on the expanded region of picocells in heterogeneous networks
TRANSCRIPT
JUNE 2011 1
On the Expanded Region of Picocells in
Heterogeneous NetworksDavid Lopez-Perez1, Member, IEEE,Xiaoli Chu1, Member, IEEE,Ismail Guvenc2, Member,
IEEE
1 Centre for Telecommunications Research, King’s College London, London WC2R 2LS, UK
2 DOCOMO Innovations, Inc., Palo Alto, CA
Email: david.lopez,[email protected], [email protected]
Abstract
In order to expand the DownLink (DL) coverage areas of picocells in the presence of an umbrella
macrocell, the concept of range expansion has been recentlyproposed, in which a positive range expansion
bias (REB) is added to the DL Received Signal Strengths (RSSs) of picocell pilot signals at User
Equipments (UEs). Although range expansion may increase DLfootprints of picocells, it also results
in severe DL inter-cell interference in picocell Expanded Regions (ERs), because ER Picocell User
Equipments (PUEs) are not connected to the cells that provide the strongest DL RSSs. In this paper, we
derive closed-form formulas to calculate appropriate REBsfor two different range expansion strategies,
investigate both DL and UpLink (UL) Inter-Cell Interference Coordination (ICIC) to enhance picocell
performance, and propose a new macrocell-picocell cooperative scheduling scheme to mitigate both
DL and UL interference caused by macrocells to ER PUEs. Simulation results provide insights on
REB selection approaches at picocells, and demonstrate thebenefits of the proposed macrocell-picocell
cooperative scheduling scheme over alternative approaches.
Index Terms
Coordination, heterogeneous, interference, picocell, radio resource management, range expansion.
EDICS - COM-NETW
I. INTRODUCTION
Driven by a new generation of wireless User Equipments (UEs)and the proliferation of bandwidth-
intensive applications, data traffic and network load are increasing in an unexpected manner, straining
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0 50 100 150 200 250 300 350 400 450 500−150
−100
−50
0
50
100
150
DL Range=4.43m
UL Range=107.94m
Distance (m)
Dis
tance (m
) DL Range=13.65m
UL Range=107.94m
DL Range=23.04m
UL Range=107.94m
DL Range=32.52m
UL Range=107.94m
DL Range=42.08m
UL Range=107.94m
Macrocell (46
Picocell (30
Equal DL RSS boundary
UL Range
dBm)
dBm)
Fig. 1. Picocell coverage area in the presence of a macrocell. The DL coverage of a PBS, i.e., the area where it provides the
strongest DL RSS, becomes smaller when it is closer to the high power MBS. The DL powers of the MBS and the PBS are
46 dBm and 30 dBm, respectively. The propagation models and other parameters used are presented in Table I.
current cellular networks to a breaking point. At the same time, as wireless services migrate from voice
centric to data centric, more UEs operate indoors, which requires increased link budget and coverage
extension to provide satisfactory user experience [1]. In this context, there have been increasing interests
in deploying low-power cellular Base Stations (BSs) such asrelay nodes, picocells and femtocells overlaid
on macrocells to bring cellular networks closer to end-customers, thus enhancing network capacity. The
resulting networks are generally referred to as Heterogeneous Networks (HetNets) [2]. Heterogeneity in
network deployments has been heralded as the most promisingapproach to increase both the coverage
and capacity of future cellular networks in a cost-effective and energy-aware manner. Developments and
deployments of HetNets are attracting much momentum in the wireless industry and research community,
and also gained the attention of standardization bodies such as the 3rd Generation Partnership Project
(3GPP) LTE-Advanced, which has several work/study items related to HetNet deployments [3].
Among the low-power nodes in a HetNet, picocell BSs (PBSs) are typically deployed by operators
within the coverage areas of macrocell BSs (MBSs) for capacity enhancement and coverage extension.
PBSs usually have the same access and back-haul features as MBSs, but operate with much lower transmit
power, for serving a few dozens of UEs within a coverage rangeof up to a hundred meters or more [4].
However, the deployments of picocells are facing technicalchallenges arising from the large difference in
DownLink (DL) transmit powers between PBSs (≈ 30 dBm) and MBSs (≈ 46 dBm) [2]. In fact, the closer
a PBS gets to an MBS, the smaller the DL coverage area of the PBSbecomes, i.e., the area in which the
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PBS provides the dominant DL Received Signal Strength (RSS)shrinks1, as shown in Fig. 1. Moreover,
the shrink of picocell DL coverage areas leads to a mismatch between the DL HandOver (HO) boundary
(i.e., the boundary along which the DL RSSs from the PBS and the MBS are equal) and the UpLink
(UL) HO boundary (i.e., the boundary determined by the UE UL transmission range), as illustrated in
Fig. 1. As a result, in HetNets, associating a UE to the cell that provides the strongest DL RSS may not
always be the best strategy, because UEs may connect to distant high-power MBSs rather than nearby
low-power PBSs, thus preventing efficient load balancing orspatial reuse. Furthermore, following the
conventional DL RSS-based cell selection procedure, UEs connected to far MBSs will severely interfere
the ULs of PBSs located in their vicinity, as illustrated in Fig. 2.
On the contrary, cell selection procedures that connect UEsto nearby BSs would enable load balancing
and spatial reuse, and mitigate UL inter-cell interferencethrough reduced UL transmit power [5]. In this
line, an approach under investigation isrange expansion[6], in which a positive range expansion bias
(REB) is added to the DL RSSs of picocell pilot signals at UEs to increase picocells’ DL coverage
footprints [3]. With range expansion, the MUE in Fig. 2 gets connected to the PBS, even though
the DL link quality is better with the MBS. However, improvedspatial reuse and UL interference
mitigation offered by picocell range expansion come at the expense of reduced DL signal quality in
picocell Expanded Regions (ERs), because ER Picocell User Equipments (PUEs) are not connected to
cells that provide the strongest DL RSSs and thus suffer fromlow DL Signal-to-Interference-plus-Noise
Ratios (SINRs) (< 0 dB). Therefore, range expansion needs to be supported by Inter-Cell Interference
Coordination (ICIC) between macrocells and overlaid ER picocells, so as to mitigate excessive DL inter-
cell interference suffered by ER PUEs.
A. Literature Review
Although the benefits of picocell range expansion have been demonstrated in recent works, there lacks
a parametric study or systematic design for picocell range expansion. Outage probability in a HetNet has
been derived as a function of REB in [7] using homogeneous Poisson point processes (PPPs) to model
the locations of MBSs and PBSs. Also using PPP models, spectral efficiencies in range expanded picocell
networks have been analyzed in [8] for the cases with and without ICIC (see also [9] for a related spectral
efficiency analysis). In [5], based on simulations, the authors show that the sum rate can be significantly
improved for both cell-edge and cell-median UEs in a HetNet by connecting UEs to the cells with
1Readers may refer to [4] for picocell coverage radius of similar range at different central frequencies and inter-BS separations.
February 23, 2012 DRAFT
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the lowest path-loss, but associating too many UEs to a picocell by a large REB may cause overload
issues. In [10], the authors evaluate the performance of range expansion in conjunction with ICIC, for
arbitrarily selected REBs such as 8 dB and 16 dB, while details of the ICIC scheme are missing. In [11],
the authors combine range expansion with a Resource Partitioning (RP) based ICIC, where the available
spectrum is divided between macrocells and picocells so that ER PUEs are protected from macrocell
DL interference. However, RP lowers spectral efficiency, since resources accessed by macrocells cannot
be reused by picocells. In [12], the authors propose an iterative cell association scheme, where a cell
evaluates a utility function in each iteration to decide whether a UE should stay connected or be handed
over to a neighboring cell. Nevertheless, as this distributed scheme requires the exchange of messages
between cells and the evaluation of utility functions through a heuristic approach, it may not be able to
respond quickly enough for mobile UE HOs, and its convergence has yet to be proven.
B. Contributions
In this paper, we
• provide general analytical expressions for calculating the REB that should be added to the DL RSSs
of picocell pilot signals at UEs, so that UEs connect to the appropriate cells in different scenarios;
• identify the necessity of not only DL ICIC but also UL ICIC to enhance the performance of UEs
located within picocell ERs; and
• propose a macrocell-picocell cooperative scheduling scheme that mitigates both the DL and UL
inter-cell interference suffered by ER PUEs from the umbrella macrocell as well as neighboring
picocells.
The rest of the paper is organized as follows. In Section II, the network and system models are
introduced. Section III describes the HO procedure for ER picocells. In Section IV, closed-form formulas
for calculating the REB to be added to picocell pilot signalsare derived. Section V presents the new
macrocell-picocell cooperative scheduling scheme. In Section VI, performance of the proposed scheduling
scheme in support of ER picocells is evaluated through extensive system-level simulations. Finally, Section
VII draws the conclusions.
II. N ETWORK AND SYSTEM MODELS
A. Network Model
We assume that inter-macrocell interference is mitigated through some form of fractional frequency
reuse scheme or sophisticated frequency allocation, thus focusing our analysis on a scenario with multiple
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MBS(xm,ym)
ER
EPB
ESB
PBS(xp,yp)
dp,e
ellipse(xe,ye)
ellipse(xe,ye)
ER
EPB
ESB
PBS(xp,yp)
dp,e
maj
or
sem
i-axismin
or
sem
i-axis
α
ΘPBS
MUE
PUE
Same DL RSS from MBS and PBS
Same Path Loss to MBS and PBS Interference
Signal
Desired Signal
Fig. 2. UL interference scenarios in macrocell-picocell deployments. The equal DL RSS boundary (ESB) and the equal path-loss
boundary (EPB) of a picocell as defined in Section IV are also plotted.
picocells overlaid on a macrocell. Hence, we define an Orthogonal Frequency Division Multiple Access
(OFDMA) network comprising an underlaid macrocell and picocells as follows:
• An umbrella macrocell:CMm with m = 1, where the superscriptM indicates a macrocell;
• A set of picocells:CP = CP1 , ..., C
Pp , ..., C
PP with 1 ≤ p ≤ P andp, P ∈ N, where the superscript
P indicates a picocell;
• A set of UEs:U = Ua1 , ..., Uau , ..., U
aU, with 1 ≤ u ≤ U and u,U ∈ N, where the superscript
a = M indicates a Macrocell User Equipment (MUE), whilea = P indicates a PUE;
• A set of Resource Blocks (RBs):K = 1, ..., k, ...,K, with 1 ≤ k ≤ K andk,K ∈ N;
• A set of Modulation and Coding Schemes (MCSs):R = 1, ..., r, ..., R with 1 ≤ r ≤ R and
r,R ∈ N (see [13], Chapter 10, Table 10.1).
B. Signal Quality
Assuming that all subcarriers within an RB experience the same radio channel condition at any given
time, i.e., frequency flat-fading in an RB [14], the DL SINRγDLm,u,k of UE UM
u served by macrocellCMm
in RB k can be modeled as
γDLm,u,k=
pm,k ·Γm,uIu,k + σ2
=pm,k · Γm,u
P∑
p=1
pp,k Γp,u+σ2
∀u ∈ Um , (1)
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whereUm is the set of UEs connected to macrocellCMm , pm,k denotes the DL power applied by cell
CMm to a subcarrier of RBk, Iu,k indicates the total DL interference power received by UEUau in RB
k, σ2 is the noise power in RBk, andΓm,u = GmGuξm,uδm,u
is the channel gain from cellCMm to UE Uau ,
with Gm being the BS antenna gain of cellCMm , Gu being the antenna gain of UEUau , ξm,u being
the wall-penetration loss suffered by the signal from the BSof cell CMm to UE Uau , andδm,u being the
path-loss between the BS of cellCMm and UEUau , which is defined as
δm,u = ϕm · (dm,u)αm , (2)
whereϕm is a constant that accounts for the system losses of cellCMm , dm,u is the distance between the
BS of cellCMm and UEUau , andαm is the path-loss exponent of cellCM
m . This model is a generalization
of the path-loss models selected by 3GPP for HetNets [15].
The UL SINRγULm,u,k of UE UM
u served by macrocellCMm in RB k is given by
γULm,u,k=
pu,k ·Γm,uIm,k + σ2
=pu,k · Γm,u
P∑
p=1
∑
u′∈Up
pu′,k Γm,u′+σ2
∀u ∈ Um, (3)
where andUp is the set of UEs connected to picocellCPp , pu,k denotes the UL power applied by UE
Uau to a subcarrier of RBk, andIm,k indicates the total UL interference power received by the BSof
cell CMm in RB k. The DL and UL SINRs of UEs connected to picocells can be modeled in a similar
manner, with the subscriptm and the superscriptM in the corresponding parameters replaced withp and
P, respectively.
C. User Capacity
When using MCSr, the bit rateBRr and the throughputTPu,r,k of UE Uau in RB k can be modeled
respectively as
BRr = Ω · ηr =Aofdma · Bofdma
Tsubframe· ηr , (4)
TPu,r,k = BRr · (1− BLER(r, γm(p),u,k)) , (5)
whereΩ is a fixed parameter that depends on the network configuration, Aofdma and Bofdma are the
numbers of data subcarriers and symbols per RB, respectively, Tsubframe is the RB duration in time
units,ηr is the efficiency in bits/symbol of MCSr [13], andBLER (r, γm(p),u,k) is the BLock Error Rate
(BLER) of RB k, which is a function of both MCSr and SINRγm(p),u,k.
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D. User Feedback
In current cellular standards, a UEUMu (UP
u ) feeds back periodically to its serving cellCMm (CP
p )
Measurement Reports (MRs) (everyTu,mr in time) to assist the cell selection procedure and Channel
Quality Indicators (CQIs) (everyTu,cqi) to assess radio channel conditions [16]. In this paper, MRs
indicate the DL RSSwpilotm(p),u of the pilot signal from cellCM
m (CPp ) measured by UEUau , while CQIs
indicate the powerIu,k of the interference suffered by UEUau in each RBk.
III. H ANDOVER PROCEDURE FOREXPANDED REGION PICOCELLS
A. Conventional Handover Procedure
Conventionally, a UEUMu will be handed over from macrocellCM
m to picocellCPp when the DL RSS
(wpilotm,u )dBm of the pilot signal from macrocellCM
m plus a hysteresis margin(Q)dB is lower than the DL
RSS(wpilotp,u )dBm of the pilot signal from picocellCP
p at the UE (the A3 condition [17]), i.e.,
(wpilotp,u )dBm > (wpilot
m,u )dBm + (Q)dB , (6)
where DL RSSs(wpilotm(p),u)dBm are usually averaged and filtered by UEs in both frequency andtime
domains to cope with signal fluctuations caused by channel fading [17]. In addition, the DL powerppilotm(p)
applied by cellCMm (CP
p ) to a pilot subcarrier is typically constant. Once the A3 condition is met for a
given time period, which is referred to as the time to trigger(TTT), the UE sends an MR to its serving
cell to initiate the HO procedure. The HO procedure is then managed by both the serving and target cells
through the exchange of HO-related command messages [18].
B. Range Expansion Handover Procedure
The range expansion of picocellCPp can be realized by UEs adding a positive REB(∆ERp)dB to the
DL RSS of the pilot signal received from picocellCPp .
• Condition of HO from a macrocell to an ER picocell:
(wpilotp,u )dBm + (∆ERp)dB > (wpilot
m,u )dBm + (Q)dB ; (7)
• Condition of HO from an ER picocell to a macrocell:
(wpilotm,u )dBm > (wpilot
p,u )dBm + (∆ERp)dB + (Q)dB . (8)
In this way, the DL coverage footprint of picocellCPp can be artificially expanded, allowing more
UEs to be connected to it even when it is not providing the strongest DL RSS. However, aggressive
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range expansion may impair network capacity due to possibleoverload at picocells and/or excessive
DL/UL inter-cell interference. It is thus important to appropriately set the value of∆ERp and employ
sophisticated ICIC for successfully deploying picocells overlaid on macrocells2. In the following sections,
both problems will be addressed.
IV. RANGE EXPANSION
In this section, we first derive analytical expressions for boundaries of picocell coverage areas with
and without range expansion. These picocell coverage area boundaries are defined as follows.
• The equal DL RSS boundary (ESB) of a picocell is comprised of 2D plane points at which the DL
RSSs from the umbrella macrocell and the picocell are the same. Conventionally, the ESB determines
the picocell DL coverage boundary.
• The equal path-loss boundary (EPB) of a picocell is comprised of 2D plane points at which the
path-loss from the umbrella macrocell and that from the picocell are the same.
• The hot spot boundary (HSB) encloses the area wherein the spatial density of UEs is high. The
radius of a picocell hot spot is specified to be40 m in [19] (Appendix A.2.1.1.2, pp. 65).
Accordingly, two different picocell range expansion strategies are proposed. In the first strategy, we
expand the picocell coverage from the area enclosed by the ESB to the whole area within the EPB, so
that users can always connect to the cell with the least path-loss. This strategy however may result in
aggressive range expansion. In the second strategy, we expand the picocell range from the ESB to the
HSB, so that the whole picocell hot spot area is covered. Closed-form formulas for calculating the REB
∆ERp will be provided for both proposed range expansion strategies.
A. Equal DL RSS Boundary (ESB)
Without range expansion, the DL coverage area of a picocell is delimited by the ESB.
Theorem 1: The ESB of a picocell is an ellipse (given by (37) in Appendix A), with the center
xe = (xe, ye) and the two semi-axess1 ands2 given as follows
xe =cd− bf
b2 − ac, ye =
af − bd
b2 − ac, (9)
2Note that in this paper, only the problem of data channel ICICis considered, and control channel ICIC will not be specifically
treated.
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s1 =
√
2(af2 + cd2 + gb2 − 2bdf − acg)
(b2 − ac) ·[√
(a− c)2 + 4b2 − (a+ c)] ,
s2 =
√
2(af2 + cd2 + gb2 − 2bdf − acg)
(b2 − ac) ·[
−√
(a− c)2 + 4b2 − (a+ c)] , (10)
wherea, b, c, d, f, g are defined in (38)-(43) in Appendix A.
Proof: See Appendix A.
It is easy to show that the rotation angle of a picocell ESB (i.e., the counter-clockwise angleΘ from
the positive x-axis to the major-axis of the ESB ellipse [20]) is given by
Θ = arctan(yp − yexp − xe
) =
0, if b = 0 anda < c
π2 , if b = 0 anda > c
12 cot
−1(a−c2b ) if b 6= 0 anda < c
π2 + 1
2 cot−1(a−c2b ) if b 6= 0 anda > c
, (11)
wherexp = (xp, yp) is the PBS position of picocellCPp . The rotation angleΘ is illustrated in Fig. 2.
Note that the centerxe of the ESB ellipse does not overlap with the PBS positionxp. Instead,xe is
on the straight line defined by the MBS locationxm = (xm, ym) andxp, with xp in betweenxm andxe,
as shown in Fig. 2, forPm > Pp, wherePm(p) = Gm(p) ppilotm(p)/(ϕm(p) ξm(p),u). Therefore, the rotation
angleΘ of the ESB ellipse is equal to the counter-clockwise angleα = arctan( yp−ymxp−xm) from the positive
x-axis to the straight line defined byxm andxp. As a consequence, the major axis of the ESB ellipse
(37) always overlaps with the straight line connectingxm andxp, regardless of the transmission power
difference between the MBS and the PBS.
B. Equal Path-Loss Boundary (EPB)
Theorem 2: The EPB of a picocell is also an ellipse (given by (45) in Appendix B). The center
x′e = (x′e, y
′e), semi-axess′1 and s′2, and rotation angleΘ′ of the EPB ellipse can be computed by
replacinga, b, c, d, f, g with a′, b′, c′, d′, f ′, g′, respectively, in (9), (10), and (11), respectively, where
a′, b′, c′, d′, f ′, g′ are defined in (46)-(52) in Appendix B.
Proof: See Appendix B.
Similar to the ESB ellipse, the centerx′e of the EPB ellipse does not overlap with the PBS position
xp, but is located on the straight line defined byxm andxp, wherexp is in betweenx′e andxm.
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C. Shifts of ESB and EPB Centers from the PBS
The distance between the ESB ellipse center and the PBS location is given bydp,e = |xe −xp|, while
the distance between the EPB ellipse center and the PBS location is given byd′p,e = |x′e − xp|.
Theorem 3: Both dp,e andd′p,e can be approximated as linear functions of the distancedm,p between
the MBS and the PBS, i.e.,dp,e ≈dm,p
Pm/Pp−1 , andd′p,e ≈dm,p
Gm/Gp−1 , whereGm = 1ϕm ξm,u
, andGp = 1ϕp ξp,u
.
Moreover,dp,e < d′p,e, and the EPB always contains the ESB.
Proof: See Appendix C.
It follows from Theorem 3 that one side of the ESB (or EPB) ellipse gets closer to the PBS with a
larger dp,e (or d′p,e), in which case it is more likely for an MUE to be closer to the PBS than a PUE,
thus causing severe UL interference to PUEs.
In Fig. 3, semi-axis lengths of the ESB and EPB ellipses are plotted versus the distancedm,p between
the BSs of macrocellCMm and picocellCP
p . We can see that the semi-axess′1 ands′2 of the EPB ellipse
(45) are always larger than the semi-axess1 and s2 of the ESB ellipse (37), withs′1 and s′2 increasing
with dm,p faster thans1 ands2, indicating that the EPB ellipse always contains the ESB ellipse. We can
also see that the gap between the EPB and the ESB is larger for apicocell located further away from
the MBS. Moreover, for typical settings of the network, we have a ≈ c anda′ ≈ c′, and consequently,
s1 ≈ s2 and s′1 ≈ s′2, which implies that both the ESB and EPB ellipses can be well approximated by
circles.
In Fig. 3, the distanced′p,e between the PBS and the the EPB ellipse centerx′e is also plotted versus
dm,p, using the theoretical value∣
∣
xp−x′e
∣
∣ based on (9) and the linear function in Theorem 3, respectively.
There is a gap between the theoretical value and the approximated linear function ofd′p,e. This is because
ψ = 3.76/3.67 is used3 in the numerical evaluation of∣
∣
xp−x′e
∣
∣ based on (9), while we assumeψ = 1 in
Appendix C to obtain the linear functions in Theorem 3. Both the theoretical value and the approximated
linear function show thatd′p,e increases withdm,p, indicating that for a picocell located at a larger distance
from the MBS, the EPB ellipse centerx′e shifts further away from the PBS locationxp (and the MBS
locationxm) along the straight line defined byxm andxp. Therefore, expanding the picocell coverage
area from the ESB to the EPB may see the PBS located much closerto one edge of its coverage area
than the other edges, and consequently some MUEs may get closer to the PBS than some ER PUEs,
causing significant UL interference to the ER PUEs.
3See the path loss models for macrocells and picocells in Table I. Note that sinceψ ≈ 1, the theoretical value also shows a
linear behavior. The linear behavior is lost asψ diverges from1.
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0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
Distance between macro BS and pico BS (m)
Dis
tanc
e (m
)
s1 (ESB ellipse)
s2 (ESB ellipse)
s′1 (EPB ellipse)
s′2 (EPB ellipse)
d′p,e
(theory)
d′p,e
(approximation, Ψ = 1)
d′p,e
Fig. 3. Semi-axis lengths (s1 and s2) of the ESB and (s′1 and s′2) of the EPB ellipses, for the same set up as in Fig. 1. Also
shown is the distanced′p,e between the PBS and its EPB ellipse center using the parameters in Table I.
In order to illustrate the UL interference issue discussed above, Fig. 4 depicts a HetNet, where an MBS
is located at (0, 0) m and a PBS is located at (202, 0) m. The ESB (37) and EPB (45) of the picocell are
also plotted. We observe that the ESB center shifts only slightly away from the PBS, while the shift of
the EPB center away from the PBS is considerable. Fig. 4 also illustrates that the distanced1 between
an ER PUE and the PBS may be larger than the distanced2 between an MUE and the PBS. If these two
UEs are assigned with the same RB, the ER PUE may suffer from strong UL interference caused by the
MUE. Therefore, expanding the picocell coverage area from the ESB to the EPB requires coordinated
radio resource allocation between MBSs and PBSs, to mitigate not only the DL interference but also the
UL interference from the macrocell to ER PUEs4.
D. Range Expansion Biases for HSB and EPB
In order to avoid aggressive range expansion, the picocell coverage area can be expanded to just cover
the targeted hot spot. The coverage area required for a hot spot should typically be known by operators,
and can be used for optimizing network deployment. Without loss of generality, we define the HSB as
4See e.g. [21]–[23] for some recent discussions in 3GPP for ULinterference mitigation in HetNets through power control.
February 23, 2012 DRAFT
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150 200 250 300 350
−100
−50
0
50
100
Distance (m)
Dis
tanc
e (
m)
d1
d2 PBS
ESB Ellipse
ER Ellipse(∆ER = 25 dB)
EPB Ellipse(Overlaps with
ER Ellipse)
User Hot SpotBoundary
EPBEllipseCenter
ESB Ellipse Center
PUE
MUE
Fig. 4. Plot of ESB and EPB ellipses using 3GPP propagation models and the parameters in Table I. The user hot spot boundary
indicates the area where PUEs are distributed, and will be discussed in Section IV-D. Even if we expand the picocell coverage
from ESB to EPB, due to the shift of the EPB ellipse center fromthe PBS, an MUE may be closer to the PBS than a PUE
(i.e., d1 > d2), causing severe UL interference to the picocell.
a circle centered atxh = (xh, yh) with a radiusrh, and assume that the ESB ellipse centerxe (which is
near the PBS location as shown in Fig. 4) overlaps with the HSBcenterxh.
Since the ESB ellipse can be well approximated by a circle (asshown in Section IV-C), the expansion
of picocell DL coverage area from the ESB to the HSB can be realized by UEs increasing the DL RSSs
of picocell pilot signals by an REB(∆ERHSBp )dB, which can be computed based on (10) and the given
HSB radiusrh. For ψ = 1, ∆ERESBp can be approximated by the following closed-form expression
∆ERHSBp =
(2r2h + d2m,p)Pm − Pmdm,p
√
d2m,p + 4r2h
2r2hPp, (12)
which is derived in Appendix D. Fig. 5 plots the REB(∆ERHSBp )dB required for providing a targeted
picocell DL coverage versus the targeted picocell coverageradius (i.e.,rh) for several values of the
MBS-PBS distancedm,p. Both the theoretical value of(∆ERHSBp )dB calculated using (10) and the
approximation in (12) are plotted. From Fig. 5, we can see that the REB increases with the targeted hot
spot radiusrh at a givendm,p, but decreases with the increase ofdm,p for a givenrh. The approximated
∆ERHSBp in (12) is about 2 dB larger than the theoretical value. This is becauseψ = 3.76/3.67 is used
February 23, 2012 DRAFT
JUNE 2011 13
0 10 20 30 40 50 60 70 80 90−20
−15
−10
−5
0
5
10
15
20
Ran
ge e
xpan
sion
bia
s (
dB)
Picocell coverage radius (m)
MBS to PBS dist. = 170m (theory)MBS to PBS dist. = 170m (approximation, Ψ=1)MBS to PBS dist. = 200m (theory)MBS to PBS dist. = 200m (approximation, Ψ=1)MBS to PBS dist. = 230m (theory)MBS to PBS dist. = 230m (approximation, Ψ=1)
Fig. 5. Plot of∆ERHSBp required for a targeted picocell DL coverage radius at several MBS-PBS distances. The vertical green
line denotes the40 m picocell hot spot radius specified in [19].
in the numerical evaluation based on (10), whileψ = 1 is assumed for (12) in Appendix D. Negative
values of(∆ERHSBp )dB indicate that the ESB without range expansion already contains the targeted HSB.
Range expansion is not necessary in this case, which will notbe considered in the sequel.
Since the EPB ellipse can also be well approximated by a circle (as shown in Section IV-C), the
expansion of the picocell DL coverage area from the ESB to theEPB can be realized by UEs increasing
the DL RSSs of picocell pilot signals by the REB(∆EREPBp )dB. The ∆EREPB
p required for range
expansion from the ESB to the EPB can be approximated by the following closed-form expression
∆EREPBp =
Gmppilotm
Gpppilotp
, (13)
which is derived in Appendix E under the assumption ofψ = 1.
V. MACROCELL-PICOCELL ICIC SCHEME
In order to prevent the jamming of ER PUEs in the DL and/or the UL, radio resource management
coordination between the umbrella macrocell and the overlaid picocells is needed. Indeed, it is necessary
for the MBS to intelligently lower power in or even stop usingthe resources allocated by PBSs to their
ER PUEs.
February 23, 2012 DRAFT
JUNE 2011 14
In this section, we propose a macrocell-picocell cooperative scheduling scheme to deal with DL and
UL inter-cell interference [24]. The main idea is that when aUE enters or stays within the ER of a
picocell, the PBS will inform the umbrella MBS about the set of RBs allocated to this ER PUE, and
then the MBS will lower its transmit power in these RBs so thata desired Quality of Service (QoS)
in terms of SINR can be guaranteed to this ER PUE. The communication between a MBS and a PBS
is through the operator’s back-haul via, e.g., LTE X2 interface [16], and it could be periodic or event
triggered. Communication delays over the operator-provided back-haul or inter-BS interface should not
be an issue, because they are planned and deployed for stringent QoS requirements.
This macrocell-picocell cooperative scheduling scheme can be implemented in two steps:
• Step 1: Decide the maximum transmit power that the MBS can usein each RB being used by ER
PUEs, in order to provide the desired SINR to ER PUEs. This step requires communication via
message passing between the MBS and PBSs.
• Step 2: The MBS assigns RBs and transmit power levels to its DLand UL UEs, respecting the
transmit power constraints determined in Step 1.
A. Calculating Macro DL Power Constraints
If the DL SINRγDLp,u,k of ER PUEUP
u is lower than its SINR targetγtargetu , then picocellCPp will advice
macrocellCMm to reduce its DL transmit power in RBk from pm,k to p′m,k, wherep′m,k ≤ pmax
m,k ,∀k ∈ K,
andpmaxm,k is the maximum transmit power that macrocellCM
m can use in RBk so that ER PUEUPu can
meet the DL SINR targetγtargetu .
To achieve the DL SINR targetγtargetu , the highest inter-cell interferenceImaxu,k that ER PUEUP
u can
tolerate in RBk is given by
Imaxu,k =
wpu,k
γtargetu
− σ2 , (14)
in which wpu,k denotes the DL RSS measured by ER PUEUPu from the carrier signal of its serving
picocellCPp in RB k, and picocellCP
p knowswpu,k from CQIs reported by ER PUEUPu .
The maximum interferenceIm,maxu,k that macrocellCM
m can create in RBk towards ER PUEUPu can
then be calculated as
Im,maxu,k = Imax
u,k −
P∑
p′=1,p′ 6=p
wp′
u,k , (15)
wherewp′
u,k is the DL RSS in RBk of the interfering signal from neighboring picocellCPp′ measured and
reported by ER PUEUPu back to the PBS ofCP
p . If more than one interfering macrocell is taken into
account, thenIm,maxu,k should be shared by all the macrocells in a proportional and fair manner.
February 23, 2012 DRAFT
JUNE 2011 15
Based on the channel gainΓm,u between the MBS ofCMm and ER PUEUP
u , picocellCPp can calculate
the maximum powerpmaxm,k that macrocellCM
m can allocate to RBk as follows
pmaxm,k =
Im,maxu,k
Γm,u, (16)
whereΓm,u is known by picocellCPp from MRs sent by ER PUEUP
u .
Since picocellCPp knowsγtargetu , wpu,k, w
p′
u,k(p′ 6= p) andΓm,u from its scheduling data and the reports
fed back by its PUEs, picocellCPp can compute the macrocell DL transmit power constraintpmax
m,k using
(14)-(16). PicocellCPp then informs macrocellCM
m of the DL power constraintpmaxm,k and RB indexk via
the back-haul. In order to reduce signalling overhead, sucha message is sent fromCPp to CM
m only if the
power constraintpmaxm,k varies by more than 1 dB.
B. Calculating Macro UL Power Constraints
If the UL SINR γULp,u,k of ER PUEUP
u is lower than its SINR targetγtargetu , then picocellCPp will
advice macrocellCMm to reduce the UL transmit power of its MUEUM
u′ in RB k from pu′,k top′u′,k,
wherep′u′,k ≤ pmaxu′,k ,∀k ∈ K, andpmax
u′,k is the maximum transmit power that MUEUMu′ can use in RB
k for ER PUEUPu to meet the UL SINR targetγtargetu .
To achieve the UL SINR targetγtargetu , the maximum inter-cell interferenceImaxp,k that ER PUEUP
u
can tolerate in RBk is given by
Imaxp,k =
wup,k
γtargetu
− σ2 , (17)
in which wup,k is the UL RSS measured by the serving PBSCPp from the carrier signal sent by its ER
PUEUPu in RB k.
Similar to (15), the maximum inter-cell interferenceIu′,max
p,k that MUE UMu′ can create towards ER
PUEUPu in RB k is estimated as
Iu′,max
p,k = Imaxp,k −
P∑
p′=1,p′ 6=p
∑
u′′∈Up′
wu′′
p,k , (18)
wherewu′′
p,k is the UL RSS in RBk measured by the serving PBSCPp of the interfering signal from PUE
UPu′′ of a neighboring picocellCP
p′ .
Based on the channel gainΓu′,p between MUEUMu′ and PBSCP
p , macrocellCMm can calculate the
maximum transmit powerpmaxu′,k that MUEUM
u′ can use in RBk as follows
pmaxu′,k =
Iu′,max
p,k
Γu′,p, (19)
February 23, 2012 DRAFT
JUNE 2011 16
whereΓu′,p is known by macrocellCMm from MRs sent by MUEUM
u′ .
Since picocellCPp knows γtargetu , wup,k andwu
′′
p,k(∀u′′ ∈ Up
′
, p′ 6= p), picocell CPp can compute the
interference constraintIu′,max
p,k using (17)-(18), and send values ofIu′,max
p,k and RB indexk to macrocell
CMm via the back-haul. In order to reduce signalling overhead, acontrol message is sent fromCP
p to CMm
only if the interference constraintIu′,max
p,k varies by more than 1 dB. Then, macrocellCMm can compute
the UL transmit power constraintpmaxu′,k using (19).
C. Macrocell-Picocell Cooperative Scheduling Scheme
Various scheduling strategies can be used by macrocellCMm to assign RBs and power levels to its DL
(UL) MUEs, subject to the power constraintspmaxm(u),k derived in the previous subsections. Motivated by
the scheduling strategies proposed in [25] and [26], where each macrocell independently allocates radio
resources in a way that its total transmit power is minimizedwhile meeting the throughput demands of
its UEs, we propose the following macrocell-picocell cooperative scheduling scheme, which can be used
for both DL and UL radio resource allocation incorporating the macrocell transmit power constraints
pmaxm(u),k. Due to limited space, we present the scheme for the DL, and indicate the UL counterparts in
brackets.
Macrocell DL (UL) MCS Selection:
Similarly to [25], MUEUMu is allocated to the MCSru that requires the least number of RBs and the
lowest transmit power to meet its throughput targetTPtargetu . Hence, the required numberDu of RBs for
MUE UMu is given by
Du =
⌈
TPtargetu
Ω · ηru
⌉
, (20)
whereηru is the efficiency of MCSru, andΩ is a network parameter defined in Section II-C.
Required Macrocell DL (UL) Transmit Power:
The transmit powerpm(u),k that MBSCMm (MUE UM
u ) has to apply in each subcarrier of RBk so that
MUE UMu can meet the SINR thresholdγru of the selected MCSru is given by
pm(u),k = γru ·Iu(m),k + σ2
Γm,u, (21)
whereΓm,u is known by MBSCMm from MRs sent by MUEUM
u , andIu,k can be obtained by MBSCMm
from CQIs fed back by MUEUMu (Im,k is known by MBSCM
m from UL measurements directly).
Problem Formulation:
February 23, 2012 DRAFT
JUNE 2011 17
The cooperative RB and Power Allocation Problem (coRPAP) tobe solved in macrocellCMm can be
formulated as the following integer linear problem:
CS = minχu,k
Um∑
u=1
K∑
k=1
pm(u),k · χu,k (22a)
subject to
Um∑
u=1
χu,k ≤ 1 ∀k ∈ 1, . . . ,K (22b)
K∑
k=1
χu,k = Du ∀u ∈ 1, . . . , Um (22c)
χu,k · pm(u),k ≤ pmaxm(u),k ∀k (∀u, k) (22d)
χu,k ∈ 0, 1 ∀u, k , (22e)
whereUm is the number of MUEs connected to macrocellCMm , (22b) ensures that an RB is assigned to
at most one MUE, (22c) guarantees that MUEUMu is allocatedDu RBs, (22d) ensures that the transmit
power constraints imposed to avoid jamming ER PUEs are respected, and (22e) defines thatχu,k = 1 if
MUE UMu uses RBk, otherwiseχu,k = 0.
In order to efficiently solve the coRPAP (22) in macrocellCMm , we define the followingnetwork flow
F = (V,E) [27]:
• Vertex set:
V := Um ∪ K ∪ s, t, (23a)
wheres, t(∈ V ) are the source and sink ofV , respectively,K is the set of RBs defined in Section II-A,
andUm denotes the set of MUEs connected to macrocellCMm . For simplicity, we rename MUEUM
u as
MUE u in (23).
• Edge set for the DL (UL):
E :=(su) : u ∈ Um ∪ (uk) : u ∈ Um,
k ∈ K∣
∣ pm(u),k ≤ pmaxm(u),k ∪ (kt) : k ∈ K, (23b)
where if pm(u),k > pmaxm(u),k, then there is no edge between MUEu and RBk, meaning that RBk cannot
be assigned to MUEu.
• Capacity function:
February 23, 2012 DRAFT
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TABLE I
SIMULATION PARAMETERS
Parameter Value Parameter Value
Simulation time 5000 s Macro path loss model 128.1 + 37.6log10(R) dB (R in km)
Carrier frequency 2.0 GHz MUE distribution radius (rm) 289 m
Bandwidth 10 MHz Macro ant. gain 14 dBi
Subframe duration (Tsubframe) 1 ms PBS transmit power 30 dBm
OFDMA data symbols per subframe (Bofdma) 11 Pico path loss model 140.7 + 36.7log10(R) dB (R in km)
Subcarriers 600 PUE distribution radius (rh) 40 m
Number of RBs (K) 50 Pico ant. gain 5 dBi
Number of subcarriers perRB (Aofdma) 12 Mobile UE avg. speed 3 km/h
Thermal noise density -174 dBm/Hz MR frequency (1/Tu,mr) 1/20 ms−1
Number of MBSs 1 Min. dist. MBS-PBS 75 m
Number PBSs per macrocell 4 Min. dist. PBS-PBS 40 m
Mobile UEs within macro range 50 DL / 50 UL Min. dist. MBS-MUE 35 m
Static UEs within pico range 50 DL / 50 UL Min. dist. PBS-PUE 10 m
MBS transmit power 46 dBm FPC P0 = −58 dBm, α = 0.6
cap(a, b) :=
Db, if a = s, b ∈ Um
1 otherwise,(23c)
• Cost function:
cost(k) :=
pm(u),k, if k ∈ K (u ∈ Um, k ∈ K)
0 otherwise.(23d)
The minimum cost network flow of capacity∑
u∈Um Du will provide the optimal solution to the
coRPAP in (22). We use thenetwork simplexalgorithm [28] implemented in the LEMON library [29] to
find the minimum cost network flow of (23).
Note that the macrocell-picocell cooperative scheduling scheme proposed in this section tends to
allocate RBs being used by ER PUEs to MUEs that are close to theMBS or have low throughput
demands (therefore requiring low transmit power). In this way, MUEs and ER PUEs can reuse the same
RBs, while satisfying their respective SINR requirements.
VI. SYSTEM-LEVEL SIMULATION RESULTS
A. Simulation Model
In this section, performance of the proposed macrocell-picocell cooperative scheduling scheme in
support of ER picocells is evaluated. The scenario used in our system-level simulations comprised 1
MBS and 4 PBSs uniformly distributed within the MBS coveragearea, defined by its radiusrm. Each
February 23, 2012 DRAFT
JUNE 2011 19
simulation lasted 5000 s and comprised 10 different random drops of PBSs within the MBS coverage
area. The minimum distance between a MBS and a PBS was 75 m, andthe minimum distance between
PBSs was 40 m. Path loss models and other set-up parameters were selected according to the 3GPP
recommendations in [15]. We used 100 MHz bandwidth to provide 50 RBs in the DL and 50 RBs in the
UL for the simulated network. There were 50 DL and 50 UL mobileUEs uniformly distributed within
the MBS coverage area. Mobile UEs moved at an average speed of3 km/h according to the model in
[30]. There was a circular hot spot centered at each PBS with aradiusrh, wherein 50 DL and 50 UL
static UEs uniformly distributed. Mobile UEs were given higher priorities than static UEs, and hence in
overloaded cells, the allocation of RBs was in favor of mobile UEs over static UEs if necessary.
In the simulations, each UE maintained its connection to a BSfor an exponentially distributed time of
meanµp, and thereafter disconnected from the BS. Once a disconnection occurred in a cell, a new UE
appeared at a random location within the coverage of the samecell. In the DL, the throughput demand
of a mobile UE is uniformly distributed in [12.2,712.5] kbps, while that of a static UE is uniformly
distributed in [256,712.5] kbps. In the UL, the throughput demand of a mobile UE is uniformly distributed
in [12.2,350] kbps, while that of a static UE is uniformly distributed in [128,350] kbps. PBSs used a
Uniform Power Distribution (UPD) to evenly allocate transmit power among subcarriers, whereas the
MBS employed the macrocell-picocell cooperative scheduling scheme proposed in Section V-C, running
at a constant frequency of120 s−1. If UPD is used in the UL, Fractional Power Control (FPC) is adopted
with P0 = −58 dBm andα = 0.6 according to [31]. The values of parameters used in the system-level
simulations are provided in Table I.
B. Schemes Used for Comparison
The following 4 approaches for setting the REB were used for performance comparison of range
expansion:
• Fixed REB of 6 dB.
• Fixed REB of 10 dB.
• REB calculated using (12) for range expansion from the ESB tothe HSB.
• REB calculated using (13) for range expansion from the ESB tothe EPB.
The following 6 resource allocation schemes were used for performance comparison:
• No REB: No range expansion is performed at any picocell. The MBS andPBSs uniformly distribute
their transmit power among subcarriers, targeting at a frequency reuse of 1. FPC is used in the UL.
February 23, 2012 DRAFT
JUNE 2011 20
• No ICIC: Each picocell is range expanded. The MBS and PBSs uniformlydistribute their transmit
power among subcarriers. No ICIC scheme is implemented at any cell. FPC is used in the UL.
• Resource Partitioning (RP): Each picocell is range expanded. The MBS and PBSs uniformlydis-
tribute their transmit power among subcarriers. Half of thetotal RBs are used by the macrocell only,
while the other half are used by the picocells only. As a result, there is no interference between the
macrocell and picocells. FPC is used in the UL.
• Almost Blank Subframes (ABSFs): Each picocell is range expanded. The MBS and PBSs uniformly
distribute their transmit power among subcarriers. The macrocell leaves certain subframes blank
following the ABSF technique considered in 3GPP. Letβ (0 ≤ β ≤ 1) denote the duty cycle of
blank subframes in the macrocell. We setβ = 0.5. The macrocell schedules transmissions only in
the odd subframes (OSFs), and leaves the even subframes (ESFs) blank. Accordingly, ER PUEs
are scheduled in the subframes that overlap with the ABSFs ofthe macrocell, i.e., ESFs, to avoid
suffering from macrocell interference [9]. FPC is used in the UL.
• RPAP: Each picocell is range expanded. Each PBS uniformly distributes its power among subcarriers.
The macrocell uses the RB and transmit power assignment scheme presented in Section V-C, but
without coordination with the overlaid picocells, i.e., there are no power constraints imposed by
picocells in the resource allocation of the macrocell.
• coRPAP: Each picocell is range expanded. Each PBS uniformly distributes its power among subcar-
riers. The macrocell employs the proposed macrocell-picocell cooperative scheduling scheme, i.e.,
the resource allocation of the macrocell needs to respect the power constraints imposed by picocells.
C. coRPAP Running Time
When utilizing thenetwork simplexalgorithm in [28] to solve (22), the sum running time of one million
different RB and power allocations was around 730.32 s. Accordingly, the average running time of a
single network simplex run is around 0.73 ms, which is less than the minimum feed back period in LTE
(2 ms [16]). Thus, the coRPAP proposed in Section V-C can be used in real-time network deployments.
D. coRPAP Intuitive Operation
Fig. 6 illustrates the DL SINR of a mobile UE when it moves across the network scenario described
in Section VI-A over a time duration of 3 minutes. We can see that when no ICIC is used, the DL
SINR of this mobile UE dramatically drops when it is handed over from the macrocell to a picocell.
This is because the macro DL RSS is much larger than the pico DLRSS in the ER. When RPAP is
February 23, 2012 DRAFT
JUNE 2011 21
no ICIC
Fig. 6. UE DL SINR versus simulation time. The dash-dot line denotes the SINR threshold (15.60 dB) of the targeted MCS.
used, the DL SINR of this mobile UE drops much less because theMBS tends to use the least possible
transmit power to serve its mobile MUEs following the proposed strategy. However, due to the lack of
macro-pico coordination, the DL SINR of this mobile UE in theER cannot be guaranteed and it may
still fall down to unacceptable values. On the contrary, when using coRPAP, the DL SINR of this mobile
UE never goes below the SINR threshold of the targeted MCS (15.60 dB)5. Note that when using RPAP
or coRPAP, fluctuations in the DL SINR occur due to the movement and varying interference condition
of the mobile UE.
E. Performance Comparison of REB Selection Methods
In order to compare the performance of the four different REBselection methods listed in Section VI-B,
Fig. 7 and Fig. 8 illustrate the CDFs of average user throughput and average network sum throughput,
respectively, when the four REB selection methods were usedin conjunction with the ABSF scheme.
Note that each sample used for calculating the CDF is the throughput of a user averaged over 100 ms.
Results are provided for both the DL and UL. Note that although DL user throughput demands are
uniformly distributed within [12.2,712.2] kbps, DL CDFs are not bounded between such range. This is
due to the effect of the ABSF duty cycleβ on users average throughputs. Because the maximum DL
throughput per RB achievable in the simulations is 732.6 kbps and due to the duty cycle ofβ = 0.5 used
5Which corresponds to the SINR threshold for64-QAM modulation with 3/4 coding rate and spectral efficiency of
4.52 bits/symbol [13].
February 23, 2012 DRAFT
JUNE 2011 22
DL
UL
Fig. 7. Average user throughput Cumulative Distribution Function (CDF) versus REB selection method.
Fixed−6dB Fixed−10dB HSB EPB0
10
20
30
40
50
60
70
80
REB selection approach
Ave
rage
net
wor
k th
roug
hput
(M
bps)
8% DL TP gains with respect to EPB
1% UL TP gains with respect to EPB
DL ABSF (all UEs)UL noICIC (all UEs)UL noICIC (mobile UEs)UL noICIC (hot spot UEs)
Fig. 8. Average network sum throughput versus REB selectionmethod.
February 23, 2012 DRAFT
JUNE 2011 23
in the ABSF scheme, the maximum DL average user throughput is732.62 = 366.3 kbps. Both Fig. 7 and
Fig. 8 show that the HSB based REB in (12) provides the best network performance in both DL and
UL, indicating that expanding the picocell DL coverage to just cover hot spot users provides the best
load balancing. In Fig. 7, the6 dB REB results in a large number of UEs with low throughput. This is
because with a small REB, picocell range expansion is insufficient, and a large number of static UEs
in hot spots would be handed over from picocells to the macrocell, thus overloading the macrocell. We
also observe that both the user throughput and network sum throughput increase with the REB, because
more UEs are served by picocells at a larger REB. The EPB basedREB in (13) performs worse than
the HSB based REB in (12), because picocells are overloaded due to aggressive range expansion.
In order to analyze UL FPC, Fig. 8 also illustrates the throughputs of the mobile UEs and the hot spot
UEs separately. When the REB increases, the picocell DL coverage increases, and then the ER PUEs at
the cell-edge use larger transmit power due to the FPC. Therefore, interference from the PUEs to the
macrocell increases, reducing the throughput of mobile UEs(which are mostly connected to the macrocell
for relatively small REB values). On the other hand, when theREB is too large, the throughput of mobile
UEs increases because most of them are connected to picocells. On the contrary, hot spot UE throughput
increases with REB, since they get connected to a picocell rather than the macrocell, which has a larger
path loss. However, when REB is too large, hot spot UE throughput decreases due to overloading in the
picocells as explained above.
F. Performance Comparison of ICIC Methods
In order to illustrate the performance of the proposed ICIC methods, i.e., RPAP and coRPAP, Fig. 9
plots the average network sum throughput with respect to different ICIC methods. Results are provided
for both DL and UL, and the HSB based approach is adopted to compute picocells’ REBs, since it
provided the best performance in the previous simulations.
Fig. 9 shows that coRPAP provides the best network performance, providing around a 36 % improve-
ment of average network throughput over ABSF in the DL, and 7 %in the UL. No REBprovided the
worst performance since the macrocell gets overloaded and picocells underutilized. WhenNo ICIC is
adopted, UL performance is enhanced due to the interferencemitigation of range expansion, but DL
performance suffers due to the large interference observedby users in the expanded region. While RP
completely removed cross-tier interference, the spectralefficiency was degraded. When ABSF is adopted,
a large performance improvement is achieved due to the effective interference mitigation. Since MUEs
and ER PUEs are scheduled in different subframes, the intrinsic DL range expansion interference problem
February 23, 2012 DRAFT
JUNE 2011 24
No REB No ICIC RP ABSF RPAP coRPAP0
20
40
60
80
100
120
ICIC approach
Ave
rage
net
wor
k th
roug
hput
(M
bps)
36% DL TP gains with respect to ABSF
7% UL TP gains with respect to ABSF
DL HSB (all UEs)UL HSB (all UEs)
Fig. 9. Average network sum throughput versus ICIC method.
is solved. Moreover, the ABSF approach achieves a good spectral efficiency as the MUEs and cell-center
PUEs reuse the same RBs. Since we assume that no subframe blanking is implemented in the UL, both
No ICIC and ABSF offer the same UL capacity.
While ABSF provides good performance improvement over other approaches, Fig. 9 shows that coRPAP
significantly outperforms it. Through a sophisticated power management, coRPAP does not need to ‘blank’
any radio resource to provide interference mitigation in contrast to ABSF. When using coRPAP, based
on the information exchanged between PBSs and the MBS, the latter was able to perform a more
efficient resource assignment, in which mobile UEs requesting low DL transmit power levels (due to
low throughput demands or short distances to the MBS) were allocated to RBs being used by ER PUEs.
In this way, coRPAP allowed for a better spatial reuse that significantly increased the average DL and
UL network throughput compared to the other approaches considered. Comparing RPAP with coRPAP,
we can observe that without macrocell-picocell cooperation, network performance degrades, but is still
comparable to that of ABSF. This indicates that minimizing cell transmit power while providing users
with their required demands outperforms approaches in which power is uniformly distributed among
subcarriers in terms of interference mitigation. Moreover, the fact that coRPAP outperformed FPC in the
UL by around 7 % in terms of average network throughput manifests the necessity of UL ICIC for ER
February 23, 2012 DRAFT
JUNE 2011 25
80 100 120 140 160 180 200 220 2400
20
40
60
80
100
120
140
Ave
rage
net
wor
k th
roug
hput
(M
bps)
Distance between macro BSs and pico BSs (m)
DL Fixed−6dBDL Fixed−10dBDL HSBDL EPBUL Fixed−6dBUL Fixed−10dBUL HSBUL EPB
Fig. 10. Average network sum throughput versus MBS to PBS distance (coRPAP case).
picocells. This can be explained by the fact that simply expanding the picocell DL coverage to the region
delimited by the EPB or HSB may result in severe UL interference from MUEs to picocells due to the
shift of the EPB or HSB center with respect to the PBS location(as illustrated in Fig. 4).
Fig. 10 illustrates the average network throughput with respect to the distance between the MBS and
the PBSs (dm,p) for the proposed REB selection methods, i.e., HSB and EPB based approaches. Overlaid
PBSs were deployed around the MBS all with the samedm,p and the same PBS to PBS distance. In
this case, coRPAP was adopted, since it provided the best performance in the previous simulations. We
can observe that the HSB based approach again provided the best network performance in both DL
and UL, in accordance with results in Section VI-E. This is because the HSB based approach is able to
compute for each picocell the appropriate REB required to cover the hot spot and achieve load balancing.
Moreover, we can see that the network throughput decreases when the PBSs are deployed closer to the
MBS, because their DL coverage areas (i.e., the area delimited by ESB) become smaller, and thus more
UEs need to be served in their ERs, creating more challenginginterference conditions.
VII. C ONCLUSIONS
In this paper, the REB values required to expand the DL coverage area of a picocell to its HSB
and EPB are derived in closed forms. Several analytical insights that may be useful in practical HetNet
February 23, 2012 DRAFT
JUNE 2011 26
deployments are provided, and the need for not only the DL butalso the UL ICIC to enhance the
ER picocell performance is demonstrated. A new macrocell-picocell cooperative scheduling scheme is
proposed to mitigate both DL and UL interference caused by the umbrella macrocell to ER PUEs.
Extensive simulation results show that expanding the picocell coverage area into its HSB yields the best
offloading gains. Moreover, the proposed scheduling scheme(CoRPAP) improves the DL and UL average
network throughputs by36% and7%, respectively, as compared with the 3GPP Release-10 ICIC methods.
ACKNOWLEDGMENT
This work has been supported by the UK EPSRC grant EP/H020268/1.
APPENDIX A: PROOF OFTHEOREM 1
For a given UEUau located on the ESB of picocellCPp , the DL RSSs from the umbrella macrocell
CMm and picocellCP
p are equal, i.e.,
ppilotm ·Gm
ξm,u δm,u= ppilotp ·
Gpξp,u δp,u
, (24)
where pilot signal transmit powerppilotm andppilotp are used since the HO process is typically driven by
pilot signals.
Plugging (2) into (24), we getPm
(dm,u)αm=
Pp(dp,u)αp
, (25)
wherePm = Gm ppilotm /(ϕm ξm,u) andPp = Gp p
pilotp /(ϕp ξp,u).
Taking the (2/αp)-th root of both sides in (25), we obtain
P2/αpm
(dm,u)2ψ=
P2/αpp
(dp,u)2, (26)
whereψ = αmαp
. Since outdoor path-loss exponents typically range from 2 to 4, while indoor path-loss
exponents can vary from 4 to 6 [32], it is likely thatαm ≤ αp and thus0 < ψ ≤ 1.
Assuming that UEUau is located at the point(x, y), its distances to the BSs of macrocellCMm and
picocellCPp are given respectively by
dm,u =√
(x− xm)2 + (y − ym)2 , (27)
dp,u =√
(x− xp)2 + (y − yp)2 , (28)
where(xm, ym) and (xp, yp) are the BS locations of macrocellCMm and picocellCP
p , respectively.
February 23, 2012 DRAFT
JUNE 2011 27
Plugging (27) and (28) into (26) and performing some manipulations, we obtain
P2/αpp (x2 + x2m − 2xmx+ y2 + y2m − 2ymy)
ψ − P2/αpm (x2 + x2p − 2xpx+ y2 + y2p − 2ypy) = 0 . (29)
Becausex2+x2m−2xmx+y2+y2m−2ymy is a polynomial of order 2 and since0 < ψ ≤ 1, the order
of (29) is at most 2. We thus approximate(x2 + x2m − 2xxm + y2 + y2m − 2yym)ψ using the following
2nd order Taylor series evaluated at point(i, j)
T (i, j) = f(i, j) + (x− i)fx(i, j) + (y − j)fy(i, j) +1
2(x− i)2fxx(i, j)
+1
2(y − j)2fyy(i, j) + (x− i)(y − j)fxy(i, j) , (30)
where
f(i, j) = (i2 + j2 − 2ixm − 2jym + x2m + y2m)ψ (31)
fx(i, j) = 2ψ[
f(i, j)]
ψ−1
ψ (i− xm) (32)
fy(i, j) = 2ψ[
f(i, j)]
ψ−1
ψ (j − ym) (33)
fxx(i, j) = 4ψ(ψ − 1)[
f(i, j)]
ψ−2
ψ (i − xm)2 + 2ψ[
f(i, j)]
ψ−1
ψ (34)
fyy(i, j) = 4ψ(ψ − 1)[
f(i, j)]
ψ−2
ψ (j − ym)2 + 2ψ[
f(i, j)]
ψ−1
ψ (35)
fxy(i, j) = 4ψ(ψ − 1)[
f(i, j)]
ψ−2
ψ (i − xm)(j − ym) . (36)
Plugging (30) into (29) and carrying out some manipulations, we get
ax2 + 2bxy + cy2 + 2dx+ 2fy + g = 0 , (37)
where
a =1
2P2/αpp fxx(i, j)− P2/αp
m , (38)
b =P
2/αpp fxy(i, j)
2, (39)
c =1
2P2/αpp fyy(i, j)− P2/αp
m , (40)
d =P
2/αpp
[
fx(i, j)− ifxx(i, j)− jfxy(i, j)]
+ 2P2/αpm xp
2, (41)
f =P
2/αpp
[
fy(i, j)− jfyy(i, j)− ifxy(i, j)]
+ 2P2/αpm yp
2, (42)
g = P2/αpp
[
f(i, j)− ifx(i, j)− jfy(i, j) +i2
2fxx(i, j),
+j2
2fyy(i, j) + ijfxy(i, j)
]
− P2/αpm
(
x2p + y2p)
. (43)
If a 6= c and b2 < 4ac, (37) is a non-degenerated ellipse, which may rotate depending on the term
2bxy. The center and the two semi-axess1 and s2 of the ellipse in (37) are given in (9) and (10),
respectively [20].
February 23, 2012 DRAFT
JUNE 2011 28
APPENDIX B: PROOF OFTHEOREM 2
For a UEUau located at point(x, y) on the EPB of picocellCPp , the path-losses from the umbrella
macrocellCMm and picocellCP
p are equal, i.e.,
Gm(dm,u)αm
=Gp
(dp,u)αp, (44)
whereGm = 1/(ϕm ξm,u) andGp = 1/(ϕp ξp,u). Following similar steps as in Appendix A, we find that
the EPB is also an ellipse, which is given by
a′x2 + 2b′xy + c′y2 + 2d′x+ 2f ′y + g′ = 0, (45)
where
a′ =1
2G2/αpp fxx(i, j)− G2/αp
m , (46)
b′ =G2/αpp fxy(i, j)
2, (47)
c′ =1
2G2/αpp fyy(i, j)− G2/αp
m , (48)
d′ =G2/αpp
[
fx(i, j)− ifxx(i, j)− jfxy(i, j)]
+ 2G2/αpm xp
2, (49)
f ′ =G2/αpp
[
fy(i, j)− jfyy(i, j)− ifxy(i, j)]
+ 2G2/αpm yp
2, (50)
g′ = G2/αpp
[
f(i, j)− ifx(i, j)− jfy(i, j) +i2
2fxx(i, j), (51)
+j2
2fyy(i, j) + ijfxy(i, j)
]
− G2/αpm
(
x2p + y2p)
. (52)
Based on (45), the center(x′e, y′e), semi-axess′1 ands′2, and rotation angleΘ′ of the EPB ellipse can
be formulated in a similar way to (9), (10), and (11), respectively.
APPENDIX C: PROOF OFTHEOREM 3
Without loss of generality, we setxm = 0, ym = 0, xp = dm,p, yp = 0, αp = 2 andψ = 1. For i = xp
andj = 0, plugging all these values into (31)-(36) yields
f(i, j) = d2m,p, fx(i, j) = 2dm,p, fy(i, j) = 0, fxx(i, j) = 2, fyy(i, j) = 2, fxy(i, j) = 0 . (53)
Substituting (53) into (38)-(43), we have
a = Pp − Pm, b = 0, c = Pp −Pm = a, d = Pmdm,p, f = 0, g = −Pmd2m,p . (54)
February 23, 2012 DRAFT
JUNE 2011 29
Based on (9) and (54), we calculatedp,e as follows
dp,e ≈ |xe − xp| =
∣
∣
∣
∣
cd− bf
b2 − ac− xp
∣
∣
∣
∣
=
∣
∣
∣
∣
−d
a− xp
∣
∣
∣
∣
=
∣
∣
∣
∣
Pmdm,pPp − Pm
+ dm,p
∣
∣
∣
∣
=dm,p
Pm/Pp − 1, (55)
which proves the linear relationship betweendp,e anddm,p. Note that forψ different than1, (55) would
be a non-linear function ofdm,p. As PmPp
→ ∞, dp,e → 0, andxe → xp, which is aligned with the
observation in [33].
In a similar way, the distance between the EPB ellipse centerand the PBS is calculated as
d′p,e ≈ |x′e − xp| =
∣
∣
∣
∣
Gmdm,pGp − Gm
+ dm,p
∣
∣
∣
∣
=dm,p
Gm/Gp − 1, (56)
which is also linearly dependent ondm,p. Note that asGm → Gp, we havedm,p → ∞, and the EPB
converges to a line which is equidistant to the PBS and the MBS.
Comparing (56) with (55), we can show thatd′p,e > dp,e, because in a HetNet we typically have
Pm >> Pp and hencePm/Pp >> Gm/Gp.
Moreover, since we have shown in Sections IV-A and IV-B that the major axis of the EPB ellipse
overlaps with that of the ESB ellipse, it is sufficient to showthat the EPB always contains the ESB if
the following condition is satisfied
|x′e − xe|+ s1 ≤ s′1 . (57)
Plugging in the values ofx′e, xe, s1, s′1 (see also Appendix D) into (57), we have
∣
∣
∣
∣
Gmdm,pGm − Gp
−Pmdm,pPm −Pp
∣
∣
∣
∣
+
√
PpPm(Pp − Pm)2
dm,p ≤
√
GpGm(Gp − Gm)2
dm,p . (58)
Upon some manipulation, (58) simplifies to
GmPp + PmGp ≥ 2√
GmGpPmPp , (59)
which is equivalent to(
√
GmPp −√
PmGp
)2≥ 0 . (60)
Since (60) is always satisfied, (57) is also satisfied, and hence the EPB contains the ESB.
February 23, 2012 DRAFT
JUNE 2011 30
APPENDIX D: DERIVATION OF REB FOR A DESIRED COVERAGE RADIUS
Similar to Appendix C, letxm = 0, ym = 0, xp = dm,p, yp = 0, ψ = 1, i = xp, j = 0, andαp = 2,
which yields (53) and (54). We also define the DL RSS enlarged by the REB∆ERHSBp as follows
P ′p = ∆ERHSB
p Pp = ∆ERHSBp Gp p
pilotp /(ϕp ξp,u) . (61)
Then, based on (10) and (54), we have
rh = s1 =
√
f2 + d2 − ag
a2= dm,p
√
P ′pPm
(P ′p − Pm)2
, (62)
whererh = s1 is used to realize the expansion from the ESB to the HSB, underthe assumption that
the PBS is placed at the HSB center, which should typically beknown by operators, and based on the
observation that the ESB center is close to the PBS location.
Solving (62) forP ′p, we obtain
P ′p =
(2r2h + d2m,p)Pm ± Pmdm,p
√
d2m,p + 4r2h
2r2h. (63)
Note that the two values ofP ′p in (63) correspond to two different circles of radiusrh. The smaller
value of P ′p results in the HSB circle around the PBS, while the larger value of P ′
p leads to a circle
surrounding the MBS instead, because the corresponding value of REB is so large that the picocell DL
coverage overwhelms that of the macrocell. Substituting the smaller value of (63) into (61) and after
some manipulation, we get the approximated expression of∆ERHSBp in (12).
APPENDIX E: DERIVATION OF REB REQUIRED TOACHIEVE EPB
The range expansion from the ESB to the EPB is achieved whens1 = s′1. Based on the same
assumptions of Appendix D and the definition ofP ′p in (61), and following similar steps in (62), we have
√
P ′pPm
(P ′p − Pm)2
=
√
GpGm(Gp − Gm)2
. (64)
Plugging the expressions ofP ′p, Pm, Gp andGm into (64), we get
Gp∆EREPBp ppilotp Gmp
pilotm
(
1
ϕpξp,u+
1
ϕmξm,u−
2
ϕpξp,uϕmξm,u
)
=G2p(∆EREPB
p ppilotp )2
ϕ2pξ
2p,u
+G2m(p
pilotm )2
ϕ2mξ
2m,u
− 2Gp∆EREPB
p ppilotp Gmppilotm
ϕpξp,uϕmξm,u. (65)
Without loss of generality, we assume thatϕp = 1, ξp,u = 1, andϕm = 1, ξm,u = 1. Plugging these
values into (65) and with some manipulation, we obtain
G2p(∆EREPB
p ppilotp )2 +G2m(p
pilotm )2 − 2GpGm∆EREPB
p ppilotp ppilotm = 0 . (66)
Solving (66) for∆EREPBp , we obtain the approximated expression of∆EREPB
p in (13).
February 23, 2012 DRAFT
JUNE 2011 31
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David Lopez-Perez (S’08-M’012) is Research Associate at King’s College London,
UK. In 2011, he received his PhD title from University of Bedfordshire (UoB), UK.
In 2005, he was with Vodafone, Spain, and in 2006, he was with Cork Institute of
Technology, Ireland. In May 2007, he was awarded with a PhD Marie-Curie fellowship
at UoB, UK. He is editor and/or author of several cellular network related books, i.e.,
”Heterogeneous Cellular Networks: Theory, Simulation andDeployment” Cambridge University Press,
2012, ”Femtocells: Technologies and Deployment”, Wiley 2010, and ”Femtocell Networks: Deployment,
February 23, 2012 DRAFT
JUNE 2011 33
PHY Techniques, and Resource Management”, Cambridge University Press, 2012. He has published more
than 50 book chapters, journal and conference papers, and heis/has also been co-chair of several journal
special issues (SIs) and workshops, e.g., 2nd IEEE 2011 GLOBECOM Workshop on Femtocell Networks
(FEMnet2011). In 2011, he was also awarded IEEE Communications Letters exemplary reviewer.
Xiaoli Chu (S’03-M’06) is a Lecturer at the Center for Telecommunications Research
at King’s College London (KCL). She received the PhD degree in Electrical and
Electronic Engineering from the Hong Kong University of Science and Technology
in 2005. From 2005 to 2006, she was a Research Associate at KCL. She received the
UK EPSRC Cooperative Awards in Science and Engineering for New Academics in
2008, the UK EPSRC First Grant in 2009, and the RCUK UK China Science Bridges Fellowship in
2011. She is or has also been co-chair of several journal SIs and workshops, e.g., IEEE GLOBECOM
2011 Workshop on Enabling Green Wireless Multimedia Communications. She is currently Chair of the
Graduates of the Last Decade Affinity Group and Secretary of the Computer Chapter within the IEEE
United Kingdom and Republic of Ireland Section.
Ismail Guvenc (S’01-M’06 - SM’10) received his Ph.D. degree in electricalengineer-
ing from University of South Florida, Tampa, FL, in 2006 (with outstanding dissertation
award). He was with Mitsubishi Electric Research Labs in Cambridge, MA, in 2005,
and since June 2006, he has been with DOCOMO Innovations, Inc., Palo Alto, CA,
working as a research engineer. His recent research interests include heterogeneous
wireless networks and future radio access beyond 4G wireless systems. He has published more than
60 conference and journal papers, and several standardization contributions. He co-authored/co-edited
three books for Cambridge University Press, is an editor forIEEE Communications Letters and IEEE
Wireless Communications Letters, and was a guest editor fortwo special issue journals on heterogeneous
networks. Dr. Guvenc holds 8 U.S. patents, and has another 15pending U.S. patent applications.
February 23, 2012 DRAFT