526 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 3, APRIL 2012
of interference management solutions. A summary of possible
solutions considered in 3GPP can be found in [15].
Last, but not least, the vision of cognitive radio networks
(CRN) [16] has revamped the academic interest in the dis-
tributed version of the channel assignment problem due to its
self-organizing nature and its potential to reduce operational
expenditures. Given the synergy between HetNets and CA in
light of CRN, the fundamental problem discussed in this paper
is the design of practical self-adjusting component carrier (CC)
selection mechanisms to deal with in terference in future LTE-
Advanced femtocell deployments.
B. Related Work
Mathematically, channel assignment is a combinatorial op-
timization p roblem which can be mapped into a conflict graph
vertex (mu lti-) coloring, hence the problem is often analy zed
in light of graph (multi-) coloring [17]–[19]. Although the
problem is known to be NP-hard [20], several centralized
and distributed color ing algorithms exist. While ear lier studies
were mostly based on the usage of (generalized) unit disk
graphs to model ad-hoc networks [21], recent proposals deal
with dense deployments of WLAN networks [22], [23].
An excellent overview and systematic performance compar-
ison of several channel allocation algorithms in the context
of circuit-switched networks can be found in [24] and [25],
respectively. An insightful theoretical analysis of the stability
of distributed dynamic channel allocation technique is pre-
sented in [26]. Readers will find a more up-to-date to overview
in [27].
With the emergence of decentralized packet switched cellu-
lar networks, dynamic spectrum approaches and cooperation
are steadily gaining momentum. These solutions typically
consider a decentralized architecture of autonomous decision
makers. Game Theory studies such interactions and has been
applied to dynamic spectrum sharing in a number o f recent
proposals [28]–[30]. A survey of dynamic spectrum man-
agement and cognitive radio (CR) developments is presented
in [31]. The coexistence problem between macrocell and
femtocell systems is also addressed by means of reinforcement
learning techniques in [32], where the authors propose a new
docitive paradigm in order to speed up the slow and complex
cognitive process. Finally, stochastic geometry and related
concepts have also been applied to investigate fully distributed
networks consisting of randomly located devices, akin, but not
limited to femtocells [33].
One important aspect that most contributions so far fail
to consider is the presence of traffic variability. Although
optimality and quick convergence may be sufficient from a
purely theoretical perspective, these are not the only concerns,
stability and robustness (minima l perturbation) are equally,
if not more, relevant. In dense deployments, femtocells can
(re-)appear at anytime and anywhere, and traffic characteris-
tics often deviate from the idealized full-buffer assumption.
Therefore, even if the system converges very quickly, uncon-
trolled/unpredictable reconfigurations remain a m ajor nuisance
and pose several practical problems. Consequently, depending
on the application, it might be preferable to exchange opti-
mality for inertia, i.e. resistance to reconfigurations.
C. Paper Overview
This paper presents a systematic evaluation of the effects
of inter-cell interference on the overall performance of fem-
tocells through detailed system level simulations. Because the
complementary co-channel cross-tier interference is already
receiving significant attention in the literature [2] –[5], this
contribution concentrates on the inter-cell interference among
femtocells operating in a dedicated band, i.e. macro cell
and femtocell users are made orthogonal through bandwidth
splitting. This is also the simplest way to avoid coverage holes
due to the presence CSG femtocells.
Among our contributions, we evaluate and compare four
distributed carrier-based interference management solutions.
Beginning with the obvious candidate: universal reuse, the
techniques are introduced in increasing order of complexity.
The ultimate goal is to identify the trade-offs and assess how
much complexity is effectively r equired to provide efficient
interference coordination on a CC level in the context of LTE-
Advanced femtocells.
The rest of the paper is organized as follows: Section II
formulates the problem and sets the scene with the h elp
of an insightful numerical example. The latter is also used
throughout the p aper to complement the observed results
via intuitive explanations. The considered solutions are de-
scribed in Section III. Most notably, we propose a novel and
decentralized “cognitive” solution that enables femtocells to
jointly determine the subset of CCs and their corresponding
transmission power levels, such that existing transmissions
from neighboring cells are not disrupted. Section IV intro-
duces our working assumptions, while Section V presents an
extensive comparative analysis of the considered alternatives.
We focus on the downlink and heed the o ften overlooked case
of time-varying interference due to random session arrivals
and finite payloads. The analysis encompasses the effects of
spatial density (network topology) and temporal sparseness
(activity factor) on n etwork performance. To the best o f our
knowledge, a comprehensive evaluation of these two aspects
is not available in the context of interference coordination
schemes for femtocells. Finally, Section VI recapitulates the
main findings and concludes the paper.
II. S
YSTEM MODEL AND PROBLEM FORMULATION
We define a network as a set of N femtocells, denoted by
N = {1,...,N} operating in a licensed band of B MHz.
The spectrum is divided into a set C of component carriers
of cardinality |C| = C. Without loss of generality, we assume
that BW(c)=B/C ∀ c ∈Cand that all CCs experience
approximately the same propagation conditions. Nonetheless,
the interference footprint o f each CC can be substantially
different due to mobility and time-varying load conditions.
The problem at hand is to find the subset Λ(n) ⊆Cof
CCs that each cell n should deploy given the topology of
the network and its current traffic conditions. We pay special
attention to the nuances of interference footprint in local
area deployments and do not address the case of co-channel
interference to/from macrocells in overlaid networks.
In order to avoid confusion, we also highlight that the
proposed selection of CCs is femtocell-specific, which differs