Network planning for IEEE 802.16j relay networks

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April 26, 2008

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Contents
1 Network Planning for IEEE 802.16j Relay Networks 1
1.1 Introduction.................................... 2
1.2 OverviewofIEEE802.16j ............................ 4
1.2.1 IEEE802.16jScope............................ 4
1.2.2 Relay Station Capabilities . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Radio Propagation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 FreeSpaceModel............................. 7
1.3.2 SUIModel................................. 7
1.4 IEEE 802.16j Network Planning Problem Formulation . . . . . . . . . . . . . 9
1.4.1 Integer Programming Model . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.2 State Space Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.3 Clustering Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 ResultsandDiscussion .............................. 17
1.5.1 Integer Programming Model . . . . . . . . . . . . . . . . . . . . . . . 18
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ii CONTENTS
1.5.2 Effect of the Constraints Reducing the State Space . . . . . . . . . . 19
1.5.3 Using the Clustering Approach . . . . . . . . . . . . . . . . . . . . . 19
1.5.4 Impact of the Ratio of the Cost of BS to RS on Solution . . . . . . . 21
1.6 Conclusion..................................... 21

Chapter 1
Network Planning for IEEE 802.16j
Relay Networks
Yang Yu , Vasken Genc, Se´an Murphy, Liam Murphy
In this chapter, a problem formulation for determining optimal node location for Base
Stations (BSs) and Relay Stations (RSs) in relay-based 802.16 networks is developed. A
number of techniques are proposed to solve the resulting Integer Programming (IP) problem
– these are compared in terms of the time taken to find a solution and the quality of the
solution obtained. Finally, there is some analysis of the impact of the ratio of Base Station
(BS)/Relay Station (RS) costs on the solutions obtained.
Three techniques are studied to solve the IP problem: (1) a standard branch and bound
mechanism, (2) an approach in which state space reduction techniques are applied in advance
of the branch and bound algorithm and (3) a clustering approach in which the problem is
divided into a number of sub-problems which are solved separately, followed by a final overall
optimisation step.
These different approaches were used to solve the problem. The results show that the
more basic approach can be used to solve problems for small metropolitan areas; the state
1

2CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
space reduction technique reduces the time taken to find a solution by about 50%. Finally,
the clustering approach can be used to find solutions of approximately equivalent quality in
about 30% of the time required in the first case.
After the scalability tests were performed, some rudimentary experiments were performed
in which the ratio of BS/RS cost was varied. The initial results show that for the scenarios
studied, reducing the RS costs results in more RSs in the solution, while also decreasing the
power required to communicate from the mobile device to its closest infrastructure node (BS
or RS).
1.1 Introduction
IEEE 802.16 technologies are advancing rapidly. The base standards have been defined,
industry is offering products to the marketplace, and network operators are deploying systems
and offering service to subscribers. Mobile variants of the technology are now receiving a
lot of attention: the WiBro system in Korea provides coverage for large population centres
and has a substantial user base; the WiMax Forum is hosting a number of events designed
to solve interoperability problems for 802.16e compliant systems, in advance of providing
certification to products.
While all this momentum behind the technology bodes well, there are still significant
issues that must be addressed before WiMax sees mass market adoption in many places
throughout the world. In many countries, changes in spectrum allocation and/or regulations
are necessary before WiMax systems can be rolled out. In some countries, the low cost
of high speed wired broadband connections make the business case for WiMax solutions
less compelling. Subscriber terminals are still evolving, but the form factor of most current
WiMax terminals is still quite large for mobility applications. So, while there are many
reasons to believe that the future is bright for mobile WiMax technology, it will be some
years before it reaches maturity.
One very important issue which is faced by network operators at initial network roll-out

1.1. INTRODUCTION 3
is how to provide maximum coverage at minimum cost. One approach which can be very
useful in this context is to employ so-called relay network architectures. The essential idea
is to use Relay Stations (RSs), which are associated with Base Stations (BSs) to effectively
increase the coverage area of the BS at low cost. If the price point of the RSs is sufficiently
low, this can result in a lower cost coverage solution than the traditional BS-based solution.
The 802.16 standards body has been developing standards for 802.16-based relay network
architectures. More specifically, it is working on standards for BSs and RSs which enable
them to work with legacy 802.16-2004 [1] and 802.16e [2] compatible devices — this will result
in the 802.16j [3] standard. The 802.16j task group are focusing on issues associated with
how to make minimal modifications to the signalling and frame structure such that operation
with legacy systems is possible, while introducing a relay-based network architecture.
While the work of the 802.16j task group is still in the relatively early stages — the
standard will most likely not be ratified until 2009 at the earliest — it is interesting to
determine how the relay network architecture will impact network design and deployment.
Because relays introduce a significant change to the network architecture, traditional network
planning approaches are no longer applicable and new approaches are required.
In this chapter, new approaches to planning of 802.16j relay are described. The contribu-
tions of this chapter are twofold. Firstly, there is a synthesis of previous proposals to solve
this problem – namely the basic branch and bound approach, the approach using state space
reduction and the clustering approach. Secondly, there is an analysis of the impact of the
ratio of BS/RS costs on the resulting solution.
The structure of the chapter is as follows. An overview of the main components of 802.16j
are first provided. This is followed by a short discussion of radio propagation models suitable
for this context. The main problem formulation is then presented, followed by a discussion of
the different solution techniques. These different techniques are then compared in terms of
scalability and solution quality and the results are presented. Finally, there is some analysis
of the impact of the BS/RS costs.

4CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
1.2 Overview of IEEE 802.16j
In IEEE 802.16j low cost Relay Stations are introduced to provide enhanced coverage and
capacity. Using such stations, an operator could deploy a network with wide coverage at a
lower cost than using only (more) expensive BSs to provide good coverage, and increasing
significantly the system throughput. As network utilisation increases, these relay stations
could be replaced by BSs as required. The mesh architecture defined in WiMAX is already
used to increase the coverage and the throughput of the system. However, this mode is
not compatible with the Point-to-MultiPoint (PMP) mode with no support of the OFDMA
PHY, fast route change for mobile station (MS) etc. Hence, the standards organisation has
recognised this as an important area of development, and today a task group is charged with
drafting a new standard: the IEEE 802.16j Mobile Multihop Relay design to address these
issues. The first draft of the IEEE 802.16j standard has just finished in August 2007.
1.2.1 IEEE 802.16j Scope
The IEEE 802.16j is aiming to develop a Relay mode based on IEEE 802.16e by introducing
RSs depending on the usage model:
•Coverage extension
•Capacity enhancement
In other words, the relay technology is firstly expected to improve the coverage reliability
in geographic areas that are severely shadowed from the BS and/or to extend the range
of a BS. In both cases the RS enhances coverage by transmitting from an advantageous
location closer to a disadvantaged SS than the BS. Secondly, it is expected to improve the
throughput for users at the edges of an 802.16 cell. It has been recognized in previous 802.16
contributions that subscribers at the edges of a cell may be required to communicate at
reduced rates. This is because received signal strength is lower at the cell edge. Finally,
it is expected to increase system capacity by deploying RSs in a manner that enables more

1.2. OVERVIEW OF IEEE 802.16J 5
aggressive frequency reuse. Figure 1.1 illustrates the different scenarios in which Relay mode
could be used. However, introducing such RSs considerably alters the architecture of the
network and raises many issues and questions. It is still unclear what system design is
appropriate and can be realised at a low cost while still providing good coverage with an
enhancement of the throughput.
The 802.16j task group’s scope is to specify OFDMA PHY and MAC enhancement to the
IEEE 802.16 standards for licensed bands. These specifications aim to enable the operation
of fixed, nomadic and mobile RSs by keeping the backward compatibility with SS/MS. In
other words, the standard will define a new RS entity and modify the BS to support MMR
links and aggregation of traffic from multiple sources. An Mobile Multi-hop Relay (MMR)
link represents a radio link between an MMR-BS and an RS or between a pair of RSs. Such
link can support fixed, portable and mobile RSs and multihop communications between a
BS and RSs on the path. An access link is a radio links that originate or terminate at an
SS/MS. Figure 1.2 illustrates the main scope of the project.
1.2.2 Relay Station Capabilities
As the standard is still evolving, it is not clear what the final variant will look like. However,
at present, it appears that two categories of RS will be defined: low capability RS (simple RS)
and high capability RS (full function RS). The simple RS is used for low cost deployment, and
operates on one OFDMA channel. It contains no control functionality (i.e., control functions
are centralized in the MMR-BS) with one transceiver and optionally supports MIMO. The
full function RS can operates on multiple OFDMA channels, implements distributed control
functions, and support MIMO. This type of RS has a further two variants: Fixed/Nomadic
full function RS and Mobile full function RS. Mobile RSs add support for handover and the
ability to deal with a varying channel due to mobility. Table 1.1 summaries the different
RSs capabilities.
At present, it is considered that a MMR network could be composed of multiple usage
models [6] including multiple RS types specifically deployed. But at present, there is only a

6CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Table 1.1: RS capabilities
Simple RS Full Function Mobile RS
Fixed/Nomadic RS
Number of OFDMA 1 ≥1≥1
channels
Duplexing on MMR TDD TDD or FDD TDD or FDD
and access links
Frequency sharing Yes Yes or No Yes or Nobetween access and
MMR links
Mobility Centralised in Centralised in Centralised in
MMR-BS MMR-BS or MMR-BS or
distributed in RSs distributed in RSs
Antenna Support SISO or MIMO MIMO MIMO
little work about the heterogeneous functionalities of the relay stations in different scenarios.
For example, a MS can move from the coverage provided inside a building by fixed/nomadic
RS to a train where the coverage is provided by a mobile RS. Furthermore, there is no direct
mapping between the usage models and the types of RS. An operator may deploy a variety
of different RS types depending on traffic, mobility, topology (2 hops or more) within the
area of each RS location for a specific usage model.
In fact, the future standard will not answer all the issues raised by the RS incorporation
to provide vendor differentiation. For instance, intelligent scheduling either at the BS (in
a centralised approach) or at the BS and RSs (in a distributed approach) is required to
minimise the interference occurs at the RSs.
1.3 Radio Propagation Models
In any wireless network planning problem, the radio model is a key component. Because
of the variety of the propagation environment, there is no universal propagation model. In
general, radio models can be almost arbitrarily complex. However, working with such models
can be very computationally intensive and it is important to find the model with the right

1.3. RADIO PROPAGATION MODELS 7
balance of abstraction and complexity for the problem under study. For the WiMax network
planning problems, two propagation models can be suitable and are described below.
1.3.1 Free Space Model
The free-space model [7] (originally published by H.T. Friis in 1946) is the simplest model
that can only be applied in open area, i.e. no obstruction on the transmission line. This
model is considered as a standard propagation model, a reference and benchmark of all other
propagation models.
The path loss of the free space model is:
Lfs(f, d) = 32.44 + 20 log10 f+ 20 log10 d(1.1)
where, Lfs is the free space path loss in decibels, dis the distance between the transmitter
and the receiver in kilometre and fis the frequency in MHz.
In the free space model, many factors, such as reflection/multi-path, shadowing, fading,
atmosphere factors, etc. that may affect radio on its transmission path are omitted. This
model, consequently, does not capture key transmission characteristics of radio, so it is not
a very appropriate model for real world scenarios.
1.3.2 SUI Model
The SUI (Stanford University Interim) model was developed for design, development and
testing in the Multipoint Microwave Distribution System (MMDS) frequency band [8] (2-
3GHz). It was recommended by the IEEE 802.16 standard body. The SUI model is valid
for radio propagation within the 2-3 GHz range and has different parameter settings for
urban, suburban and rural scenarios. The maximum path loss (type A) is hilly terrain with
moderated-to-heavy tree density. The minimum path loss (type C) is mostly flat terrain
with light tree densities. The intermediate path loss condition is type B.

8CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
The SUI model is used for receiver’s antenna height between 2m and 10m. The path loss
model is given by:
LSU I (d, f, hm) = A+ 10δlog10 µd
d0¶+Xf+Xh+s, for d > d0(1.2)
with the correction factors for the operating frequency and for the CPE antenna height of
the model:
Xf= 6 log10 µf
2000¶(1.3)
Xh=−10.8 log10
hm
2,for terrain type A and B (1.4)
Xh=−20 log10
hm
2,for terrain type C (1.5)
where, LSU I is the SUI path loss in decibels, dis the distance between the base station
(BS) and the CPE antennas in metres, d0= 100m, hmis the CPE height above ground, s
is a lognormally distributed factor that is used to account for the shadow fading owing to
trees and other clutter and has a value between 8.2dB and 10.6dB. The other parameters
are defined as:
A= 20 log10
4πd0
λ(1.6)
δ=a−bhb−c/hb(1.7)
where, hbis the base station height above the ground in metres and should be between
10m and 80m. The parameters a,b,care constants dependent on the terrain type and are
shown in Table 1.2.
Table 1.2: Constant values for the SUI model parameters
Model Parameters Terrain Type A Terrain Type B Terrain C
a4.6 4.0 3.6
b0.0075 0.0065 0.005
c12.6 17.1 20
The SUI model was chosen to be used in the following network planning models based on
the following reasons: 1) the model was accepted by the IEEE 802.16 standard body; 2) it

1.4. IEEE 802.16J NETWORK PLANNING PROBLEM FORMULATION 9
has a good compromise between simplicity and accuracy, i.e. it models the key characteristics
of the radio frequency and it is simple computationally with a relatively small number of
parameters.
1.4 IEEE 802.16j Network Planning Problem Formulation
Here, a specific problem formulation for planning of multi-hop 802.16 networks is developed.
The following inputs are assumed:
•a set of candidate BS and RS sites;
•user demand, modelled by a set of discrete Test Points (TPs);
–this approach has been widely used in previous work and originally appeared in
[10];
•a suitable propagation model;
•a set of costs associated with BS and RS.
The objective is to determine the set of BSs and RSs from the total set of candidate
BS/RS sites that can accommodate the user demand at lowest cost.
The propagation model used here is the well-known SUI channel model. to use the model,
it is necessary to define a number of parameters: terrain type, frequency of operation, antenna
height, etc. In the experiments described below a single set of parameters were used as in
Table 1.3.
Table 1.3: Parameters used in SUI model
Parameter Name Value
Height of BSs and RSs Random value between 10 and 80m
Height of TPs 1.6m
Frequency 2.5GHz
Terrain Type C, mostly flat terrain with light tree densities

10 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
The height of BSs and RSs is the general height of a building, radio tower or other
constructions that can be mounted a BS/RS. The height of TP is average height of an adult.
2.5GHz is the frequency recommended by WiMax forum for mobile WiMax systems.
1.4.1 Integer Programming Model
The following problem inputs are defined:
•S={1, . . . , m}: Candidate site for BSs;
•R={1, . . . , n}: Candidate site for RSs;
•T={1, . . . , t}: TPs;
•cb
j(j∈S): Cost of each BS;
•cr
j(j∈R): Cost of each RS;
•ui(i∈T): Traffic demand for each TP (number of connections).
The set of BS sites differs from those of RS, as a BS is larger than a RS in size and has
more functionalities. Also, the multi-hop concept is limited to nodes which are at most two
hops from the BS: hence Subscriber Stations (SSs) can connect to an RS which is connected
to the BS, or they can connect directly to the BS.
The gain matrices are determined based on the SUI model:
•gb
ij (0 < gb
ij <1, i ∈T , j ∈S): Propagation factor of the radio link between TP iand
candidate site of BS j;
•gr
ij (0 < gr
ij <1, i ∈T , j ∈R): Propagation factor of the radio link between TP iand
candidate site of RS j;
•gij (0 < gij <1, i ∈R, j ∈S): Propagation factor of the radio link between candidate
site of RS iand candidate site of BS j.

1.4. IEEE 802.16J NETWORK PLANNING PROBLEM FORMULATION 11
The decision variables of the problem are a set of binary variables as follows:
yj=




1,if a BS is installed in j
0,otherwise
for j∈S(1.8)
zj=




1,if a RS is installed in j
0,otherwise
for j∈R(1.9)
xb
ij =




1,TP iis assigned to BS j
0,otherwise
for i∈Tand j∈S(1.10)
xr
ij =




1,TP iis assigned to RS j
0,otherwise
for i∈Tand j∈R(1.11)
rij =




1,RS iis assigned to BS j
0,otherwise
for i∈Rand j∈S(1.12)
It is now possible to write the objective function:
min
x,y,z,r "Ã m
X
j=1
cb
jyj+
m
X
j=1
cr
jzj!+λ1Ãt
X
i=1
m
X
j=1
ui
1
gb
ij
xb
ij !+
λ2Ãt
X
i=1
n
X
j=1
ui
1
gr
ij
xr
ij !+λ3Ãn
X
i=1
m
X
j=1
1
gij
rij !# (1.13)

12 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
subject to the following constraints:
m
X
j=1
xb
ij +
n
X
j=1
xr
ij = 1,∀i∈T(1.14)
m
X
j=1
rij =zi,∀i∈R(1.15)
xb
ij 6yj,∀i∈T, ∀j∈S(1.16)
xr
ij 6zj,∀i∈T, ∀j∈R(1.17)
rij 6yj,∀i∈R, ∀j∈S(1.18)
In the objective function (1.13), the first term constitute the cost of installing the BSs and
RSs. The next two terms relate to the transmit power of the mobile stations — it is desirable
to limit the required transmit power for the mobile devices since the mobile devices normally
have less power and thus the radio frequency can transmit shorter than that from a BS. The
first of these terms relates to the transmit power of those devices that are communicating
directly with the BS, while the second relates to devices that are using the relays. The final
term ensures that RSs are associated with their closest BSs. The parameters λ1,λ2and
λ3are weight parameters which determine how much weight is given to each of these terms
in the optimisation process. Note that this formulation is somewhat independent of node
transmit power — it simply tries to find a solution with lowest path loss between nodes.
The set of constraints are quite natural. Constraint (1.14) ensures every TP is assigned
to either a BS or an RS. Constraint (1.15) ensures every RS assigned to only one BS; also if
the RS is not installed, it cannot be assigned to a BS. Constraints (1.16), (1.17) and (1.18)
ensure that TPs are not assigned to BSs that are not present, TPs are not assigned to RSs
that are not present and RSs are not assigned to BSs that are not present.
1.4.2 State Space Reduction
The above problem formulation is a 0-1 IP (Integer Programming) problem. Standard ap-
proaches can be used to solve this problem, such as the branch and bound algorithm. How-

1.4. IEEE 802.16J NETWORK PLANNING PROBLEM FORMULATION 13
ever, since it is an NP-hard problem, it can take huge amount of time to solve when the
problem size scales up. In order to reduce the execution time, some more constraints could be
added to reduce the problem state space. These extra constraints derive from understanding
of the problem.
As each TP is connected to only a single RS or BS which is close to it, it is possible to add
constraints which limit the set of RSs/BSs that any given TP can be associated with. In this
way, the problem state space can be reduced considerably. There are two natural choices to
determine whether it should be possible to allocate a TP to an RS/BS: the decision could
be based on distance or path loss. In this work, the latter was chosen because the path
loss reflects naturally the received signal quality. By means of close, a percentage parameter
is set during the experiments and the first percentage number of TPs are considered close
to the corresponding BS or RS (Refer to Section 1.5.2). The following matrices were then
introduced:
fb
ij =




1,TP iis close to BS j
0,otherwise
for i∈Tand j∈S(1.19)
fr
ij =




1,TP iis close to RS j
0,otherwise
for i∈Tand j∈R(1.20)
fij =




1,RS iis close to BS j
0,otherwise
for i∈Rand j∈S(1.21)
And the following constraints are added for this variant of the problem:
xb
ij 6fb
ij ,∀i∈T, ∀j∈S(1.22)
xr
ij 6fr
ij ,∀i∈T, ∀j∈R(1.23)
rij 6fij ,∀i∈R, ∀j∈S(1.24)

14 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Constraint (1.22) and (1.23) ensure that TPs can only be associated with nearby BSs or
RSs, respectively. Constraint (1.24) ensures that RSs will only be associated with nearby
BSs.
1.4.3 Clustering Approach
Clustering is a very standard technique for grouping entities together which are somehow
related. In this case, these entities are related due to their geographical proximity. The
main idea behind the clustering approach described here is to divide the larger problem into
a number of smaller problems, each of which can be solved separately using the formulation
above. The advantage of this is that the resulting time to find a solution is significantly
lower. A clustering approach is used rather than more primitive methods of dividing the
state space, as it tends to result in fewer problems at the boundaries between the different
clusters [11].
The clustering approach employed here comprises of three steps:
1. Use standard k-means clustering based on a particular metric to divide the state space
into kseparate clusters;
2. Use the problem formulation described above to solve the problem for each of the
clusters independently;
3. Given the resulting set of RS and BS locations, perform a reallocation of TPs to RS/BS
and RS to BS using another Integer Programming formulation.
The first two steps mentioned above are quite intuitive; the purpose of the third step is
to address the problems that arise at the boundary. More specifically, it is possible that TPs
or RSs at the boundary of a cluster are associated with a RS/BS within that cluster when
there is a much closer RS/BS in a neighbouring cluster: the third step above enables such
points to be associated with nodes in other clusters.
The first step — generating clusters — was performed by generating clusters of nodes

1.4. IEEE 802.16J NETWORK PLANNING PROBLEM FORMULATION 15
(TP, BS, RS) which have similar path losses to all other nodes (BS, RS) in the system. Note
that this is a variant of an approach in which distance to other nodes is used as the metric.
A large gain matrix is first generated as input to the problem. This gain matrix comprises
of all path losses between all nodes in the system as shown below:
M=



A B
C D
E F




(1.25)
In which, A,B,C,D,Eand Fare all matrices, as follow:
A=



l1,1· · · l1,m
.
.
.....
.
.
lt,1· · · lt,m




;B=



l1,m+1 · · · l1,m+n
.
.
.....
.
.
lt,m+1 · · · lt,m+n




;
C=



lt+1,1· · · lt+1,m
.
.
.....
.
.
lt+n,1· · · lt+n,m




;D=



lt+1,m+1 ··· lt+1,m+n
.
.
.....
.
.
lt+n,m+1 ··· lt+n,m+n




;
E=



lt+n+1,1· · · lt+n+1,m
.
.
.....
.
.
lt+n+m,1· · · lt+n+m,m




;
F=



lt+n+1,m+1 · · · lt+n+1,m+n
.
.
.....
.
.
lt+n+m,m+1 · · · lt+n+m,m+n




; (1.26)
where matrix Arepresents the gain matrix between TPs to BSs, matrix Brepresents
the gain matrix between TPs to RSs, matrix Crepresents the gain matrix between RSs to
BSs, matrix Drepresents the gain matrix between RSs to RSs, matrix Erepresents the gain
matrix between BSs to BSs, matrix Frepresents the gain matrix between BSs to RSs. Thus,
the matrix Mhas a dimension of t+n+mby m+n.
The k-means clustering algorithm is then applied using the above gain matrix to obtain

16 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
kclusters: the nodes in each cluster are characterised by similar path loss to all RS and BS
in the system. This results in kdistinct, non-overlapping clusters, typically of comparable
size for realistic node distributions.
In step 2, the standard branch and bound algorithm was used to obtain RS and BS
locations for each cluster. This resulted in solutions for each cluster in which the TPs were
allocated to RSs/BSs in that specific cluster.
A new problem formulation was developed for the final step to overcome the boundary
issues. This problem differs from the original in that the RS and BS locations are now
fixed, and the focus is on determining the relationships between TPs, RSs and BSs: more
specifically, which TPs should be allocated to which RS/BS and which BS each RS should
be associated with.
The problem can be stated as follows:
min
x,r "λ1Ãt
X
i=1
m
X
j=1
ui
1
gb
ij
xb
ij !+λ2Ãt
X
i=1
n
X
j=1
ui
1
gr
ij
xr
ij !+λ3Ãn
X
i=1
m
X
j=1
1
gij
rij !# (1.27)
subject to:
m
X
j=1
xb
ij +
n
X
j=1
xr
ij = 1,∀i∈T(1.28)
m
X
j=1
rij =zi,∀i∈R0(1.29)
xb
ij 6yj,∀i∈T, ∀j∈S0(1.30)
xr
ij 6zj,∀i∈T, ∀j∈R0(1.31)
rij 6yj,∀i∈R0,∀j∈S0(1.32)
where S0and R0are the sets of BS and RS locations, respectively. As the formulation is very
similar to that presented earlier, it is reasonably clear what the objective is and what the
constraints represent.

1.5. RESULTS AND DISCUSSION 17
1.5 Results and Discussion
The objective of these tests can be divided into two parts. One is to obtain an understanding
of the scalability of the problem formulation — the basic and the state space reduction model.
More specifically, the objective was to understand if this problem formulation can be used
to solve problems of realistic size. Given that it is, in principle, an NP-hard problem, it is
important to understand the range of problems for which standard solution techniques are
appropriate and the range of problems which require the development of heuristics which
employ domain knowledge.
The second is to determine how the clustering approach compares with the more rudi-
mentary approaches. The comparison was performed based on both the time taken to obtain
a solution and the quality of the resulting solution; naturally, the former relates directly to
the scalability characteristics of the approach and its applicability for realistic scenarios.
A number of tests were performed in which the number of BSs, RSs and TPs were varied.
All tests were done using a standard desktop computer — Centrino Duo 2.0GHz, 1GB
Memory, Windows Vista. 12 tests were performed each time and the mean execution time
taken. As there was some variation in the results the minimum and maximum execution
times were removed and the mean taken over the remaining 10 results.
Problems were generated at random. The locations of each of the BSs, RSs and TPs
were chosen randomly from an area of size 3km ×3km. The (x, y) co-ordinates of each node
were chosen by selecting two random variable from the distribution U(0,3000). For each of
the problems the same set of weight parameters were used: λ1= 8, λ2= 8 and λ3= 20,
However, it is worth noting that the values of these parameters have little impact on the
time required to find solutions. In each of the problems, the BS cost was chosen at random
and was 3 times the cost of the RS.
In all of the following tests, the branch and bound method found the optimal solution
to the given problem. Figure 1.3 shows one possible result for planning a network with 20
candidate BSs, 60 candidate RSs and 200 TPs. In the solution, 10 BSs are selected with 36
RSs.

18 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
1.5.1 Integer Programming Model
Four sets of tests were performed with the basic variant of the problem to determine its
sensitivity to different parameters.
In the first experiment, all three parameters were scaled — the number of candidate
BSs, candidate RSs and TPs. The number of BSs was varied and the numbers of RSs and
TPs were 3 times and 10 times this figure, respectively. Figure 1.4 shows how the time
required finding a solution scales up. As can be seen, the problem can be solved for up to 80
candidate BSs and 240 RSs with ease. Further, the results show that the problem complexity
is scaling up quite rapidly. Indeed, further experiments were performed in which the number
of candidate BSs was increased to 120 and the resulting execution mean time was under 30
minutes. The system is exhibiting scaling properties which are quite non-linear, although
some basic curve fitting has shown that for the available data set, the scaling is considerably
less than exponential.
Figure 1.5 shows the calculation time when only the number of BSs is scaling. The number
of RSs is set to 90 and the number of TPs is set to 300 in all tests.
A similar experiment was performed in which the number of RSs was scaled up and the
number of BSs and TPs remained constant. Again it is clear that the system is scaling up
linearly in this parameter (see Figure 1.6). The number of BSs is set to 30 and the number
of TPs is set 300 in all tests.
Finally, in this set of experiments, the sensitivity to the number of TPs was considered.
The same characteristic is again observed: the system scales linearly as can be seen from
Figure 1.7. The number of BSs is set to 30 and the number of RSs is set to 90 in all tests.
From the figures, it can be seen that this algorithm should suit small size network planning
problems since the time cost is very short for small number of BSs. The time varies almost
linearly if individual parameter is varying. For the problem sizes studied — which are
typical for small metropolitan scenarios — the solution can be found quickly on typical
desktop computers, e.g. under 2 minutes for problems with 50 candidate BS sites, and

1.5. RESULTS AND DISCUSSION 19
approximately 10 minutes for problems with 100 candidate BS sites. The time cost for the
planning could increase to one day long or a few days to plan a larger network, e.g. around
500 candidate sites, but it is still practicable.
1.5.2 Effect of the Constraints Reducing the State Space
Based on the test results, the additional constraints do not affect the planning result obtained
but shortened the execution time significantly:
Figure 1.8 shows the effect of the state space reduction in solving different problem sizes.
The execution time of applying and not applying the state space reduction constraints are
shown in the figure. The problem size are varying depends on the number of candidate BS,
which scaling between 30 to 75. The three parameters are scaling in the same manner as in
Figure 1.4. It can be seen that it reduces half of the execution time.
Figure 1.9 shows the effect of the parameter which defines the term ”close to” as in Section
1.4.2. The parameter defines the percentage of the state space is reduced. It vary between
0 to 75 percent which means the rest of the nodes, i.e. 100 to 25 percent of all the other
nodes (TP/RS that can connect to the node itself ), are considered ”close to” the node it
self. In all tests, the number of candidate BSs is set to 80, the number of candidate RSs is
set to 240 and the number of TPs is set to 800. From the figure, it is very obvious that the
additional constraints could increase the performance and the more percentage of the state
space is reduced, the more time can be saved.
1.5.3 Using the Clustering Approach
Before considering the final output of the clustering approach, it is interesting to consider
how well the clustering algorithm works. Figure 1.10 shows a clustering output of a network
with 20 candidate BSs, 60 candidate RSs and 200 TPs. There, it can be seen that the
clustering algorithm divides the nodes into 4 groups of approximately equal size.

20 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Once the clusters were obtained, the performance of the full approach was considered.
Figure 1.11 compares the calculation time of using the clustering algorithm with that of
using the basic model. Two variants of the clustering approach were considered: one in
which the number of clusters was 2 and one in which 4 clusters were used.
The results show that the clustering approach results in significant improvements — the
amount of time required obtaining the solution decreases by up to 60 percent. The results
show that the 4-cluster solution operates significantly faster: this is to be expected, as it
involves the solution of significantly smaller problems.
It is interesting to consider further the impact of the number of clusters. Figure 1.12
shows the calculation time of the whole clustering model with different kvalues. All other
parameters remain the same: 80 candidate BSs, 240 candidate RSs and 800 TPs. When
k= 1, the clustering model is the same as the basic model.
From the Figure 1.12, it can be seen that the calculation time drops as the number
of clusters increases. As the number of clusters increases, the execution time drops to 20
percent of the non-clustered approach. It is worth noting, however, that the number of
clusters reduces to have much impact above 4-6 clusters, for the problem size studied. This
indicates that it is not necessary to have a large number of clusters to obtain significant
savings: further, increasing the number of clusters does not result in further savings. It
is anticipated, however, that larger problems could benefit from slightly larger numbers of
clusters.
It is insufficient to consider execution time alone: it is necessary to consider the quality
of the resulting solution. Figure 1.13 shows how the overall cost changes with k. The figure
shows the variation normalised to the known optimal solution obtained via branch and
bound. The scenarios are the same as those in Figure 4. While it is clear that kdoes have
an impact on the resulting overall cost — with increasing kresulting in poorer solutions —
the difference is so small as to be considered negligible. Further, there is a small improvement
which results from the final step that reduces this difference.

1.6. CONCLUSION 21
1.5.4 Impact of the Ratio of the Cost of BS to RS on Solution
It is also worth to notice how the ratio of the cost of BS and RS affects the site selection.
Intuitively, as the ratio raising, the RS becomes relatively cheaper, so it should tend to select
more RS compare to the BS and connections from TP to RS should increase. Figure 1.14
shows the trend. It shows number of connections between TP and BS and between TP and
RS as the cost ratio varying from 1 to 10, i.e. from the cost of BS equals to the cost of
RS to the cost of BS 10 times the cost of RS. Figure 1.15 shows the corresponding average
path loss between each TP and its communicating node. It can be seen that the path loss is
decreasing which means the quality of the radio received becomes higher as the cost of RS
becoming lower.
Figure 1.16 and Figure 1.17 shows two extreme cases. In both cases, the number of
candidate BS sites is 50, the number of candidate RS sites is 150 and the number of TP is
500. Figure 1.16 shows the plan of the cost of BS equals to the cost of RS. In this case, there
are 38 BSs and 50 RSs being selected; 177 connections between TP and BS; 320 connections
between TP and RS. Figure 1.17 shows the plan of the cost of BS 10 times to the cost of
RS. In this case, there are 28 BSs and 75 RSs being selected; 133 connections between TP
and BS; 367 connections between TP and RS.
1.6 Conclusion
In this chapter a model for planning 802.16-based relay networks is proposed. An integer
programming formulation was developed and an investigation of the applicability of standard
algorithms to this problem was performed. The results show that the standard branch and
bound algorithm can find optimal solutions to problems of reasonable size on standard
hardware. More specifically, these techniques can be used to solve planning problems for
small metropolitan areas or areas of a city. Further, the results show that the time required
to obtain solutions scales linearly with each of the individual parameters of the problem.
However, when all parameters are scaled, the time complexity increases more quickly.

22 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
A simple state space reduction mechanism was also considered. While the performance
of this can vary, it was found to reduce the computing time required by 50% for realistic
cases. A clustering approach was also proposed and it was shown to deliver significant time
improvements over the two previous approaches, finding solutions in 30% of the time required
by the basic model with negligible impact on solution quality. The analysis found that the
system has some sensitivity to the number of clusters used: for the size of problems studied,
4-6 clusters are optimal in terms of execution speed and quality of resulting solution. This
new approach enables larger problems to be solved in realistic time on typical computing
hardware.
Some analysis of the impact of the ratio of BS/RS cost was also performed. This analysis
showed that as the cost of RS decreases (relative to that of the BS), the solutions comprise
of more RSs. Further, the path loss between the mobile node and the infrastructure node is
lower in the case that the RS cost is lower.
This initial work clearly leaves many questions unanswered. Future work will involve
investigation of frequency reuse in this context, addition of QoS constraints to the model,
further study of the impact of power constraints and some investigation of the impact of the
weighting parameters. Also heuristic techniques are necessary to be studied to significantly
reduce computation complexity and present corresponding results.
References
[1] IEEE, IEEE Std 802.16-2004, ”IEEE Standard for Local and Metropolitan Area Net-
works, Part 16: Air Interface for Fixed Broadband Wireless Access Systems,” October
2004
[2] IEEE, IEEE Std 802.16e-2005, ”IEEE Standard for Local and Metropolitan Area Net-
works, Part 16: Air Interface for Fixed Broadband Wireless Access Systems. Amend-
ment for Physical and Medium Access Control Layers for Combined Fixed and Mobile
Operation in Licensed Bands,” February 2006
[3] IEEE 802.16j MMR Work Group, http://www.ieee802.org/16/relay

1.6. CONCLUSION 23
[4] Y. Yu, S. Murphy, L. Murphy, ”Planning Base Station and Relay Station Locations in
IEEE 802.16j Multi-hop Relay Networks”, Consumer Communications and Networking
Conference, CCNC 2008, 2nd IEEE BWA Workshop
[5] M. Nohara, J. Puthenkulam, M. Hart, M. Asa, J. Cho, IK. Fu, et al., ”IEEE 802
Tutorial: 802.16 Mobile Multihop Relay,” March 2006
[6] J. Sydir, ”IEEE 802.16 Broadband Wireless Access Working Group C Harmonized Con-
tribution on 802.16j (Mobile Multihop Relay) Usage Models,” July 2006
[7] V.S. Abhayawardhana, I.J. Wassell, D. Crosby, et al., ”Comparison of Empirical Prop-
agation Path Loss Models for Fixed Wireless Access Systems,” IEEE VTC 2005.
[8] V. Erceg, K. V. S. Hari, et al., ”Channel Models for Fixed Wireless Applications,” tech.
ep., IEEE 802.16 Broadband Wireless Access Working Group, January 2001
[9] E. Amaldi, A. Capone, and f. Malucelli, ”Planning UMTS Base Station Location: Op-
timization Models with Power Control and Algorithms,” IEEE Trans on Wireless Com-
munication, Vol. 2, No. 5, pp. 939-952, September 2003
[10] K. Tutschku, ”Demand-Based Radio Network Planning of Cellular Mobile Communi-
cation Systems,” Proc. IEEE INFOCOM’98, vol. 3, pp. 1054-1061, April 1998
[11] H. Zhang, H. Gu, Y. Xi, ”Planning Algorithm for WCDMA Base Station Location
Problem Based on Cluster Decomposition,” Control and Decision, Vol. 21, No. 2, pp.
213-216, February 2006

24 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Figure 1.1: IEEE 802.16j example use cases [6]
Figure 1.2: IEEE 802.16j project scope

1.6. CONCLUSION 25
Figure 1.3: A typical output of the planning tool
Figure 1.4: Calculation time when three parameters are scaled at the same time

26 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Figure 1.5: Calculation time when only the number of BS is scaled
Figure 1.6: Calculation time when only the number of RS is scaled

1.6. CONCLUSION 27
Figure 1.7: Calculation time when only the number of TP is scaled
Figure 1.8: Comparison of the calculation time, with and without the additional constraints

28 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Figure 1.9: Trend of the calculation time when different filtered percentage is applied
Figure 1.10: A clustering output with 4 clusters in which different shapes represent different
clusters

1.6. CONCLUSION 29
Figure 1.11: Comparison of the calculation time, with and without the state space reduction
constraints and the clustering approach
Figure 1.12: Calculation time for different kvalues

30 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Figure 1.13: BS and RS costs for different kvalues
Figure 1.14: Number of connections between TP and BS and between TP and RS as the
ratio of the cost of BS and RS is varied

1.6. CONCLUSION 31
1 2 3 4 5 6 7 8 9 10
179.7
179.8
179.9
180
180.1
180.2
180.3
180.4
180.5
180.6
180.7
Ratio of cost of BS to RS
Average path loss
Figure 1.15: Average path loss between each TP and its communicating node as the ratio
of the cost of BS and RS is varied
Figure 1.16: An output of the planning tool when the ratio of the cost of BS and RS is 1

32 CHAPTER 1. NETWORK PLANNING FOR IEEE 802.16J RELAY NETWORKS
Figure 1.17: An output of the planning tool when the ratio of the cost of BS and RS is 10