IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
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Relay Deployment in Cellular Networks:
Planning and Optimization
Weisi Guo, Tim O’Farrell
Department of Electrical and Electronic Engineering
University of Sheffield, United Kingdom
Email: {w.guo, t.ofarrell}@sheffield.ac.uk
Abstract— This paper presents closed-form capacity expressions for interfere-limited relay channels. Existing theoretical
analysis has primarily focused on Gaussian relay channels, and
the analysis of interference-limited relay deployment has been
confined to simulation based approaches. The novel contribution
of this paper is to consolidate on these approaches by proposing
a theoretical analysis that includes the effects of interference
and capacity saturation of realistic transmission schemes. The
performance and optimization results are reinforced by matching
simulation results.
The benefit of this approach is that given a small set of network
parameters, the researcher can use the closed-form expressions to
determine the capacity of the network, as well as the deployment
parameters that maximize capacity without committing to protracted system simulation studies. The deployment parameters
considered in this paper include the optimal location and number
of relays, and resource sharing between relay and base-stations.
The paper shows that the optimal deployment parameters are
pre-dominantly a function of the saturation capacity, pathloss
exponent and transmit powers.
Furthermore, to demonstrate the wider applicability of the
theoretical framework, the analysis is extended to a multiroom indoor building. The capacity improvements demonstrated
in this paper show that deployment optimization can improve
capacity by up to 60% for outdoor and 38% for indoor users.
The proposed closed-form expressions on interference-limited
relay capacity are useful as a framework to examine how key
propagation and network parameters affect relay performance
and can yield insight into future research directions.
I. I NTRODUCTION
Relays have been proposed as a solution to solving the
challenge of improving local capacity in Long-Term-Evolution
Advanced (LTE-A) and 802.16 j/m standards. Its primary
purpose is to either increase the capacity of an existing area or
to extend the coverage area of the parent cell-site. The Qualityof-Service (QoS) provided by an operator is not necessarily
determined by the average performance, but by that achieved
by a certain bottom percentage of customers. This is generally
customers operating either on the interference limited celledge or indoors. Statistically, over 70% of the mobile traffic
is carried to indoor users, therefore there is an urgency in
addressing how to enhance capacity for users in both of these
scenarios. This paper presents a novel closed-form capacity
expression for an interference-limited relay-assisted cellular
network, with consideration to the capacity saturation of realistic transmission schemes, as well as both outdoor and indoor
users. The benefit of this approach is that given a small set of
network parameters, the researcher can determine the capacity
of the network, as well as the deployment parameters that
maximize capacity without committing to protracted system
level simulation studies.
A. Review
The topic of relays in cellular networks has been well
studied in the past [1] [2]. In terms of analysis, existing
theory has largely focused on extending the original work on
Gaussian relay channels. Closed-form expressions on optimal
relay deployment in Gaussian channels was proven in [3]
for location and in [4] for resource allocation. In a realistic
cellular system, the effects of inter-cell interference [5] and
capacity saturation of realistic modulation schemes have a
significant impact on both the capacity of the system and the
optimal solutions, as shown in [6]. For relay deployment in
a multi-cell interference-limited network, the characterization
of capacity and outage performance has been limited to
simulation based studies [5] [7]. Interference-limited stochastic
geometric theoretical methods have not yet been extended
to relay channels [8]. The optimization of relay deployment
location [9], resource allocation [1] [5], and cost efficiency
[10] is conducted using iterative numerical approaches on
simulation results.
From a system designer perspective, there is a dichotomy
in the theoretical and simulation approaches. The lack of
tractable interference-limited relay capacity expressions means
that one either has to rely on closed-form Gaussian channel
expressions or extensive multi-cell simulation results. This
has restricted the insight into how and why key network and
channel parameters affect the relay performance and optimal
deployment solutions.
B. Contribution
The novelty of this paper is to consolidate the theoretical
and simulation based approaches by proposing an interferelimited theoretical framework that considers capacity saturation. The paper presents closed-form capacity expressions
for a relay-assisted base-station and maximizes the capacity
with respect to deployment parameters. The benefit of this
approach is that, for any set of network parameters, the system
designer is able to characterize and optimize the multi-cell
network performance without resorting to extensive multicell simulations. The proposed analysis is also validated by
a multi-cell simulator. Furthermore, to demonstrate the wider
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
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(λ), AWGN power (n) and antenna gain (A):
|hi |2 λi 10
γs,i =
n+
Fig. 1. Example system setup for a particular relay-node (RN) configuration
(3-sector BS with 5-relays per sector): a) 19-BS RAN model; b) BS with
RNs; c) Mean received SINR plot.
applicability of the theoretical framework, the analysis is
extended to a multi-room indoor building. The theoretical
analysis in this paper are validated by multi-cell simulation
results from our own simulator and existing work.
II. S YSTEM M ODEL
The system considers a Multi-Cell-Multi-User (MCMU)
Radio-Access-Network (RAN), where the base-stations (BSs)
are homogeneously deployed, and are assisted by relay-nodes
(RNs). The homogeneous deployment offers an upper-bound
to the RAN performance, in comparison to other irregular
cell distribution methods such as spatial poisson-point-process
(SPPP) distribution [8]. The RN-assisted BS establishes a high
quality BS-RN channel by providing a LOS BS-RN channel,
as recommended by 802.16j/m specifications [11]. The paper
considers non-cooperative Decode-and-Forward (DF) relaying
protocol due to its low CSI estimation complexity and relatively strong system level performance compared to AF relaying [12]. The relays in this paper operate in the transparent
mode, whereby the parent BS is responsible for scheduling the
packet transmission of each user with knowledge of the relay
deployment. The traffic model assumes that it is full-buffer
and given that relays can yield a higher overall capacity, the
authors expect that the relays can in fact reduce congestion
delay.
The system layer simulation results are derived from our
own proprietary VCESIM LTE Dynamic System Simulator
[13], which is bench-marked against 3GPP tests and has
been verified by our sponsors Fujitsu and Nokia Siemens
Networks. Each BS’s throughput considers 2-tiers of inter-BS
interference, which is sufficiently accurate [5]. The simulation
system model is shown in Fig. 1a, where a 19 BS network
is created with wrap-around [5]. The relays are deployed near
the cell-edge of each BS, where the cell-edge is defined as
the region where the interference power from other cells is
similar or stronger than the signal power from the serving
BS. An illustration of one form of relay deployment is shown
in Fig. 1b, and the corresponding average received SINR is
shown in Fig. 1c.
In simulations, the instantaneous received signal to interference plus noise ratio (SINR) of a single sub-carrier of a single
user is a function of: the transmit power of BS (P ), pathloss
Si +A(θi )
10
PNcell
j=1,j6=i |hj
|2 λ
j 10
Ps,i
Sj +A(θj )
10
,
(1)
Ps,j
where the values of each parameter is given in Table. I in
the Appendix. The parameters h and S are the multi-path
and log-normal shadow fading components, defined in [14].
The pathloss component can be expressed as a function of the
distance x: λ = Kx−α ; where K is the frequency dependent
pathloss constant and α is the pathloss exponent. The downlink
throughput employs an adaptive-modulation-coding results are
taken from a physical link layer simulator [15].
III. A NALYTICAL M ODEL
A. Interference-Limited Capacity
The analytical model considers a simplified and tractable
SINR expression of (1), based on a serving cell (i) and
dominant interference cell (j), as shown in Fig. 2. This is
similar to the analytical models in [16], whereby it has been
shown that the effects of fading on capacity, when averaged
over time, are small compared to the effects of pathloss. The
complete SINR expression in (1) can be approximated to:
x−α
Pi
i
, by not assuming that the interference power is
γi ≈ x−α
Pj
j
greater than AWGN power.
The downlink throughput is found using the Shannon expression, with consideration to mutual information saturation:
Cs
for: 0 < xi < ds
Ci =
(2)
alog2 (1 + bγi )
for: ds < xi < r
where at the distance ds or less away from the serving cell,
the the maximum achievable capacity in LTE is Cs = 4.3
bit/s/Hz, for a modulation and coding scheme of 64QAM
and 6/7 Turbo Code. The factors a = 0.8 and b = 0.6
are the Shannon adjustment values to compensate for coding
losses in mutual information [17]. It has been shown that
if the capacity saturation of channels is not considered, the
optimization solution can often be skewed towards awarding
high capacity links with more resources, when in reality these
channels have already been saturated [6]. The value of the
distance at which capacity saturation occurs (ds ) can be found
as a function of the inter-BS distance (2r), pathloss exponent
(α) and the saturation capacity (Cs ):
2r
ds ≤
1+(
Cs
(2 a
−1)Pj 1
)α
bPi
,
(3)
which is proven in Lemma 1 in the Appendix.
The paper’s simulation results and analytical model considers both the mean capacity and the edge capacity, as defined
by:
• Mean Capacity: the mean capacity achieved is dominated by BS centre users that achieve a large received
SINR. By stating that SINR (γ) of each position is large
enough for the approximation log(1 + γ) ≈ log(γ) to
hold, the margin of error averaged across the BS is small
(0.1%). This is proven in Lemma 2 of Appendix.
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
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Fig. 2. Analytical (top) System Model and Simulated (bottom) Capacity for: a) Homogeneous BS; and b) Heterogeneous Outdoor-Outdoor Network with
BS and Relays.
(x = 0):
C̄ =
1
r
Z
where ds =
r
0
ds
1
Cdx ≈ {Σ + a | ds log2 [(
)−α ]
r
2r − ds
2r − ds
) |},
−2αrlog2 (
r
2r
1
1+γsα
(5)
is given by expression (3) and Σ = Cs ds .
The full proof is given in Lemma 3.
The edge capacity achieved is between 2 closest BSs
deployed, as illustrated in Fig. 2 at location 1. The minimum
capacity (edge) occurs when (x = r):
Cedge = alog2 (1 + b
Fig. 3. Baseline downlink throughput results for simulation (symbols) and
theory (lines) with BS coverage sizes.
Edge Capacity: the capacity achieved by cell-edge users
that has the lowest received SINR, which determine the
Quality-of-Service (QoS).
The paper will now consider the cellular capacity for a baseline
outdoor system in Section III.
•
B. No Relay
In the baseline outdoor capacity analysis, the paper considers an omni-directional 1-sector BS, as shown in Fig. 2. The
capacity of a single sector BS with co-frequency interference
from other BSs can be expressed as:

for: 0 < x < 2r 1
 Cs
1+γsα
C=
(4)
bx−α
2r
 alog2 (1 + (2r−x)
)
for:
<
x
<r
1
−α
1+γsα
The mean capacity achieved is the average capacity achieved
from edge of BS coverage (x = r) to the base of the BS
r−α
).
(2r − r)−α
(6)
The results of the theoretical analysis and the simulation model
is presented in Fig. 3, where similar to the conclusion in [18], a
reasonably good match was found (margin of error is 1.2% for
mean capacity and 16% for edge-capacity). The paper will now
introduce the interference-limited relay capacity and maximize
the capacity with respect to: RN location, number of RNs and
resource shared between BS and RN.
IV. O UTDOOR R ELAYING (OR)
The paper assumes that the RNs are deployed in places
where the channel between the parent BS and the RN is Lineof-Sight (LOS) based [14]. All other channels are assumed to
be NLOS-based in the theoretical framework, and probability
between NLOS and LOS based in the simulation framework
(see Section I). When co-frequency RNs are inserted into a
BS to improve outdoor capacity, the dominant interference
coupling is between the parent BS and the RN, and not from
the neighbouring BSs. This is due to the fact that signal
power is dominated by propagation distances, despite the RN’s
significantly lower transmit power.
For an UE in the BS, there is a handover point where the
mean received SINR from the BS-UE and the RN-UE is equal,
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
Fig. 4. Relaying downlink capacity variation with RN distance: Mean and
Edge capacity for Gaussian relay channels without interference and capacity
saturation (simulation in symbols and theory in lines).
4
Fig. 5.
Relaying downlink capacity variation with RN distance: Mean
and Edge capacity for interference-limited network with capacity saturation
(simulation in symbols and theory in lines).
A. Mean Capacity Optimization
as shown in Fig. 2. This distance from the BS, is denoted dHO
and is shown to be the following in Lemma 4:
dHO =
dr
1
1 + ( PPrc ) α
,
(7)
where dr is the distance of the RN from the serving BS. If the
RN and BS transmit at the same power, the handover distance
is half-way between the RN and the BS.
The capacity of co-frequency outdoor-relaying (CF-OR) can
therefore be represented as:

Cs
for: 0 < x < ds1


 alog (1 + bPc x−α ) for: d < x < d


s1
HO
2
Pr (dr −x)−α

bPr (dr −x)−α
CCF-OR =
alog2 (1 +
) for: dHO < x < ds2
Pc x−α



C
for: ds2 < x < ds3
s



bPr (x−dr )−α
alog2 (1 +
) for: ds3 < x < r
Pc x−α
(8)
which is for dHO > ds1 and holds true if the BS-RN channel
is always stronger than the RN-UE channel, as proven in
Lemma 5. The values for the break-point distances ds1 , ds2
and ds3 can be found via Lemma 1 and Lemma 4 and is
presented in Lemma 6. Figure 4 shows the downlink capacity
(CCF-OR ) variation with BS-RN distance dr . In Fig. 4, the
classical Gaussian relay channel is considered, whereby no
capacity saturation and interference are modelled. The results
show that the optimal RN location is generally less than halfway (dr /r < 0.5), similar to the results obtained in for a
cooperative DF relaying [3] [4]. By introducing the co-channel
interference and capacity saturation, the optimization solution
shifts to deploying the RN away from the BS to dr /r ' a.
This will be more closely explained in the next section. The
mean capacity results show a good match between simulation
and theoretical capacity. The detailed proof on optimization
for mean and edge capacity is given below.
The mean capacity achieved is the average capacity
achieved from edge of BS (x = r) to the base of the BS
(x = 0):
Z
1 0
1
(9)
C̄CF-OR =
CCF-OR dx ≈ {ΣCF-OR + | aFΣ |},
r r
r
where ΣCF-OR contains the BS and RN saturation capacity
terms, and FΣ is a composite logarithm term that contains
the non-saturated terms, as explained in Lemma 6.
In order to maximize the mean capacity with respect to
the location of the RN, expression (9) is differentiated with
respect to dr . The optimal BS-RN distance that maximizes
mean capacity is:
d∗r,CF-OR,mean-opt. ≈ 0.4FΣ [1 + (γs
Pr − 1
) α ],
Pc
(10)
where FΣ is a constant and the full optimization proof is
shown in Lemma 6 of the Appendix.
The conclusion is that the optimal RN location is almost
entirely dependent on the power ratio between the RN and
the BS ( PPrc ), the pathloss exponent (α), and the saturation
SINR threshold (γs ):
• A lower γs (worse transmission technique) means the
RN should be placed further to the parent-BS, because
most of the coverage area near the BS is saturated.
Therefore the RN is only beneficial at the cell-edge and
the effectiveness of RN deployment is also reduced.
• A lower RN to BS transmit power ratio means the RN
should be placed further from the parent-BS, because the
stronger the BS transmit power, the stronger the effect of
the BS’s coverage.
• A lower α (more LOS based propagation) means the RN
should be placed further from the BS, because the weaker
the pathloss effect, the stronger the effect of the serving
BS’s coverage.
The results in Fig. 4 show that the optimal RN location for
Gaussian channels is generally less than half-way (dr /r <
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
Fig. 6. Optimal Number of RNs for simulation and theory for a variety of
RN and BS transmit powers.
0.5) [3] [4]. By introducing the co-channel interference and
capacity saturation (Fig. 5), the optimization solution in (10)
shifts to deploying the RN to dr /r ' 0.8, yielding a capacity
improvement of 55%. This generally agrees with existing
recommendations (dr /r ' 0.66 to 0.8) on relay deployment
in a multi-cell environment [7] [9].
The results in Fig. 5 also show that the mean capacity is
significantly diminished when the RNs are placed too close to
the BS, but the edge-capacity generally remains undiminished.
This is because regions close to the BS are already operating
with a saturated capacity and by adding RNs, the capacity
can only be degraded via increased interference. However, the
edge-capacity is at the inter-BS location and is thus largely
unaffected by RNs placed near the BS.
Fig. 7.
•
5
Downlink Capacity for Non-Co-Frequency Relaying (NCF).
stronger the BS transmit power, the stronger the effect of
the serving BS’s coverage.
A lower α means the RN should be placed further from
the parent-BS, because the weaker the pathloss effect, the
stronger the effect of the serving BS’s coverage.
The relation’s insight is very similar to that found for the mean
capacity in expression (10), without the capacity saturation
parameter. This is because capacity saturation can not be
achieved on the cell-edge and poor coverage areas. There
is a conflict of interest between maximizing mean-capacity
and edge-capacity by deploying the RN at either (10) or (12)
respectively. However, as the results in Fig. 5 indicate, by
sacrificing a small percentage of edge-capacity, the maximum
mean-capacity can be achieved. This sacrifice in edge-capacity
is negligible in the theoretical framework and approximately
4% from the simulation results.
B. Edge Capacity Optimization
For a BS with coverage radius (r), the edge capacity occurs
at one of the 2 possible low SINR locations, as illustrated in
Fig. 2:
1) the traditional inter-BS edge (x = r),
2) the handover point between BS and RN (x = dHO ),
whereby the minimum of the capacity at these 2 locations
determines the edge-capacity:
C. Number of Relays
So far, the paper’s analytical framework has considered
relaying only on a 1-dimensional level (distance away from
parent BS). In order to consider the impact of increasing the
number of RNs (Nr ) evenly distributed around the parent-BS,
the analytical model is expanded in the following logic:
•
CCF-OR,edge = min[CCF-OR (x = dHO ), CCF-OR (x = r)]. (11)
In order to maximize the edge capacity, neither of the aforementioned capacity terms can be smaller than the other and
thus, equating the terms in expression (11) leads to the optimal
RN location and maximum edge-capacity to be:
d∗r,CF-OR,edge-opt. = r[1 − (
Pr 1
) α ].
Pc
(12)
The insight here is that the optimal RN location is almost
entirely dependent on the power ratio between the RN and the
BS ( PPrc ) and the pathloss exponent (α):
• A lower RN to BS transmit power ratio means the RN
should be placed further from the parent-BS, because the
•
Increasing the number of RNs can improve the capacity,
provided that the mutual interference between RNs does
not exceed the interference from the BS.
The inter-RN interference dominates performance when
the inter-RN distance is small (RN density is large).
Furthermore, the paper defines that additional RNs are deployed equal distant to the BS and that the propagation channel
between RNs is NLOS based. Given these assumptions and
conditions, the theoretical maximum number of beneficial RNs
can be shown to be the following:
∗
NRN,opt.
< bπ(
2Pr − 1
) α c,
Pc
(13)
with the full proof in Lemma 7. The insight here is that
the optimal RN number is almost entirely dependent on the
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
Fig. 8.
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Mean and Edge capacity tradeoff for different relaying techniques.
power ratio between the RN and the BS ( PPrc ) and the pathloss
exponent (α):
• A higher RN transmit power means fewer RNs should be
placed to reduce mutual interference.
• A lower α means more RNs should be placed.
• The optimal number of RNs is largely independent of the
BS coverage size (r).
In Fig. 6, the results show that the theory matched very
well with the simulation results for the optimal number of
RNs that maximizes mean capacity for a variety of transmit
power levels. The theoretical results are validated by our own
simulation results and existing literature [10].
Fig. 9.
Directional and Omni-Directional RN Deployment SINR Plots.
shown in Lemma 5 that if the user position is smaller than a
threshold from the RN, the 2-hop relay capacity becomes BSRN limited. Adaptive NCF (A-NCF) dynamically balances
the BS-RN and RN-UE capacity to be equal, by prioritizing
2-hop relay transmission over direct BS-UE transmission. With
the aid of Lemma 5, the proportional increase in bandwidth of
the BS-RN channel Bδ required for capacity parity between
the 2-hop relay channels is:
D. BS-RN Resource Sharing
This section of the paper examines non-co-frequency (NCF)
relaying and what the resource block sharing ratio should be
between the parent BS and RNs. Generally speaking WCDMA
and LTE cells are deployed with frequency reuse pattern 1
[14] and there is debate on what the optimal frequency reuse
pattern is for RNs in different scenarios [1] [5]. In order to
maximize the edge-capacity, the edge-capacity of the BS and
the RN should be equal:
(
0.5
for low density of RNs
∗
,
Br,opt. ≈
log(Φ) −1
(1 + log(Ψ)
)
for high density of RNs
(14)
where Φ =
dHO
2r−dHO
1
and Ψ =
−
α dr
q2
.
4π 2 2
1+ N
dr
RN
If the RN density
is low, such that the worst coverage area is at the inter-BS
edge, then the optimal resource block sharing fraction is approximately 0.5. As shown in Fig. 7, the theoretical expression
in (14) is validated with our own multi-cell simulations and
those in existing literature [5]. The numerical search methods
in simulations found that Br is optimally between 0.45-0.6 in
order to maximize edge capacity.
A further capacity enhancing technique is to grant users that
benefit from relaying constant channel capacity parity between
the BS-RN and RN-UE channels. For example, it has been
Bδ '
r
log( drx−x
)
r
β
α
dr
)
log( 2r−x
r
,
(15)
where the value of Bδ can be above or below unity depending
on the user location (xr ). The results in Fig. 8 show that the CF
relaying offers the greatest mean capacity. The NCF relaying
yields a mean capacity degradation, but an improvement in
edge-capacity compared to no relaying. The A-NCF relaying
yields the greatest edge-capacity improvement due to its
channel parity scheme, but it does suffer a mean capacity
degradation compared to the CF relaying, due to the resources
sacrificed in the BS-UE channel (15).
The paper also extends the research to directional BS and
RN antennas. The rationale is whether directional RNs can not
only achieve a capacity improvement for the relaying region,
but also reduce the radiated interference to the other regions
of the BS that do not require relaying. It was found that
directional RNs can further enhance the capacity by 26%,
when the bore-sight of the RNs are directed along the celledge, as shown in Fig. 9.
V. I NDOOR R ELAYING (IR)
A. Indoor System Setup
Previously, the paper discussed how the worst performance
users are usually on the inter-BS edge or indoors. This
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
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Fig. 10. Analytical System Model for Indoor Network with Outdoor BS and
RN.
section shows that the interference-limited relay analysis can
be extended to analyze the indoor capacity. The analysis
demonstrates that the interference-limited framework is robust
and can model a variety of novel scenarios.
The capacity of a user at a distance of x from the nearest
wall to the parent BS is:
Fig. 11. Indoor Mean Capacity as a function of Building Location for a
BS-size r = 500m and L = 20m, with Simulation (Symbols) and Theory
(Lines).
x
Cindoor ' alog2 (1 + b
Pc (D + x)−α Wout Wink−1 10− 20
), (16)
Pc (2r − D)−α Wout
assuming that the serving BS’s signal power is predominantly
from one direction and the interference powers are from
all directions. The indoor capacity is generally below the
saturation capacity Cs , unless the building has no internal
walls (Nwall = 0) and is very close to the serving cell.
The paper now considers the addition of a closed-access cofrequency relay to improve coverage to the indoor users. The
main research theme of this section considers whether the RN
should be placed outside or inside the building, as a function
of building size (L) and distance from the serving BS (D). By
using the same analysis as previously shown in Lemma 5, the
paper’s indoor analytical model assumes the following:
• RN is outside building: the BS-RN channel is always
stronger than the RN-UE channel
• RN is inside building: the BS-RN channel is always
weaker than the RN-UE channel
• The rooms in the building are equally spaced in this
analysis
Note that the simulation results make no assumptions regarding the strength of channels. The results below will show that
these theoretical assumptions yield accurate approximations to
simulated results.
The paper considers a building with length L with Nwall
evenly spaced internal walls and is located at a distance D
from the serving BS (as shown in Fig. 10. The mean indoor
capacity achieved is the average capacity achieved from one
end of the building x = 0 to the other x = L, and it can be
shown to be approximately:
L −α
alog2 (b PPrc ( D
) )
outside RN
, (17)
C̄IR '
D
alog2 (1 + b( 2r−D
)−α ) inside RN
where the full mean capacity proof is given in Lemma 8.
B. Indoor Relay Placement
In order to maximize mean capacity, the location of the RN
(outside or inside the building) depends on the distance of the
building (D) from the serving BS. From expression (17), the
two capacity expressions are equal when:
r
Pr 1
Pr 1
∗
(18)
D = 0.5[ 8rL( )− α − L( )− α ].
Pc
Pc
Therefore, the adaptive deployment guideline that maximizes
indoor capacity for a multi-room building is:
•
•
Deploy RN inside if the building is at D < D∗ .
Deploy RN outside if the building is at D > D∗ .
The results in Fig. 11 show that deploying a RN can significantly improve the indoor capacity, especially for buildings
that are far away from the parent-BS. In order to maximize
the benefit of RNs, the RNs should be placed adaptively either
inside or outside the building depending on the location of
the building (D), as given by expression (18). The results
show that a mean capacity improvement of up to 38% can be
obtained in the adaptive RN deployment strategy. It should be
noted that if the pathloss exponent is different for when the RN
is inside compared to outside, the optimization expression (18)
can be adjusted relatively easily. The challenge of addressing
non-uniform distribution of rooms and users is non-trivial and
is not considered in the scope of this paper.
The results in Fig. 12 show that by deploying a fixed omnidirectional closed-access RN outside the building to cover
indoor users, the interference it causes to the outdoor network
leads to a mean capacity degradation of 44%. By adopting
an adaptive deployment based on the guideline devised in
(18), the outdoor mean capacity degradation is 31%, an
improvement of 20% over the fixed strategy. That is to say, not
only does the adaptive indoor RN deployment benefit indoor
users (30% improvement), it also benefits outdoor users (20%
improvement). By employing a directional RN, whereby a
RN radiates the directional bore-sight (4dBi) into the targeted
building and radiates the backside (-10dBi) towards the outdoor network, a further 13% capacity gain can be obtained
compared to the omni-directional RNs.
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
8
be achieved, the following must hold true:
alog2 (1 + bγs ) = alog2 (1 + b
ds =
Pi d−α
s
)
Pj (d − ds )−α
d
P
1
1 + (γs Pji ) α
(19)
.
B. Lemma 2: Integral Approximation for High SINR
By encompassing RNs, the mean capacity expression needs
to be approximated with log(1 + x) ' log(x). This has a
margin of error of ε, which is:
ε=
Fig. 12. Simulated outdoor capacity as a function of the distance of the
interfering RN to the parent-BS.
VI. C ONCLUSIONS
The purpose of this paper is to propose a tractable theoretical framework that can characterize and optimize the
performance of a relay-assisted network. The novelty is that
the theory considers the effects of cellular interference and
capacity saturation of realistic transmission schemes. The paper distinguishes itself from existing work, which have largely
considered theoretical Gaussian relay channels or multi-cell
results based on simulations.
The benefit of this approach is that given a set of essential
network parameters, the researcher can use the expressions
to determine the capacity of the network, as well as the
relay deployment parameters that maximize capacity. The
framework can therefore be used to dimension and plan a
network before committing to protracted system level simulations. Compared to Gaussian relay channel optimization,
the interfere-limited analysis yields a 55% improved capacity
in a cellular environment. The theory in this paper have been
validated by multi-cell simulation results.
Furthermore, the theoretical framework is general enough
to be extended to optimizing resource sharing between basestation and relay, as well as optimizing the relay location for
an indoor multi-room building. The capacity improvements
demonstrated in this paper show that optimization of the
aforementioned parameters can improve capacity by up to 60%
for outdoor and 38% for indoor users. The novel interferencelimited relay capacity expressions are useful as a framework to
examine how key propagation and network parameters affect
relay performance and can yield insight into future research
directions.
(1 + γs )1+γs
1
)
log2 (
γs
γsγs
where γs is the saturation SINR for a realistic modulation and
coding scheme and R is the coverage radius of the considered
BS. For a LTE BS operating with 2x2 SFBC MIMO, the value
of γs = 18dB, which achieves a saturated spectral efficiency
of Cs = 4.3 bit/s/Hz. The resulting expression for margin of
error is: ε = 0.1 %.
C. Lemma 3: Mean Capacity (No Relays)
The mean capacity achieved is the average capacity
achieved from edge of BS (r) to the base of the BS:
Z
Z ds
1 0
1
C̄outdoor =
Cdx = {Cs ds +
Coutdoor dx}
r r
r
r
1
ds
(21)
= {Σ+ | a(ds log2 [(
)−α ]
r
2r − ds
2r − ds
)) |},
− 2rαlog2 (
r
where ds =
2r
1
1+γsα
and Σ = Cs ds .
D. Lemma 4: BS-RN Handover Location
The handover distance from the serving BS, when a cofrequency RN is deployed dr away from the BS is (γBS-UE =
γRN-UE ):
dHO =
1
1 + ( PPrc ) α
,
(22)
E. Lemma 5: Relay Channels
It can be proved that the BS-RN channel is always superior
to the RN-UE channel due to the LOS propagation characteristic of the system setup. Consider a RN located at dr from the
parent-BS and a UE located at xr from the RN. The following
must hold true for the BS-RN to be always equal or greater
than the RN-UE capacity (CBS-RN ≥ CRN-UE ):
dr
xr ≥
In order to find the maximum distance away from the
serving BS where saturated spectral efficiency (Cs ) can still
dr
where Pc and Pr are the transmit power for the BS and RNs
respectively.
A PPENDIX
A. Lemma 1: Capacity Saturation Range
(20)
1+
−β
dr α (2r
1
− dr )( PPrc )− α
(23)
which assumes that from an interference perspective, the users
are close to the RN so that 2r − xr ∼ 2r − dr . The value of xr
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 7, SEPTEMBER 2012
as a percentage of BS coverage radius (r) is no more than 2%
for system values given in Table I. That is to say the relaying
capacity is limited by the RN-UE channel.
F. Lemma 6: Outdoor Mean Capacity (Relays)
The values for the break-point distances are as follows,
dr
, ds1 =
using Lemma 1 and Lemma 4: dHO =
1
−1
dr
1
1+(γs ρ−1 ) α
, ds2 =
dr
1
1+(γs ρ) α
, and ds3 =
1+(ρ
dr
)α
1
1−(γs ρ) α
. The mean
capacity of a co-frequency BS and RN setup is therefore:
Z
1
1 0
CCF-OR dx = {Cs (ds1 + ds3 − ds2 )
C̄CF-OR =
r r
r
+ | alog2 [F1 (ds1 , dHO )F2 (ds2 , dHO )F3 (r, ds3 )]
(ds1 − dr )(ds2 − dr )(ds3 − dr )
− aαdr log2 (
) |},
(dHO − dr )2 (r − dr )
(24)
(
)a
ba
(
ba
)a
where F1 (a, b) = ( ( drbb−a )b )−α , F2 (a, b) = ( ( drbb−a )b )α ,
(
ba
dr −b
)a
dr −b
r
aF3 (a, b) = ( ( a−d
)α ; and ΣCF-OR = Cs (ds1 + ds3 − ds2 ).
bb
)b
9
TABLE I
S YSTEM PARAMETERS FOR LTE S IMULATOR
Parameter
LTE Operating Frequency
LTE System Bandwidth
Path-loss Model
NLOS Pathloss Exponent
LOS Pathloss Exponent
Shadow Fading variance
Capacity Saturation
SINR Saturation
AWGN power per subcarrier
BS Transmit Power
Directional Antenna Pattern
Relay Transmit Power
Building Length
Building Distance to BS
External Wall Loss
Internal Wall Loss
Number of Internal Walls
Symbol
f
BW
λ
α
β
2
σsd
Cs
γs
n
Pc
Acell
Pr
L
D
Wout
Win
Nwall
Value
2600MHz
20MHz
[14]
3.67
2.2
9dB
4.3 bit/s/Hz
18dB
6 × 10−17 W
10-40W
[14]
0.5-5W
20m
50-500m
20dB
10dB
4
b−dr
The below work shows the proof for optimal BS-RN distance by differentiating the mean capacity term with respect
to the BS-RN distance parameter (dr ):
D ' D + L. For indoor users being served by a RN on the
inside, the mean capacity (IR,i) is:
1
dC̄CF-OR
1
1
2(γs ρ) α
FΣ
= {
}. (25)
+
1 + a
ddr
r 1 + (γs ρ−1 ) α1
dr
α
1 − (γs ρ)
The optimal BS-RN distance that maximizes mean capacity
is:
d∗r,CF,mean−opt.
≈ 0.4FΣ [1 + (γs ρ)
1
−α
].
(26)
G. Lemma 7: Optimal Number of Relays
Assume a BS with NRN RNs deployed on the circumference
of a circle around the BS with radius dr . At each RN, in order
for the dominant interference power of 2 nearby RNs to be
stronger than the interference power from the serving BS, the
following must hold:
−α
2Pr Kd−α
rr > Pc Kdr
∴
NRN
where:
drr ∼
2Pr − 1
< 2π(
) α,
Pc
2πdr
NRN
(27)
which is only accurate when the number of RNs is above 2
and high.
C̄IR,i = alog2 (1 + b(
D
)−α ).
2r − D
(29)
I. System Modeling Parameters
The parent-BSs and RNs are assumed to be on rooftops and have Line-of-Sight (LOS) propagation, whereas the
interference from adjacent BSs and RNs are assumed to be
Non-Line-of-Sight (NLOS) based [14]. The parameter |h| is
the magnitude of the complex fading coefficient h, which
Rayleigh distributed and generated from an auto-regressive
AR(n) process, where by the value of n is dependent on the
delay spread [14] [19]. The BS-UE and the RN-UE channels
are assumed to be based on a probabilistic model, whereby
the probability of being in LOS:
x
x
18
)(1 − e− 36 ) + e− 36 ,
(30)
x
where x is the distance from the serving BS. The serving
BS-RN channel is assumed to be in LOS [11] [20].
℘LOS = min(1,
H. Lemma 8: Indoor Mean Capacity (Relays)
For indoor users being served by a RN on the outside, the
mean capacity (IR,o) is:
Z
bPr x−α
1 0
C̄IR,o =
alog2 (1 +
)dx
L L
Pc (D + x)−α
(28)
Pr L −α
' alog2 (b ( ) ), for: D L,
Pc D
which holds true for when the building size (L) is significantly
smaller than the distance from the serving BS (D), so that
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Weisi Guo received his B.A., M.Eng.,
M.A. and Ph.D. degrees from the
University of Cambridge. He is currently
an Assistant Professor at the University
of Warwick and is the author of the
VCESIM LTE System Simulator. His
research interests are in the areas of
self-organization, energy-efficiency, and
10
multi-user cooperative wireless networks.
Tim O’Farrell holds a Chair in Wireless Communication at the University
of Sheffield, UK. He is the Academic
Coordinator of the MVCE Green Radio Project. His research encompass resource management and physical layer
techniques for wireless communication
systems. He has led over 18 research
projects and published over 200 technical papers including
8 granted patents.