Performance of Decentralized Interference
Coordination in the LTE Uplink
Jan Ellenbeck, Hussein Al-Shatri, and Christian Hartmann
Institute of Communication Networks
Technische Universität München
Email: jan.ellenbeck@tum.de
Abstract—Interference management techniques like inter-cell
interference coordination (ICIC) will play a key role in enabling
high spectral efficiency in future wireless OFDMA-based cellular
systems. The aim of ICIC is to lower inter-cell interference by
coordinating the usage of spectrum resources among neighboring
cells. Especially for the cell-edge users, avoiding the reuse of the
same resources in neighboring cells yields a significant increase in
SINR and thus capacity. In this paper, we consider decentralized
ICIC schemes for the uplink of an LTE system in which base
stations perform selfish resource allocation decisions. System level
simulations in a multi-cell scenario show the convergence of
the distributed schemes towards Nash equilibria. The mean cell
throughput as well as the 5% CDF user throughput are compared
to those achieved by frequency reuse 1 and 3 deployments. The
simulation results show that the proposed schemes adapt well to
varying uniform and especially non-uniform traffic loads.
I. I NTRODUCTION
Inter-cell interference coordination (ICIC) has been included
as a Radio Resource Management (RRM) aspect of UTRAN
Long Term Evolution (LTE) since Release 8 [1]. The aim of
ICIC is to lower inter-cell interference by coordinating the
reuse of spectrum resources which are called physical resource
blocks (PRBs) in LTE. A reduction of inter-cell interference
can be achieved by using only a subset of the total systemwide resources in each cell. The resulting lower interference
per PRB allows a higher capacity per resource. However, the
lower number of available PRBs per cell reduces the total
capacity so that the total cell capacity depends on the trade-off
between lower interference and higher resource availability.
Of course, a reduction of interference by restricting the
usage of PRBs is only achieved if neighboring cells reuse
the spectrum in a coordinated way. A traditional static coordination scheme (reuse 3) consists of forming cell clusters
of 3 cells that each use a different third of the resources.
It achieves a good coordination of resources and thus low
inter-cell interference but drastically limits peak data rates and
cannot adapt to varying traffic load between cells. Therefore,
LTE in principle allows a full reuse (reuse 1) of resources but
seeks to keep inter-cell interference under control by dynamic
and possibly self-organizing ICIC techniques.
As part of the System Architecture Evolution in LTE the
radio network controllers have been abolished. Therefore,
ICIC will have to be handled decentrally by the base stations (evolved NodeBs, eNBs). To facilitate such an inter-cell
coordination, certain means to exchange information via the
X2 interface connecting the eNBs have been foreseen. For the
uplink (UL), Interference Overload (IO) and High Interference
(HI) indicators have been standardized [2]. However, the ICIC
mechanism itself is not specified which leads us to propose two
schemes suitable for the uplink in this paper. The first scheme
allows autonomous adaptations by the eNBs but does not reach
complete convergence in practice. The second scheme uses
signaling between cells and can be shown to converge to a
stable resource allocation.
Our approach is based on a non-cooperative game model
[3] in which the eNBs as the players of the game compete
by selecting the PRBs in a selfish way. In a previous study
[4] we could show the convergence of the distributed scheme
to stable Nash equilibria in a simplified scenario. Now, we
study the convergence and performance in a realistic powercontrolled LTE uplink. As shown in [4], the resulting equilibria
are typically sub-optimal but the simplicity of the approach
compared to complex centralized optimization justifies this
“price of anarchy”.
Besides the conventional schemes like reuse 1 and reuse
3, so-called fractional frequency reuse schemes [5] achieve
a compromise by allowing full reuse for cell-center users
while protecting cell-edge users with a reuse 3 scheme. The
disadvantage of these schemes is that they do not easily adapt
to varying traffic loads. More similar to our approach, the authors in [6] present a mechanism that leads to self-organizing
fractional frequency reuse patterns among neighboring cells in
an OFDMA system. However, their focus is on the downlink
where they assume a closed-loop power control algorithm.
The remainder of the paper is organized as follows. In
the next section we first describe the general non-cooperative
game model and how the eNBs can converge to a stable
interference situation. Then, in Section III we describe the two
proposed schemes based on the approach introduced in Section
II. In Section IV we establish the framework used to evaluate
the schemes’ performance by system level simulations. The
results of these will be discussed in Section V before we draw
our conclusions in Section VI.
II. S ELFISH INTERFERENCE COORDINATION BY E NB S
The presented hierarchical resource allocation process separates the decisions which PRBs are available in each cell
from the scheduling of users onto resources. That way, suitable
frequency-selective schedulers can still realize a (somewhat
reduced) multi-user diversity gain while enjoying reduced
interference levels at the same time.
A. Non-cooperative game model
Both schemes are based on a non-cooperative game model
[4] in which the eNBs as the players strive to selfishly select a
subset of PRBs that offers them the highest utility – in this case
the lowest interference. The schemes differ in the way how
the eNBs obtain their knowledge of the current interference
situation.
We denote the choice of player i by the binary vector
xi ∈ Bm with xi,k = 1 meaning that PRB k is among the
chosen subset of the m PRBs available in total in the system.
Depending on its own decision xi and the selection of all
other eNBs denoted by x−i , an eNB will experience a certain
interference situation Ii,k (x−i ) for each PRB k that it uses.
Note that the actual interference situation per PRB in
the uplink of an actual multi-cellular system will not only
depend on the subsets used in other cells but also on the UE
scheduling at a specific time instant. The experienced intercell interference can differ significantly depending on whether
a center-cell UE with low transmit power or a cell-edge UE
with high power was scheduled in a neighboring cell. In the
following, we will assume that we can nevertheless express
PRB k’s utility to player i by assuming a certain interference
situation Ii,k solely based on the PRB allocations (xi , x−i ).
Our simulation results show that this assumption is justified.
We express the utility an eNB obtains from its own allocation xi while experiencing the interference caused
m by the other
cells’ allocations x−i as Ui (xi , x−i ) = − k=1 xi,k Ii,k . To
avoid the trivial solution xi = 0, we require each eNB to
allocate a fixed number Di > 0 of resources. In lowering their
own experienced interference, the players will try to avoid
allocations of other players leading to an anti-coordination
game.
If the interference from cell j in cell i equals the interference
cell i causes to cell j on some PRB k, the interference
situation is symmetric and the game can be shown to admit
a potential function Φ(xi , x−i ) [4]. In this case, the game
will have one or multiple Nash Equilibria (NEs) (xi ∗ , x∗−i )
[7]. These NEs present stable system-wide resource allocations
because no player has an incentive to deviate from his chosen
allocation x∗i assuming all other players keep their allocations
x∗−i constant.
Reaching such a stable allocation is highly desirable. However, collectively agreeing upon a specific Nash equilibrium is
difficult for the players because, for combinatorial reasons,
there will be many different Nash equilibria with possibly
equal utilities. Thus, players trying to reach a common NE
cannot know in advance which one to aim for. In such
situations, players can sometimes agree upon or learn [8] a
common NE by playing many successive rounds of the game.
For potential games, it can be easily shown [4] that sequential
unilateral best-response adaptations to the previous player’s
move will ultimately lead to a NE.
B. Simultaneous adaptation algorithm
The adaptation algorithm for both of our schemes employs
such a best-response approach but allows for simultaneous
re-allocations. In contrast, the above-mentioned learning approach allows only one adaptation at a time. This avoids
situations in which multiple eNBs choose the same lowinterference PRB but does not allow for fast convergence
in large scenarios. We thus proposed an algorithm [4] that
de-facto always converges under simultaneous adaptations by
including a better PRB only with some probability Psel . If
chosen correctly, on average only one eNB in a neighborhood
will switch to a better resource so that conflicts creating high
interference are avoided.
The eNBs in our simulations periodically check each radio
frame if some PRB k of their Di PRBs could be replaced by
another one that now has lower interference based on the latest
interference information Iˆi,k . If this is the case, the PRB is
replaced by the better one with probability Psel = 0.1 but only
if the interference is lower by some threshold ΔI. The latter
check helps to make the interference situation as stable and
predictable as possible by avoiding small-scale fluctuations.
Due to the probabilistic element, the convergence cannot be
guaranteed for this scheme but in practice it always converges
with much higher speed than a sequential solution, see [4].
III. P ROPOSED SCHEMES
We now introduce the two concrete schemes that will be
evaluated in Section V. They both follow the general scheme
outlined above but differ in the way they obtain the interference information Iˆi,k . The advantage of the first scheme is
that it does not rely on any inter-cell signaling to determine
Iˆi,k . However, its convergence cannot be guaranteed. On the
other hand, the second scheme provably converges but needs
inter-cell signaling to do so. The algorithmic complexity of
both schemes is very low. The eNBs just need to identify the
PRBs with the lowest interference by sorting them according
to Iˆi,k . The update of the allocated PRB subset can then
be performed in a single loop replacing current PRBs with
better but previously unused PRBs (subject to the interference
threshold ΔI and the selection probability Psel ).
A. Autonomous scheme
In this scheme, we assume that the eNBs periodically
measure the interference across all PRBs themselves. As
they are the target receivers for all uplink transmissions,
no signaling between eNB and UEs is involved. Also, no
communication with other eNBs is necessary allowing for
completely autonomous operation.
As mentioned above, the inter-cell interference not only
depends on the PRB allocations in neighboring cells but also
on the user scheduling yielding a high variance. To combat
these fluctuations we measure the current actual interference
Ii,k,t on all PRBs every 10 ms radio frame and derive an
exponentially averaged value Iˆi,k,t = αIi,k,t + (1 − α)Iˆi,k,t−1 .
In our simulations, α = 0.005 and an interference threshold
of ΔI = 1 dB have yielded both good performance and
convergence behavior.
As mentioned in Section II, the interference coordination
game has a potential and thus a NE if interference impacts
between cells are symmetric. However, this is in general not
The ICIC schemes shall adapt to traffic and UE mobility
and consequently operate on timescales of seconds to hours.
We therefore do not consider small-scale effects like fast
fading. We only model pathloss, see Table I. To evaluate the
achievable throughput depending on the received Signal to
Interference and Noise Ratio (SINR), denoted by γ, we use a
model from [9] that assumes an implementation loss of 60%
compared to Shannon’s capacity bound S(γ) = log2 (1+γ). It
further requires an SINR of γ > γmin = −10 dB and imposes
an upper limit of 2.0 bps/Hz of spectral efficiency provided
by the actual modulation and coding schemes, cf. (1).
Fig. 1. 27 cells scenario indicating UE and eNB positions as well as downlink
reuse 1 SINR = γ in dB
always the case. Switching one UE in cell i from PRB k to
l might lead to lower interference in cell i but, depending
on UE positions, the total system-wide interference might
increase. This happens if the reduction on resource k (cell
i now does not create interference on that PRB anymore)
does not outweigh the total increase on PRB l. Therefore,
convergence will not be guaranteed with this scheme.
B. Inter-cell signaling based scheme
The motivation for this scheme is to guarantee the convergence of the interference coordination mechanism. The idea
is to play the game based on “virtual” interferences Iˆi,k that
are chosen to be symmetric even if the actual interference Ii,k
would not be exactly symmetric. This way the decentralized
coordination process will always converge.
We aim to make this virtual interference scenario as meaningful as possible with respect to the real one. Therefore, we
compute the virtual interference Iˆi,k that an eNB i experiences
by summing up the pre-computed interference contributions
center
that a UE in the center of cell j would create for
Ii,j
all cells that use the same PRB k. Due to the sectorized eNB
center
center
= Ij,i
. Thus, we average
antenna patterns, we have Ii,j
them to achieve a mean interference impact that we will use
for both cells. In order to know which other cells create intercell interference on PRB k we make use of the HI indicators
as specified in [2]. They allow the eNB to exchange bitmaps
among each other to indicate which PRBs are used (with high
power in the UL). Together with the symmetric interference
impact values this allows us to compute virtual Iˆi,k values
that still closely reflect the real interference situation. No
exponential averaging is required here and the interference
threshold can be lowered to ΔI = 0.5 dB.
IV. P ERFORMANCE E VALUATION F RAMEWORK
In order to evaluate the performance of the two schemes
compared to standard schemes like reuse 1 and reuse 3, we
conducted system level simulations in a multi-cell scenario.
As the main focus is on evaluating the ICIC schemes and how
they trade-off resource availability against interference level,
we do not model packet-based traffic or the LTE protocol stack
in detail.
⎧
⎨
γ < γmin
γmin < γ < S −1 (T hmax )
αS(γ) ≥ T hmax
(1)
Uplink transmissions are power controlled in LTE. We
model the open-loop power control scheme as defined in [10]
[11], cf. Table I for details.
An exemplary scenario snapshot is shown in Fig. 1. We
assume 27 eNBs each covering a 120◦ sector. Within these
cells UEs are dropped at uniformly chosen random positions.
To investigate the behavior with uneven UE distributions,
between 0% and 80% of UEs are relocated among random
cell pairs. The same algorithms are performed in each cell with
the same level of detail. However, only the results from the
shaded center cells are evaluated. No mobility is considered
but different random drops are realized for every simulation
run.
In the system and in every cell there are 36 PRBs with a
bandwidth of 180 kHz each available for uplink transmissions.
Every transmission time interval (TTI) of 1 ms we assign each
UE to a PRB unless there are more users than PRBs. This
implies that we do not consider throughput requirements for
individual UEs as every UE gets at most one PRB yielding
an SINR-dependent throughput. Thus, the number of UEs per
cell determines the traffic load of that cell. It also determines
the number of PRBs the ICIC coordination scheme selects for
use in that cell. Note that the reuse 1 scheme does not impose
any restrictions so that all 36 PRBs are available. The reuse
3 scheme avoids PRB reuse within the cell cluster and makes
12 PRBs available in each cell.
Due to a lack of mobility, the number of UEs per cell will
remain fixed and consequently the number of allocated PRBs
will be constant. However, the mapping of UEs to PRBs will
be randomly permuted each TTI. That way, we model the
effect of a frequency-selective scheduler on the assignment
of PRBs to UEs. This has two consequences: First, it results
in highly varying inter-cell interferences as interferences on
a PRB k might come from completely different origin UEs
in a neighboring cell. This makes adapting to the inter-cell
interference situation difficult for our autonomous scheme.
Second, this improves the performance of the reuse 1 scheme
as the used PRBs are always spread out over all 36 PRBs
causing a kind of interference averaging effect.
T h[bps/Hz] =
0 :
α S(γ) :
⎩
T hmax :
TABLE I
OVERVIEW OF RADIO SIMULATION PARAMETERS
eNB Antenna pattern [12]
Scenario size
Number of eNBs
Number of UEs
Inter-site distance
Pathloss model [12]
Max. Tx Power in UL
Uplink power control
Link-level
model [9]
performance
Simulation time
Value
2000 MHz
36
180 kHz
-121 dBm per PRB,
figure
5 dB noise
2
A(Θ) = − min 12 ΘΘ
, Am
3dB
Θ3dB = 70◦ , Am = 20 dB
1500 m x 1500 m
27 (9 sites with 3 cells/sectors each)
10, 20, or 30 with 0% to 80% relocated
between random cell pairs
500 m
L = 128.1 + 37.6 log10 (R[km])
scenario (1) in [12]
Pmax = 24 dBm per PRB
P = min{Pmax , P0 + αL} per PRB
Open-Loop Power Control [10] [11]
with P0 = −48 dBm and α = 0.7
see equation (1) with these parameters:
α = 0.4
γmin = −10 dB
T hmax = 2.0 bps/Hz
5 seconds with 3 seconds transient phase
V. S IMULATION RESULTS
System level simulations have been performed using the
openWNS simulator [13]. For each combination of ICIC
schemes including reuse 1 and reuse 3, number of UEs, and
degree of uneven UE distribution, results are merged from the
simulation of 8 random topologies.
A. Convergence of Decentralized Coordination
Figure 2 shows the convergence behavior of the dynamic
schemes during a representative simulation run. The y-axis
gives a measure of how many PRBs are still seen by the
algorithms as more favorable (in terms of interference) to
be used by the respective eNBs, than the currently assigned
PRBs. The signaling-based scheme fully converges in a very
short time. The autonomous scheme also starts converging
very fast, however, not completely so. Due to the asymmetry
of the interference impact and the memory of the exponential
averaging, slight changes in the observed interference remain.
However, instability is easily avoided by the applied interference threshold.
B. Performance under different traffic loads
A comparison of the mean cell throughput over 8 random
drops is provided in Figures 3(a) through 3(c) as a function
of the standard deviation of the number of users per cell, i.e.,
as a function of the spatial inhomogeneity of the traffic. From
Fig. 3(a) we observe that in the homogeneous case (exactly
10 users per cell, std. dev. = 0) reuse 3 actually provides the
best results because it guarantees low inter-cell interference,
while the fixed number of 12 PRBs per cell is sufficient to
serve the 10 users. When the traffic inhomogeneity grows
beyond a standard deviation of two users from the mean, the
performance of the reuse 3 scheme starts to degrade because
the likelihood grows to have a higher number of users in
one cell than PRBs available. In comparison, the reuse 1
VLJQDOLQJEDVHG
DXWRQRPRXV
250
200
# of PRBV
Parameter
Carrier frequency
Number of PRBs
Bandwidth per PRB
Thermal noise power
300
150
100
50
0
0
1
2
3
4
5
Time [sec]
Fig. 2.
Convergence behavior example
scheme has always enough PRBs available, however due to the
lack of coordination between neighboring cells, the inter-cell
interference limits the throughput. The two dynamic schemes
perform very similar to each other, starting only slightly worse
than the reuse 3 scheme. With growing traffic inhomogeneity
the benefit of the adaptive nature of these schemes becomes
evident from the fact that their performance hardly degrades
with growing standard deviation of the number of users.
Beyond a standard deviation of two users per cell, the dynamic
schemes perform better than both fixed schemes. When the
overall traffic grows to a mean number of 20 users per cell
(Fig. 3(b)), reuse 1 and reuse 3 switch positions, i.e. reuse 1
starts performing better than reuse 3. This is due to the fact that
reuse 3 is now permanently suffering from a low number of
available PRBs in comparison to the number of users per cell.
The dynamic schemes adapt to the growing traffic as well as
to the inhomogeneity and thus perform better than the fixed
schemes, throughout. Finally, when the system load further
grows (Fig. 3(c)), the performance of the reuse 1 scheme
approaches that of the dynamic schemes, since the number
of users per cell is becoming similar to the number of PRBs
available to the system, limiting the potential of coordination
for the dynamic schemes.
Figures 4(a) through 4(c) show the 5% CDF cell throughput
for the different scenarios, reflecting mainly the performance
of the cell edge users who are suffering from low SINR. The
relative behavior of the compared schemes is very similar
to that of the mean cell throughput. Comparing the overall
performance of all schemes, we can observe that the average
cell throughput will grow with increasing traffic, while the
performance of the cell-edge users degrades, as expected.
C. Comparison of dynamic schemes
The performance of the two dynamic schemes is almost
identical. This means that the autonomous scheme adapts well
to the real interference situation yielding a significant reduction even when it does not completely converge (cf. Fig. 2).
On the other hand, the complete convergence of the intercell signaling based scheme does not contribute a significant
additional improvement as its virtual interference scenario
does not exactly reflect the actual interference situation.
5500
5000
5000
4500
4000
3500
2500
2
4
6
8
autonomous
signaling-based
reuse 1
reuse 3
10
Std. dev. number of mobiles per cell with mean=10
2500
12
(a) 10 users
Fig. 3.
350
20000
2
4
6
8
10
3000
2500
12
2
4
6
8
10
Std. dev. number of mobiles per cell with mean=10
5% CDF individual UE throughput (Kbps)
12
(a) 10 users
Fig. 4.
10
12
(c) 30 users
autonomous
signaling-based
reuse 1
reuse 3
150
100
50
00
8
200
100
50
6
250
150
100
4
300
200
150
2
autonomous
signaling-based
reuse 1
reuse 3
Std. dev. number of mobiles per cell with mean=30
350
autonomous
signaling-based
reuse 1
reuse 3
250
200
20000
(b) 20 users
Mean cell throughput for different variations in user density
300
250
autonomous
signaling-based
reuse 1
reuse 3
Std. dev. number of mobiles per cell with mean=20
350
autonomous
signaling-based
reuse 1
reuse 3
300
3500
3000
5% CDF individual UE throughput (Kbps)
3000
5% CDF individual UE throughput (Kbps)
4500
4000
3500
00
5000
4500
4000
20000
Mean total cell throughput (Kbps)
6000
5500
Mean total cell throughput (Kbps)
6000
5500
Mean total cell throughput (Kbps)
6000
2
4
6
8
10
Std. dev. number of mobiles per cell with mean=20
12
50
00
(b) 20 users
5% CDF cell throughput for different variations in user density
VI. C ONCLUSION
In this paper, we introduced low-complexity decentralized
resource allocation schemes aiming at interference coordination among cells in future wireless networks. Through
system simulations we could show that the dynamic schemes
converge well. In contrast to fixed reuse, the proposed schemes
adapt to changing traffic loads and specifically to inhomogeneous traffic situations, providing almost in all cases the best
throughput in comparison. Comparing an inter-cell signaling
based scheme and a completely autonomous scheme we could
show that the latter might not fully converge but offers the
same performance without any signaling between cells. This
is remarkable because it allows the implementation of effective dynamic inter-cell interference coordination mechanisms
without introducing standardization requirements. Future work
will focus on further improving the proposed schemes as well
as on investigating the performance using a full LTE protocol
stack.
ACKNOWLEDGMENT
Part of this work was funded by the German Research
Foundation DFG.
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