Io2415011509

Sultan F. Meko / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1501-1509
Optimal Relay Placement Schemes In OFDMA Cellular Networks
Sultan F. Meko
IU-ATC, Department of Electrical Engineering
Indian Institute of Technology Bombay, Mumbai 400 076, India

ABSTRACT
The Wireless services such as Skype and otherwise it is blocked. Depending on the SINR
other multimedia teleconferencing require high experienced by an arriving user, the BS computes the
data rate irrespective of user’s location in the subcarriers that need to allocate to the user so as to
cellular network. However, the Quality of Service provide the required rate. If the required sub-channels
(QoS) of users degrades at the cell boundary. (i.e., a group of subcarriers) are available, then the
Improvement in capacity and increase in coverage user is admitted. Note that the SINR decreases as the
area of cellular networks are the main benefits of distance between the BS and the user increases. Thus,
Fixed Relay Nodes (FRNs). These benefits of the users at the cell boundary can cause blocking
FRNs are based on the position of relays in the probability to be high. Since the number of admitted
cell. Therefore, optimal placement of FRNs is a users is directly proportional to the revenue of the
key design issue. We propose new schemes service provider, it is imperative to design solutions
optimal FRN placement in cellular network. Path- that allow accommodating a large number of users.
loss, Signal to Interference and Noise Ratio This motivates us to propose a Fixed Relay based
(SINR) experienced by users, and effects of cellular network architecture that is well suited to
shadowing have been considered. Our analysis improve the SINR at the cell boundary, and thus can
give more emphasis on supporting users at the possibly increase the number of admitted users.
cell-boundary (worst case scenario). The results Relaying is not only efficient in eliminating coverage
show that these schemes achieve higher system holes throughout the coverage region, but more
performance in terms of spectral efficiency and importantly; it can also extend the high data rate
also increase the user data rate at the cell edge. coverage range of a single BS. Therefore bandwidth
and cost effective high data rate coverage may be
Keywords - FRN deployment, OFDMA, multi- possible by augmenting the conventional cellular
hop, outage probability, Sectoring. networks with the relaying capability.

1. INTRODUCTION
Increase in capacity, coverage and
throughput are the key requirements of future cellular
networks. To achieve these, one of the solutions is to
increase the number of Base Stations (BS) with each
covering a small area. But, increasing the number of
BSs requires high deployment cost. Hence, a cost
effective solution is needed to cover the required area
while providing desired Signal to Interference plus
Noise Ratio (SINR) to the users so as to meet the
demand of the future cellular networks. To achieve
the high data rate wireless services, Orthogonal
Frequency Division Multiple Access (OFDMA) is
one of the most promising modulation and multiple
Fig.1 Layout of FRN based Cellular system
access techniques for next generation wireless
communication networks. In OFDMA, users are
dynamically allocated sub-carriers and time-slots so We consider a cellular system with six fixed
that it is possible to minimize co-channel interference relay nodes (FRNs) that are placed symmetrically
from neighboring cell by using different sub-carriers. around the BS as shown in Fig. 1. Mobile stations
Therefore, OFDMA based multi-hop system offers (MSs) in outer regions AR1 to AR6 can use relaying
efficient reuse of the scare radio spectrum. to establish a better path than the direct link to BS.
The key design issues in such systems are the
We consider an OFDMA-based cellular following: (1) How sub-channels should be assigned
system in which users arrive and depart dynamically. for (a) direct MS to BS links, (b) FRN to BS links,
Each arriving user demands rate 𝑟. If the required and (c) MS to FRN links. Algorithm for this is
rate can be provided, only then a user is accepted, referred to as the channel partitioning scheme. (2)
How sub-channels can be used across various cells.
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Algorithm for this is referred to as channel reuse system can be maximized while providing each user
scheme. with its required rate.
Effective channel partitioning maximizes
utilization of every channel in the system, and thus The paper is organized as follows. In
obtains high spectrum efficiency in cellular systems Section 2, we describe our system model. In Section
[3]. For a cellular system enhanced with FRNs, the 3, we propose our relay placement schemes based
main idea of channel partitioning is to optimally Path-loss, SNR and Shadowing. In Section 4, we
assign the resources to the MS-BS, FRN-BS, and evaluate the performance of the proposed schemes
MS-FRN links. Such intra-cell spectrum partitioning using numerical computations and simulations. In
along with the channel reuse scheme not only grant Section 5, we conclude the paper.
the data rate demanded by each user, but also
manages the inter-cell interference by controlling the 2. SYSTEM MODEL AND DESCRIPTION
distance between any pair of co-channel links. 2.1 System Configuration
We consider a cellular system consisting of
The concept of channel partitioning for FRN regular hexagonal cells each of edge length D. Each
based cellular system has been discussed in [4], [5], cell has a BS and certain number of FRNs situated
[2], [8], [7], [14]. In [4], full frequency reuse scheme symmetrically around the BS at a distance dr from the
was proposed. The authors divided the cell in to center and dm from the cell edge as shown in Fig.1.
seven parts and allocated six sets of subcarriers to Let the total bandwidth available for the downlink be
FRN link and the remaining to BS. The authors W units. Let the minimum SNR/SIR experienced by
aimed at exploiting the multiuser diversity gain. the user at furthest location from BS/FRN be γ1.
However, sectoring the inner region can further Similarly, let the minimum SNR/SIR experienced by
reduce the co-channel interference. In [5], frequency FRN at furthest location from BS be γ2, i.e, both MS
reuse scheme was proposed based on dividing the and FRN are placed at a location that they
outer region in to six and also sectoring the inner experienced minimum SNR or SIR. Therefore, these
region. In [2], a preconfigured relay channel selection locations are the effective boundary for each link (i.e
algorithm is proposed to reuse the channels that are MS-BS, FRN-BS and FRN-BS). For a given MS
already used in other cells on the links between FRNs position, let the distance from BS be d* and nearest
and MSs. This scheme may suffer from high co- FRN be d*m. If d* ≤ d, then MS communicates with
channel interference on FRN-MS links. In [7], [14], the BS directly; otherwise it communicates through
frequency partitioning and reuse schemes for cellular the nearest relay using two hop route. Because of the
WLAN systems with mobile relay nodes are specified routing scheme, a cell can be partitioned
proposed. Relays are mobile as the MSs themselves into seven regions as shown in Fig.1. We define the
act as a relay for other MSs. Since the relay is region covered by BS as the inner region (A1) and the
mobile, the channel between relay and the BS can region covered by FRNs as outer region (A2). Outer
change, which will result in a large number of inter- region is further divided into A2k, for k=1, ..., 6. All
relay handoffs. Furthermore, MSs acting as relays the MSs in region A1 communicate directly to the BS,
may not be cooperative because of the power and the MSs in kth A2 region communicate to BS
consumption and the security issues. In [8], a through relay kth FRN. Both the number of FRNs (K)
coverage based frequency partitioning scheme is and the size of each region in a cell (d*m and D) are
proposed. The scheme assumes that the relay nodes determined by the optimal relay placement algorithm.
are placed at a distance equal to the two-third of the
2.2 Channel Partitioning and Reuse Scheme
cell radius, and does not consider optimal relay
The channel partitioning scheme, partitions
placement. Some other proposals for frequency
the downlink bandwidth into 2K+1 orthogonal
management include the use unlicensed spectrum
segments, viz. W1, W2,k and W3,k for k = 1, . . . ,K.
[12], and the use of directional antennas [1].
The band W1 is used by the MSs in region A1, the
band W2,k is used by kth FRN to communicate with
In our paper [6], we proposed a channel
the BS, and the band W3,k is used by the MSs in kth
partitioning and a channel reuse scheme for
A2 region to communicate with kth FRN. Let 𝑊2 =
increasing system capacity to support some preceding 6 6
standards like Global System for Mobile 𝑊 and 𝑊3 =
𝑘 =1 2,𝑘
𝑊 . Because of the
𝑘=1 3,𝑘
Communications (GSM). In this paper, we extend the channel partitioning, there is no intra-cell
channel partitioning and channel reuse scheme for interference, and the system performance is mainly
OFDMA cellular networks which results in increased determined by inter-cell co-channel interference.
system capacity and spectral efficiency. We also
consider the optimal relay placement based on For channel reuse scheme, we assume that
different parameters. We show that with the the frequency reuse distance is 1, i.e., each cell uses
appropriate relay placement, the system performance the complete bandwidth W for the downlink
can be improved significantly. As a result, the communication [11]. In each
number of users that can be accommodated in the

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cell, inner region uses the same band W1. While kth the “BS-MS, BS-FRN and FRN-MS links”,
FRN uses band W2k to communicate with BS and MS henceforth, we use both terms interchangeably. On
in kth A2 region uses W3k band to communicate with these three links, we assume that each link has
kth FRN. minimum SNR requirement (threshold). When the
received SNR exceeds a threshold, the message is
correctly decoded. The distance of user from
2.3 Propagation Model
BS/FRN, where the received SNR equals the
Wireless channel suffers from fading. threshold is defined as the effective radius of
Fading is mainly divided into two types, slow and BS/FRN; it inturn determines the optimal FRN
fast. Slow fading is due to path-loss and shadowing, location. In the next subsections, we describe our
while fast fading is due to multi-path. In this paper, proposed methods to deploy FRNs optimally based
we assume that the code lengths are large enough to on path-loss and SNR.
reveal the ergodic nature of fast fading. Hence, we do
not explicitly consider multi-path effect. We focus on
the path-loss and shadowing in the analysis. Because 3.1 Relay Placement based on Path-loss
of the path-loss, the received signal power is In this subsection, we propose a simplified
inversely proportional to the distance between the relay placement algorithm that depends on the path-
transmitter and the receiver. In general, the path-loss loss. Path-loss is signal attenuation between a source
PL between a transmitter and a receiver is given as, (BS/FRN) and a receiver (MS) which depends on the
propagation distance.
2 𝛾
𝑃𝑇 4𝜋𝑓 𝑑∗
𝑃𝐿 = 𝐺𝑇 𝐺𝑅 = (1)
𝑃𝑅 𝑐 𝑑0

where PT is the transmitted power; PR is the received
power, GT and GR are the antenna gain of transmitter
and receiver respectively; f is the carrier frequency, c
is the speed of light; d* is separation between the
transmitter and receiver; d0 is the reference distance,
and γ > 0 is the path-loss exponent [11].

3. RELAY PLACEMENT SCHEMES
Improvement in capacity and increase in
coverage area are the main benefits of FRNs. These
benefits of FRNs are based on the position of relays
in the cell. Deploying FRNs around the edge of the Fig.2 Layout of FRN enhanced Cellular system
cell help the edge users. However, when they are illustrating the coverage of MS-BS, FRN-BS and
placed at inappropriate locations, may cause MS-FRN regions.
interference to the edge users of the neighboring cell. We consider a simplified cellular
Therefore, optimal placement of FRNs is a key configuration consisting of BS and FRNs as shown in
design issue. Consider the downlink scenario where Fig.2. Initially, FRNs are placed at random position
the BS encodes the message and transmits it in the in a cell. MS moves from BS towards the cell
first time slot to nearby MSs and FRNs. FRNs boundary along a straight-line trajectory.
transmits the message to MSs at the cell boundary in Determination of optimal position is based on the
the second time slot. FRNs are either Decode-and- received signal strength and distance measurements
Forward (DF) type, which fully decodes and re- along the path. MS evaluates the received signal
encodes the message, or Amplify-and-Forward (AF) strength till the signal strength becomes equal to the
type, which amplifies and forwards the Message to preset threshold value.
MSs in the second hop. Note that the reverse will be
for uplink scenario. In downlink scenarios, we As the MS moves away from the BS/FRN, if
consider non-transparent type relays, i.e., MSs in the the received signal strength decreases below a
first hop communicate to BS while MSs in the second threshold value and the MS is not able to
hop communicate only to FRNs [15]. communicate with the BS. At this position where the
received signal strength is too weak, appropriately
In this section, we propose two types of placed FRN can enhance the signal quality of the
Relay placement schemes to deploy FRNs optimally MS.
in the cell. We analytically determine the position of
FRNs within the cell so that the QoS requirement of Now, we describe our path-loss based FRN
each user is satisfied. In each scheme we evaluate the placement algorithm as follows: Referring to Fig.2,
signal strength on the three links (BS-MS, BS-FRN, let PBS and PFRN be the power transmitted by BS and
and FRN-MS links). The term “three links” denote FRN respectively. Let Pb be the power received by

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MS located at the distance (d) from BS; P r be the transmitted signal is diffracted due to a tree or the top
power received by FRN located at the distance (dr) of a building along the path of propagation. Let Г 𝑏𝐵𝑀 ,
from BS; Pm be the power received by MS located at Г 𝑏𝐵𝑅 and Г 𝑏𝑅𝑀 be the SNR experienced by the user on
the distance (dm) from one of FRNs. When MS BS-MS, BS-FRN and FRN-MS links respectively. In
follows straight line trajectory, then BS, MS and this paper the term SNR is used to denote the effects
FRN are collinear and the radius of the cell D is of noise and shadowing, henceforth, we use SNR to
computed as D = d + 2dm and also dr = d + dm. represent the effect of SNR plus shadowing. This
Assume that the threshold Pb = Pm and Pb ≠ Pr, the algorithm is based on evaluation of SNR on three
path-loss (1) is redefined for the three links as: links as follows,
𝛾𝑏
𝑑0 Г 𝑏𝐵𝑀 = 𝑃 𝐵𝑆 − 10𝛾 𝑏 log 𝑑 + 𝜉 𝑏 − 𝑁 𝑏 (9)
𝑃 𝑏 = 𝐾1 𝑃 𝐵𝑆 (2)
𝑑
𝛾𝑟 Г 𝑏𝐵𝑅 = 𝑃 𝐵𝑆 − 10𝛾 𝑟 log 𝑑 𝑟 + 𝜉 𝑟 − 𝑁 𝑟 (10)
𝑑0 Г 𝑏𝑅𝑀 = 𝑃 𝐹𝑅𝑁 − 10𝛾 𝑚 log 𝑑 𝑚 + 𝜉 𝑚 − 𝑁 𝑚 (11)
𝑃𝑟 = 𝐾2 𝑃 𝐵𝑆 (3)
𝑑𝑟
𝛾𝑚
𝑑0 Note that we use subscript b, r and m in this paper to
𝑃 𝑚 = 𝐾3 𝑃 𝐹𝑅𝑁 (4)
𝑑𝑚 refer to the three links BS-MS, BS-FRN and FRN-
where K1, K2 and K3 are constants; γb, γr and γm are MS respectively. ξb, 𝜉 r and 𝜉 m are Gaussian random
the path-loss exponent on BS-MS, BS-FRN and variable with standard deviation of σb, σr and σm on
FRN-MS links respectively. Based on (2), (3), (4) the three links mentioned above. Similarly, Nb, Nr
and simple algebraic manipulation, the ratio and Nm denote the thermal noise.

𝑃 𝐵𝑆 𝑑𝛾𝑏 This algorithm evaluates the SNR of each
= 𝛾𝑟 (5) link. We consider SNR as a decision parameter for
𝑃 𝐹𝑅𝑁 𝑚 𝑑𝑟
𝛾 the success/failure of a transmission on a link; the
𝑃𝑏 𝑑𝑟𝑟
= 𝛾𝑏 (6) received message is correctly decoded when the SNR
𝑃𝑟 𝑑𝑚 experienced by MS on each link exceeds a threshold
SNR. Hence, the effective radius of the three links
remain constant. Based on these expressions, we can be obtained from the threshold SNR on the three
define the optimal radius for BS-MS link or direct links. Let the threshold SNR on BS-MS, BS-FRN
link (𝑑 ) and that of FRN-MS link or relaying link and FRN-MS links are denoted as Гb, Гr and Гm
(𝑑 m) as, respectively. Accordingly, the probability of
successful decoding with direct transmission over
𝑑 = max 𝑑 , BS-MS (Prb) is given as,
𝑑 >0
𝑠. 𝑡 𝑠𝑎𝑡𝑖𝑠𝑓𝑦𝑖𝑛𝑔 𝑡𝑕𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠 (7)
𝑃𝑟 𝑏 = 𝑃𝑟 Г 𝑏𝐵𝑀 > Г 𝑏
𝑖𝑛 𝐸𝑞𝑢. 5 𝑎𝑛𝑑 6
= 𝑃𝑟 𝑃 𝐵𝑆 − 10𝛾 𝑏 log 𝑑 + 𝜉 𝑏 − 𝑁 𝑏 > Г 𝑏
𝑑𝑚 = argmax 𝑑𝑚 , = 𝑃𝑟 𝜉 𝑏 > 10𝛾 𝑏 log 𝑑 + 𝑁 𝑏 + Г 𝑏
𝑑 𝑚 ∈(0, 𝑑 𝑟 −𝑑 ) − 𝑃 𝐵𝑆 (12)
𝑠. 𝑡 𝑠𝑎𝑡𝑖𝑠𝑓𝑦𝑖𝑛𝑔 𝑡𝑕𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠 (8) 10𝛾 𝑏 log 𝑑 + 𝑁 𝑏 + Г 𝑏 − 𝑃 𝐵𝑆
𝑖𝑛 𝐸𝑞𝑢. 5 , 6 𝑎𝑛𝑑 7 = 𝑄
𝜎𝑏
We consider that for a given user position, if
We choose threshold greater than the probability that the received SNR above the threshold
minimum signal strength below which call drops. is 95%, then the user has good link with the BS.
Thus all admitted calls never drop. Since the effects Therefore such users do not require relaying support.
noise, shadowing and interference from neighboring The effective radius for direct link (𝑑 ) is the
cells are not considered in this model, this algorithm maximum distance where the above criteria is
provides the simplified estimate of FRN placement satisfied. Hence, optimum value of effective radius
scheme. In the next subsection, we propose a scheme
for direct link (𝑑 ) is given as,
that considers the effect of noise and shadowing.
𝑑 = max 𝑑 ,
𝑑>0
3.2 Relay Placement based on SNR and
10𝛾 𝑏 log 𝑑 +𝑁 𝑏 +Г 𝑏 − 𝑃 𝐵𝑆
Shadowing 𝜎𝑏
= 𝑚𝑎𝑥 10 (13)
Relay placement algorithm based on SNR
and shadowing considers the case of isolated cell, 𝑠. 𝑡 𝑑 > 0; 𝑃𝑟 𝑏 ≥ 0.95,
where interference from neighboring cells is not Similarly, the probability of successful decoding on
considered. In addition to signal attenuation due to BS-FRN link ( 𝑃𝑟 𝑟 ) and on FRN-MS link ( 𝑃𝑟 𝑚 ) can
path-loss, we consider the effects of noise and be expressed as,
shadowing. Shadowing effects happen when a

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10𝛾 𝑟 log 𝑑 +𝑁 𝑟 +Г 𝑟 − 𝑃 𝐵𝑆 𝐷𝐹
𝑃𝑟 𝑟 = 𝑄 (14) 𝑠. 𝑡 𝑃suc ≥ 0.95 ; 𝑃𝑟 𝑏
𝜎𝑟
≥ 0.95. (19)
10𝛾 𝑚 log 𝑑 + 𝑁 𝑚 + Г 𝑚 − 𝑃 𝐹𝑅𝑁
𝑃𝑟 𝑚 = 𝑄 (15)
𝜎𝑚 3.3.2. Amplify and Forward Relaying
The equivalent SNR over two-hop transmission In amplify and forward relaying scheme, the
depends on the type of relaying scheme. In this paper AF relay amplifies the analog signal received from
we consider Decode and Forward Relaying (DF) and the BS and transmits an amplified version of it to the
Amplify and Forward Relaying (AF) relaying MSs [14]. Let the experienced SIR for this scheme
schemes. be Г 𝐴𝐹 , then it is computed as follows.

3.2.1 Decode and Forward Relaying Г 𝑏𝐵𝑅 Г 𝑏𝑅𝑀
Consider a downlink scenario, where each Г 𝐴𝐹 = (20)
Г 𝐵𝑅 + Г 𝑏𝑅𝑀 +1
𝑏
FRN decodes the signal received from BS-FRN link
and re-transmits to MS on the FRN-MS link. In this
scheme, the end to end rate achieved from BS to MS Let Г be the threshold SIR. If the experienced SIR
is determined by the minimum rate achieved among falls below the threshold, the user is said to be in
the rates of BS-FRN and FRN-MS links, i.e., if the 𝑜𝑢𝑡
outage and outage probability is given as 𝑃 𝐴𝐹 out for
required rate for this scheme is RDF, then AF scheme [14].

2𝑅 𝐷𝐹 ≤ 𝑚𝑖𝑛 log 2 1 + Г 𝑏𝐵𝑅 , log 2 1 + Г 𝑏𝑅𝑀 (16) 𝑜𝑢𝑡
Г 𝑏𝐵𝑅 Г 𝑏𝑅𝑀
𝑃 𝐴𝐹 = 𝑃𝑟 ≤Г (21)
Г 𝐵𝑅 + Г 𝑏𝑅𝑀 +
𝑏
1
If the required rate is not achieved on either of the
link, then user is said to be in outage. Let the outage It is difficult to obtain the exact closed-form
𝐷𝐹 solution for outage probability of (21) [10]. However,
probability in DF scheme be Гout , it can be expressed
several literatures give the closed-form lower bound
as
and upper bound. We are interested in upper bound
solution to compute the effective radius of relaying
𝑃out = Pr 𝑚𝑖𝑛 log 2 1 + Г 𝑏𝐵𝑅 , log 2 1 + Г 𝑏𝑅𝑀
𝐷𝐹
link. Accordingly, the optimum radius for relaying
≤ 2𝑅 link ( 𝑑 𝑚 ) due to AF relay is given as:
= 1 − Pr 𝑚𝑖𝑛 log 2 1 + Г 𝑏𝐵𝑅 , log 2 1 + Г 𝑏𝑅𝑀
≥ 2𝑅 𝑑𝑚 = argmax 𝑑𝑚 ,
𝐷𝐹 𝑑 𝑚 ∈ 0, 𝑑 𝑟 −𝑑
= 1 − 𝑃suc (17)
𝑃 𝐹𝑅𝑁 − 𝑁 𝑚 − Г 𝑚 −𝜎 𝑚 .𝑄 −1 ( 𝑃 𝑟 𝑚 )
If user does not go into outage, this means there is 10𝛾 𝑚
successful transmission on BS-FRN and FRN-MS = argmax 10
𝐷𝐹 𝑑 𝑚 ∈(0, 𝑑 𝑟 −𝑑 )
links. Let the 𝑃suc be the probability of successful 𝐴𝐹
transmission on DF scheme, then it can be computed 𝑠. 𝑡 𝑃suc ≥ 0.95 , (22)
as [9],
3.3 Optimal Number of FRNs
𝑃suc = 𝑃𝑟 Г 𝑏𝐵𝑅 > Г 𝑟 . 𝑃𝑟 Г 𝑏𝑅𝑀 > Г 𝑚
𝐷𝐹
Assume that users are distributed uniformly
10𝛾 𝑚 log 𝑑 𝑚 + 𝑁 𝑚 + Г 𝑚 − 𝑃 𝐹𝑅𝑁 in the cell. Hence, the approximate number of FRNs
= 𝑄 . required in a cell can be obtained by computing the
𝜎𝑚
10𝛾 𝑟 log 𝑑 𝑚 + 𝑁 𝑟 + Г 𝑟 − 𝑃 𝐵𝑆 area of inner region A1 and that of outer region A2.
𝑄 After simple mathematical steps, the number of FRN
𝜎𝑟 required in a cell is also computed as 𝑁 𝐹𝑅𝑁 =
= 𝑃𝑟 𝑟 𝑃𝑟 𝑚 (18) 𝑑
4( + 1) . Since the entire cell radius is defined as
𝑑 𝑚
We consider the criterion 𝐷𝐹
𝑃suc
≥ 95% for D = d + 2dm, the number of FRN that can support the
deploying FRNs in cellular networks. Therefore, the users in outer region depend on optimal value of d
effective radius (𝑑 m) for relaying link (FRN-MS) will and dm. We choose optimal value of d and d m that
be optimal distance which 5% outage probability is minimizes the number of FRN used in the cell. The
𝐷𝐹
satisfied, i.e., 𝑃out ≥ 0.05. Hence, the optimum optimization equation is described as,
radius for FRN-MS link is given as,
𝑁 𝐹𝑅𝑁 = arg min 𝑁 𝐹𝑅𝑁 ,
𝑑𝑚 = argmax 𝑑𝑚 , 𝑠. 𝑡 𝑑 , 𝑑 𝑚 𝑎𝑛𝑑 𝑑 𝑚 𝑠𝑎𝑡𝑖𝑠𝑓𝑦𝑖𝑛𝑔 𝐸𝑞𝑢. 19 𝑎𝑛𝑑 22 ,
𝑑 𝑚 ∈ 0, 𝑑 𝑟 −𝑑 𝑑 𝑎𝑛𝑑 𝑑 𝑚 𝑠𝑎𝑡𝑖𝑠𝑓𝑦𝑖𝑛𝑔 𝐸𝑞𝑢. 8 (23)

𝑃 𝐹𝑅𝑁 − 𝑁 𝑚 − Г 𝑚 −𝜎 𝑚 .𝑄 −1 ( 𝑃 𝑟 𝑚 )
3.4 Outage performance analysis
10𝛾 𝑚 Co-channel interference and shadowing
= argmax 10
𝑑 𝑚 ∈(0, 𝑑 𝑟 −𝑑 ) effects are among the major factors that limit the

1505 | P a g e

capacity and link quality of a wireless consider correlation among interferers and also the
communications system. In this section, we use correlation that may exist between interferer and
Gauss-Markov model to evaluate the statistical desired signals
characteristics of SIR in Multihop communication
channels. By modeling SIR as log-normally 4. RESULTS AND DISCUSSION
distributed random variable, we investigate the In this section, we present the analytical and
performance of relay placement schemes discussed in simulation results to illustrate the performance of our
Subsection 3.1 and 3.2. We make a comparison proposed FRN placement algorithms. We use Matlab
between the above models in terms of performance simulation for modeling cellular networks under
evaluation where outage probability is a QoS varying channel conditions. We analyze the
parameter. Further more the result is used to find the performance of relay placement schemes based on
more realistic way of channel partitioning and relay path-loss and SNR as described in previous section.
FRN placement schemes. The list of simulation parameters are mentioned in
Table 1.
The co-channel uplink interference to the
BS/FRN of interest is assumed to be from MSs or Table 1. List of the simulation parameters.
FRNs that links to first tier or upper tier cells (MS i′s
or FRNK′s). Including the shadowing effect on the Parameters Values
three links, the SIR on each link can be described as; Carrier Frequency 5GHz
𝑁 −1 System Bandwidth (W) 25.6MHz
10 𝜉𝑏 10 1 Standard Deviation 8, 5, 8 dB
Г 𝑏𝐵𝑀 = 𝛾𝑏
𝑑 𝛾𝑏 𝑑 𝑖 10 𝜉𝑏𝑖 10 ( σ𝑑, 𝜎𝑟and 𝜎𝑚)
𝑖=1
Correlation Coefficient 0.5
𝛾𝑏 𝜉𝑏𝑖 −𝜉𝑏
−1
= 𝑁 𝑑
10 10 (24) Path-loss Exponent 3.5, 2.5, 3.5
𝑖=1 𝑑𝑖 (𝛾𝑑, 𝛾𝑟 and 𝛾𝑚)
𝑁 −1 BS Transmit Power (PBS) 40dBm
10 𝜉𝑟 10
1 FRN Transmit Power (PFRN) 20dBm
Г 𝑏𝐵𝑅 = 𝛾𝑟 𝛾𝑟
𝑑𝑟 𝑑 𝑟𝑖 10 𝜉𝑟𝑖 10 MS transmit Power (PMS) 2dBm
𝑖=1
Threshold (Г) -10dBm
𝛾𝑟 𝜉𝑟𝑖 −𝜉𝑟 −1
𝑁 𝑑 Thermal Noise (N) -100dBm
= 𝑖=1 10 10 (25)
𝑑 𝑟𝑖

𝑁 −1 The optimal FRNs placement results are summarized
10 𝜉𝑚 10
1 in the Table 2.
Г 𝑏𝑅𝑀 = 𝛾𝑚 𝛾𝑟
𝑑𝑚 𝑑 𝑚𝑖 10 𝜉𝑚𝑖 10
𝑖=1
Table 2. Results of optimal FRNs placement based on
𝛾𝑚 𝜉𝑚𝑖 −𝜉𝑚 −1
= 𝑁 𝑑
10 10 (26) path-loss and SNR.
𝑖=1 𝑑 𝑚𝑖

where d and dr are the location of desired MS and Parameters Based on Path-loss Based on SNR
FRN from the BS0 on direct link, d m is the location of dr 2120m 2076m
desired MS from desired FRN under the second hop. d 1611m 1522m
Similarly, di and dri are the location of co-channel dm 509m 554m
interferer MS and FRN from the BS0, while dmi NFRN 6 6
denotes the location of co-channel interferer MSs
from FRN that is associated to BS0. Shadowing for
the desired links are denoted as ξb, 𝜉 r and 𝜉 m For Fig. 3 illustrates the outage probability of
interfering links shadowing is expressed as ξbi, 𝜉 ri and downlink cellular network where the optimal FRN
𝜉 mi to denote the interfering link of MS-BS, FRN-BS placement scheme is based on path-loss. This figure
and MS-FRN; in all cases, i∈ {1, ..., 18}. compares the outage probability of relay enhanced
cellular system of direct link and relay link along
Basically, the outage probability analysis for with the scheme without FRNs. Furthermore, Fig. 3
the three links (MS-BS, FRN-BS and MS-FRNs) is demonstrates that outage probability is significantly
similar to the expression given in Section 3.2. improved in relay enhanced cellular system with
However, interference from neighboring cells is optimal FRN placement. As it can be shown in this
considered here. We compute the mean and standard figure, at SIR threshold of 0 dB, the outage
deviation of both desired and interference signal probability of the scheme without FRNs is 40%. But,
based on Fenton-Wilkinson′s and Schwartz-Yeh′s the outage probability of our proposed scheme for
method [13]. Shadowing is usually represented by FRN-MS link is nearly 0%. This means that due to
i.i.d. log-normal model in wireless multi-hop models. optimal placement of FRNs, outage probability at
However, shadowing paths are correlated. Hence, we cellular boundary improves by 40%. Since the users
at the cell boundaries dominate the system
1506 | P a g e

performance, our optimal relay placement scheme Fig. 5. Outage probability versus SIR threshold of DF
significantly improves the outage probability of MSs relay enhanced cellular system with 1200 sectoring in
of second hop link. the inner region; proposed optimal FRN placement
Simulation of cellular radio system 00 Sectorization schemes are compared with FRNs location at 2/3rd of
100
cell radius.
90 without FRN
With FRN (direct link MS-FRN)
Fig. 4 illustrates the outage probability
Outage Probability (%) based on Pathloss

80 With FRN (2nd hop link MS-FRN)
versus SIR threshold for DF relay where the inner
70
region of the cell is sectored in to 600 sectoring (refer
60 Fig.1). We compare our proposed optimal FRN
50
placement schemes with a scheme that places FRNs
at 2/3rd position of the cell radius. The results show
40
that our proposed schemes achieve significant
30 improvement on the performance of the cellular
network. In Fig.4, at SIR threshold of -20 dB, the
20
outage probability of a system when FRNs are placed
10 at 2/3rd of cellular radius is 50% whereas, the outage
0 probability of our proposed scheme for FRN-MS link
-50 -40 -30 -20 -10 0 10 20 30
Threshold SIRo (dB) is only 2%. However, there is no significant
difference in performance among our proposed
Fig. 3. Outage probability versus SIR threshold of DF
schemes. As can be shown in Fig.4, Fig.5 and Fig.6,
relay enhanced cellular system with no sector in the
comparing the performance of our two proposed
inner region; optimal FRN placement is based on schemes, the outage probability of optimal FRNs
path-loss. placement scheme which depends on path-loss and
Simulation of cellular radio system 600 Sectoring (DF)
100 that of the scheme which depends on SNR are nearly
equal. Hence, either of the two proposed schemes can
90
be implemented for optimal FRNs placement to
80 achieve the same QOS requirement.
Simulation of cellular radio system 00 Sectorization (DF)
70 100
Outage Probability (%)

FRN placement at
60 2/3 of total radius 90

Optimal FRN placement
50 based on pathloss 80

Optimal FRN placement Relay placement
70
40 based on SNR based on pathloss

Relay placement
60 based on SNR
30
Relay placement at
50 2/3 of total radius
20
40

10
30

0 20
-50 -40 -30 -20 -10 0 10 20 30
Threshold SIRo (dB)
10

Fig. 4. Outage probability versus SIR threshold of DF 0
-50 -40 -30 -20 -10 0 10 20 30
relay enhanced cellular system with 600 sectoring in Threshold SIRo (dB)

the inner region; proposed optimal FRN placement
schemes are compared with FRNs location at 2/3rd of Fig. 6. Outage probability versus SIR threshold of DF
cell radius. relay enhanced cellular system with no sectoring in
100
Simulation of cellular radio system 1200 Sectoring the inner region; proposed optimal FRN placement
schemes are compared with FRNs location at 2/3rd of
90
cell radius.
80

70 Fig.4, Fig.5 and Fig.6 also illustrate that
sectoring the BS-MS direct link of the cell

60
Optimal Relay placement significantly improves the outage performance of the
50 based on pathloss
Optimal Relay placement
cell in which FRNs are placed at 2/3rd of the cell
40 based on SNR
radius while sectoring has no significant effect on the
Relay placement at 2/3 of
30
cell radiusased on pathloss cellular networks that use the proposed optimally
20
FRNs placement schemes. Even though sectoring
lowers the effect of co-channel interference, it also
10
degrades system capacity.
0
-50 -40 -30 -20 -10 0 10 20 30
Threshold SIRo (dB)

1507 | P a g e

Fig.7 shows the performance of path-loss effects of co-channel interference, but decreases
based optimal FRNs placement schemes for 6 and 18 system capacity.
co-channel interferers. We evaluate the performance
of the two hop cellular network with AF and DF 5. CONCLUSION
relay. Since AF relay scheme amplifies the required This research work proposed two optimal
signal and noise, the cellular network performance FRNs placement schemes which are based on path-
decreases with the increase in number of co-channel loss and SNR. The proposed schemes also compute
cells. We also observe that, outage probability of the optimal number of FRNs that are required to enhance
system at -20 dB SIR threshold is improved by 80% the QoS of cellular system. Our schemes also
when the co-channel decreases from two tire (18 cell) investigate effects of sectoring the inner region of the
to one tier (6 cells) cell. However such effect is not cell on optimal FRN placements. Sectoring the inner
significantly observed in DF relaying scheme. region for improves the outage probability. Our
optimal relay node placement schemes significantly
Simulation of cellular radio system 00 Sectorization reduce the outage of the cellular system and provide
100
better QoS for users at cell boundaries.
90

80 6. ACKNOWLEDGMENT
Outage Probability (%) based on Pathloss

70 This research work is supported by India-UK
60
Advanced Technology Centre (IU-ATC) of
Excellence in Next Generation Networks Systems
50
DF Relay 6 cochannel cells
and Services.
40 AF Relay 6 cochannel cells
DF Relay 18 cochannel cells
30 AF Relay 18 cochannel cells References
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