Chapter
1
Introduction to Cellular Radio
This book is concerned with two digital mobile radio systems: the global system for mo-
bile communications (GSM); and a code division multiple access (CDMA) system that
was originally known as the American interim standard 95, or IS-95 and is now called cd-
maOne [1–7]. While GSM was conceived and developed through the concerted efforts of
regulators, operators and equipment manufacturers in Europe, cdmaOne owes its existence
to one dynamic Californian company, Qualcomm Inc. The authors have been involved
with both the pan-European mobile radio system, which became GSM, and the Qualcomm
CDMA system for a number of years. The GSM system predates cdmaOne.
The two systems are very different. The radio interface of GSM relies on time division
multiple access (TDMA), which means that its radio link is very different to that of cd-
maOne. Also GSM is a complete network specification, from the subscriber unit through
to the network gateway. Indeed its fixed network component is perhaps its most advanced
feature [1, 2]. cdmaOne, by contrast, has a more complex and advanced radio interface, and
only later were fixed network issues addressed [3, 7].
In the chapters to follow, the GSM and cdmaOne systems will be described and analysed
while the final chapter deals with their evolution to third generation systems. This chapter is
meant to provide background information on cellular radio [1–11]. The reader who is well
acquainted with the fundamentals of mobile radio communications should therefore bypass
this chapter.
For the reader who has elected to read this chapter we should state at the outset that
our goal is to provide a clear exposition of the concepts of the subject rather than detailed
analyses, which will follow in the later chapters. The first point to make is that a mobile
radio network has a radio interface that enables a mobile station (MS) to communicate
with the fixed part of the mobile network. Both components, the radio interface that fa-
cilitates user mobility, and the fixed network that enables the mobile to communicate with
1
eter Gould
Wiley & Sons Ltd

directional, which means that power is directed over a solid angle rather than over all an-
gles. This means that compared with isotropic radiator there is a gain G
(
θ

φ
)
of power in
the θ and φ directions, where θ and φ are angles measured in the vertical and horizontal
directions, respectively.
As the transmitted energy spreads out from the BS, the amount of power the MS antenna
can receive diminishes [12, 13]. The mobile’s antenna is usually located only one to two
metres above the ground whereas the BS antenna may be at a height from several metres
to in excess of a hundred metres. The heights of the antenna affect the path loss, i.e. the
difference in the received signal power at the MS antenna compared with the BS transmitted
power. The path loss (PL) is usually measured in decibels (dB). As an example, for the plane
earth model there are two paths, a direct line-of-sight (LOS) path and a ground-reflected
1.1. A SINGLE CELL
3
path. The expression for PL is
PL
=

h
T
h
R
d
2


(
θ

φ
)
are the gains of the
transmitter and receiving antenna, respectively. When written in decibels, the path loss, L
p
,
becomes
L
p
=
10log
10
PL
=
20log
10
h
T
+
20log
10
h
R

40log
10
d

where λ is the wavelength of the radiated wave.
The plane earth model is useful but may deviate significantly from reality. In the plane
earth model, L
p
decreases at 40 dB per decade increase in distance, i.e. if the distance
increases by 10 times, the path loss will increase by 40 dB. This rate is often used in prac-
tical situations, although measurements show it may be closer to 35 dB per decade. If
the transmitted power is sufficiently high a MS will often travel beyond the LOS of the
BS antenna. When a mobile goes behind a large building the average received power will
decrease and when it emerges from the building that casts the electromagnetic shadow, the
average received power will rise. The fading due to large obstacles that produce electromag-
netic shadows is called shadow fading. As a result of this fading effect, as the MS travels
away from the BS the received power at the MS and the BS is subjected to considerable
variations. These variations due to shadowing effects can be represented by a log-normal
distribution of a shadow fading random variable ζ. Specifically we introduce this variable
into Equation (1.2) to give
L
p
=
20log
10
h
T
+
20log
10
h
R

40log

10log
10
P

10n log
10
d
+
ζ (1.5)
4
CHAPTER 1. INTRODUCTION TO CELLULAR RADIO
or, when not in decibels, the expression becomes
S
=
Pd

n
10
ζ
=
10

(1.6)
where P is the transmitted power from the BS and n is called the exponent of the PL.
Observe that when we employ Equations (1.5) or (1.6), the terms relating to antenna heights
and antenna gains are absent. This is because we often ignore the effects associated with the
antennas on the path loss when we are concerned with signal-to-interference ratios (SIRs)
since these parameters tend to cancel out on the signal and interference paths. Equation (1.6)
is used extensively in Chapters 3 and 5.
The MS is not only subjected to shadow fading, but also to small scale fading, i.e. due

ing another delta function that is also Rayleigh distributed. This process of each received
ray causing a group of scattered rays that can be represented by a Rayleigh distributed delta
function yields a channel impulse response that is itself made up of a number of impulses
or delta functions at epochs 0, τ
1
, τ
2
:::
, as shown in Figure 1.1. Since each delta function
is fading independently the spectrum of the radio channel no longer fades uniformly for all
frequencies. This type of fading is called frequency selective fading, which means that in
the time domain the depths of the fades are, in general, much less than for flat fading. In
the latter case the fading can be very deep, typically up to 40 dB, and this may cause bursts
of symbol errors. As a consequence, having a wideband channel means that the signal is
less likely to drop below the receiver sensitivity for a given transmitted power compared
1.1. A SINGLE CELL
5
with a narrow band channel. However, the wideband channel has a wider impulse response,
and since the received signal is the convolution of the transmitted signal with the impulse
response of the radio channel, one data symbol is smeared into other symbols. This effect,
called intersymbol interference (ISI), requires the receiver to un-smear the symbols. This
is achieved using a channel equaliser in GSM and a RAKE receiver in cdmaOne. We will
return to channel equalisation and RAKE receivers in some detail in later sections.
As a MS travels away from the BS, the received signal at the MS decreases as the path
loss increases. The received signal will also exhibit large scale (shadowing) fading and small
scale fading. Figure 1.2 shows an example of the variations in the received signal level (in
dBs) as the MS travels. The dotted line represents the change in received signal level due
to shadow fading. The rapid changes in the received signal level are the consequence of
small scale fading, which for a particular carrier frequency depends on the MS speed. The
faster the MS travels, the more rapid is the fading. A stationary MS may be in a deep fade.

-110
-100
-90
-80
-70
-60
-50
-40
0 0.2 0.4 0.6 0.8 1
Time (s)
Received signal level (dBm)
Figure 1.2: Combined shadow and fast fading.
f
c
+(
ν
=
λ
)
cosα
i
,whereν is the speed of the MS and λ is the wavelength of the carrier
(
=
3

10
8
=
f

Conversely, when the received signal level drops below the receiver sensitivity, the MS is
1.2. MULTIPLE CELLS
7
no longer able to receive signals of an acceptable quality from the BS. The point in space at
which this threshold occurs represents a boundary point for the down-link or forward link,
i.e. the transmissions from the BS to the MS.
What about the up-link or reverse link, i.e. the transmission from the MS to the BS?
The two links are never the same. They are similar in GSM and radically different in
cdmaOne. The MS transmitter operates at significantly lower power levels than the BS and
so the maximum radiated power levels are lower than those at the BS. The BS is able to
compensate for the MS deficiencies by being able to operate at a lower receiver sensitivity
and by employing techniques such as space diversity to enhance the received signal from
the MS. It is important to note that the signal characteristics that we have already discussed
in relation to the down-link (i.e. path loss, fast and slow fading, Doppler shift and ISI) will
also be present in the received up-link signal. To simplify our discussion, we will assume
that our boundary point is the same for either link, unless specifically stated.
If the MS takes a number of different routes away from the BS and on each route notes
the location where the received signal goes below the receiver sensitivity, then by joining up
these location points on a map we will form a contour around the BS. A stylised arbitrary
irregularly shaped contour is shown in Figure 1.3. The area enclosed within the boundary
is called a cell.
1.2 Multiple Cells
The dimensions of a cell are limited by the transmitter and receiver performances, the path
loss, shadow fading and other factors described in the previous section. If we are going to
cover wide areas we will need to tessellate cells, and switch a MS between BSs as it roams
throughout the network. If hundreds or thousands of cells are required, then some cells must
operate with the same carrier frequencies. This phenomenon is called frequency reuse.
BS
Figure 1.3: A single cell.
8

same channel sets.
The number of cells in the cluster, M, is called the reuse factor. The value of M depends
on the SIR. If, for an acceptable BER, the SIR is required to be high, then we must have
many cells in the cluster in order to space the ‘reuse cells’ sufficiently far apart such that the
interference is low enough to satisfy the minimum SIR requirement. We will see that GSM
requires M

3, while cdmaOne can operate with M
=
1.
Why is a low cluster size good? By operating with a smaller number of cells in a cluster
the number of channels per cell, equal to
(
N
=
M
)(
W
=
B
c
)
, is high, since M is low. The carried
C
D
A
B
Cluster 1
C
D

access scheme is complex and will be addressed at a later stage. What we must note is that,
given a modulation and multiple access scheme resulting in a cluster size of M, the number
of users on the network is greatly increased if the cells, and thereby the clusters, are small.
This is because each cluster carries a traffic of MA
c
Erlangs, where A
c
is the carried traffic
at each BS, and if a cluster occupies an area S
c
then the traffic carried per km
2
is MA
c
=
S
c
Erlangs/km
2
for a bandwidth W . Using small cells, often called microcells, means S
c
is
small and the traffic density that may be supported is high.
1.2.1 Hexagonal cells
These types of cells are conceptual. The cell site is located at the centre of each hexagon,
and the hexagonal cells are tessellated to form clusters [15]. Although these cells are fic-
titious, they are often used for comparing the performances of different cellular systems.
Figure 1.6 shows clusters of tessellated hexagonal cells. Observe that for hexagonal cells
there are always six near cochannel cells, irrespective of the cluster size. This is because
10

=
2

D

(1.7)
cos ψ
=
i
+(
j
=
2
)
D

(1.8)
and as
sin
2
ψ
+
cos
2
ψ
=
1

(1.9)
D

1.2. MULTIPLE CELLS
11
4
Re-use distance
D
3
3
1
1
3
1
1
2
3
4
2
4
2
1
4
3
2
R
4
1
3
2
1
2
4


l
2
+
lm
+
m
2

1
2

(1.14)
A cluster of hexagonal cells can be approximated by a large hexagon of dimension R
c
as
shown in Figure 1.9. The number of cells, M, in this cluster is the ratio of the area of the
cluster to the area of the cell, which is equal to the ratio of the distance squared between
the centres of the clusters to the distance squared between the centres of adjacent hexagonal
cells, i.e.
M
=
D
2
(
2µ
)
2
=
l

with practical antennas, and in general they do not create significant interference between
sectors.
To simplify analysis we consider idealised antenna patterns that span a fixed number
of degrees exactly, and ignore overlapping areas. Figure 1.11 shows a three-cell cluster
arrangement with three sectors per cell, whereas Figure 1.12 is a four-cell cluster with
again three sectors per cell but with different shaped sectors. As seen from the zeroth cell
site there are only two sectors that cause significant interference. From Equation (1.14),
D
=
2
p
3µ and 4µ for the three- and four-cell per cluster arrangements, respectively. For an
unsectorised arrangement, there are six significant interferers located at the same distances
of 2
p
3µ and 4µ. Consequently the interference is decreased by a factor of three.
While sectorisation does significantly increase the SIRs, it often decreases the carried
traffic in time division multiple access (TDMA) and frequency division multiple access
(FDMA) systems. Dividing the number of channels, N, at an omnidirectional cell site into
three groups while maintaining the same probability of a cell being blocked means that the
14
CHAPTER 1. INTRODUCTION TO CELLULAR RADIO
SECTOR 2
Overlap region
SECTOR 3
SECTOR 1
Cell site
Figure 1.10: Antenna patterns for a cell site having three 120

sectors.

each sector and there will be no trunking efficiency loss. In a system with perfect sec-
torisation the increase in capacity at a cell site will be equal to the number of sectors, i.e. a
three-fold increase for three sectors. In practice, interference caused by overlapping antenna
patterns and side and back lobes reduces this gain to around 80% of the ideal case.
1.3 The TDMA Radio Interface
1.3.1 Multiple access procedure for TDMA
In mobile radio communications, multiple users access the allotted radio spectrum in order
to communicate, via the fixed component of the mobile network, with another user in the
PSTN/ISDN or in its own or other mobile networks. There are different multiple access
16
CHAPTER 1. INTRODUCTION TO CELLULAR RADIO
methods but the basic one is FDMA in which each user is assigned a sub-band of the spec-
trum for the duration of the call. The sub-bands that support a traffic channel are arranged to
be contiguous, as shown in Figure 1.13. Note that user k transmits on frequency f
uk
on the
up-link, so-called because it is from a mobile at a low elevation to a BS antenna at a higher
elevation. The up-link is also referred to as the reverse link. The forward or down-link is
used for transmissions from the BS to the MS, and therefore the MS receives on frequency
f
dk
. It is usual that each user has a pair of up-link and down-link channels that are always
spaced apart by a frequency f
dup
. Transmitting and receiving at the same time but on dif-
ferent frequencies is called frequency division duplexing (FDD). To assist the duplexer in
protecting the strong transmitted signal from affecting the weak received signal, f
dup
is suf-
ficiently large to ensure that the transmitted energy at f

corresponding to 40 channels. For the 5 MHz band we have 24 carriers (allowing for a
1.3. THE TDMA RADIO INTERFACE
17
up-link FDMA channels
uk
user k
dup
down-link FDMA channels
dk
frequency
user k
Figure 1.13: FDMA radio channels for FDD operation.
1 Slot
6 78
1 Frame
312 45 26781 34 5
Figure 1.14: Transmitter TDMA framing structure.
Frequency
FDMA
TDMA
Figure 1.15: Channel occupancy of a single FDMA and TDMA channel (note that eight users can
be accommodated per TDMA carrier).
18
CHAPTER 1. INTRODUCTION TO CELLULAR RADIO
guard band), and it is these carriers that are deployed in our cellular structure. Thus, if there
are four cells per cluster and three sectors per cell, we may have two carriers or 16 channels
per sector. Adjacent carrier frequencies must not be used at the same site as they will
interfere with each other. This is known as adjacent channel interference. Planning which
carriers to use in each sector is complex, and is known as frequency planning.Caremust
be exercised to maximise both the signal-to-cochannel interference ratios and the signal-

base station transmitter and mobile receiver). The transmitter consists of a speech encoder
that digitises the speech signal from the microphone. Both GSM and cdmaOne use the
analysis-by-synthesis type of codecs. The GSM codec is a regular pulse excited linear
predictive codec (RPE-LTP) that generates bits at a fixed rate. A variable rate code excited
linear predictive codec (CELP) is used in cdmaOne. Since our analysis of both GSM and
cdmaOne presupposes that the speech is in a coded format, we advise the interested reader
to read Chapters 3 and 8 in Reference [2] which deal with analysis-by-synthesis speech
coding.
Both GSM and cdmaOne employ convolutional coding which accepts the digitised speech
and essentially adds redundancy bits prior to transmission in order that the convolutional
decoder can correct some of the bit errors that occurred as a result of transmission over
1.3. THE TDMA RADIO INTERFACE
19
Sequence
Generation
and Baseband
Modulator
speech
input
Speech
coder
coder
FEC
Modulator
TDMA
buffer
burst
Transmitter
interleaver
bit

Figure 1.16: The basic TDMA mobile radio link.
the mobile radio channel. It is therefore appropriate that we say a few words concerning
convolutional coding, but for a more comprehensive discourse consult Reference [2].
Let us start by saying that mobile radio channels are not benign like optical channels or
even copper wire links in the PSTN. Mobile radio channels often cause high error rates
unless considerable counter measures are deployed. We have mentioned that as the mo-
bile travels away from the BS there is an increasing path loss, there is shadow fading,
fast fading, dispersion effects, receiver noise, co-channel interference and adjacent channel
interference. All of these factors may impair the received signal, and cause bits to be erro-
neously regenerated at the receiver. A host of measures are therefore employed to decrease
the probability of bit errors, and if bit errors do occur, the role of forward error correction
(FEC) codes is to correct as many of them as the power of the code will allow. In FEC
coding the coder generally takes k input message bits at a time and maps them into n-bit
code words. The amount of redundancy introduced by the coder is measured by the ratio
n
=
k, and the inverse of it, namely k
=
n, is defined as the coding rate. The redundancy bits,
n

k, are used to increase the relative Hamming distance, which is the number of different
symbols between two code words or coded symbol sequences. An FEC decoder is able to
provide error correction, although this is limited by the Hamming distance provided.
We are interested in convolutional codes as they are used by both cdmaOne and GSM. A
convolutional coder accepts the latest k-bit and the previous
(
K

1

101
]
and g
2
=
111
]
(1.17)
and the corresponding code word

c
2

c
1
]
,where
c
1
=
2
6
4
b
2
b
1
b
0
3

generator vectors is two generator polynomials
g
1
(
z
)=
1
+
z
2
and g
2
(
z
)=
1
+
z
+
z
2

(1.19)
where 1 denotes the present input bit, and z and z
2
represent the previous input bits having
one and two clock period delays, respectively, and
+
is modulo 2 addition. The convo-
lutional coder is a finite-state machine which can be described by its state diagram. Fig-

3
)
is shown in Figure 1.19,
where the dashed and solid lines correspond to the latest input bit of 1 and 0, respectively.
In the trellis diagram, each node, represented by a dot, corresponds to the state shown on
the left-hand side of the figure. Similar to the state diagram of Figure 1.18, the dashed and
solid lines indicate the state transitions due to an input bit of 1 or 0, respectively. For a
input data sequence of 01101, the corresponding paths in the trellis diagram are displayed
by thick dashed and solid lines, and the coded symbol sequence is shown at the bottom
of the figure. Since the error correction performance of convolutional codes is related to
their Hamming distance, we redraw the state diagram as shown in Figure 1.20 to examine
the Hamming distance of cc
(
2

1

3
)
. Instead of labelling each branch with its correspond-
ing output code word, we label it with D
0
=
1, D
1
=
D or D
2
, where the exponent of D
represents the Hamming distance corresponding to that branch compared with the all-zero

00
state IV
11
00
01
00
01
01
10
01
10
01
01
11
state II
10
state I
00
state III
01
11
Figure 1.19: The trellis diagram for cc
(
2

1

3
)
.

DX
III

X
V
=
D
2
X
IV
:
(1.20)
For an infinite-length coded symbol sequence, the transfer function of the cc
(
2

1

3
)
code is
defined as
T
(
D

H
)=
X
V

H
3
+ :::+
2
k
D
k
+
5
H
k
+
1
+ :::
=
∞
∑
d
=
5
2
d

5
H
d

4
D
d

f
, of the code.
1.3. THE TDMA RADIO INTERFACE
23
D
D
DH
D
2
H
DH
D
2
X
I
H
X
V
X
IV
X
III
1010
00
01
11
X
II
00
Figure 1.20: An alternative state diagram for cc

form a packet. The input to the buffer is at the coded rate r
code
and will be removed from
the buffer as a burst in its assigned time slot and at the much higher rate r
burst
.Theburstdata
modulate an FDMA carrier and are transmitted. By opting for TDMA, the RF equipment
is simplified, but the signal processing at baseband in the receiver is increased. This is a
24
CHAPTER 1. INTRODUCTION TO CELLULAR RADIO
consequence of the TDMA structure transmitting and receiving data at a high rate due to
the method of bursty transmissions. As a crude approximation the burst rate r
burst
is r
code
increased by the number of slots per frame. Transmitting at high bit rates introduces ISI
where one bit is smeared over many. The radio channel is therefore dispersive, and in order
to regenerate the bits at the receiver we need to equalise the radio channel in order to remove
these dispersive effects. This in turn requires us to estimate the complex impulse response
of the mobile radio channel, and to achieve this we need to sound the channel. Rather than
apply an impulse to the radio channel, or rather an approximation to one, we opt to send
a pseudo-random sequence that has an autocorrelation function (ACF) that is impulse-like.
By this means we can estimate the channel impulse response. However, sending a pseudo-
random sequence in each TDMA packet represents a costly overhead in that, if it were not
required, the bits could be assigned to the speech or FEC coding.
Referring to Figure 1.16, we have now described that speech is encoded, followed by
channel coding and bit interleaving to combat bit error bursts. We also see that the packetiser
accepts both the interleaved coded speech and a sounding bit sequence. This sounding
sequence is placed in the centre of the packet with the coded data on either side. If the
sounding sequence were placed at the front of the packet, then the estimation of the channel

ing sequence. The latter is applied to a matched filter to provide an estimate of the channel
impulse response. We have previously mentioned that both the modulator and the mobile
radio channel cause each received bit to have a duration that no longer spans the original bit
period, but a number of bit periods. This means that each modulation symbol will interfere
with both its preceding and successive bits, an effect known as intersymbol interference
(ISI). We know the amount of ISI that was deliberately introduced by the modulator to re-
strain the bandwidth occupancy of the modulated signal. We now have to decide how much
additional bit spreading, or dispersion, caused by the channel, we wish to accommodate.
There is a trade-off between the amount of channel dispersion that can be accommodated
and the receiver complexity, i.e. the larger the dispersion we wish to accommodate, the
higher the complexity of the channel equaliser at the receiver. Having decided how much
spreading will be accommodated, say three bits for the modulator and two for the radio
channel, then spreading in excess of five-bits may cause regenerated bits to be in error. We
know that five bits can be arranged in 32 different ways, and we apply each five bit se-
quence to a baseband digital modulator identical to the one used at the transmitter. Now we
see why we needed to sound the radio channel and get an estimate of its impulse response;
because, armed with this response, we convolve each of the 32 local modulated signals to
get 32 estimates of the received signal. These 32 estimates, or templates, apply to receiving
a logical 1 or 0 with all the combinations that the two adjacent bits on either side of the bit
being processed could have.
When the traffic data are processed, each traffic bit is compared with all 32 templates, and
the mean square error between the actual data bit and each of the 32 template waveforms
yields 32 incremental metrics that are used in the Viterbi processor [16]. Note that if the
channel estimate were perfect, then one of these incremental metrics would be zero. A de-
scription of the Viterbi processor is beyond the scope of this book and the reader is referred
to Reference [2] for a comprehensive description. Suffice to say here that the Viterbi pro-
cessor used for channel equalisation is similar to the workings of the convolutional decoder.
The equalisation process requires these incremental metrics, and hence channel sounding is
essential. The data in the burst are not regenerated until the last bit is finally processed.
This entire process has effectively equalised the effects of the radio channel (and the