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Planning Base Station and Relay Station Locations
for IEEE 802.16j Network with Capacity
Constraints
Yang Yu
School of Computer Science
and Informatics
University College Dublin
Dublin, Ireland
Email: yang.yu@ucd.ie
Se´
an Murphy
School of Computer Science
and Informatics
University College Dublin
Dublin, Ireland
Email: sean.murphy@iname.com
Liam Murphy
School of Computer Science
and Informatics
University College Dublin
Dublin, Ireland
Email: liam.murphy@ucd.ie
Abstract—In this paper, two formulations for planning Base
Station (BS) and Relay Station (RS) locations are proposed:
a rather complex 0-1 integer programming model which can
be used to determine which of a set of locations should be
selected from a given set of BS and RS locations and a
simpler decomposition approach which focuses first on the BS
location problem followed by the RS location determination.
The two approaches are compared and the results show that
the simpler decomposition approach can find solutions using
significantly less resources which are very minimally lower in
quality than that found by the more complex formulation. Hence,
the decomposition approach can be used to solve larger 802.16j
network planning problems.
I. INT ROD UC TI ON
WiMax technology continues to receive considerable atten-
tion within the community with increasing numbers of roll-
outs happening worldwide: the Clearwire XOHM deployment
probably being the most ambitious and noteworthy. Although
there is much debate how WiMax will fare relative to LTE,
it is still quite clear that WiMax has much potential and is
the most advanced radio system of its kind that is currently
shipping.
WiMax technology, however, is not standing still - the
standardisation body is continually developing more advanced
variants of the technology. One such variant is the 802.16j
multi-hop relay system. The IEEE 802.16j standard [1] has just
been approved and published by IEEE in June. The standard
provides coverage and capacity improvements through the
introduction of new nodes called Relay Stations (RS). The
system is compatible with the Point-to-Multi Point (PMP)
mode of operation with slightly altered Base Stations (BS)
to support the RSs.
IEEE 802.16j has the potential to deliver higher capacity
networks at lower cost than more conventional single hop
wireless access technologies. This is attractive to network
operators. Previous literature has shown the capacity gains
that can be delivered by the system, but planning approaches
for such systems have received little attention. While relay
technologies are not an entirely new concept, large-scale
deployment of standardised relay-based technology is new.
Hence, there is a need for new approaches to network planning
to obtain solutions for operators considering how to rollout a
relay-based solution.
In this paper, a novel formulation of the multi-hop network
planning problem is first proposed. The resulting problem is
complex and hence an alternative formulation which is based
on a decomposition of the original formulation is introduced.
The paper compares these two approaches to solving the
problem, in particular comparing time to obtain a solution and
resulting solution quality.
The rest of the paper is organised as follows. Section II
discusses the related work. In Section III the system model
and some related aspects are described. Section IV presents
the proposed problem formulations. In Section V numerical
results are presented which compare time to obtain solution
and resulting solution quality. Finally Section VI concludes
the paper.
II. RE LATE D WOR K
There have been quite a number of contributions to the lit-
erature which demonstrate that relays can deliver performance
gains in different contexts.
Hoymann et al in [2] analysed the inter-cell interference, up-
link and downlink throughput of WiMax multi-hop networks.
The results show that both intracell and intercell interference
in relay based solutions are manageable and can deliver
performance gain over single hop wireless solutions.
In [3], the work was specifically focused on the uplink.
Through both analytical and simulation modelling, gains of
up to 40% were observed.
In [4], the system capacity of IEEE 802.16j transparent
mode was investigated for different number of RSs and trans-
mission power. The study found that an overall throughput
gain of 125% and 55% can be obtained with and without
spatial reuse respectively compared to 802.16e system.
There have not been many contributions on cellular network
planning for relay systems. In our preliminary work [5], [6],
we developed an integer programming formulation for the
problem of realising coverage in relay architectures. However
an important aspect – capacity of the system – is not taken
into account in the study.
In [7], [8], the authors considered the problems of optimal
RS placement – for a single RS and for two RSs in a cell –
in an 802.16j context using cooperative relaying technology.
While co-operative relaying is mentioned in the standard, it is
an optional capability: many deployments will not have this
and it is not considered in this work.
In [9], the performance of some variant of LTE-Advanced
relay system on particular real world data is considered. The
authors utilised ray-tracing techniques to determine how to
deploy relays judiciously in a central London area. They found
that 3-4 relays per sector and 3 sectors per BS can achieve
significant gain.
The problem of planning a relay enabled telecommunica-
tion network is in nature a hierarchical capacitated location
facility problem and it is known to be NP-hard. In [10],
the authors reviewed over 70 studies of hierarchical facility
location models in the last two decades including those in
telecommunications area. The main difference between the
work described here and previous contributions arises from
the nature of the capacity constraints. Unlike previous work,
this problem presents capacity constraints only at the top level
of the hierarchy, i.e. BSs. This increases the complexity of the
constraints.
III. SYS TE M MOD EL
The problem focused on in this work is a BS and RS
location planning problem of an 802.16j two-hop network with
the following inputs:
∙a set of candidate BS and RS sites;
∙a set of costs associated with BSs and RSs.
∙user demand, modelled by a set of discrete Test Points
(TPs) each associated with a capacity requirement;
The objective is to determine the set of BSs and RSs that
can accommodate the user demand at the lowest cost.
Before describing the problem formulation, it is necessary
to describe some aspects of the relay system under study. This
section provides a brief overview of IEEE 802.16j transparent
mode of 802.16j system, some path selection issues that arise
in relay systems and the radio propagation model used.
A. Transparent Relay Mode
In transparent relay mode, the SS receives the synchronisa-
tion and frame header information from the BS and receives
data from the RS as if there were no RS. This mode requires
that an SS must be in the coverage area of a BS to enable
relay transmissions. Transparent mode is used mainly to give
capacity enhancements in contrast of non-transparent mode
which is mainly used to provide coverage extension.
B. Path Selection and Weights
As the SS can be associated with either a BS or an RS, a
basic issue is to determine to which node – BS or RS – any
particular SS should be associated.
Modulation QPSK 16-QAM 64-QAM
Coding rate 1/2 3/4 1/2 3/4 1/2 2/3 3/4
Bit rate (b/s) 1 3/2 2 3 3 4 9/2
Weight 9/2 3 9/4 3/2 3/2 9/8 1
TABLE I
OFDMA MCS, BIT RATE A ND WEI GH T LOOK UP TAB LE [1]
As a number of options for communication between SS
and BS can exist, it is necessary to have some mechanism to
determine which of these is most appropriate. In this work, a
weight was associated with each link, SS-RS, SS-BS and RS-
BS, which reflects the efficiency of this link. These weights
were then used for path selection, with the path with the lowest
cumulative weight being the most efficient option for SS-BS
communications. Note that if the weight of the direct link is
smaller than any two-hop path, it is chosen.
The weighting scheme is directly related to the Modulation
and Coding Scheme (MCS) used on the link. It is inversely
proportional to the bit rate as shown in Table I. An infinite
weight is set when the channel condition is so poor that it is
not possible to establish connection between two nodes using
any of the defined MCS.
As the weight reflects link efficiency, it is also used when
considering the load on any link in the work below.
C. Propagation Model
The radio propagation model is a key component in any
wireless network planning problem. The propagation model
used in this work is the modified SUI model recommended
by the standardisation body [11]. The parameters of the SUI
model used in this work are in Table II below.
Parameter Name Value
Carrier frequency 2.5GHz
Height of BS 60m
Height of RS 20m
BS transmission power 40dBm
RS transmission power 30dBm
Height of SS 2m
Terrain type
BS-SS, A, Macro-cell suburban, ART to BRT
RS-SS for hilly terrain with moderate to
heavy tree densities.
BS-RS D, Macro-cell suburban, ART to ART.
TABLE II
PARAMETERS USED I N CHAN NE L MODE L
IV. PROBLEM FORMULATIONS
In this section, the system parameters used are introduced
first. This is followed by the two problem formulations pro-
posed for planning the BS and RS locations for 802.16j
network.
A. System Parameters
The following inputs to the problem are defined:
∙𝐵={1,2, . . . , 𝑏}: Set of candidate BS sites
∙𝑅={1,2, . . . , 𝑟}: Set of candidate RS sites
∙𝑇={1,2, . . . , 𝑡}: Set of Test Points (TP)
∙𝑐𝑏
𝑖(𝑖∈𝐵): Cost of BS
∙𝑐𝑟
𝑖(𝑖∈𝑅): Cost of RS
∙𝑢𝑖(𝑖∈𝑇): Traffic demand of TP
∙𝑙𝑏
𝑖,𝑗 (𝑖∈𝑇, 𝑗 ∈𝐵): BS-TP link path loss
∙𝑙𝑟
𝑖,𝑗 (𝑖∈𝑅, 𝑗 ∈𝐵): BS-RS link path loss
∙𝑙𝑡
𝑖,𝑗 (𝑖∈𝑇, 𝑗 ∈𝑅): RS-TP link path loss
∙𝑤𝑏
𝑖,𝑗 (𝑖∈𝑇, 𝑗 ∈𝐵): BS-TP link weight
∙𝑤𝑟
𝑖,𝑗 (𝑖∈𝑅, 𝑗 ∈𝐵): BS-RS link weight
∙𝑤𝑡
𝑖,𝑗 (𝑖∈𝑇, 𝑗 ∈𝑅): RS-TP link weight
Coverage of a site (BS or RS) is reflected by the weights
of the link between a node and the site. An indicator function,
𝑓𝑐(𝑤), is used to determine whether two nodes are within
coverage of each other.
∙𝑓𝑐(𝑤) = {0, 𝑤 =∞(node out of coverage of site)
1, 𝑤 ∕=∞(node in coverage of site)
∙𝑟𝑏
𝑖,𝑗 =𝑓𝑐(𝑤𝑏
𝑖,𝑗 )(𝑖∈𝑇, 𝑗 ∈𝐵): BS-TP coverage
∙𝑟𝑟
𝑖,𝑗 =𝑓𝑐(𝑤𝑟
𝑖,𝑗 )(𝑖∈𝑅, 𝑗 ∈𝐵): BS-RS coverage
∙𝑟𝑡
𝑖,𝑗 =𝑓𝑐(𝑤𝑡
𝑖,𝑗 )(𝑖∈𝑇, 𝑗 ∈𝑅): RS-TP coverage
The following decision variables are defined:
∙𝑥𝑏
𝑖,𝑗 ∈ {0,1}(𝑖∈𝑇, 𝑗 ∈𝐵): BS-TP link existence
∙𝑥𝑟
𝑖,𝑗 ∈ {0,1}(𝑖∈𝑅, 𝑗 ∈𝐵): BS-RS link existence
∙𝑥𝑡
𝑖,𝑗 ∈ {0,1}(𝑖∈𝑇, 𝑗 ∈𝑅): RS-TP link existence
∙𝑦𝑖∈ {0,1}(𝑖∈𝐵): whether BS is installed
∙𝑧𝑖∈ {0,1}(𝑖∈𝑅): whether RS is installed
B. Problem Formulation with Linear Constraints
In a typical problem formulation, there would be separate
decision variables associated with each link. In this case, the
approach would lead to a large number of quadratic constraints
on the problem which results in significant complexity.
Here, new variables which represent the radio conditions on
TP-RS-BS path are introduced. This makes the Formulation
with Linear Constraints (FLC) a 0-1 integer programming
formulation. Thus, additional system parameters are needed:
∙𝑙𝑖,𝑗,𝑘(𝑖∈𝑇 , 𝑗 ∈𝑅, 𝑘 ∈𝐵): average of path loss of TP-
RS-BS link
∙𝑤𝑖,𝑗,𝑘(𝑖∈𝑇 , 𝑗 ∈𝑅, 𝑘 ∈𝐵): sum of weights of TP-RS-
BS link
The decision variables are:
∙𝑥𝑖,𝑗,𝑘 ∈ {0,1}(𝑖∈𝑇, 𝑗 ∈𝑅, 𝑘 ∈𝐵): TP-RS-BS link
existence
∙𝑚𝑖,𝑗 ∈ {0,1}(𝑖∈𝑅, 𝑗 ∈𝐵): BS-RS link existence mask,
makes sure each RS is only connected to one BS
The objective function is then defined as:
min
𝑥,𝑦,𝑧 [( 𝑏
∑
𝑖=1
𝑐𝑏
𝑖𝑦𝑖+
𝑟
∑
𝑖=1
𝑐𝑟
𝑖𝑧𝑖)+
⎛
⎝
𝑡
∑
𝑖=1
𝑟
∑
𝑗=1
𝑏
∑
𝑘=1
𝑙𝑖,𝑗,𝑘𝑥𝑖,𝑗,𝑘 +
𝑡
∑
𝑖=1
𝑏
∑
𝑗=1
𝑙𝑏
𝑖,𝑗 𝑥𝑏
𝑖,𝑗 ⎞
⎠⎤
⎦
subject to:
𝑡
∑
𝑖=1
𝑟
∑
𝑗=1
𝑥𝑖,𝑗,𝑘𝑢𝑖𝑤𝑖,𝑗,𝑘 +
𝑡
∑
𝑖=1
𝑥𝑏
𝑖,𝑘𝑢𝑖𝑤𝑏
𝑖,𝑘 ≤𝐶, ∀𝑘∈𝐵(1)
𝑥𝑖,𝑗,𝑘 ≤𝑟𝑡
𝑖,𝑗 𝑟𝑏
𝑖,𝑘,∀𝑖∈𝑇 , ∀𝑗∈𝑅, ∀𝑘∈𝐵(2)
𝑥𝑏
𝑖,𝑗 ≤𝑟𝑏
𝑖,𝑗 ,∀𝑖∈𝑇, ∀𝑗∈𝐵(3)
𝑚𝑖,𝑗 ≤𝑟𝑟
𝑖,𝑘,∀𝑖∈𝑅, ∀𝑘∈𝐵(4)
𝑟
∑
𝑗=1
𝑏
∑
𝑘=1
𝑥𝑖,𝑗,𝑘 +
𝑏
∑
𝑘=1
𝑥𝑏
𝑖,𝑘 = 1,∀𝑖∈𝑇(5)
𝑏
∑
𝑗=1
𝑚𝑖,𝑗 =𝑧𝑖,∀𝑖∈𝑅(6)
𝑥𝑖,𝑗,𝑘 ≤𝑚𝑗,𝑘,∀𝑖∈𝑇 , ∀𝑗∈𝑅, ∀𝑘∈𝐵(7)
𝑥𝑏
𝑖,𝑗 ≤𝑦𝑗,∀𝑖∈𝑇, ∀𝑗∈𝐵(8)
𝑚𝑖,𝑗 ≤𝑦𝑗,∀𝑖∈𝑅, ∀𝑗∈𝐵(9)
In the objective function of FLC, the first term corresponds
to the total installation cost of BS and RS; the second term
relates to the path loss between nodes and ensures that nodes
are associated with nearby nodes thus ensuring efficient use
of the medium.
Constraint (1) ensures that the load of each BS does
not exceed the maximum capacity. Due to the requirement
of transparent mode, constraint (2) ensures that each relay
connected TP is in coverage of both of the RS and the BS.
Constraint (3) and (4) ensure that every directly connected TP
and RS is in coverage of a BS respectively. Constraint (5)
ensures that each TP is either connected to an RS or a BS.
Constraint (6) and (7) ensure that each RS if installed, is only
connected to one BS. Constraint (8) and (9) ensure that every
TP or RS can only be connected to the BSs that are chosen
to be installed.
Basing the problem on paths rather than links introduces a
large number of decision variables. A State Space Reduction
(SSR) approach can help to reduce the number of decision
variables significantly.
The number of variables in the problem can be reduced sig-
nificantly by eliminating variables associated with infeasible
links, i.e. links for which the path loss is so high that it is
unrealistic to consider establishing a link. Thus, the variables
𝑥𝑖,𝑗,𝑘 are removed if 𝑤𝑖,𝑗,𝑘 ≥𝑤𝑏
𝑖,𝑘,∀𝑖∈𝑇 , ∀𝑗∈𝑅, ∀𝑘∈𝐵.
C. Decomposition Formulation
As all TPs must be in coverage area of the serving BS,
the choice of which RSs are installed does not have a
significant impact on how TPs are associated with BSs. For
this reason, it is possible to decompose the problem into two
smaller problems, one focuses on planning on BS locations,
ignoring RSs and the other focuses on RS location, given
BS locations. This can also be useful for scenarios in which
RSs are added incrementally after a BS installation has been
designed/deployed.
1) Association of TPs with BS: The first step solves a single
hop network planning problem:
min
𝑥,𝑦 ⎛
⎝
𝑏
∑
𝑗=1
𝑐𝑏
𝑗𝑦𝑗+
𝑡
∑
𝑖=1
𝑏
∑
𝑗=1
𝑙𝑏
𝑖,𝑗 𝑥𝑏
𝑖,𝑗 ⎞
⎠
subject to:
𝑡
∑
𝑖=1
𝑥𝑏
𝑖,𝑗 𝑢𝑖𝑤𝑏
𝑖,𝑗 ≤𝐶, ∀𝑗∈𝐵(10)
𝑏
∑
𝑗=1
𝑥𝑏
𝑖,𝑗 = 1,∀𝑖∈𝑇(11)
𝑥𝑏
𝑖,𝑗 ≤𝑦𝑗,∀𝑖∈𝑇, ∀𝑗∈𝐵(12)
𝑥𝑏
𝑖,𝑗 ≤𝑟𝑖,𝑗 ,∀𝑖∈𝑇, ∀𝑗∈𝐵(13)
Constraint (10) limits the maximum capacity of each BS.
Constraint (11) ensures every TP is assigned to only one BS.
Constraint (12) ensures every TP is only assigned to BSs that
are installed. Constraint (13) ensures every TP is in coverage
of a BS.
2) Incorporating relays: The objective of the second step
is to introduce RSs so as to reduce the overall load on any of
the BSs - each BS is considered in isolation. The load can be
reduced if an RS can facilitate a two-hop path which is more
efficient than the direct path.
The following new parameters are defined:
∙𝑇′={1,2, . . . , 𝑡′}: TPs that are associated with the BS
∙𝑅′={1,2, . . . , 𝑟′}: RSs that are in coverage of the cell
∙𝑐′𝑟
𝑖(𝑖∈𝑅′): cost of RS
∙𝑢′
𝑖(𝑖∈𝑇′): traffic demand of TP
∙𝑑′
𝑖,𝑗 (𝑖∈𝑇′, 𝑗 ∈𝑅′): capacity gain realised by connecting
TP 𝑖to BS 𝑛via RS 𝑗:
𝑑′
𝑖,𝑗 ={𝑤𝑡
𝑖,𝑛 −(𝑤𝑟
𝑖,𝑗 +𝑤𝑏
𝑗,𝑛), 𝑤𝑡
𝑖,𝑛 −(𝑤𝑟
𝑖,𝑗 +𝑤𝑏
𝑗,𝑛)>0
0, 𝑤𝑡
𝑖,𝑛 −(𝑤𝑟
𝑖,𝑗 +𝑤𝑏
𝑗,𝑛)≤0
∙𝑟′
𝑖,𝑗 (𝑖∈𝑇′, 𝑗 ∈𝑅′): indicator variable, 1 if RS 𝑗can
support more efficient path to BS for TP 𝑖, 0 otherwise
𝑟′
𝑖,𝑗 ={1, 𝑑′
𝑖,𝑗 >0
0, 𝑑′
𝑖,𝑗 ≤0,∀𝑖∈𝑇′,∀𝑗∈𝑅′
The decision variables are the following for each cell:
∙𝑧′
𝑖∈ {0,1}: whether RS 𝑖is installed
∙𝑥′𝑟
𝑖,𝑗 ∈ {0,1}: TP-RS link
Objective function:
min
𝑥′,𝑧′⎛
⎝
𝑟′
∑
𝑖=1
𝑐′𝑟
𝑖𝑧′
𝑖−
𝑡′
∑
𝑖=1
𝑟′
∑
𝑗=1
𝑥′𝑟
𝑖,𝑗 𝑑′
𝑖,𝑗 𝑢′
𝑖⎞
⎠
subject to:
𝑟′
∑
𝑗=1
𝑥′𝑟
𝑖,𝑗 ≤1,∀𝑖∈𝑇′(14)
𝑥′𝑟
𝑖,𝑗 ≤𝑧′
𝑗,∀𝑖∈𝑇′,∀𝑗∈𝑅′(15)
𝑥′𝑟
𝑖,𝑗 ≤𝑟′
𝑖,𝑗 ,∀𝑖∈𝑇′,∀𝑗∈𝑅′(16)
The objective function is comprised of a term reflecting the
RS costs and another reflecting the load reduction on the BS.
Constraint (14) ensures that each TP is at most assigned to one
RS. Constraint (15) ensures that each TP is assigned to an RS
that is installed. Constraint (16) ensures that a TP is assigned
to an RS only if the RS can realise a throughput gain.
V. RESULTS
Analytical and numerical results are presented in this section
in order to compare the performance of the above approaches.
First, a basic complexity analysis of the two formulations is
presented. This is followed by comparison of time required to
obtain solutions for the two formulations. Finally, the quality
of the resulting solutions is compared.
A. Number of Variables and Constraints
The number of variables and constraints naturally reflects
the complexity of a formulation. It is a function of the problem
size 𝑛which is defined as the number of candidate BS sites
in this context. The number of candidate RS sites and TPs are
correlated to 𝑛.
Table III shows a list of the maximum order and approx-
imate number when 𝑛= 20 of the number of variables
and constraints of the formulations. From the table it can be
seen that the FLC formulation has a relative large number
(cubic) of variables and constraints even with SSR. The DF
formulation significantly reduces both the number of variables
and constraints indicating that it is simpler to solve.
Formulation No. variables No. constraints
FLC 𝑂(𝑛3)≈20000 𝑂(𝑛3)≈29000
DF-step1 𝑂(𝑛2)≈2000 𝑂(𝑛2)≈4000
DF-step2 𝑂(𝑛)≈500 𝑂(𝑛)≈1000
TABLE III
LIST OF NUMBER OF VARIABLES AND CONSTRAINTS
B. Execution time
Experiments were performance to collect the statistics of
the execution time of FLC with SSR and DF formulations.
Figure 1 shows the comparison of the execution time of both
formulations. Obviously even with SSR, the scalability of FLC
is very poor compared to DF and it is clearly not suitable for
any real size problems. However since it can be used to obtain
an optimal solution to the planning problem, it is used in the
next section as a benchmark to investigate the performance of
the DF model.
C. Quality of Results
The solutions obtained using the FLC and DF approaches
are compared in this section by comparing results obtained for
a number of network planning problems. A 3km×3km area
with 20 candidate BSs, 200 RSs and 500 TPs was considered.
A set of 100 different scenarios were generated and the
planning problem solved for each of these. Some experiments
were also conducted for larger problems (30 candidate BSs
in 4km×4km area) and similar results were obtained. In this
section, then, the results are compared in terms of BS/RS cost
per scenario, number of RS chosen per cell and the system
capacity gain achieved through use of the RSs.
Figure 2 and 3 compares the costs of the BSs and RSs
respectively obtained using the FLC and DF approaches. The
results are presented as Probability Distribution Functions
20 40 60 80 100 120 140 160 180 200
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
Number of candidate BSs
Calculation time(s)
DF
FLC
Fig. 1. Execution time
−0.5 0 0.5 1 1.5 2 2.5 3
10
20
30
40
50
60
70
80
90
BS cost difference (%)
PDF (%)
Fig. 2. BS cost comparison
−20 −10 0 10 20 30
10
20
30
40
50
RS cost difference (%)
PDF (%)
Fig. 3. RS cost comparison
0 1 2 3 4 5 6 7 8 9
5
10
15
20
25
Number of RSs per cell
PDF (%)
FLC
DF
Fig. 4. Number of RS per cell
10 20 30 40 50
10
20
30
40
50
Capacity gain (%)
PDF (%)
FLC
DF
Fig. 5. Capacity gain per cell
(PDFs) which show how the results compare over all 100
scenarios. The FLC costs are taken as the reference and the
DF costs are compared to these.
In Figure 2, it can be seen that 90% of the scenarios result
in approximately the same BS costs and for the remaining
cases, the difference is small. The maximum difference in a
single scenario is 2.6%. This means that the two approaches
predominantly chose the same set of BSs.
From Figure 3, it can be seen that difference in RS costs is
a little larger: on average the cost of RSs using DF is 6.7%
more than FLC. This is consistent with Figure 4 which shows
that the DF solution typically results in slightly more RSs per
cell when compared with the FLC solution. This shows that
there is some slight cost to using the DF approach.
Another important metric is the capacity gain that can be
attained using the RSs. Figure 5 illustrates the capacity gain
using both FLC and DF. As with the RS costs, there is a slight
difference: in both cases, the capacity gain can be over 45%,
but on average, the gain for DF is 31.5% compared with a gain
of 35% for the FLC case. Again, it can be seen that the DF
based solution obtains results which are slightly suboptimal.
VI. CONCLUSIONS
In this work, two formulations of 802.16j BS/RS location
planning problems were proposed and evaluated. Experimental
results show that the DF formulation is much more scalable at
a very small cost in terms of solution quality. Hence, it can be
used for planning of larger networks. Also, the decomposition
approach has the advantage of decoupling the BS and RS
planning problems, meaning that RSs can, in principle, be
easily added to classical BS-only installations.
ACK NOW LE DG ME NT
Y. Yu and S. Murphy would like to acknowledge the support
of the EU FP7 CARMEN project. Y. Yu would also like to
acknowledge the support of the UCD Ad Astra scheme.
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