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- Third-Generation Systems and Intelligent Wireless Networking
J.S. Blogh, L. Hanzo
Copyright © 2002 John Wiley & Sons Ltd
ISBNs: 0-470-84519-8 (Hardback); 0-470-84781-6 (Electronic)
Third-Generation CDMA Systems
K. Yen and L. Hanzo
1.1 Introduction
Although the number of cellular subscribers continues to grow worldwide [27], the predom-
inantly speech-, data- and e-mail-oriented services are expected to be enriched by a whole
host of new services in the near future. Thus the performance of the recently standardised
Code Division Multiple Access (CDMA)third-generation (3G) mobile systems is expected
to become comparableto, if not better than, that of their wired counterparts.
These ambitious objectives are beyond the capabilities of the present second-generation
(2G) mobile systems such as the Global System for Mobile Communications known as
GSM [28], the Interim Standard-95 (IS-95) Pan-American system, or the Personal Digital
Cellular (PDC) system[29] in Japan. Thus, in recent years, a range of new system concepts
and objectives were defined, and these will be incorporated in the 3G mobile systems. Both
the European Telecommunications Standards Institute (ETSI) andthe International Telecom-
munication Union (ITU) are defining a framework for these systems under the auspices of
the Universal Mobile Telecommunications System (UMTS) [27,29-331 and the International
Mobile Telecommunications scheme the year 2000 (IMT-2000)'[30,31,34].
in
Their objectives and the system concepts will bediscussed in more detail in later sections.
CDMA is the predominant multiple access technique proposed the 3G wireless commu-
for
nications systems worldwide. CDMA was already employed in some 2G systems, such as
the IS-95 system and it has proved to be a success. Partly motivated by this successer, both
the Pan-European UMTS and the IMT-2000 initiatives have opted for a CDMA-based sys-
tem, although the European system also incorporates an element of TDMA. In this chapter,
we provide a rudimentary introductionto a range of CDMA concepts. Then the European,
American and Japanese CDMA-based3G mobile system conceptsare considered, followed
by a research-oriented outlook on potential future systems.
' Formerly known as Future Public Land Mobile Telecommunication Systems
1
- 2 CHAPTER 1. THIRD-GENERATION
SYSTEMS CDMA
The chapter is organised as follows. Section 1.2 offers a rudimentary introduction to
CDMA in order to make this chapter self-contained, whereas Section 1.3 focuses on the basic
objectives and system concepts of the 3G mobile systems, highlighting the European, Amer-
ican and Japanese CDMA-based third-generation system concepts. Finally, our conclusions
are presented in Section 1.4.
1.2 Basic CDMA System
CDMA is a spread spectrum communications technique that supports simultaneous digital
transmission of several users’ signals in a multiple access environment. Although the de-
velopment of CDMA was motivated by user capacity considerations, the system capacity
provided by CDMA is similar to that of its more traditional counterparts, frequency division
multiple access (FDMA), and time division multiple access (TDMA) [35]. However, CDMA
has the unique property of supporting a multiplicity of usersin the same radio channel with a
graceful degradation in performance due to multi-user interference. Hence, any reduction in
interference can lead to an increase in capacity [36]. Furthermore, the frequency reuse factor
in a CDMA cellular environment can be as high as unity, andbeing a so-called wideband sys-
tem, it can coexist with other narrowband microwave systems, which maycorrupt the CDMA
signal’s spectrum in a narrow frequency band without inflicting significant interference [37].
This eases the problem of frequency management as well as allowing a smooth evolution
from narrowband systems to wideband systems. But perhaps the most glaring advantage of
CDMA is its ability to combat or in fact to benefit from multipath fading, as it will become
explicit during ourfurther discourse.
In the forthcoming sections, we introduce our nomenclature, which will be usedthrough-
out the subsequent sections. Further in-depth information on CDMA can be found in a range
of excellent research papers [35,37,38] and textbooks [3942].
1.2.1 SpreadSpectrumFundamentals
In spread spectrum transmission, the original information signal, which occupies a bandwidth
of B Hz, is transmitted after spectral spreading to a bandwidth N times higher, where N is
known as the processing gain. In practical terms the processing gain is typically in the range
of 10 - 30 dB [37]. This frequency-domain spreading concept is illustrated in Figure 1.1.
The power of the transmitted spread spectrum signal is spread over N times the original
bandwidth, while its spectral density is correspondingly reduced by the same amount. Hence,
the processing gain is given by:
B
N = L
B’
where B, is the bandwidth of the spread spectrum signal while B is the bandwidth of the
original information signal. As we shall see during our further discourse, this unique tech-
nique of spreading the information spectrum is the key to improving its detection in a mobile
radio environment, and it also allows narrowband signals exhibiting a significantly higher
spectral density to share the same frequency band [37].
There are basically two main types of spread spectrum (SS) systems [35]:
- 1.2. BASIC CDMA SYSTEM 3
Power
density
/ p watts/Hz
watts/Hz
7
- z
I -- I ?
Frequency
B,=BxN >
I-
Figure 1.1: Power spectral density of signal before and after spreading.
0 Direct Sequence (DS) SS systems and
0 Frequency Hopping (FH)SS systems.
1.2.1.1
Frequency
Hopping
In FH spreading, which was invoked in the 2G GSM system the narrowband signal is trans-
mitted using different carrier frequencies at different times. Thus, the data signal is effectively
transmitted over a wide spectrum. There are two classes of frequency hopping patterns. In
fast frequency hopping,the camer frequency changesseveral times per transmitted symbol,
while in slow frequency hopping, the carrier frequency changes typically after a number of
symbols or atransmission burst. In the GSM system each transmission burst of 114 channel-
coded speechbits was transmitted on a different frequency andsince the TDMA frame dura-
tion was 4.615 ms,the associated hopping frequency its reciprocal, that is, 217 hopdsec.
was
The exact sequenceof frequency hoppingwill be made known only to the intended receiver
so that the frequency hopped pattern may be dehopped in order to demodulate the signal [37].
Direct sequence (DS) spreading more commonlyused in CDMA. Hence, our forthcoming
is
discussions will be in the context of direct sequence spreading.
1.2.1.2
Direct
Sequence
In DS spreading, the information signal is multiplied by a high-frequency signature sequence,
also known as a spreading code or spreading sequence. Thisuser signature sequence facili-
tates the detection of different users’ signals in order to achieve a multiple accesscapability
in CDMA. Althoughin CDMA this user ‘separation’ is achieved using orthogonal spreading
codes, in FDMA and TDMA orthogonal frequencyslots or time-slots are provided, respec-
tively.
We can see from Figure1.2 that each information symbol duration T, is broken into N ,
of
equi-spaced subintervals of duration T,, each of which is multiplied with a different chip of
- 4 CHAPTER 1. THIRD-GENERATION
SYSTEMS CDMA
X
Figure 1.2: Time-domain waveforms involvedin generating a direct sequence spread signal.
m c o s w,t
Figure 1.3: BPSK modulated DS-SS transmitter.
the spreading sequence. Hence, N , = 9.The resulting output is a high-frequency sequence.
For binary signalling T, = Tb, where Tb is the data bit duration. Hence, N , is equal to
the processing gain N. However, for M-ary signalling, where M > 2, T, # Tb and hence
N , # N . An understanding of the distinction between N, and N is important, since the
values of N , and N have a direct effect on the bandwidth efficiency and performance of the
CDMA system.
The block diagramof a typical binary phase shift keying (BPSK) modulated DS-SS trans-
mitter is shown in Figure 1.3. We will now express the associated signals mathematically.
The binary data signal may be written as:
W
- 1.2. BASIC 5
where Tb is the bit duration, bj E {+l, -l} denotes the jth data bit, and F T b ( t ) is the pulse
shape of the data bit. In practical applications, rT(t)has a bandlimited waveform, such as a
raised cosine Nyquistpulse. However, for analysis and simulation simplicity, we will assume
that FT ( t )is a rectangular pulse throughout chapter, which is defined as:
this
1, O S t < T ,
rT(t) = 0, otherwise.
Similarly, the spreading sequencemay be written as
M
+
where ah E { 1,-l} denotes the hth chip and FT, (t)is the chip-pulse with a chip duration
of Tc.The energyof the spreading sequence
over a bit duration of Tb is normalised according
to:
As seen in Figure 1.3, the data signal and spreading sequence are multiplied, and the
resultant spread signal is modulated on carrier in order to produce the wideband signal s ( t )
a
at the output:
s ( t ) = a b ( t ) a ( t )COS w,t, (1.6)
where P is the average transmittedpower. At the intended receiver, the signal is multiplied
b
by the conjugate of the transmitter's spreading sequence,which is known as the despreading
sequence, in order to retrieve the information. Ideally, in a single-user, nonfading, noise-
less environment, the original information can be decoded without errors. This is seen in
Figure 1.4.
In reality, however, the conditions are never so perfect. The received signal will be cor-
rupted by noise, interfered by both multipath fading- resulting in intersymbol interference
(IS) - and by other users, generating multi-user interference. Furthermore, this signal is
delayed by the time-dispersive medium.It is possibleto reduce the interference due to multi-
path fadingand other users by innovative signal processing methods,which will bediscussed
in more detail in later sections.
Figure 1.5 shows the block diagramof the receiver for a noise-compted channel using a
correlator for detecting the transmitted signal, yielding:
(i+l)Tb
bi = sgn{
fl
J
1iTb a * ( t ) [ s ( t+ n(t)]
) coswct dt
where = Tb x P is the bit energy and sgn(z) is the signum function of x,which returns
b
a value of 1, if x > 0 and returns a value of -1, if z < 0. In a single-user Additive White
- 6 CHAPTER 1. THIRD-GENERATION
SYSTEMS CDMA
X
l- T, = N , x
Figure 1.4: Time-domain waveforms involvedin decoding a direct sequence signal
l
cos wet a* ( t )
Signature
sequence
Figure 1.5: BPSK DS-SS receiver for AWGN channel.
Gaussian Noise (AWGN) channel, the receiver shown in Figure 1.5 is optimum. In fact, the
so
performance of the DS-SS system discussed far is the same as that of a conventional BPSK
modem in an AWGN channel, wherebythe probability of bit error P T b ( c ) is given by:
where
&(x) = l
l o "
eVY2/'dy (1.9)
is the Gaussian Q-function. The advantages spread spectrum communications and CDMA
of
will only be appreciated in a multipath multiple access environment. The multipath
aspects
and how the so-called RAKE receiver [5,43] be used to overcome the multipath effects
can
will be highlighted in the next section.
1.2.2 The Effect of Multipath Channels
In this section, we present an overview of the effects of the multipath wireless channels en-
countered in a digital mobile communication system, which treated in depth for example
was
- 1.2. BASIC CDMA SYSTEM 7
in [ 1l]. Interested readers may also refer to the recent articles written by Sklar in [44,45] for
a brief overview on this subject,
Since the mobile station is usually close to the ground, the transmitted signal is re-
flected, refracted, and scattered from objects in its vicinity, such as buildings, trees, and
mountains [35]. Therefore, the received signal is comprised of a successionof possibly over-
lapping, delayed replicas of the transmitted signal. Each replica is unique in its arrival time,
power, and phase [46]. As the receiver or the reflecting objects are not stationary, such re-
flections will be imposed fading on the received signal, where the fading causes the signal
strength to vary in an unpredictable manner. This phenomenon is referred to as multipath
propagation [ 1l].
There are typically two types of fading in the mobile radio channel [44]:
0 Long-term fading
0 Short-term fading
As argued in [l l]long-term fading is caused by the terrain configuration betweenthe base
station and the mobile station, such as hills and clumps of buildings, which result in an
average signal power attenuation as a function of distance. For our purposes the channel
can be describedin terms of its average pathloss, typically obeying an inverse fourth power
law [35] and a log-normallydistributed variation around the mean. Thus, long-termshadow
fading wasalso referred to as log-normal fading in [ 11,441 .
On the other hand, short-term fadingrefers to the dramatic changes in signal amplitude
and phase as a result of small changes in the spatial separation between the receiver and
transmitter, as we noted in [ 11,441.
Furthermore, the motion betweenthe transmitter and receiver results in propagation path
changes,such that the channelappears to be time-variant. The time-variant frequency-
selective channel was modelled as a tapped delay line in [ 1l], where the complex low-pass
impulse response can be modelled as:
(1.10)
where la1 ( t ) , ~ ( t ) and 7 are the amplitude, phase, and delayof the Zth path, respectively,
I I 1
and L is the total number of multipath components. wasargued in [ 1l] that the rate of signal
It
level fluctuation is determined by the Doppler frequency,fo, which in turn is dependent on
the carrier frequency, fc, and the speed of the mobile station W according to (see also page 16
of [47]):
(1.11)
where c is the speed of light.
Typically, the short-term fading phenomenon modelled statistically by a Rayleigh,Ri-
is
cian, or Nakagami-m distribution [48]. The Rayleigh and Rician distributions were char-
acterised for example in [l l]. There have been some contrasting views in the literature as
to which of these distributions best describes the fast-fading channel statistically. Although
empirical results have shown that the fading statistics are best described by a Nakagami dis-
tribution [49], in most cases a Rayleigh-distributed fadingused for analysis and simulation
is
- 8 CHAPTER 1. THIRD-GENERATION
SYSTEMS CDMA
I'O
0.9 1
0.8
0.7
0 1 2 3 4 5 6 7 8 9 1 0
Time Delay [PS]
Figure 1.6: COST 207 BU impulse response.
because of simplicity, and it serves as a useful illustrative example in demonstrating the ef-
fects of fading on transmission. Moreover, the Rayleigh distribution is a special case of the
Nakagami distribution, when m, known as the fading parameter, is equal to unity (see page
48 in [5]).The Rician distribution is more applicable to satellite communication, due to the
presence of a dominant signal component known as the specular component [44], than to
large-cell terrestrial communication, where often there is no Line-of-Sight (LOS) path be-
tween the terrestrial base station and the mobile station. However, in small microcells often
the opposite is true. In our investigations in this chapter, Rayleigh-distributed frequencyse-
lective fading is assumed.
The delay is proportional the length of the corresponding signal path between trans-
to the
mitter and receiver. The delay spread due to the path-length differences between the multi-
path components causes Intersymbol Interference (ISI) in data transmission, which becomes
particularly dominant for high data rates.
A typical radio channel impulse response isshown in Figure 1.6. This channel impulse
response is known as the COST 207 bad urban (BU) impulse response[50].It can be clearly
seen that the response consists of two main groups of delayed propagation paths: a main
profile and a smaller echo profile following the main profile at a delay of 5 p . The main
profile is caused by reflections of the signal from structures in the vicinity of the receiver
with shorter delay times. On the other hand, the echo profile could be caused by several
reflections from a larger but more distant object, such as a hill [51]. In either case, we can
see that both profiles approximately follow a negative exponentially decaying function with
respect to the time-delay.
Figure 1.7 shows the impairments of the spread spectrum signal travelling over a multi-
path channel with L independent paths, yielding the equivalent baseband received signal of:
L
(1.12)
- 1.2. BASIC CDMA SYSTEM 9
Figure 1.7: Multipath propagation model of the transmitted signal.
where q ( t ) is the time-variant complex channel gain, which is given by J a l ( t ) l e j @ p , (in)
t
Equation l . 10 with a Rayleigh-distributed amplitude, uniformly distributed phase over the
interval [ -7r . . .7r] and g ( t - 71) is the equivalent baseband transmitted spread spectrum signal
from Equation l .6 delayed by 71. The above equation shows the Zth path is attenuated by
that
the channel coefficient a ( t )and delayed by 71. Without intelligent diversity techniques [ 5 ] ,
1
these paths are added together at the receiver and any phase or delaydifference between the
paths may result in a severely multipath interfered signal, corrupted by dispersion-induced
intersymbol interference (1.31).
Figure 1.8 shows the effect of a nonfading channel and a fading channel on the bit er-
ror probability of BPSK-modulated CDMA. Without diversity, the bit error rate (BER) in
a fading channel decreases approximately according to Prb(6) M &, where rc the av-
is
erage Signal-to-Noise Ratio (SNR), and hence plotted on a logarithmic scale according to
log Prb(c) = - log47, we have a near-linear curve [ 5 ] . This is different from a nonfad-
ing, or AWGN, channel, wherebythe BER decreases exponentially with increasing the SNR.
Thus, in a fading channel, a high transmitted power is required to obtain alow probability of
error. As we shall see in the next section, diversity techniques can be used to overcome this
impediment.
1.2.3 RAKE Receiver
As mentioned previously, spread spectrum techniques can take advantage of the multipath
nature of the mobile channel in order to improve reception. This is possible due to the sig-
nal's wideband nature, which has a significantly higher bandwidth than the multipath chan-
nel's coherence bandwidth [52]. In this case, the channel was termed a frequency selective
- 10 CHAPTER 1. THIRD-GENERATION
SYSTEMS CDMA
Figure 1.8: Performanceof BPSK modulated CDMA overvariousRayleigh-fadingchannels.The
curves were obtained using perfect channel estimation, and there was no self-interference
between diversity paths.
fading channel, since different transmitted frequencies faded differently if their separation
was higher than the previously mentioned coherence bandwidth. Suppose that the spread
spectrum has a bandwidth of B , and the channel’s coherence bandwidth is B,, such that
B, > B,. Thus, the number of resolvable independent paths - that is, the paths that fade
>
near-independently - L R is equal to
(1.13)
where . is the largest integer thatless than or equal to The number of resolvable paths
j1 is x.
L R varies according to the environment, and it is typically higher in urban than in suburban
areas, since in urban areas the coherence bandwidth is typically lower due to the typically
higher delay-spread of the channel [35]. More explicitly, this is a consequence of the more
dispersive impulse response, since the coherence bandwidth is proportional to the recipro-
cal of the impulses responses delay spread, as it was argued in [ 5 2 ] . Similarly to frequency
diversity or space diversity, these LR resolvable paths can be employed in multipath diver-
sity schemes, which exploit the fact thatstatistically speaking, the different paths cannot be
in deep fades simultaneously; hence, there is always at least one propagation path, which
provides an unattenuated channel. These multipath components are diversity paths.
Multipath diversity can only be exploited in conjunction with wideband signals. From
Equation 1.13, for a narrowband signal, where no deliberate signal spreading takes place,
- 1.2. BASIC 11
the signal bandwidth B, is significantly lower than B,. In this case, the channel was termed
frequency nonselectivein [52]. Hence, no resolvable diversity paths can be observed, unlike
in a wideband situation, and this renders TDMA and FDMA potentially less robust in a
narrowband mobile radio channel CDMA.than
Multipath diversity is achieved, for example, by a receiver referred to as the RAKE re-
ceiver invented by Price and Green [43]. This is the optimum receiver for wideband fading
multipath signals. It inherited its name fromthe analogy of a gardenrake, whereby the fingers
constitute the resolvable paths. The point where handle and fingers meet is where diversity
the
combining takes place. There are four basic methods of diversity combining, namely[53]:
0 Selection Combining (SC).
0 Maximal Ratio Combining (MRC).
0 Equal Gain Combining (EGC).
0 Combining of the n best signals (SCn).
The performance analysis of selection combining in CDMA can be found in [54,55], while
a general comparison of the various diversity combining techniques can be found in [53]
for Rayleigh-fading channels. Maximal ratio combining gives the best performance, while
selection combining is the simplest to implement. The number of resolvable paths that are
combined at the receiver, represents the order of diversity of the receiver, which is denoted
here as L P . We note, however, that in practical receivers not all resolvable multipath compo-
<
nents are combined dueto complexity reasons, that is, L p LR.
There are two basic demodulation techniques, namely coherent noncoherent demod-
and
ulation [5]. We will highlight the basics of coherent demodulation in this section in the
context of CDMA. However, before demodulation can take place, synchronisation between
the transmitter and the intended receiver has to be achieved.
Synchronisation in DS-CDMA is performed by a processknown as code acquisition and
tracking. Acquisition is usually carried out by invokingcorrelation techniques between re- the
ceiver’s own copy of the signature sequence andthe received signature sequence and search-
ing for the displacement between them -associated with specific chip epoch that results
a -
in the high correlation [37,56,57]. Once acquisition has been accomplished,usually a code
tracking loop [58] is employed to achieve fine alignment of the two sequences andto main-
tain their alignment. Thedetails of code acquisition and trackingare beyond the scope of this
chapter. Interested readers may refer to [59-62:1 and the references therein for an in-depth
treatise on this subject. Hence, in this chapter, we will assume that the transmitter and the
intended receiver are perfectly synchronised.
For optimum performanceof the RAKE receiver using coherent demodulation,the path
attenuation and phase must be accurately estimated. This estimation is performed by an-
other process knownas channel estimation, which will be elaborated onin Section l .2.6. In
typical low-complexity applications, known pilot symbols can be inserted in the transmit-
ted sequence in order to estimate the channel’s attenuation and phase rotation. However, for
now, let us assume perfect channel estimation order to assess the performance of the RAKE
in
diversity combiner.
Figure 1.9 shows the block diagram of the HPSK RAKE receiver. The received signal
is first multiplied by the estimated channel coefficients a1 ( t ) , . . , a ( t ) in each RAKE
. ~ ~
- 12 CHAPTER 1. THIRD-GENERATION
SYSTEMSCDMA
a;(t) a*(t - 7 1 )
I I
Figure 1.9: RAKE receiver.
branch tuned to each resolvable path. For optimumperformance of the RAKE receiver using
maximal ratio combining, these channel coefficient estimates should be the conjugates of the
actual coefficients of the appropriate paths in order to invert the channel effects.* Note that
for equal gain combining only the phase is estimated, and the various path contributions are
multiplied by a unity gain before summation. The resulting signals in each RAKE branch
are then multiplied by the conjugate signature sequences as wehaveseenin Figure 1.3,
delayed accordingly by the code acquisition process. After despreading by the conjugate
signature sequencesa*(t - T I ) , . . . , a*(t - T L ~ )the outputs of the correlators in Figure 1.9
,
are combined in order obtain the decoded symbolof'
to
(1.14)
Normally, the first term of Equation 1.14, which contains the useful information, is much
larger than the despread, noise-related second term. This is because the first term is pro-
portional to the sum of the absolute values of the channel coefficients, whereas the second
term in Equation 1.14 is proportional to the vectorial sum of the complex-valued channel
'c~leJ91 c~le-J4I = a2
X
1'
3Here we assumed that there is no multipath interference. This interference can be considered as part of multi-
user interference, which will be discussed in the next section.
- 1.2. BASIC SYSTEM 13
Figure 1.10: CDMA system model.
coefficients. Hence, the real part of the first term is typically larger than that of the second
term. Thus, the RAKE receiver can enhance the detection of the data signal in a multipath
environment.
Refemng back to the BER curves of Figure 1.8, we can see that the performance of the
system is improved when multipath diversity is used. Better performance is observed by
increasing the number of diversity paths LP. However, this also increases the complexity of
the receiver, since the number of correlators has to be increased, which is shown in Figure 1.9.
1.2.4 Multiple Access
So far, only single-user transmission was considered. The system is simple and straight-
forward to implement. Let us now consider how multiple user transmission can affect the
performance of the system.
Multiple accessis achieved in DS-CDMA by allowing different users to share a common
frequency band. Each transmitter and its intended receiver are assigned adistinct user signa-
ture sequence. Onlythe receivers having the explicit knowledge of this distinct sequence are
capable of detecting the transmitted signal. Consider a CDMA scenariowith K number of
active users, transmitting simultaneously. The baseband equivalent system model is shown in
Figure l. 10. For simplicity, it is assumed that there is no multipath propagationand perfect
power control is maintained.
The mathematical representation of the kth user’s data signal is similar to that shown in
Equation 1.2, except for an additional superscript, denoting multi-usertransmission. Hence,
it is written as:
(1.15)
+
where b i k ) E { 1,-l}. There is a distinct user signature sequence ( t )associated with
the kth user, which is similar to that of Equation 1.4, with the exception of a superscript,
- 14 CHAPTER 1. THIRD-GENERATION
SYSTEMSCDMA
differentiating between users:
(1.16)
h=-m
The lcth user’s data signal b(”(t) and signature sequence a(”(t) are multiplied in order to
produce an equivalent baseband wideband signal, namely,
(1.17)
where Pi’) is the average transmit power of the lcth user’s signal. The compositemulti-user
baseband received signal is:
where d k ) is the propagation delay plus the relative transmission delay of the lcth user with
respect to other users, and n ( t )is the AWGN with a double-sided power spectral density of
+ WMZ.
1.2.4.1 Downlink
Interference
In the downlink (base station to mobile), the base station is capable of synchronising the
transmission of all the users’ signals, such that the symbol durations are aligned with each
other. Hence the composite signal is received at each mobile station with d l i ) = 0 for
IC = l,2, . . . , K . This scenario is also known as symbol-synchronous transmission. Using
the conventional so-called single-user detector, each symbol of the jth user is retrieved from
the received signal r ( t ) by correlating it with the jth user’s spreading code in order to give:
(1.19)
- 1.2. BASIC CDMA SYSTEM 15
Substituting Equation 1.18 into Equation 1.19 yields:
= sgn
--
5
@b!j)
wanted
signal
+
k=l
k#j
&,k)bik)Rjk
noise
multiple access interference
white
(1.20)
where R j k is the cross-correlation of the spreading codes of the kth and jth user for iTb 5
+
t 5 (i l)Tb, which is given by:
(1.21)
There will be no interference from the other users if the spreading codesare perfectly orthog-
onal to each other. That is, R j k = 0 for all k # j . However, designing orthogonal codes a
for
large number of users is extremely complex. The so-called Walsh-Hadamard codes [63] used
in the IS-95 system excel terms of achieving orthogonality.
in
1.2.4.2 Uplink Interference
In contrast to the previously considered downlinkscenario, in practical systems perfect or-
thogonality cannotbe achieved in the uplink (mobileto base station), since there is no coor-
dination in the transmission of the users' signals. In CDMA, all users transmit in the same
frequency band in an uncoordinated fashion. Hence, d k ) # 0, and the corresponding sce-
nario is referred to as an asynchronous transmission scenario. In this case, the time-delay
d k ) , k = 1, ..., K , has to be included in the calculation. Without loss of generality, it can
be assumed that = 0 and that 0 < T ( ~ < d 3 ) < ... < d K ) < T b . In contrast to the
)
synchronous downlink scenario Equation 1.19, the demodulation of the ith symbol of the
of
jth user is performed by correlating the received signal r ( t ) with a ( j ) * t )delayed by #,
(
- 16 CHAPTER 1. THIRD-GENERATION
SYSTEMSCDMA
yielding:
(1.22)
where i ( j ) is the estimated time-delay at receiver.
the
Substituting Equation1.18 into Equation 1.22 assuming perfect code acquisition and
and
tracking yield:4
4For perfect code acquisition and tracking, ? ( j ) = ~ ( j ) .
- 1.2. BASIC CDMA SYSTEM 17
-
wanted
signal
k=L
p
multiple access interference
k=l k=.7+l
v
multiple access interference
K -
(1.24)
k=j+l ~ white-noise I
multiple access interference
where R j k ( i ) and f i j k ( i ) ,i E { + l ,0 , - l } represent the cross-correlation of the spreading
codes due to asynchronous transmissions, which are given by [64]:
(1.25)
and
and is limited to +l,0 , - 1, since the maximum path delay is assumed to be limited to one
symbol duration, asmentioned in Section 1.2.2.
Equations 1.24 and 1.20 represent the estimated demodulated data symbol of the jth user
at the base station and mobile station, respectively. Both contain the desired symbol of the
j t h user. However, thisis corrupted by noise and interference from the other
users. This inter-
ference is known as multiple access interference (MAI). It contains the undesired interfering
signals from the other ( K - 1 ) users. The MA1 arises due to the nonzero cross-correlation
of the spreading codes. Ideally, the spreading codes should satisfy the orthogonality property
such that
(1.27)
However, it is impossible to design codes thatare orthogonal for all possible time offsets im-
posed by the asynchronous uplink transmissions. Thus there will always be MA1 in the up-
link. These observations are augmented by comparing the terms of Equations 1.20 and 1.24.
On the other hand, multipath interference is always present in both the forward and re-
verse link. Multipath interference is due to the different arrival times of the same signal via
- 18 CHAPTER 1. THIRD-GENERATION
SYSTEMSCDMA
the different paths at the receiver. This is analogous to the signals transmitted from other
users; hence, multipathinterference is usually analysed in the same way as MAI.
As the number of users increases, the MA1 increases too. Thus, the capacity of CDMA
is known to be interference limited. CDMA is capable accommodating additional users at
of
the expense of a gradual degradationin performance in a fixed bandwidth, whereas TDMA
or FDMA would require additional bandwidth to accommodate additional users. Intensive
research has been carried out to find ways of mitigating the effects of MAI. Some of the
methods include voice activity control, spreading code design, power control schemes, and
sectored/adaptive antennas[65]. These methods reduce MA1 to a certain extent.
the
The most promising uplink method so far has been in the area of multi-user detection,
which was first proposed by Verdii [66]. Multi-user detection [6749], which will be dis-
cussed in more depth in the next chapter, invokes the knowledge of all users’ signature se-
quences and all users’ channel impulse response estimates order to improve the detection
in
of each individual user. The employment of this algorithm is more feasible for the uplink,
because all mobiles transmit to the base station and the base station has to detect all the
users’ signals anyway. The topic of multi-user detection is however beyondthe scope of this
chapter, since it will be discussed in a little more detail in the next chapter, namely in Chap-
ter 2. For a more indepth treatment the interested readers are referred to Verdu’s excellent
book [70], which provides a comprehensive discussion on topic. A generalreview of the
the
various multi-user detection schemes further references can also be found, for example,
and
in Moshavi’s contribution[65].
Another shortcomingof CDMA systemsis their susceptibility to the near-far problem to
be highlighted below. If all users transmit at equal power, then signals from users near the
base station are received at a higher power than those from users at a higher distance due to
their different path-losses. The effects of fading highlighted in Section 1.2.2 also contribute
to the power variation. Hence, accordingto Equation 1.24, if the jth user is transmitting from
the cell border and all other users are transmitting near the base station, then the desired jth
user’s signal will be masked by the other users’ stronger signals, which results in a high bit
error rate. In order to mitigate this so-called near-far problem, power control is used to ensure
that all signals from the users are received at near-equal power, regardless of their distance
from the base station.
There are typically two basic types of power control [38]:
0 open-loop power control
0 closed-loop power control
Open-loop power control is usually used to overcome the variation in power caused by
pathloss. On the other hand, closed-loop power control is used to overcome shadow fad-
ing caused by multipath. The details of the various power control techniques will not be
elaborated onin this chapter. Readers may refer to [7l] for more information.
1.2.4.3 Gaussian
Approximation
In order to simplify any analysis involving multi-user transmission in CDMA, the MA1 is
usually assumed to be Gaussian distributed by virtue of the central limit theorem [72-741.
This assumption is fairly accurate even for K < 10 users, when the BER is lop3 or higher.
- 1.2. BASIC 19
We will use the standard Gaussian approximation theory presented Pursley [72] to repre-
by
sent the MAI. When the desired user sequence is chip- and phase-synchronous with all the
interfering sequences, wherethe phase-synchronous relationship is defined as in the absence
of noise, the worst-case probability of error Prb ( E ) performance was given by Pursley [72]
as:
(1.28)
where Q(.) is the Gaussion Q-functionof Equation 1.9, since the synchronous transitions do
not generate pure random Gaussian-like impairments. This formula would be characteristic
of the synchronous downlink scenario Section l .2.4.1. However, in practical uplink situa-
of
tions as augmented in Section 1.2.4.2, there is always some delay among users, and each
the
received signal will be phase-shifted independently. In this case, according to Pursley, the
probability of error in the absence of noise will be [72]:
(1.29)
Equation 1.29 represents the best performance corresponding to Gaussian-like impair-
ments. In between these two extremes are situations whereby, in the first case, the desired
sequence andthe interfering sequence are chip synchronousbut not phase synchronous. The
probability of error in the absence of noise is given by [72]:
(1.30)
In the second case, the desired sequence and
interfering sequence are phase synchronous
but not chip synchronous. Hence, the probability of error in the absence of noise is given
by [72]:
(1.31)
Analysing the above equations,it can be seen that by increasing the number of chips N ,
per symbol,the performance of the system will be improved. However, there is alimitation to
the rate of the spreading sequence based on Digital Signal Processing (DSP) technology. Fig-
ure 1.1 1 compares the simulated results with the numerical results given by Equations 1.28
to I .3 1 for a binary systemwith a processing gain 7. The figure shows that the assumption
of
of Gaussian distributed MA1 is valid, especially for a high number of users. It also demon-
strates that CDMA attains its best possible perfolmance an asynchronous multi-user trans-
in
mission system. This is an advantage over TDMA and FDMA because TDMAand FDMA
require some coordination amongthe transmitting users, which increases the complexity of
the system.
- 20 CHAPTER 1. THIRD-GENERATION
SYSTEMSCDMA
A Chip & phase sync
0 Phase sync
0 Chipsync
0 Async
,n-4 I I
Figure 1.11: Probability of error against number of users using Equations 1.28, 1.29, 1.30, and 1.31.
Markers: Simulation;solid line: Numerical computation. The processing gain is 7.
1.2.5 Spreading Codes
As seen previously, the choice of spreading codes plays an important role in DS-CDMA. The
a
main criteria for selecting particular setof user signature sequences in CDMA applications
are that the number possible differentsequences in the set forany sequence length must be
of
high inorder toaccommodate a high number of users in a cell. The spreading sequences must
also exhibitlow cross-correlations for the of reducing the multi-user interference during
sake
demodulation. A high autocorrelation main-peak to secondary-peak ratio - as indicated
by Equation 1.27 - is also essential, in order to minimise the probability of so-called false
alarms during code acquisition. This also reduces the self-interference among the diversity
paths. Below we provide a brief overview of a few differentspreading sequences.
1.2.5.1 m-sequences
Perhaps the most popular set of codes known are the m-sequences[ 5 ] . An m-sequence with
a periodicity of n = 2" - l can be readily generated by an m-stage shift register with linear
feedback, as shown in Figure 1.12.
The tap coefficients c l , c2, . . . , c, can be either 1 (short circuit) or 0 (open circuit). In-
formation on the shiftregister feedback polynomials, describing the connections between the
register stagesand the modulo-2 adders can be found, for example, in [5]. Note that in spread
spectrum applications, theoutput binary sequences of 0,l are mapped into a bipolar sequence
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