases,
while they decrease their transmission rate in response to an
increased number of active interfering users. The number of
active interfering users is broadcast to the mobile users by the
central base station (BS). In this contribution, the performance
of the DS-CDMA systems using the proposed VSF-assisted
adaptive rate-transmission scheme is evaluated when commu-
nicating over additive white Gaussian noise (AWGN) channels.
0018-9545/04$20.00 © 2004 IEEE
YANG AND HANZO: ADAPTIVE RATE DS-CDMA SYSTEMS USING VARIABLE SPREADING FACTORS 73
Fig. 1. State-transition diagram modeling the number of active interfering users with the aid of a Markov chain having
K
states.
The reasons for us to consider only AWGN channels are as
follows. First, as we have mentioned above, the fading effects
encountered in power-controlled DS-CDMA systems can be
efficiently mitigated by using RAKE receivers and multiple
transmitter/receiver antennas. Second, our aim is to study the
effects of the MUI in isolation, without the obfuscating effects
of the channel’s fading, and then gain insight into the effects of
the MUI on the system’s effective throughput when the conven-
tional matched filter receiver is considered. Note that our study
can be readily extended for considering various fading channels
as well as to multicell CDMA systems. Our results show that
by employing VSF-assisted adaptive rate transmissions, the
effective throughput of a DS-CDMA system may be increased
by 40% upon exploiting the Markovian-distributed number of
active users in the system. The increased effective throughput
is achieved without wasting power and without increasing the
bit error rate (BER).
The remainder of this contribution is organized as follows. In
the next section, we give a rudimentary overview in the con-
text of DS-CDMA systems and introduce the Markov model
describing the number of active users, while providing simula-
tion results. In Section III, we describe the VSF-assisted adap-
tive rate-transmission scheme. Section IV derives the effective
throughput of a DS-CDMA system when the proposed adaptive
rate-transmission scheme is employed and provides the corre-
sponding BER expression. Our numerical results are provided
in Section V and, finally, in Section VI we present our conclu-
sion.
II. S
YSTEM OVERVIEW
We consider a single-cell DS-CDMA system, where a single
BS is located at the center of the cell, while the mobile users are
uniformly distributed in the area covered by this BS. The BS is
capable of simultaneously processing a maximum number of
calls, i.e., the maximum number of active users supported by the
cell is
. We assume that each active user’s data is BPSK mod-
ulated and is transmitted to the BS asynchronously over AWGN
channels. Furthermore, we assume ideal power control, i.e., the
received power of each active user is the same at the BS. Based
on the above assumptions and assuming furthermore that there
are
active users (the reference user plus interfering
users), then the received signal at the BS can be expressed as
[18]
(1)
where
is the AWGN having a two-sided spectral density of
represents the power received from each active user,
is the spreading code, is the binary data signal, and
is the time-delay parameter that accounts for the propagation
delay as well as for the lack of synchronism between the trans-
mitters, while
is the phase angle due to carrier modulation
and channel delay.
According to the analysis of [18], the bit errors in DS-CDMA
systems communicating over AWGN channels are caused by the
effect of multiple-access interference and the AWGN. The BER
of an asynchronous DS-CDMA system having received signals
given by (1) can be closely approximated by [19]
(2)
where
represents the signal-to-noise
ratio (SNR) per chip and
is the chip duration, while repre-
sents the spreading factor (number of chips per bit). In our fur-
ther discourse,
will be controlled as a function of the number
of active users and the parameter
can be derived from [19]
(3)
Furthermore, in (2) the Gaussian
-function is given by
.
The number of interfering users
can be modeled with the
aid of a Markov chain having
states [14]. The state-transition
diagram modeling the number of users determining the interfer-
ence level is shown in Fig. 1, which represents a
queueing system [14].
1
The arrival rate of new calls or users
corresponds to the probability of the event that a new interfering
user is activated within a unit-length time duration, while the
average service time of
is the average duration of an active
interfering connection. For the
queueing system,
1
In the
M=M=m=m
queueing system [14], the first parameter
M
indicates
that the arrival process is a Poisson process, the second that
M
indicates that the
service time obeys a negative exponential distribution, the third that
m
quanti-
fies the number of servers, while the last (
m
) indicates the limit of the number
of customers in the system.
74 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 1, JANUARY 2004
(a)
(b)
Fig. 2. Markov characteristics of the number of active interfering users.
the probability that there are active interfering users (cus-
tomers) can be expressed as [14]
(4)
where the probability of simultaneously supporting
users is known as the Erlang B formula [14], which determines
the call blocking probability of the system considered.
Fig. 2 shows the number of active users generated by the
above-mentioned Markov chain for the first 3000 normalized
time slots [Fig. 2(a)] and for the normalized time slots spanning
the index-range of 1000–2000 [Fig. 2(b)]. The parameters used
for the simulations were
, and the max-
imum number of users supported was
. From Fig. 2(a)
and (b), we can observe that the number of active interfering
users is a slowly time-variant variable, fluctuating as a function
of the normalized time-slot index.
It is widely recognized that DS-CDMA systems are interfer-
ence-limited systems and that the systems’ BER performance is
Fig. 3. BER performance versus the number of active users for the parameters
of
=
0 dB and spreading factors of
N
=
8, 16, 24, 40, 56, 80, 112, and 120
computed from (2).
highly sensitive to the number of interfering users. Fig. 3 shows
the achievable BER performance with respect to the number
of active users for a DS-CDMA system communicating over
AWGN channels when the spreading factors of
8, 16, 24,
40, 56, 80, 112, and 120 are employed. From the results of Fig. 3,
we can infer following observations.
• For a given spreading factor, the BER increases when sup-
porting an increased number of active users.
• For a given number of users, the BER decreases upon in-
creasing the value of the spreading factor.
• For a given target BER—for example, for
—and for a given number of active users, there
exists a spreading factor that results in a specific BER for
the DS-CDMA system matching the target BER require-
ment. A DS-CDMA system using a higher spreading
factor is capable of supporting a higher number of active
users than that using a lower spreading factor, while
maintaining the target BER.
Therefore, based on the Markov chain characterized in Fig. 2
and on the BER performance of the DS-CDMA system as a
function of the number of active users shown in Fig. 3, we argue
that an appropriate spreading factor can be employed within a
specific time slot for maximizing the number of bits transmitted
by this specific time slot, while maintaining the required BER
performance. Furthermore, when the number of active users
dynamically fluctuates, variable spreading factors can be em-
ployed by the DS-CDMA system for achieving the maximum
throughput, while guaranteeing the required BER performance.
In other words, a VSF-assisted adaptive DS-CDMA system is
capable of increasing the effective throughput of the system
while maintaining a given target BER.
In this section, we have reviewed the behavior of interference-
limited DS-CDMA systems and highlighted the philosophy of
an adaptive DS-CDMA system in order to increase the effective
throughput of the system when the number of active interfering
users is time varying. Let us now investigate the behavior of
adaptive VSF-assisted schemes in more detail.
YANG AND HANZO: ADAPTIVE RATE DS-CDMA SYSTEMS USING VARIABLE SPREADING FACTORS 75
Fig. 4. Data structure of the transmitted signal in adaptive rate DS-CDMA systems using VSF-assisted adaptive rate transmissions.
III. A
DAPTIVE-TRANSMISSION SCHEME
The requirements for adaptive rate DS-CDMA systems may
be listed—without completeness—as follows.
• The rate adaptation of each active user may be controlled
independently, i.e., without cooperation with other active
users. Hence, the associated complexity is reasonably low.
• Since DS-CDMA systems are typically interference lim-
ited, an adaptive rate-transmission scheme must not im-
pose extra interference on the system. Hence, an attractive
adaptive rate DS-CDMA scheme is expected to maintain
the interference state, regardless of the active users’ trans-
mission rates. In other words, an active user’s interference
environment is expected to be affected only by the number
of active users corresponding to a certain level of MUI,
but not by their individual transmission rates. The trans-
mission rate and the achievable quality of service (QoS)
of a user have to obey a tradeoff for this particular user,
regardless of the other users of the system.
• For DS-CDMA systems, where some active users may
communicate at constant rates while the remaining ac-
tive users communicate at a variable rate, the BER and
throughput of the active users communicating at constant
rates is expected to be unaffected by those communicating
using adaptive rate transmissions.
• For adaptive DS-CDMA systems using VSF, the set of le-
gitimate spreading factors must be appropriately designed,
so that the effective throughput can be maximized with the
aid of readily realizable spreading codes.
Below we propose and investigate a specific adaptive rate-
transmission scheme that is capable of meeting the above re-
quirements. Let us assume that each user transmits a block of
data, as shown in Fig. 4. As shown in Fig. 4, the data block is
divided into
frames, where is assumed to be a random vari-
able distributed over a certain range, potentially extending to
.
We assume that at the beginning of the
th frame there are in-
terfering users, which is the a priori knowledge for determining
the required spreading factor, and the corresponding transmis-
sion rate during the
th frame. Let us assume that each frame
consists of a constant number of chips, which is expressed as
, i.e., each frame has a constant duration of s. Let us
also assume that there are
spreading factors having values ex-
pressed as
, where each is a factor of .
Furthermore, let us assume that the target BER is
. Then, the
required spreading factor of the
th frame and the corresponding
number of bits conveyed by the
th frame can be determined as
follows.
• A specific spreading factor is selected from the set
according to (2), based on the number
of interfering users
and on the target BER such that
the selected spreading factor’s value is as low as possible
while guaranteeing the required BER performance. We
denote the selected spreading factor by
.
• Once the spreading factor
of the th frame was
selected, the corresponding number of bits
conveyed by the th frame can be determined as
(5)
Based on (5) and on our previous arguments, it is readily
seen that the maximum or minimum throughput of the
th
frame is obtained when using the lowest or the highest
spreading factor from the set
, respec-
tively. Specifically, the maximum throughput of the
th frame
is given by
bits s
bits chip , while the minimum throughput is
given by
bits s
bits chip .
The proposed adaptive-transmission scheme is capable
of meeting the requirements listed at the beginning of this
section. Specifically, each user’s rate adaptation procedure is
independent of that of the other users’. The knowledge required
by each mobile user for adjusting his or her transmission rate
is the number of actively interfering users at the beginning
of each transmitted frame. This knowledge can be broadcast
to each mobile user by the BS. Second, since each user’s
received power is constant when different spreading factors as
well as different bit durations are used, the interference level
is only a function of the number of active interfering users.
However, the SNR per bit expressed as
exhibits
different values when various spreading factors or date rates
are employed. Finally, the communication environment of
the mobile users employing constant rate transmissions is not
76 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 1, JANUARY 2004
TABLE I
N
UMBER OF
BITS
TRANSMITTED IN A
FRAME BY
ASSUMING
THAT THE
TOTAL
NUMBER OF CHIPS
PER FRAME
IS
N
=
1680 = 2
2
3
2
5
2
7
WHEN THE
SPREADING
FACTORS
SEEN IN THE
RIGHT
COLUMN ARE
EMPLOYED.
R
ANDOM
SPREADING CODES
WERE
ASSUMED
affected by the rate-adaptation operations of the mobile users
invoking adaptive rate transmissions.
In [9], Goldsmith and Chua have shown that the highest effec-
tive throughput can be achieved by using continuous rate adapta-
tion. Hence, the results of [9] suggest that we should use as many
different spreading factors as possible and, simultaneously, have
a near-continuous spreading factors value set. Tables I and II
show two design examples for the appropriate choice of the
spreading factors. In Table I, we assumed that random spreading
sequences that have various length were employed and that the
frame’s length is
chips. As
shown in Table I, we can obtain 40 different spreading factors
and, hence, can support 40 different transmission rates. In the
context of Table II, we assumed that orthogonal spreading se-
quences were employed and that the frame’s length is also
chips. These orthogonal spreading se-
quences having variable length were derived based on the fact
that there exist
Hadamard matrices, provided
that
, where is a positive integer. Table II shows that
there exist 26 different orthogonal spreading codes having dif-
ferent VSF values in conjunction with
. Hence, the
DS-CDMA systems using the spreading factors of Table II are
capable of supporting 26 different transmission rates.
IV. T
HROUGHPUT AND BER ANALYSIS
In this section, we analyze the effective throughput as well
as the resultant average BER when achieving this effective
TABLE II
N
UMBER OF BITS TRANSMITTED IN A FRAME BY ASSUMING THAT THE TOTAL
NUMBER OF CHIPS PER FRAME IS
N
= 1680 = 4
2
2
2
3
2
5
2
7
WHEN THE VARIOUS SPREADING FACTORS SEEN IN THE RIGHT
COLUMN ARE EMPLOYED.ORTHOGONAL WALSH–HADAMARD
SPREADING CODES WERE ASSUMED
throughput. The effective throughput is defined as the total
number of bits successfully transmitted within a unity-duration
time interval by all users supported by the system. Our analysis
is based upon the following assumptions.
1) All active users communicate using adaptive rate trans-
missions based upon the same set of spreading factors, as
described in Section III. The transmitted data block length
of each active user obeys an independent identical distri-
bution (i.i.d).
2) Assuming that the number of interfering users at the
beginning of the
th frame is , the probability of
increasing or decreasing this number by one within
a frame’s time duration is given by
or
, respectively. The probability of increasing
or decreasing the number of interfering users within
a frame’s time duration by more than one is zero.
Therefore, the probability that the number of interfering
users remains unchanged, i.e.,
, within a frame’s time
duration can be expressed as
(6)
3) When the number of active interfering users increases by
one or decreases by one within the
th frame, we assume
that this happens at the moment having a time difference
of
from the beginning of the th frame (see Fig. 4), where
is assumed to be uniformly distributed over the interval
.
The effective throughput can be derived as follows. Ac-
cording to our analysis in Sections II and III, we know that
the spreading factor
as well as the number of bits
transmitted during the th
frame are determined by the number of active interfering users
