Chapter 1 - Introduction
Page 2
1.2 Cellular systems
The cellular concept was a major breakthrough in solving the problem of limited-
bandwidth and user capacity. It offers a very high capacity in a limited spectrum
allocation without any major technological changes. The cellular concept is a system
level idea which calls for replacing a single, high power transmitter (large cell) with
many low power transmitters (small cells), each providing coverage for a small area.
Each base station is allocated a portion of the total number of channels available to the
whole system, and nearby base stations are assigned different groups of channels so that
all the available channels are assigned to a relatively small number of neighbouring base
stations.
1.2.1 Static resource allocation
The classical resource allocation scheme that is found in all early mobile telephone
systems is the Fixed Channel Allocation (FCA). In this scheme each cell is assigned a
certain fixed number of channels. If the expected number of active mobiles is the same in
all cells of the network, the number of channels assigned to each base station should be
the same in order to provide the same level of service in all parts of the system.
1.2.2 Frequency reuse
We can consider M available channels, let us divide them in N groups of
approximately same size. Each cell is assigned a group of
=
N
M
C ( 1.1 )
channels. N is know as the cluster size. The cell has the right to freely use these channels
to communicate with its mobiles, but cannot use any channel from another group. The
group size C is a rough measure of the capacity of the system since it indicates the
maximum number of simultaneous connections that can be supported in each cell. To
maintain a sufficiently high carrier-to-interference ratio (CIR), the channels in a group
cannot be reused in a cell that is too close to the reference cell. We call this minimum
distance the reuse distance D. Clearly using many channel groups, it means a big N, it is
obvious it is less difficult to maintain a large D corresponding to a high CIR .
The penalty paid for such a procedure is that the number of channels that each cell has at
its disposal C , becomes small, it means the capacity of the system will be low. On the
other hand, if we can allow a low CIR , D can be allowed to be small. In this case only a
few channel groups are necessary and the capacity will be high.
Chapter 1 - Introduction
Page 3
1.2.3 Cell planning
The actual radio coverage of a
cell is known as the footprint and
it is determined from field
measurements or propagation
prediction models. Practically, for
design, we use the hexagonal cell
shape. It is conceptual and a
simplistic model of the radio
coverage for each base station, but
it has been universally adopted
since the hexagon permits easy
and manageable analysis of a
cellular system.
The cell plan shown in figure
1.1 is an example of a hexagonally
symmetric cell plan. Such cell
plans are characterized by the
property that the patterns formed
by the cells carrying the
same colour (label) are identical (just shifted) for all colours (labels) . Further, in such a
cell plan, each cell has nearest 6 co-channel neighbours, all at the same (minimum reuse)
distance D. For hexagonally symmetric cell plans one can show that the following
relationship between D and N holds,
N
R
D
Q 3== ( 1.2 )
The parameter Q , called the co-channel reuse ratio , is related to the cluster size and it’s
possible to show that symmetric cell plans exist for all integers N in the set
.0,1,2,3,..ji, }ji)ji(N:n{ =⋅−+==Ν
2
( 1.3 )
To find the nearest co-channel neighbours of a
particular cell, one must do the following steps :
1) Move i cells along any chain of hexagons ;
2) Turn 60 degrees counter-clockwise ;
3) Move j cells ;
as it is shown in figure 1.2 for a 7-cluster cell plan.
1
2
3
4
5
6
7
1
1
1
1
1
Cluster
R
D = Reuse distance
N = 7
Figure 1.1
Figure 1.2
Chapter 1 - Introduction
Page 4
Clearly, different cluster sizes mean different cell-patterns. In the figures below some
patterns are shown, highlighting the co-channel sets of cells for typical cluster sizes.
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Figure 1.4 - Cluster size = 4
Radius
Radius
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
Figure 1.6 - Cluster size = 9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Radius
Radius
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
Figure 1.8 - Cluster size = 13
Radius
Radius
Figures 1.3-8 Co-channel sets for different cluster sizes
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Figure 1.3 - Cluster size = 3
Radius
Radius
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Figure 1.5 - Cluster size = 7
Radius
Radius
-15 -10 -5 0 5 10 15
-10
-8
-6
-4
-2
0
2
4
6
8
10
1
2
3
4
5
6
7
8
9
Figure 1.7 - Cluster size = 12
Radius
Radius
Chapter 1 - Introduction
Page 5
In figure 1.9 we focus on a 7-cell pattern, looking at the first tier of closest co-channel
neighbours, which is usually chosen as a quick approximation.
Figure 1.9
A small value of Q provides large capacity since the cluster size N is small, whereas a
large value of Q improves the transmission quality, due to a smaller level of co-channel
interference. A trade off must be made between these two objectives in actual cellular
system design.
i j
)jiji(N ⋅++=
22
NRDQ 3==
1 0 1 1.73
1 1 3 3.00
2 0 4 3.46
2 1 7 4.58
3 0 9 5.20
2 2 12 6.00
3 1 13 6.24
Table 1.1 - Co-channel reuse ratio vs. frequency reuse pattern
1.2.4 Dynamic resource allocation
The most common method to improve network capacity is the introduction of
microcells. These micro-cellular structures suffer from the problem that they are to a
Chapter 1 - Introduction
Page 6
much greater extent sensitive to variations of traffic and interference than is the case with
macrocells.
It’s clear that fixed channel allocation seems not to be adequate for microcells, a
dynamic channel allocation (DCA) is required.
One of the major requirements of a mobile radio communication system is the
maintenance of the required transmission and service quality throughout a radio
connection independent of the movement of the subscribers. This is automatically
achieved performing handover actions as soon as the defined quality criteria are no
longer met.
DCA introduces intra-cell handovers, in other words, a channel reassignment, which
increases adaptability to traffic and interference, and co-channel reusage.
Further capacity enhancements can be obtained by combining FCA and DCA. In (fast)
dynamic channel allocation, cells share a common pool of potentially all channels. The
selection of a channel from a pool can be based on traffic load and/or interference power
in the cell. If channel reuse is determined by the number or identity of other cells
employing the channel, the scheme is called traffic adapted. If reuse is determined by the
interference, it is called interference adapted.
1.2.5 Intra-cell handovers
Intra-cell handovers are managed by the base station control, to save signalling
bandwidth, without involving mobile terminals, except to notify them of the completion.
They, of course, must be performed successfully and as infrequently as possible, being
imperceptible to the users. Voice communication can tolerate handovers as short breaks
in communication go undetected by the human ear. However, such breaks can lead to
complications in data transfer to/from a mobile host.
1.3 Multi-user receivers
An important issue in future mobile communication systems is to achieve a high
spectral efficiency. Increase of spectral efficiency allows for higher data rates or for more
users to operate simultaneously in the same bandwidth. In the third generation mobile
communication system (UMTS), code division multiple access is applied to achieve this
goal. In CDMA, the user signal is coded with a user signature which makes it possible to
distinguish and detect users which occupy simultaneously the same channel at the cost of
a large increase of the bandwidth required. In this thesis, power control techniques for
narrowband multi-user receivers are investigated. In this type of receivers no spreading
gain or bandwidth expanding signature coding is applied to separate the users like in
CDMA. The maximum likelihood joint detection of all users is the narrowband multi-user
detection that is studied most, another promising digital signal processing technique is the
analytical constant modulus algorithm , which is based on the exploitation of the constant
modulus property of phase-modulated signals.
Chapter 1 - Introduction
Page 7
The multi-user receiver thought to be used in this thesis is a subtractive narrowband
multi-user receiver. The main difference with CDMA schemes is that in the narrowband
case, the signals are separated by differences in amplitude, phase, timing and data, and
not by the use of orthogonal codes. It is based on successive signal detection and
subtraction of co-channel users. This principle is known as onion peeling [3] and in
figure 1.10 an example with Q signals is shown. In this receiver, the major signal is
detected and estimated in the first detector, the estimate is subtracted from the total input
signal, subsequently the next largest signal is detected, estimated and subtracted, and so
on.
.
.
.
.
.
.
detector
detector
detector
-
-
+
+
τ
τ
r(t)
d
1
(t)
d
2
(t)
d
x
(t)
s
1
(t)
s
2
(t)
Figure 1.10 – Subtractive narrowband
multi-user receiver
detector
d
3
(t)
Considering a cellular system, this technique allows in principle for in-cell channel
reuse, it means the assignment of multiple signals to the same channel within a cell.
When no antenna diversity is used, a certain power ratio (PR) between the received
signals is required in order to guarantee good detection performance. The required PR
depends on the modulation technique that is used. If antenna diversity is applied, the PR
requirements can be reduced, and the number of active signals can be increased. If users
with sufficiently different channel gains exist, they can be assigned to the same channel
for only a small penalty in total transmitted power in the cell. A user with a low channel
gain anyhow must transmit with a large power, whereas a user with a good channel gain
can reach the base station with much less power. The sum of these powers being about
the same as the maximum power of the two signals.
Chapter 1 - Introduction
Page 8
1.4 Lay out
The reminder of this report is organized as follows : Chapter 2 gives a description of
the system model, Chapter 3 describes the transmitting power control theory, Chapter 4
depicts the admission control, finally Chapter 5 and 6 present results of the simulations
and some conclusions.
The simulations are run in order to fill the system complying with constraints on
maximum transmitting power levels and running the power control algorithm, at first in a
single-channel scenario and then extending them to a multi-channel one. In order to test
the system performances, different types of filling are investigated, taking into account
the time evolution.
The admission control investigates the strategies to assign users in a multi-channel
scenario aiming to improve the performances and gives some theoretical suggestions
about a possible reshuffling.
Chapter 2 – System Model
Page 9
Chapter 2
SYSTEM MODEL
In this Chapter a brief description of the system is given, focusing on the radio
propagation model adopted and the generation of the arriving users, in a time and in a
spatial domain.
2.1 Mobile radio propagation
Radio-wave propagation can in general be attributed to three basic propagation
mechanisms : reflection, diffraction, scattering and path-loss. Reflection occurs when a
propagating radio-wave encounters an obstructing object with dimensions very large
compared to the wavelenght of the radio wave. Reflections from the surface of the earth
and from buildings produce waves that can interfere constructively or destructively at a
receiver.
Scattering occurs due to reflection of the radio-wave on objects with dimensions that
are on the order of the wavelenght or less, found in the vicinity of the receiver. Scattering
causes rapid variations in received signal strenght, which is called multipath.
Diffraction occurs when the radio path between the transmitter and the receiver is
obstructed by an impenetrable object. Although there is no direct path between the
transmitter and the receiver, secondary waves can be formed behind the obstructing
object. This phenomenon is called shadowing because the diffracted field can reach a
receiver even when it is shadowed by an object. Whereas multipath fading, which is
dependent on phase differences between wave components, is very rapid, the shadow
fading is mostly quite slow. The signal level variations will depend on the relative
position of the mobile to the shadowing objects. Since these object may have
considerable physical dimensions (hundreds of meters) it may take some time for the
mobile to move out of a shadow region.
For the next chapters, dealing with power control, we assume that multipath fading is
resolved by appropriate coding and interleaving techniques. That is, we assume that the
averaging interval is so long that the effects of the fast fading are averaged out.
It follows that the local-mean received power at time t in the cell i, when transmitting
in cell j , is
)t(P)t(G)t(P
jj,i
rx
j,i
⋅= ( 2.1 )
The link gain G
i,j
(t) is modelled as a product of two factors, a large scale propagation
loss L
i,j
(t) , and a shadow fading component A
i,j
(t),
Chapter 2 – System Model
Page 10
)t(A)t(L)t(G
j,ij,ij,i
⋅= ( 2.2 )
In the following , we assume reciprocal propagation conditions, which means that
uplink gains )t(G
u
j,i
and downlink gains )t(G
d
j,i
are identical.
In figure 2.1 the behaviour of received power is shown taking into account path-loss,
multipath and shadowing, moving away from the transmitter.
The following paragraphs deal with the relevant factors in the definition of the link
gain, path-loss and shadowing, and the time indipendent approximation we assumed in
the simulations.
2.1.1 Large scale propagation loss
The large scale propagation loss is very well modelled by the following power law
model,
)t(d)t(L
j,ij,i
α−
= ( 2.3 )
where d
i,j
(t) is the distance between transmitter j and receiver i at time t , and α is a
propagation constant. For macrocellular environments, the path-loss exponent, α , is
usually given in the range 42 ≤≤ α , where α =2 corresponds to free space propagation,
as it is shown in the table 2.1.
Received
Power
distance
Path loss
Path loss + Shadowing
Path loss + Shadowing
+ Multipath fading
Figure 2.1 Channel & propagation
- contributions -
Chapter 2 – System Model
Page 11
Environment
Path-loss exponent
Free space 2
Ideal specular reflection 4
Urban cells 2.7 - 3.5
Urban cells, shadowed 3 – 5
In building, line-of-sight 1.6 – 1.8
In building, obstructed path 4 - 6
In factory, obstructed path 2 - 3
Table 2.1 – Path-loss exponent in different scenarios
This propagation model is valid in the frequency range between 900 MHz and 1.8
GHz. Further, since it is reciprocal, we can use it both in the uplink and in the downlink.
2.1.2 Shadow fading
The shadowing factor A
i,j
(t) is assumed to be log-normally distributed with a log-
mean of 0 dB , and a log-variance of σ
2
dB. Its probability density function is
2
2
2
2
1
σ
σπ
a
e)a(p
−
= ( 2.4 )
Furthermore, we assume that the shadow fading processes for each of the mobile users
are mutually independent.
2.1.3 Time independent analysis
To completely evaluate the performance of radio resource management algorithms
require full scale simulations and extensive field trials. This is of course not practically
possible and we have to do with simpler evaluation strategies.
Assuming that the power control algorithms converge much faster compared to the
changes in the link gains due to mobility and shadowing, we can do a snapshot analysis,
time independent. A snapshot is essentially an observation of the system at a random
instant of time. All actions made up to the time instant for the observation, are excluded
in the analysis. If we relate this to the time dependent case, we can interpret the
algorithms as making infinitely fast updates. Hence, performance results which we obtain
Chapter 2 – System Model
Page 12
under this assumption constitute upper bounds on the performance of the algorithms in a
time varying scenario.
According to time independent assumption, we will work on the stationary link gain
matrix G.
2.2 Generation of the users
To evaluate the performances of the system-filling procedures, the users have to be
generated, in a random way, following a model close to a feasible configuration. In this
paragraph a spatial and a time model generation are described.
The users are considered uniformly distributed
within a cell and we represent their position in
polar coordinates with the pair (r,θ ), as it is shown
in figure 2.2.
Our aim is to express the probability density
function ( pdf ) to have one user at distance r from
the cell center at an angle θ .
The latter is simply uniform within the interval
[0,2π ).
About the former, we know that the probability
that the user lies within a given finite area A
equals the ratio
2
R
A
π
.
Thus if we consider an infinitesimal ring of width dr and its own correspondent area,
()( ) ()drrdrdrrrdrrdA 22
22
2
πππ ≅+=−+⋅= ( 2.5 )
we obtain the continuous pdf p(r) by the following relationship,
drr
RR
drr
R
dA
drrp
222
22
)( ===
π
π
π
( 2.6 )
and thus,
[]
>
∈
=
Rr
Rrr
R
rp
,0
,0,
2
)(
2
( 2.7 )
The cumulative density function C(r) shows a parabolic behaviour in the range [0,R] as
shown below
),r( ϑ
Figure
2.2
Chapter 2 – System Model
Page 13
[]
>
∈
=
Rr
Rrr
R
rC
,0
,0,
1
)(
2
2
( 2.8 )
Now let us define the time arrival model. We consider the number of users arriving
and leaving in each cell following a Poisson distribution. Thus the time intervals between
consecutive occurrences (interarrival times) are independent random variables identically
distributed according to the exponential distribution with parameter λ (figure 2.3).
0 e )(f >=
−
τλτ
λτ
( 2.9 )
(memory less)
Poisson Process
t soccurrence Average
0,1,2,...k
!k
) t (
e ] kX(t) [ P
t](o,timein occuring events of number )t(X
k
t-
λ
λ
λ
=
===
=
( 2.10 )
t
start
=τ
1
t
2
= t
start
+τ
2
t
3
= t
2
+τ
3
…
t
stop
= t
stop-1
+τ
stop
(τ
i
= random iid exp variable )
t
stop
< average duration of a call = T
Time flows : birth and death of users are taken into account during the reference time
interval (t
start
, t
stop
).
Arrivals
t
start
t
2
t
3
… … … t
stop
Number of average calls
stop
tλ
Figure 2.4
Figure 2.3 - Exponential probability density function
time/lambda
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