Dynamic ICIC for Post-Scheduling Outage Probability Minimization in Small Cell Networks

Abstract

We propose a distributed radio resource allocation method based on macrocell/picocell partial Channel State Information (CSI) sharing for small cell networks with range expansion. The Macro Base Station (MBS) predicts the cell-edge Pico users’ Resource Block (RB) allocation based on these shared CSIs, and reduces its transmit power only in RBs with high allocation probabilities. Unlike most previous works, we analyze the post-scheduling outage probability encompassing the effects of channel-based scheduling and random user positions. Thanks to the analysis, we can easily find the MBS power constraint that minimizes this outage probability. The results show that the proposed scheme largely improves outage probability and macrocell user offloading, compared to conventional methods.

Full text

Dynamic ICIC for Post-Scheduling Outage
Probability Minimization in Small Cell Networks
Megumi Kaneko∗, Kazunori Hayashi†
∗National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan
†Graduate School of Engineering, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
Email: ∗megkaneko@nii.ac.jp,†{kazunori}@eng.osaka-cu.ac.jp
Abstract—We propose a distributed radio resource allocation
method based on macrocell/picocell partial Channel State In-
formation (CSI) sharing for small cell networks with range
expansion. The Macro Base Station (MBS) predicts the cell-edge
Pico users’ Resource Block (RB) allocation based on these shared
CSIs, and reduces its transmit power only in RBs with high
allocation probabilities. Unlike most previous works, we analyze
the post-scheduling outage probability encompassing the effects
of channel-based scheduling and random user positions. Thanks
to the analysis, we can easily find the MBS power constraint
that minimizes this outage probability. The results show that
the proposed scheme largely improves outage probability and
macrocell user offloading, compared to conventional methods. 1
I. INTRODUCTION
To meet the high capacity and coverage demands of fu-
ture 5th Generation (5G) systems, Heterogeneous Networks
(HetNets) with dense small cells are regarded as one of the
promising solutions. HetNets were introduced in Long Term
Evolution (LTE)-Advanced, where small cells created by low-
power Base Stations (BSs) such as Pico BSs (PBSs) are
overlaid within a large macrocell coordinated by a Macro BS
(MBS). However, to achieve high spectral efficiency, these
small cells share the same frequency band as the macrocell,
leading to major inter-cell interference issues. In addition,
to enhance the data offloading from macrocell to picocells,
Cell Range Expansion (CRE) was introduced for expanding
the picocell radius [1]. Although User Equipments (UEs) are
normally served by the BS with the highest Reference Signal
Received Power (RSRP), CRE allows a Macro UE (MUE)
to be offloaded from the MBS to a PBS with a weaker
RSRP, by adding a positive offset value to the RSRP from
PBS. However, these offloaded PUEs in the range-expanded
region, referred to as extended Pico UEs (ePUEs), are subject
to severe downlink interference from the MBS due to its
high transmit power [2]. To mitigate this interference, Inter-
Cell Interference Coordination (ICIC) using Almost Blank
Subframes (ABSs) has been proposed [1][2]. In this method,
MBS reduces its transmit power in the ABS subframes where
the ePUEs can be scheduled. Thus, PBSs need the information
of the ABS patterns configured by the MBS, which requires
coordination among different BSs using the X2 interface
[3] or additional signaling bandwidth [4]. Moreover, such
1This work was supported by the Grants-in-Aid (JSPS Kakenhi) for
Scientific Research no. 26820143, 17K06453, 15K06064, and 15H2252 from
the Ministry of Education, Science, Sports, and Culture of Japan.
subframe-based blanking/power reduction methods offer lower
allocation freedom as compared to dynamic frequency-domain
methods. Therefore, there has been an increased interest for
distributed and self-organized ICIC with dynamic frequency-
domain allocation. But in most existing works, ICIC mainly
aims at protecting cell-edge users, as in [4] whose MBS power
limitation can be harmful to MUEs as their number is much
higher than that of ePUEs, or as in our initially proposed
method [5][6] based on partial Channel State Information
(CSI) sharing, from which the MBS predicts the ePUEs’
Resource Block (RB) allocation and protects them from its
interference. However, this approach only protects ePUEs at
the expense of the inner PUEs (iPUEs), i.e., the PUEs within
the original picocell area before CRE.
Therefore in this work, unlike in [5][6], we propose a
distributed radio resource allocation method that not only
mitigates the MBS interference to ePUEs, but also enables to
minimize the outage probability at a global level, i.e., for any
user type - MUEs, iPUEs or ePUEs. We consider the post-
scheduling rate outage probability, i.e., the probability that
short-term average rates for any user are below a minimum
rate, which is analytically intractable. This is why most pre-
vious works considered deterministic user positions as in [7]
or only raw Signal-to-Interference plus Noise Ratio (SINR)
fluctuations without channel-based scheduling considerations
as in [8] or [9] based on stochastic geometry. Therefore, one of
our significant contributions is the analysis of post-scheduling
rates, i.e., the actually perceived user rates that are function
of the effective SINRs after channel-based radio resource
allocation and of random user positions. This analysis enables
to compute the outage probability numerically, and hence to
set the ePUEs allocation prediction’s decision threshold θthat
minimizes the global outage probability. Then, the MBS limits
its power only on RBs whose ePUEs’ allocation probabilities
exceed threshold θ. The simulation results show that, using
the optimal decision threshold validated by analysis, the pro-
posed scheme enables to jointly increase data offloading from
macrocell to picocells and to reduce global outage probability.
II. SY ST EM MO DE L
The target HetNet model, where Ipicocells coexist within
a macrocell, is depicted in Fig. 1. A picocell is divided into its
original area APand the CRE area AE, based on the RSRP
criteria given a CRE offset value [1]. As in [2], MUEs are

MBS
ePUE CSI
feedback
PBS
ePUE
MUE CSI
feedback
iPUE CSI
feedback
iPUE
MUE
Fig. 1. Heterogeneous Small Cell Network: system model
Fig. 2. RB mapping in PUCCH
distributed within AM, a disk of radius Rmacro from the MBS,
excluding the picocell areas AP∪ AE.KMUEs, LiiPUEs,
LeePUEs are randomly distributed within AM,AP, and AE,
respectively. Li,Piand Le,Piare the numbers of iPUEs and
ePUEs in picocell i, respectively.
In each macro and picocells, UEs feedback their CSI on
a per-frame basis to their serving BSs. We adopt the CSI
feedback sharing method of [5][6], where the MBS allocates
a portion of its UL control channel, i.e., the Physical Uplink
Control Channel (PUCCH), to ePUEs as in Fig. 2, so that
it obtains the CSIs of all ePUEs to their serving PBSs. For
example, RB#1 of the MBS’s PUCCH is allocated to ePUE#1,
so MBS can get the CSI of the PBS to ePUE#1 channel
2. The MBS doesn’t allocate any of its UL control channel
resources to iPUEs, as it drastically reduces the amount of
usable resource for UL data transmission on the Physical
Uplink Shared Channel (PUSCH). Therefore, the MBS obtains
the ePUEs’ CSI only, not that of iPUEs, which was shown to
give the best throughput-signaling overhead trade-off [6].
The instantaneous received Signal-to-Noise Ratio (SNR) of
MUE kfrom MBS Mand PUE lfrom its serving PBS Pat
RB n, respectively denoted by γ(M)
k,n and γ(P)
l,n are defined as
γ(M)
k,n =
P(M)
nL(M)
kh(M)
k,n 
2
N0
, γ(P)
l,n =
P(P)
nL(P)
lh(P)
l,n 
2
N0
,
where each element is defined in Table I. In particular, we
2In Fig. 2, RBs with the same indexes on the MBS’s and the serving PBS’s
PUCCHs are assigned to an ePUE, so there is no problem if both PUCCHs
interfere. If PUCCHs of multiple PBSs interfere, the different ePUEs’ CSIs
can be retrieved based on the orthogonal sequences identifying each cell.
TABLE I
SYMBOL NOTATIO NS
h(M)
k,n ,h(˜
Mr)
k,n channel fading coefficients in RB nfrom MBS M
to MUE k, from interfering MBS Mrto k
h(P)
l,n ,h(˜
Pj)
l,n channel fading coefficients in RB nfrom PBS P
to PUE l, from interfering PBS ˜
Pjto l
L(M)
k,L(˜
Mr)
kpath losses from MBS Mto MUE k, MBS ˜
Mrto k
L(P)
l, L(˜
Mr)
lpath losses from PBS Pto PUE l, MBS ˜
Mrto l
P(M)
n,P(P)
ntransmit power allocated on RB nby MBS M,
and PBS P
assume Rayleigh fading channels, i.e., h(M)
k,n , h(P)
l,n ∼ CN (0,1).
N0is the Additive White Gaussian Noise (AWGN) power.
As in [2], we adopt the generalized expression of the path
loss models selected by 3GPP for HetNets, namely
L(M)
k=CM1
r(M)
kαM
, L(P)
l=CP1
r(P)
lαP
,(1)
where CMand CPare constants accounting for system losses,
r(M)
k, r(P)
lthe distances from MBS Mto MUE kand from
PBS Pto PUE lrespectively, and αM, αPdenote the path
loss exponents for macrocells and picocells, respectively.
Similarly, the instantaneous received SINR of MUE kand
PUE lat RB n,ζ(M)
k,n and ζ(P)
l,n respectively, are given by
ζ(M)
k,n =
P(M)
nL(M)
kh(M)
k,n 
2
I(˜
M)
k,n +I(˜
P)
k,n +N0
, ζ(P)
l,n =
P(P)
nL(P)
lh(P)
l,n 
2
I(M)
l,n +I(˜
P)
l,n +I(˜
M)
l,n +N0
,
where I(˜
M)
k,n =rP(˜
Mr)
nL(˜
Mr)
kh(˜
Mr)
k,n 
2
and I(˜
P)
k,n =
jP(˜
Pj)
nL(˜
Pj)
kh(˜
Pj)
k,n 
2
denote the sum-interference towards
MUE kon RB nfrom surrounding MBSs and from all PBSs,
respectively. Similarly, I(M)
l,n =P(M)
nL(M)
lh(M)
l,n 
2
denotes the
interference towards PUE lon RB nfrom its umbrella MBS
M;I(˜
P)
l,n =jP(˜
Pj)
nL(˜
Pj)
lh(˜
Pj)
l,n 
2
the sum-interference from
all other PBSs ˜
Pj; and I(˜
M)
l,n =rP(˜
Mr)
nL(˜
Mr)
lh(˜
Mr)
l,n 
2
, the
sum-interference from surrounding MBSs. All symbols are
defined similarly as those given in Table I.
Each UE’s CSI packet is composed of the per-RB in-
stantaneous received SNRs, for the channel from its serving
BS. These SNRs can be estimated by the UE from the
pilot subcarriers with a fixed power Pref
N, where Pref is the
total power for pilot signals and Nis the number of RBs3.
Note that the instantaneous interference pattern varies every
frame depending on the distributed scheduling decisions of
neighboring cells and on the interference channel fadings,
whereas the SNR is rather constant over several frames in low-
mobility scenarios4. This is why as shown in [11], SNR-based
scheduling offers higher robustness towards the future interfer-
ence compared to SINR-based scheduling such as [12]. Thus,
the strength of our method is to predict the future scheduling
decisions of interfering cells, by sharing instantaneous CSIs.
Remark: Alternatively, PBSs may transmit their allocation
3UEs can estimate SNRs instead of SINRs from the orthogonal sequences
among cells, i.e., the Cell-specific Reference Signal (CRS) or CSI-RS, and
CSI-Interference Measurement (IM) reports in Release 11 [3][10].
4As in [2], we assume low user mobility since channel-based scheduling
itself is inefficient in high mobility case.

Fig. 3. Overview of the proposed ICIC scheme
decisions to the MBS with increased overhead. Although this
may suit static scheduling, it is not the case for dynamic
frequency domain methods, as such decisions are obsolete for
the future frame. To summarize, in the proposed scheme, the
scheduling decisions are based on SNRs, but the perceived
rates depend on SINRs as shown in the sequel.
III. PROP OS ED ICI C SC HE ME
For clarity, we first recall the radio resource allocation in [6]
based on normalized Proportional Fairness Scheduling (PFS),
and explain the proposed ICIC method. As in Fig. 3, each
UE feeds back its CSI to its serving BS. Each BS performs
RB and power allocation in two-steps based on these CSIs,
since this was shown to be a low-complexity near-optimal
solution [12]. However, note that the proposed method is
widely applicable to other channel/priority-based schedulers.
MBS estimates the RB allocation at PBSs based on the shared
CSIs, and limits its transmit power on RBs where the ePUEs’
allocation probabilities exceed the decision threshold θ.Pi
denotes the i-th PBS in macrocell M, where i= 1, ..., I.
・Step 1: Resource Block Allocation to UEs: Normalized
PFS is performed by each BS, i.e., it selects the UE whose
ratio ˆγ(M)
k,n (ˆγ(Pi)
l,n ) between instantaneous SNR γ(M)
k,n (γ(Pi)
l,n ) on
RB nand average SNR over RBs γ(M)
k(γ(Pi)
l) is maximum,
k∗(n) = argmax
k
γ(M)
k,n
γ(M)
k
(.
= ˆγ(M)
k,n ) for MBS M,
l∗
Pi(n) = argmax
l
γ(Pi)
l,n
γ(Pi)
l
(.
= ˆγ(Pi)
l,n ) for PBS Pi, i = 1,· · · , I.
・Step 2: Power Allocation for each RB: At each BS, power
allocation is made over RBs already allocated to a specific UE,
so the user index will be dropped. Let pndenote the power for
RB n, and p= [p1, . . . , pN]T. Sum-rate maximization over
allocated UEs is performed [12],
popt = argmax
p
N

n=1
log (1 + pnΓn),
s.t.
N

n=1
pn≤Pmax, pn≥0, pn≤σn∀n, (2)
where Γnis the received SNR of RB nnormalized to unit
transmit power, and the maximum transmit power Pmax is
Pmacro
max for MBS and Ppico
max for PBS. The power limitation
σnfor RB nis given by σmacro
nfor MBS and Ppico
max for
PBSs, where σmacro
nis introduced to mitigate the interference
to ePUEs from the MBS, and determined based on the ePUEs’
CSI feedback. The optimal solution of (2) is given by iterative
water-filling [12]. Then, we set a power limitation if there is at
least one picocell with an ePUE whose allocation probability
exceeds the prediction’s decision threshold θ, namely
σmacro
n=δ
γ(MPi)
l
,if ∃Pis.t.(∃l∈ LE, F (ˆγ(Pi)
l,n )≥θ),
Pmacro
max otherwise.
δis a parameter controlling the allowed interference level and
γ(MPi)
lis the average SNR from MBS Mto ePUE l, estimated
from the received power of CSI signals at the MBS [11]. LEis
the set of ePUEs in AE. The allocation probabilities of every
ePUE of each PBS have been derived in [5] as F(ˆγ(Pi)
l,n ) =
1−exp −ˆγ(Pi)
l,n Li,Pi.
In addition, the probability pred that MBS reduces its power
on RB ncan be controlled by the decision threshold θ, as
pred = 1 −
I

i=1
Pr Fmax
l∈LE
ˆγ(Pi)
l,n ≤θ= 1 −
I

i=1
θ
Le,Pi
Li,Pi.(3)
IV. POS T-SCHEDULING OUTAGE PROBA BI LI TY ANALYS IS
We consider the optimization of the ePUEs allocation pre-
diction’s decision threshold θ. The goal is to minimize the
probability that short-term average user rates after scheduling
¯
Rare smaller than a target rate RT, i.e., the post-scheduling
outage probability Pr[ ¯
R(x, y;θ)< RT], marginalized over
all user positions. Unlike previous works such as [8][9][13]
that consider deterministic user positions and/or raw SINR
without channnel-based scheduling, here each user’s short-
term average rate is obtained by averaging over small-scale
channel fluctuations on its allocated RBs, and is a function of
the user’s random position (x, y). Unfortunately, the closed-
form expression of this outage probability is intractable due
to the complexity of the short-term average user rates after
scheduling and random user positions. However, we derive
an analytical expression of these user rates, which can be
easily computed by standard numerical methods. Due to space
limitation, we only detail the analysis for MUE rates. For sake
of clarity, we assume one PBS and analyze the basic on/off
MBS power case, with equal power allocation over RBs. MBS
and PBS are located at (0,0) and (xPBS, yPBS ), respectively.5
Proposition 1. The average perceived rate of the allocated
MUE kwith position (x, y)on the considered RB is given by
¯
RMUE(x, y;θ) = θ
Li,P
Le,P∞
0
log(1 + zk)I1(zk;x, y)dzk,(4)
where
I1(zk;x, y) = G(M)
k
G(P)
kz2
k
exp N0
G(P)
kK−1

n=0
Cn
K−1(−1)nG(M)
k
G(P)
kzk
+n+ 1−2
.
Proof. Dropping the MBS and PBS indexes, we define the
random variables ηj=|h(M)
j,n |2,j= 1 · · · K, and zk=
5The extension to multiple PBSs is straightforward but space consuming,
so its details will be given in the follow-up journal.

G(M)
k|h(M)
k,n |2
G(P)
k|h(P)
k,n|2+N0
,k= 1 · · · K. Given CM=CP=c
4πf 2
with fthe carrier frequency and cthe speed of light, we have
G(M)
k=P(M)
nL(M)
k=P(M)
nc
4πf 21
x2+y2αM
,
G(P)
k=P(P)
nL(P)
k=P(P)
nc
4πf 21
(x−xPBS)2+ (y−yPBS )2αP
.
The average perceived rate of the allocated MUE kwith
coordinates (x, y)on the considered RB can be written as
¯
RMUE(x, y ;θ) = ∞
0
log(1 + zk)fZk(zk|x, y)dzk
×Pr Fmax
l∈LE
ˆγ(P)
l,n ≤θ,(5)
where zkis the actual SINR on the allocated RB and
fZk(zk|x, y).
=I1(zk;x, y)is the p.d.f. of zk, given by
I1(zk;x, y) = ... C1
f(zk, η1, ..., ηK|x, y)dη1...ηK,(6)
where C1={(η1,· · · , ηK)|maxj=kηj≤ηk}. Note that
maxj=kηj≤ηkmeans that RB nis allocated to MUE k,
as the PFS metric is given by γk,n/¯γk=|h(M)
k,n |2=ηk.
In (5), the probability Pr Fmaxl∈LEˆγ(P)
l,n ≤θthat MBS
doesn’t reduce its transmit power on RB nis given from
(3) as θ
Li,P
Le,P. In (6), we have f(zk, η1,· · · , ηK|x, y) =
fZk(zk|ηk, x, y)j=kf(ηj), given users’ channel indepen-
dency. For Rayleigh fading channels, f(ηj) = e−ηj. After
some calculations, we can write
fZk(zk|ηk, x, y) = exp −G(M)
k
G(P)
kzk
ηk+N0
G(P)
kG(M)
kηk
G(P)
kz2
k
.
Marginalizing f(zk, η1,· · · , ηK|x, y )in the range
maxj=kηj≤ηk, we get I1(zk;x, y)below (4).
Thanks to the expression of ¯
RMUE in Proposition 1 (along
with those of ¯
RiPUE,¯
RePUE obtained similarly), the outage
probability can be easily derived numerically. Then, by plot-
ting this expression against θ∈[0,1], the optimal value of the
decision threshold θ∗satisfying
θ∗= min
θ∈[0,1] Pr[ ¯
R(x, y;θ)< RT](7)
can be determined offline very efficiently, i.e., without requir-
ing large-scale time-consuming simulations.
V. NUMERICAL RE SU LTS
The simulation parameters based on [2][10] are listed in
Table II. We consider one or several range expanded PBSs at
140m distance from the MBS. UEs are uniformly distributed
within the macro, pico and expanded areas as in [2], and
cell selection is based on RSRP criteria. All channels undergo
Rayleigh fading. As reference, we evaluate the Conventional
ICIC with Reduced-Power ABS of [1][2][4], where MBS re-
duces its transmit power in 100×β%subframes termed ABSs,
and PBS schedules ePUEs within these protected subframes, as
in Fig. 4. PBSs need to obtain the information about the ABS
patterns configured by the MBS, which is exchanged using
the X2 interface [3] or additional feedback [4]. However, here
TABLE II
SIMULATION PARAMETERS [2][10]
Carrier freqency f2GHz
System bandwidth 10MHz
Number of RBs N50
Number of PBSs I1, 6
Radius of the macrocell Rmacro 289m
Distance between MBS and PBSs 140m
Maximum transmit power of MBS 46dBm
Maximum transmit power of PBSs 30dBm
Antenna gain of MBS 14dBi
Antenna gain of PBSs 5dBi
Pathloss exponent αM, αP3.76
Noise power spectral density -174dBm/Hz
Minimum per-user required rate 0.3bps/Hz
Number of UEs 30, 100
Fig. 4. Conventional ICIC with Reduced-Power ABS
this conventional scheme will be evaluated with optimal ABS
ratios to provide an ideal performance benchmark.
First, we confirm the validity of the outage probability anal-
ysis of Section IV. We consider one PBS and 30 UEs. In Fig. 5,
we plot the analytical (“analysis (EP)”) and simulated (“sim-
ulation (EP)”) outage probabilities of the proposed scheme
versus the ePUEs allocation prediction’s decision threshold
θ∈[0,1]. We can see that the analytical curve matches
with the simulated one under the same equal power allocation
assumption despite the various approximations, showing the
validity of our analysis. In both cases, the optimal decision
threshold is obtained by θ∗= 0.97. Although “simulation
(WF)” with optimal power allocation outperforms “analysis
(EP)”, both optimal threshold values still match at θ∗= 0.97,
showing the effectiveness of our analysis.
We further evaluate the proposed method under this op-
timized parameter. We observe from Fig. 6 that our scheme
largely outperforms all other methods at its optimal value θ∗=
0.97. Moreover, the comparison with “Allocation known”, the
proposed method with perfect PUEs’ allocation knowledge,
shows that reducing the MBS power over all ePUEs’ RBs leads
to poor outage performance. Instead, the proposed method
allows to fine-tune the threshold θsuch that outage is gobally
minimized, without prioritizing specific user types (ePUEs or
MUEs), unlike most ICIC schemes.
Finally, we consider 6 PBSs placed at 140m distance
from the MBS, and 100 UEs. Interferences from surrounding
macrocells are also taken into account. Parameter δin (3) is
set to -115dBm [11]. For fair comparison, the ratio of RBs
where MBS reduces its transmit power is fixed to the same
value βfor conventional and proposed methods, by computing
the corresponding decision threshold θfrom (3) for each β.
Then, both schemes are evaluated given the MBS reduced-
power ratio βon the horizontal axis of Fig. 7. The proposed

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Allocation Probability Threshold θ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Outage Probability
simulation (EP)
analysis (EP)
simulation (WF)
Fig. 5. Analytical and simulated outage probability performances
Fig. 6. Outage probability of proposed and reference schemes
method outperforms the conventional ideal method over the
whole range of ABS ratios, with a much lower minimum
outage probability: 0.04 against 0.21, i.e., an 80% reduction.
Finally, we evaluate the outage probability of both schemes
against varying CRE offset values within the range 0–18 dB.
This time, the ratios of reduced-power RBs are optimized
for each value of the CRE offset for each scheme; for the
proposed scheme, this is based on our analysis. From Fig. 8,
the proposed method also outperforms the conventional one
regardless of the CRE offset value. Moreover, the optimal CRE
offset values are 9and 12 dBs for conventional and proposed
methods, respectively. Thus, more MUEs can be offloaded to
picocells by the proposed method, while reducing the overall
post-scheduling outage probability from 0.2down to 0.04.
VI. CONCLUSION
We have proposed a distributed ICIC method with CSI
sharing for small cell networks using CRE, where the MBS
predicts the ePUE’s RB allocation and reduces its power in
RBs where ePUE’s allocation probability is estimated to be
high. Based on our post-scheduling outage probability analy-
sis, the optimal allocation prediction’s decision threshold could
be determined. The important improvements of the proposed
method against conventional ICIC have been shown, both in
terms of global outage probability and macrocell offloading
which are essential features towards the design of 5G HetNets.
ACK NOW LE DG ME NT
The authors would like to acknowledge Mr. Takuya Ka-
menosono, former Master student in Kyoto University.
Fig. 7. Outage probability performance against the reduced power ratio
Fig. 8. Outage probability performance against the CRE offset value
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