wireless sensor networks

1. 3108 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
Congestion Control, Routing, and Scheduling in
Wireless Networks With Interference
Cancelation Capabilities
Long Qu, Jiaming He, and Chadi Assi, Senior Member, IEEE
Abstract—Recently, there has been strong interest in exploiting
advanced physical-layer techniques to increase the capacity of
multihop wireless networks. Several recent studies have emerged
with a particular focus on successive interference cancelation
(SIC) as an effective approach to allow multiple adjacent concur-
rent transmissions to coexist, enabling multipacket reception. This
paper is in line with those efforts in that we attempt to understand
the benefits of SIC on the throughput performance of wireless
networks. We consider a cross-layer design for the joint congestion
control, routing, and scheduling problem in wireless networks
where nodes are endowed with SIC capabilities and under the
general physical signal-to-interference-plus-noise ratio (SINR) in-
terference model. We use duality theory to decompose the joint
design problem into congestion control and routing/scheduling
subproblems, which interact through congestion prices. This de-
composition enables us to solve the joint cross-layer design prob-
lem in a completely distributed manner. Given that the problem
of scheduling with SIC and under the SINR interference regime is
NP-hard, this paper develops a decentralized approach that allows
links to coordinate their transmissions and, therefore, efficiently
solve the link scheduling problem. Numerically, we show that our
decentralized algorithm achieves similar results to those obtained
by other centralized methods (e.g., greedy maximal scheduling).
We also study the performance gains SIC brings to wireless net-
works, and we show that flows in the network achieve up to twice
their rates in most instances, in comparison with networks without
interference cancelation capabilities. These gains are attributed
to the capabilities of SIC to better manage the interference and
promote higher spatial reuse in the network.
Index Terms—Cross-layer design, distributed scheduling, net-
work utility maximization (NUM), successive interference cance-
lation (SIC).
Manuscript received November 24, 2013; revised April 3, 2014 and July 11,
2014; accepted August 15, 2014. Date of publication August 27, 2014;
date of current version July 14, 2015. This work was supported in part
by the Scientific and Technological Innovation Teams of Zhejiang Province
under Grant 2010R50009, Grant 2012R10009-11, Grant 2012R10009-12,
Grant 2012R10009-19, and Grant 2012R10009-20; by the Mobile Network
Application Technology Key Laboratory of Zhejiang Province under Grant
2010E10005; and by the Open Funding of Zhejiang Province under Grant
xkxl1305. The review of this paper was coordinated by Prof. J. Tang.
L. Qu and J. He are with the School of Information Science and Engineering,
Ningbo University, Ningbo 315211, China (e-mail: qulongonline@gmail.com).
C. Assi is with the Concordia Institute for Information Systems Engineering
(CIISE), Montreal, QC H3G 1M8, Canada (e-mail: assi@ciise.concordia.ca).
This first author is currently visiting Concordia University.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2014.2352551
I. INTRODUCTION
THE capacity of wireless networks is strongly dependent
on the number of concurrent active transmissions that can
be accommodated by the network, which is commonly referred
to as the level of spectrum spatial reuse [1]. Determining a
set of concurrent active transmissions is the link scheduling
problem, and optimal scheduling has been widely studied and
shown to be complex and combinatorially hard to solve [2]–[4].
In a wireless network where the spectrum is shared among all
communicating links, neighboring communications may cause
strong interference on adjacent links causing transmissions on
these links to collide and, therefore, be corrupted. Thus, the
problem of scheduling asks for finding a subset of links that can
be simultaneously active without causing strong interference in
the network, and the optimal scheduling asks for a maximal
such subset [6], [7]. The problem of optimal scheduling is dif-
ficult to solve given the complex relationship governing trans-
mission concurrence and interference. Most often, simplified
interference models are used to solve the scheduling problem,
such as the graph based or protocol based; such models have
been shown to underestimate the interference in the network,
and thus, the obtained schedules may not be feasible in practice
[8]. Alternatively, other models, such as the physical model
or the signal-to-interference-plus-noise ratio (SINR) [4], are
more realistic in capturing the cumulative interference at each
receiver; however, they are more challenging to deal with,
and link scheduling under such models is shown to be NP-
complete [5], [6].
Now, although link scheduling is an effective method for
managing the activation of interfering links and, thus, achieving
optimal spatial reuse, there has recently been growing interest
in increasing concurrence by exploiting interference rather
than avoiding it through scheduling [18]. Here, the network
allows interfering adjacent transmissions to coexist and relies
on advanced physical techniques to remove interference and,
thus, decode intended signals at their receivers. For instance,
successive interference cancelation (SIC) [9], [15] gives a
receiver the ability to decode two or more concurrent signals
successively: first by decoding the strongest signal (if it can be
decoded) and subtracting it from the combined one and, then,
in turn, decoding other stronger signals successively until the
signal of interest intended to this particular receiver is obtained.
At each step of the decoding, the receiver must ensure that the
signal being currently recovered meets the SINR requirement;
otherwise, no further decoding is possible.
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2. QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3109
Clearly, efficient link scheduling together with SIC help in
promoting better spatial reuse as well as transmission con-
currence, resulting in increased throughput performance. In
this paper, we consider a wireless network where nodes are
endowed with SIC capabilities, and we study the problem of
link scheduling, under the SINR interference model, in the
context of a cross-layer network design.
We consider a network utility maximization (NUM) problem
(similar to [25] and [26]) in a multihop wireless network and
decouple the cross-layer optimization into congestion control
and routing/scheduling subproblems. The congestion control
subproblem can easily be solved at the source node of each flow
by only using local information, and following a back pressure
framework, the routing/scheduling subproblem is converted
into a weight scheduling problem where the weight information
can be illustrated as some scale of the queue length at each
node. However, as mentioned earlier, previous work has shown
that the link scheduling under a binary interference model is
an NP-hard problem [2] and under the SINR model as NP-
complete [5], both with and without SIC, and polynomial-time
approximation algorithms are presented (e.g., [10] and [24]).
Scheduling methods such as maximum weight scheduling [11]
and greedy maximal scheduling (GMS) [12] have shown to
achieve 100% throughput in most practical wireless networks
with the second method being more amenable to distributed
implementation. In this paper, we will consider the GMS ap-
proach for solving the link scheduling problem under the SIC
constraints and the physical interference model; now, given the
complexity of the scheduling problem in centralized settings,
we develop a decentralized method for solving it. Our main
contributions are as follows. First, we revise the interference
localization method in [19] and show that it can be used to
maintain the interference constraints in a network with SIC
capabilities. Second, we present a search-based method for
determining the minimum interference neighborhood of each
link. Our design reveals that the network throughput perfor-
mance is mainly dependent on how much local information
can be coordinated at each communication link. We show that
our decentralized algorithm yields the same maximal schedule
obtained by the centralized GMS method.
The rest of this paper is organized as follows. In Section II,
we briefly survey the work related to cross-layer optimization
with and without SIC. Our system model, the interference
localization technique, and problem formulation are presented
in Section III. Section IV presents the dual decomposition for
decoupling the cross-layer design problem as well as the design
of our decentralized scheduling method. Finally, numerical
results are presented in Section V, and conclusions are drawn
in Section VI.
II. RELATED WORK
Recently, there have been growing interests to exploit inter-
ference among adjacent concurrent transmissions to increase
the network throughput. Mitran et al. in [13] formulated a
cross-layer design optimization to solve the joint problem of
routing and scheduling in a multihop wireless network with
advanced physical-layer techniques for interference cancela-
tion, such as SIC, superposition coding, and dirty-paper coding.
The authors formulated the problem of routing and scheduling
under the physical interference model as a max–min optimiza-
tion problem and developed a column generation method for
solving it efficiently. The authors have shown that SIC signifi-
cantly improves the network performance and, in particular, the
max–min per node throughput. Jiang et al. in [18] noted that
SIC is a very promising interference exploitation technique for
increasing the network throughput due to its ability in enabling
multiple concurrent transmissions. Upon developing a cross-
layer optimization framework for the routing and scheduling
problem, the authors studied the optimal interaction between
interference exploitation, through SIC, and interference avoid-
ance, through link scheduling. The authors have shown that
substantial performance gains can be achieved when both tech-
niques are combined.
Now, the asymptotic transmission capacity of ad hoc net-
works with SIC is studied in [15] and [16]; the former con-
sidered that all signals within one hop from transmitters can be
successfully decoded, and the latter supposed a more realistic
SIC model in their analysis. Sen et al. in [17] studied the extent
of throughput gains that is possible under SIC from a MAC-
layer perspective. They argued that only little gains could be
achieved in restricted scenarios (mainly for upload traffic in
wireless local area networks). Furthermore, when transmitters
choose their bit rates independently, not much gain can be
achieved. However, the authors showed (in a two-transmitter
scenario) that one way to maximize the gain is through transmit
power level selection such that the feasible bit rate is equal for
both transmissions. Lv et al. in [22] proposed a layered protocol
model and a layered physical model (to model the interference)
and studied the problem of link scheduling to characterize the
advantages of SIC. The authors analyzed the capacity of a net-
work with SIC and demonstrated the importance of designing
SIC-aware scheduling. It was shown that significant through-
put gains (20%–100%) can be obtained in chain/cell network
topologies. The problem of link scheduling with interference
cancelation using the SINR interference model is studied in
[23] where Yuan et al. assumed multiuser decoding receivers.
The authors showed that the optimal scheduling problem with
(successive or parallel) interference cancelation is NP-hard
and developed compact linear programming (LP) methods for
obtaining exact solutions. The authors showed that in the lower
SINR regime, interference cancelation yields significant im-
provements. Similarly, in [24], Goussevskaia and Wattenhofer
studied the same problem but developed approximation algo-
rithms for solving the scheduling problem in polynomial time.
SIC has shown to achieve up to 20% performance gains over
networks that do not have interference cancelation capabilities.
It should be noted that all of the aforementioned methods
solve the link scheduling problem in a centralized manner;
given the complexity of the problem, decentralized methods are
more practical. In [25], a distributed method that jointly adapts
decisions made by different layers is proposed. Chen et al.
presented then a dual driven decomposition approach for the
original problem, which is further decomposed into two sub-
problems (one for congestion control and another for routing/
scheduling), and the three are correlated through Lagrangian

3. 3110 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
multipliers. A fully distributed algorithm following the
decomposition is then presented. In [31] and [32], Joo and
Shroff and Joo et al., respectively, revised the distributed
scheduling methods in wireless networks and classified them
into different categories. For the graph-based interference
model, the authors mainly focused on the problem of schedul-
ing and proposed a revision of the GMS algorithm to satisfy the
distributed design. For the more practical interference model,
Le et al., in [19], investigated the link scheduling problem by
considering GMS; to simplify the complex relationship govern-
ing the interference, the authors presented a method to localize
the interference around each link, thereby each link coordinates
its scheduling within a local neighborhood while maintain-
ing scheduling feasibility. The authors subsequently devel-
oped a decentralized scheduling method, which was shown to
yield maximal link scheduling similar to the centralized GMS
method. These decentralized methods did not however consider
network with interference cancelation capabilities.
Note that our work is similar to [25] and [26] in that we
try to design an efficient distributed cross-layer method to
improve the performance of wireless multihop networks. Our
work, however, differs from previous work in that we consider
networks with SIC capabilities in our distributed cross-layer
design with the SINR interference model. This makes the
design of a decentralized method more complicated because of
the particularity of the SIC constraints.
III. SYSTEM MODEL
A. Network Model
We consider a network of N nodes and L links; we assume
stationary nodes, each equipped with SIC capability. Let dn,n
be the Euclidean distance between two nodes n and n , and let
Gnn be the channel gain from n to n such that Gnn = d−pl
n,n ,
where pl is the path-loss index. The transmission power at each
node is assumed to be fixed and equal to Pw. Let F be the set of
flows in the network, where each flow f (f ∈ F) is identified by
a source s(f) and a destination d(f) and a transmission rate yf .
B. Interference Model With SIC
In the physical interference model (also known as the ad-
ditive interference model), in the presence of concurrent trans-
missions on neighboring links, one transmission (e.g., on link i)
is successful if the SINR at the intended receiver is above a
certain threshold β. Then, the physical interference model can
be formulated as
SINRt(i),r(i) =
PwGt(i),r(i)
η + ∀ n∈NA−t(i) PwGn,r(i)
≥ β (1)
where η is the background noise power. NA is the set of all
active nodes in the network, and t(i) and r(i) are the transmitter
and the receiver of link i. β is the minimum SINR threshold
that must be maintained to support a successful transmission
on link i while guaranteeing a tolerable bit error rate. If the
SINR requirement is not met, then the received packet cannot
be correctly extracted from the received signal. In this paper,
we assume β ≥ 1.
Now, SIC allows a signal to be correctly decoded in the
presence of other concurrent transmissions. Here, the receiver
starts decoding the strongest signal from the combined received
signal; then, the decoded signal is subtracted, and the process
is repeated on the residual signal until the signal of interest is
either decoded or no more decoding is possible. This technique
therefore allows a signal to be correctly received given that
other stronger signals are decoded first. Next, we illustrate the
SINR constraints in the presence of SIC. Consider two links
i and i adjacent to each other. Denote by P1
r(i)(P2
r(i)) the
strength of the signal received at destination r(i) from t(i)
(respectively, from t(i )) and suppose P2
r(i) > P1
r(i). Here, r(i)
will attempt to decode the signal received from t(i ) first; this
signal can be decoded if
SINR2
r(i) =
P2
r(i)
η + P1
r(i)
≥ β. (2)
If the signal of t(i ) is successfully decoded at r(i), then r(i)
will subtract it from the combined signal and will attempt to
decode the signal arriving from t(i), i.e.,
SINR1
r(i) =
P1
r(i)
η
≥ β. (3)
The given procedure can be generalized in a straightforward
manner to any number of transmissions.
C. Link Scheduling With Interference Localization
We consider a time-division-multiple-access-based MAC
layer where time is divided into slots of equal length, and each
time slot has two parts: a schedule and a transmission. The
schedule part has several intervals, and each interval is further
divided into minislots. We define the set of links that can be
concurrently active in the same time slot (without violating the
SINR requirements) as a (feasible) configuration (or conf for
short). Then, our objective is to generate a new configuration
during the “schedule” period under SIC constraints and trans-
mits data during the “transmission” period (each active link will
transmit one packet during the “transmission” period). Note
that, in a wireless network without SIC capabilities, in [19],
Le et al. noted that only those concurrent transmissions within
a neighborhood of a particular link may create significant
cumulative interference at the receiver of this link. Accordingly,
they presented an “interference localization” technique that
allowed them to decentralize the link scheduling problem. The
authors presented a method to determine for each link a neigh-
borhood such that interference from active links outside this
neighborhood will have negligible impact on received signal
at the receiver of this link. Namely, for link l, the maximum
interference that can be tolerated is
Imax
l =
PwGt(l),r(l)
β
− η. (4)
Let INl and nINl denote the interference neighborhood
and noninterference neighborhood of link l. INl is a circle

4. QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3111
centered around the receiver of l and whose radius will be
determined later. All links whose transmitters are inside INl
will be able to exchange information (therefore coordinate)
with the transmitter of link l for scheduling purposes. nINl
(complement of INl) contains the set of links whose cumula-
tive interference is assumed to be negligible at rl. Le et al. in
[19] have shown that given a constant (0 < < 1), for link l
to be feasible, the upper bound on the interference coming from
active links located in INl should not exceed (1 − )Imax
l , and
the total interference coming from links located in nINl cannot
exceed Imax
l . Therefore, when all active links in some set are
feasible, we obtain a feasible configuration.
Now, to account for the SIC property of the nodes in the
network, we first revise the interference localization technique
presented earlier as follows. For a particular link l, we divide the
network into three regions: the strongest signal area, the inter-
ference area, and the noninterference area. The strongest signal
area (Al) refers to a circular area with radius dt(l),r(l) centered
around the receiver of link l. The interference area refers to the
ring-like area (INl − Al) with radius from dt(l),r(l) to a certain
length λ(l) (λ(l) ≥ dt(l),r(l)) centered around the receiver of
link l. The noninterference area denotes the region outside the
interference area (nINl). Next, we introduce the definition of
vector
−→
λ .
Definition 1: For any feasible link l, λ(l) denotes the lower
bound of the radius of the interference neighborhood (INl)
such that the total interference coming from links located in
the noninterference area does not exceed Imax
under SIC
constraints.
We assume that each link l (l ∈ L) is able to communicate
with any link whose transmitter is located in INl, or any link l
such that t(l) ∈ INl , to exchange link weight information and
coordinate the link scheduling. Definition 1 implies that there is
a relationship between and
−→
λ (we will present a procedure to
compute
−→
λ based on in the following section). Furthermore,
can be used to control the potential scheduling overload, and
we will verify in Section V that will have a significant effect
on the achievable network performance.
Note that, in any feasible configuration, we assume that all
“active” links l (such that t(l ) ∈ Al) have stronger received
signals at r(l) than the signal arriving from t(l), and therefore,
using SIC, r(l) is capable of successively decoding those
signals prior to decoding the signal arriving from t(l).
Definition 2: Given a certain
−→
λ , Θ(
−→
λ ) is a class of schedul-
ing algorithms such that a particular scheduling method will
belong to Θ(
−→
λ ) if it yields an active schedule satisfying
the following constraints: 1) For any active link l ∈ L, the
total interference coming from active transmitters located in
INl − Al does not exceed (1 − )Imax
(l); and 2) let k de-
note the link from any active transmitter located in Al to
r(l); then, the cumulative interference at r(k) = r(l) coming
from active transmitters located in INk − Ak does not exceed
(1 − )Imax
(k).
The second constraint in the given definition implies that all
active transmitters within the neighborhood of r(l) (i.e., in Al)
should have their signals decoded at r(l) prior to decoding the
signal arriving from t(l). Here, r(l) will attempt to success-
fully decode each of these arriving signals (using SIC); this is
possible because for each signal, we assume that the cumulative
interference from active transmitters located in INk − Ak does
not exceed (1 − )Imax
(k), which is required for successful
decoding of the signal of t(k) at r(l).
Combining Definitions 1 and 2, it can be shown that for any
(0 < < 1), there exists a vector
−→
λ and a class of scheduling
methods Θ(
−→
λ ) such that any scheduling algorithm belonging
to Θ(
−→
λ ) will result in a feasible schedule satisfying the SIC
constraints. This is summarized in the following theorem.
Theorem 1: Given any 0 < < 1, there exists a vector λ
that satisfies Definition 1, and the result of schedule Θ(λ) that
satisfies Definition 2 is feasible under SIC constraints.
D. Problem Formulation
Following the given discussion, we assume that all active
links in one conf can simultaneously transmit. Denote by E
the set of all possible configurations/schedules, where each
conf is indexed by e. Each conf (e) is represented by a
|L|-dimensional rate vector −→r e
, where for each link l, re
l can
be defined as
re
l =
c, if l ∈ e
0, otherwise
(5)
where c is a constant link transmission rate. We define the
feasible rate region Γ as the convex hull of these rate vectors.
We assume through time sharing that all interior points of Γ
are attainable. We define a link-flow matrix v to describe the
routing of flows in the network, where each element vlf ∈
v(∀ l ∈ L, f ∈ F) corresponds to the fraction of flow f deliv-
ered over link l. We assume a utility function U(yf ) to be twice
differentiable, increasing, and strictly concave [25]. Our design
target can be summarized in the following utility maximization
problem:
[OBJECTIVE]
max
yf ≥0,∀ f∈F
f∈F
U(yf ). (6)
Similar to [26], a feasible routing must satisfy two constraints:
the interference and link capacity constraints (7) and the flow
balance constraints (8).
[CONSTRAINTS]
f∈F
vlf ∈ Γ ∀ l ∈ L (7)
yif + Υ−
if ≤ Υ+
if ∀ i ∈ N, f ∈ F (8)
where yif (i ∈ N, f ∈ F) denotes the node-flow variable such
that yif = yf when i = s(f), and otherwise yif = 0. Υ−
if =
l∈L:r(l)=i vlf and denotes the fraction of flow f incoming
into node i, and Υ+
if = l ∈L:t(l )=i vl f denotes the fraction
of flow f outgoing of node i.

5. 3112 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
IV. DISTRIBUTED CROSS-LAYER DESIGN WITH
SUCESSIVE INTERFERENCE CANCELLATION
A. Dual Decomposition
Similar to [25] and [26], we resort to the dual driven
Lagrangian decomposition approach to get a distributed so-
lution. For completeness, we briefly describe the process of
decomposition, and the detailed demonstration can be found in
[25]. Consider the dual problem of primal problem (6), i.e.,
min
uif ≥0,∀ i∈N,f∈F
D(u) (9)
with partial dual function
D(u) = max
yf ≥0,v∈Γ
×
⎧
⎨
⎩
f∈F
U(yf ) −
f∈F i∈N
uif yif + Υ−
if − Υ+
if
⎫
⎬
⎭
(10)
where uif is a Lagrangian multiplier, and u = [uif ]i∈N,f∈F .
Then, (10) can be further decomposed into the following two
subproblems:
D1(u) = max
yif ≥0
f∈F i∈N
(U(yif ) − yif uif ) (11)
D2(u) = max
v∈Γ
f∈F i∈N
uif Υ−
if − Υ+
if . (12)
Here, D1(u) can be solved by (13), which is the standard rate
control problem at the source node of each flow, i.e.,
yf = U −1
(uf ) (13)
where uf = uif if node i = s(f). For the routing/scheduling
problem D2(u), we have the following identity:
D2(u) = max
v∈Γ
l∈L
vlf∗ max
f∈F
ut(l)f − ur(l)f (14)
where f∗
= arg maxf∈F {ut(l)f − ur(l)f }, l ∈ L.
Based on (14), the routing/scheduling problem can be solved
by the following two-step process.
Step 1) For each link l, we can use local informa-
tion u to find a flow f∗
that satisfies f∗
=
arg maxf∈F {ut(l)f − ur(l)f }. Let wl = ut(l)f∗ −
ur(l)f∗ be the weight of link l. Here, wl can also
be interpreted as the scaled queue length at link l
with flow f∗
. In each time slot, the links in one
conf can be active to send data to the receivers (we
assume one packet transmission per active link per
time slot). The given algorithm can be interpreted as
a back pressure process to solve the routing problem.
Step 2) We convert (14) into its reduced form as follows:
D2(u) = max
v∈Γ
l∈L
vlf∗ wl. (15)
The formulation of (15) can be seen as an ordinary link
scheduling problem where each link is associated with its
weight wl. However, it is difficult to solve the scheduling prob-
lem because the interference relationship under the physical
interference model (SINR) is nonconvex and combinatorial. In
the sequel, we present a simplified distributed link scheduling
method taking into account the SIC constraints and using the
interference localization technique presented earlier. We first
propose a method to calculate the vector
−→
λ under a certain ,
and then, a distributed scheduling method is proposed under
SIC constraints.
B. Identifying the Interference Neighborhood
Here, we present a binary-search-based method to determine
vector
−→
λ under a certain value of . Recall that, according
to Definition 1, λ(l) is the lower bound of the radius of the
interference neighborhood INl, which guarantees that, under a
feasible scheduling method (see Definition 2), the total interfer-
ence coming from links in the noninterference region (nINl)
does not exceed Imax
. For a link l, denote dmax
(l) as the
distance from the farthest node in the network to the receiver of
link l. The search procedure for link l starts from dmax
(l), and
we use a bisection search method to reduce the gap between
the current search radius and the optimal λ(l). At every level
of current radius, we have to determine the maximum inter-
ference coming from the active links whose transmitters are
located outside the current radius. One simple way to decide the
maximum interference is to sum up the received signals from
all transmitters outside the current radius; it should be noted
that since some of these transmitters may not be active in our
configuration, this calculated maximum interference represents
an upper bound. An alternative approach is to solve a simple
SIC-based scheduling problem on the links whose transmitters
are located outside the current radius. We repeat this procedure
(of updating the radius of interference neighborhood) for link
l until a tolerable performance is attained. This procedure is
illustrated in Algorithm 1. Note that Algorithm 1 is a central-
ized procedure that needs to be performed only once for a static
wireless network.
All links in the area outside the current radius are initially
stored in a link set Ψ. For current link l, we associate weight
attribute wal(l ) = PwGt(l ),r(l), ∀ l ∈ Ψ and 0 otherwise. We
also define a binary variable pi(i ∈ L), which is equal to 1 when
link i is active, and otherwise, it is zero. Then, we define our
optimization objective as
Maximize :
i∈L
wal(i)pi. (16)
Similarly, we define another binary variable qt(j)(j ∈ L),
which is equal to 1 when node t(j) is an active transmitter,
and otherwise, it is zero. Let L+
n be the set of links whose
transmitter is node n and L−
n be the set of links whose receiver
is node n. Therefore, we have
qt(j) =
i∈L+
t(j)
pi (17)
i∈L+
n
pi ≤ 1. (18)

6. QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3113
In this paper, we only consider the half-duplex mode at each
node. Then, our half-duplex constraints can be written as
pi + pj ≤ 1 ∀ n ∈ N : i ∈ L−
n, j ∈ L+
n . (19)
Similar to [18], we use the concept of residual-SINR or r-SINR
for short. Due to its interference cancelation capability, a
receiver node can sequentially cancel all interfering signals,
which are stronger than the one of interest; therefore, one only
needs to consider the interference from senders whose signals
are weaker than that of the intended one. The r-SINR can be
defined as
r_SINRt(i),t(i) =
PwGt(i),r(i)
Gt(k),r(i)≤Gt(i),r(i)
k=i,t(i)=t(k) PwGt(k),r(i)qk + η
.
(20)
Indeed, when scheduling variable vp
i = 1 (link i is active), this
implies that all other stronger received signals from adjacent
senders at r(i) have been correctly decoded, and the decoding
of the signal of interest at link i is also successful. Namely, if
vp
i = 1, then the following two constraints should be satisfied:
r_SINRt(i),r(i) ≥ β, (pi = 1, i ∈ L) (21)
r_SINRt(j),r(i) ≥ β, j =i, t(j)=t(i), Gt(j),t(i) ≥Gt(i),r(i),
pj = 1, j, i ∈ L) . (22)
To convert the SIC constraints into an LP format, we define a bi-
nary variable ρi,t(j) to describe the relationship of pi and qt(j).
Let ρi,t(j) = 1 if and only if pi = 1 and qt(j) = 1; otherwise, it
is zero. Then, the relationship can be written as follows:
pi ≥ ρi,t(j) (23)
qt(j) ≥ ρi,t(j) (24)
ρi,t(j) ≥ pi + qt(j) − 1. (25)
Now, we can use mathematical programming to describe
constraints (21) and (22) as
PwGt(j),r(i) −
Gt(j),r(i)≥Gt(k),r(i)
t(k)=t(j)
βPwGt(k),r(i)qt(k) − βη
≥ 1 − ρi,t(j) Mi,t(j)
Mi,t(j) = PwGt(j),r(i)
−
Gt(j),r(i)≥Gt(k),r(i)
t(k)=t(j)
βPwGt(k),r(i) − βη (26)
PwGt(i),r(i) −
Gt(i),r(i)≥Gt(k),r(i)
t(k)=t(i)
βPwGt(k),r(i)qk − βη
≥ (1 − pi)Hi
Hi =PwGt(i),r(i) −
Gt(i),r(i)≥Gt(k),r(i)
t(k)=t(i)
βPwGt(k),r(i)−βη. (27)
Algorithm 1: Determination of Interference Neighbourhood
1 Initialize (0 < < 1);
2 Initialize itrCut;
3 for l : l ∈ L do
4 Initialize curr.decision = 1;
5 Initialize curr.radius = dmax
(l);
6 Initialize success.radius = dmax
(l);
7 Initialize curr.decision = 1;
8 for i = 1 to itrCut do
9 curr.interval = (dmax
(l) − dt(l),r(l))/2i
;
10 curr.radius = curr.radius + (1 − curr.
decision) ∗ curr.interval − curr.decision ∗
curr.radius;
11 Generate wal based on curr.radius;
12 Solve optimal objective (16) under constraints
(17)–(19), (23)–(27);
13 if (16) > Imax
then
14 curr.decision = 0;
15 else
16 success.radius = curr.radius;
17 curr.decision = 1;
18 end
19 λ(l) = success.radius;
20 end
21 end
C. Distributed Scheduling Algorithm With SIC
Based on Algorithm 1, we can calculate
−→
λ under a certain
value of . Let Δ1
l be the set of all links k such that t(l) is
located in Ak, Δ2
l be the set of all links k such that t(l) is
located in INk − Ak, and Δl = Δ1
l Δ2
l . At the beginning
of each scheduling period, each link l broadcasts its weight
information (wl) to links in Δl and ΔIN
l [the set of links whose
transmitters are located in the interference neighborhood of link
l (i.e., in INl)]. We further divide ΔIN
l into two link sets:
ΔIN1
l and ΔIN2
l . The former denotes the set of links k such
that t(k) is located in Al, and the latter denotes the set of links
k such that t(k ) is located in INl − Al. The weight of link
l is computed as illustrated in Section IV-A. We assume that
each link l(l ∈ L) maintains two local link sets, i.e., the current
active link set (currsl for short) and a candidate link set (cansl
for short). The former contains links that have been added
into a feasible configuration conf in a particular scheduling
period, and the latter contains links that are candidate links
to be added into conf. At the beginning of each scheduling
period, we initialize currsl = ∅ and cansl = {l, Δl ΔIN
l }.
Each scheduling period consists of several intervals, and in each
interval, each link l makes a decision as to whether it should
be added into currsl or removed from cansl. Therefore, the
purpose of our scheduling method is to generate a new con-
figuration that satisfies the SIC constraints under the physical
interference model such that the sum of the weights of the
links in this configuration is the largest possible. Our scheduling
method follows the classical GMS method but is implemented
in a distributed manner.

7. 3114 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
To make sure that the new configuration, which has been
generated, satisfies the SIC constraints under the physical in-
terference model, each link will execute two main procedures
as follows. At the beginning of each scheduling interval, each
link l (l ∈ cansl) compares its weight to the weights of links
in cansl. If link l has the largest weight among all links in
cansl, it will run Algorithm 2 to try to add itself into currsl.
The detailed process is illustrated next. Link l first broadcasts a
REQ message to links in Δl. Any link in Δl will add link l into
a local auxiliary link set (auxs for short); now, any link l ∈
{currsl auxsl} will determine whether it remains feasible
under SIC constraints upon adding link l to the current schedule
as follows. For each link l ∈ {currsl auxsl}, we define the
SIC link set (sicsl for short) as the set of links whose trans-
mitters are in ΔIN1
l {currsl auxsl } and receivers are
r(l ). According to Theorem 1, any link l ∈ {currsl auxsl}
satisfies SIC constraints if 1) the total interference (I1) coming
from ΔIN2
l is ≤ (1 − )Imax
(l ) and 2) all links k ∈ sicsl
are feasible (i.e., total interference (I2) coming from ΔIN2
k is
≤ (1 − )Imax
(k)).
According to the given procedure, if any link l ∈
{currsl auxsl} does not satisfy the SIC constraints, then
link l will send an ERROR message to link l indicating that link
l cannot be added to the configuration (that is, link l is causing
strong interference making the current schedule not feasible).
If link l ∈ auxsl does not receive any ERROR message from
its neighbors, it adds itself into currsl, removes itself from
cansl, auxsl, and broadcasts a SUCCESS message to all its
neighbors to update their local link sets (cans, currs, and
auxs). Otherwise, it removes itself from cansl, auxsl and
broadcasts a REMOVE message to all its neighbors to update
their local link sets (cans, auxs). The given process enforces
that when adding a new link to a feasible configuration, the
current schedule remains feasible under SIC constraints.
The main purpose of our second procedure is to remove links
in cans (e.g., link l ∈ cansl), which have no chance of being
added into currs. After the new conf is generated at each
interval, all links l (l ∈ cansl) need to make a decision as to
whether they satisfy SIC constraints as follows. For each link
l ∈ cansl, we define another SIC link set (sicsl for short) as
the set of links whose transmitters are in ΔIN1
l currsl and
receiver is r(l). Similar to the process in the first procedure,
any link l ∈ cansl does not satisfy SIC constraints if 1) the
total interference (I1) coming from ΔIN2
l is > (1 − )Imax
(l)
or 2) for any link k ∈ sicsl is infeasible (i.e., total interference
(I2) coming from ΔIN2
k is > (1 − )Imax
(k )). After the given
process, if there is a link l in cansl that does not satisfy
SIC constraints, then link l will remove itself from cansl and
broadcast a REMOVE message to all its neighbors to update
their local link sets (cans, currs). The given process makes
sure that each link in cans satisfies SIC constraints with the
current schedule.
In our distributed implementation, we set the number of inter-
vals per scheduling period to a fixed value. In each scheduling
interval, each link will run Algorithms 2 and 3 to generate new
feasible schedule/configuration during the scheduling period.
Once a schedule is obtained, links that have been selected will
transmit in the transmission period one packet each.
Algorithm 2: Distributed Scheduling Method With SIC
(Link l)
1 Link l broadcast REQ message to all links in Δl;
2 for link l in Δl {currsl auxsl} do
3 if link l received REQ message from link l then
4 Link l adds link l into auxsk;
5 Link l calculates cumulative interference I1;
6 if I1 > (1 − )Imax
(l )) then
7 Link l broadcasts ERROR message to link l;
8 else
9 Generate sicsl ;
10 for k : k ∈ sicsl do
11 Link k temporarily calculates cumulative
interference I2;
12 if I2 > (1 − )Imax
(k) then
13 Link l broadcasts ERROR message to link l;
14 end
15 end
16 end
17 end
18 end
19 if Link l receives no ERROR messages then
20 currsl = currsl l;
21 cansl = cansl − l;
22 auxsl = auxsl − l;
23 link l broadcasts a SUCCESS message to all its neigh-
bors to update their local link sets(cans, currs, auxs);
24 Goto Algorithm 3;
25 else
26 cansl = cansl − l;
27 link l broadcasts a REMOVE message to all its neigh-
bors to update their local link sets(cans, auxs);
28 end
Algorithm 3: Distributed Scheduling Method With SIC
(Part II)
1 for link k in Δl cansl do
2 if link k received a SUCCESS message from link l then
3 Link k calculates cumulative interference I1;
4 if I1 > (1 − )Imax
(k)) then
5 Link k broadcasts a REMOVE message to its neigh-
bors to update their local link sets(cans);
6 else
7 Generate sicsk;
8 for i : i ∈ sicsk do
9 Link i calculates cumulative interference I2;
10 if I2 > (1 − )Imax
(i) then
11 Link k broadcasts a REMOVE message to its
neighbors to update their local link sets(cans);
12 end
13 end
14 end
15 end
16 end

8. QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3115
D. Joint Transport, Routing, and Scheduling With SIC
Consider the dual problem (9) and suppose that the function
D(u) is not necessarily differentiable. Therefore, (9) can be
solved using the subgradient method. Now, it is easy to verify
that
v+
if (u) − yif (u) + v−
if (u) (28)
is a subgradient of D(u) at point u. Thus, based on the subgradi-
ent method, the update algorithm can be formulated as follows:
uif (t+1)= uif (t)+α v+
if (u(t))− yif (u(t))+v−
if (u(t))
+
(29)
where α is a positive step size. Equation (29) achieves optimal-
ity when α is set to a sufficiently small value [25]. The given
dual algorithm (presented in Section IV-A) solves the cross-
layer problem through a distributed manner where at the trans-
port layer, nodes in the network individually update their prices
according to (29) and the source of each flow f individually
adjusts its rate (y) according to the local congestion price (u);
for solving the routing/scheduling subproblem, we generate a
new conf at each time slot by using Algorithms 2 and 3, which
work in a distributed manner. We summarize our joint conges-
tion control, routing, and scheduling with SIC in Algorithm 4.
Algorithm 4: Distributed Cross-Layer Design With SIC
1 Initialize max iteration count as itrmax;
2 Initialize y, v, u;
3 for i = 1 to itrmax do
4 for n ∈ N do
5 node n updates u by calculating (29);
6 end
7 for f ∈ F do
8 Source node of flow f updates y by calculating (13);
9 end
10 for l ∈ L do
11 link l updates wl;
12 end
13 Generate a feasible conf by Algorithms 2 and 3;
14 Data Transmission based on currently obtained
schedule;
15 end
E. Complexity Analysis
The whole procedure includes a centralized process for
identifying the interference neighborhood (see Algorithm 1)
and a link scheduling process under SIC, which is done in
a distributed manner at each iteration (see Algorithms 2 and
3). To analyze the complexity of the first part, we convert the
inverse LP (ILP) problem into a complete binary tree for the
worst case of solving the optimal objective (16). A route that
starts from the root of the tree to the leaf is a feasible solution
(or schedule). Based on backtracking, it is clear that the time
Fig. 1. Eight-node network topology.
complexity of a tree traversal search is O(2n
), where n is the
number of links in wal. However, in most cases, there is no need
for a complete traversal search, owing to the SINR constraints
between links. In practice, we can prune some invalid branches
(i.e., the branch-and-cut method [34]) to improve the efficiency
of the search.
For the run time complexity of the distributed scheduling
with SIC, we omit the communication overload during the
scheduling interval and only focus on the worst case compu-
tation analysis. As shown in Algorithms 2 and 3, it is easy to
verify that the time complexity of links in cansl is O(n) +
O(n2
) = O(n2
) (i.e., the weight comparison and the order of
SIC decoding), where n is the number of feasible neighbors
(i.e., active links) for link l. Given that there is no need to com-
pare the weight information in links in currsl auxsl sicsl,
their run time complexity is O(n2
). For each link that is not in
cansl currsl auxsl sicsl, it keeps silent and therefore
no calculation. Hence, the worst-case run time at each link is
O(n2
), which is polynomial.
V. NUMERICAL RESULTS
Here, we present numerical results to study the performance
of the cross-layer design method for solving the problem of
joint transport, routing, and scheduling (JTRS) in wireless
networks with interference cancelation. We are particularly in-
terested in studying the efficiency of the distributed scheduling
(JTRDS) method with SIC, and we present comparisons with
centralized scheduling methods [JTRCS; both Pick & Com-
pare (P&C) and GMS]. We also present comparisons of our
cross-layer design method with and without SIC to assess the
benefits of interference cancelation (JTRDS-SIC and JTRDS,
respectively). We use a CPLEX solver to solve the ILP problem
in Algorithm 1 to determine the radius of the interference
neighborhood for each link. For our evaluation, we consider two
random networks (Network 1 and Network 2), with eight nodes
(48 links) and 15 nodes (124 links), each randomly distributed
in a square region of 100 m × 100 m. The topologies of
the networks are shown in Figs. 1 and 2. Under the physical
interference model, the transmission power of each node is set
to Pw = 0.001 W. We assume the path-loss index pl = 4; the
background noise η is set to 10−10
W; the SINR threshold for
a successful transmission is β = 1, = 0.05 (unless otherwise
specified); and the transmission capacity of each link is c = 1
(packet/time slot). We assume that there are two flows and four
flows in Network 1 and Network 2, respectively.

9. 3116 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
Fig. 2. Fifteen-node network topology.
Fig. 3. Utility achieved by JTRDS-SIC ( = 0.05) and JTRCS-SIC (P&C).
We start by evaluating the performance benefits of JTRDS-
SIC in Network 1. There are two flows in the network (Flow 1:
node 1 → node 8; Flow 2: node 3 → node 7). We compare our
distributed method with P&C, which is a centralized scheduling
method and is shown to achieve 100% throughput [19], [20]. In
the P&C scheduling method, we randomly generate a maximal
schedule under SIC constraints at each time slot (by randomly
selecting links to be included in the schedule as long as they
satisfy the interference constraints) and compare the current
schedule with the schedule generated in the previous time slot;
the schedule with larger weight (sum of the link weights) is
always selected for data transmission at each time slot. In our
distributed method, we set = 0.05. Figs. 3 and 4 show the
utility and the congestion price of both methods. Clearly, the
figures show that our distributed method quickly converges
to the optimal solution and oscillates around it; however, the
centralized P&C has slower convergence time, which is due to
the random selection of transmission links to be included in the
schedule. To better understand the obtained results, we look at
how these two methods route the two flows and the achievable
individual flow rate; the results are shown in Tables I and II. We
observe that both methods select different routes for the flows
and that flow 1 achieves an optimal rate of 0.8519 (using the
centralized P&C scheduling method), whereas flow 1 achieves
Fig. 4. Congestion prices of JTRDS-SIC ( = 0.05) and JTRCS-SIC (P&C).
TABLE I
AVERAGE RATES OF FLOWS THROUGH DIFFERENT
LINKS WITH JTRCS-SIC (P&C)
TABLE II
AVERAGE RATES OF FLOWS THROUGH DIFFERENT
LINKS WITH JTRDS-SIC
TABLE III
SOURCE NODE, DESTINATION NODE OF EACH FLOW IN THE NETWORK
a flow rate of 0.8332 using the proposed distributed scheduling
method and a gap of 2% between the two methods. Flow 2,
however, achieves the same flow rate of 1 in both methods. It
is to be noted that GMS achieves exactly similar results to our
method (results are omitted in the figures).
Next, we consider the larger network (Network 2) with four
flows (Flow1–Flow4: Table III). We start by studying the effect
of the parameter on the achievable flow rate. We numerically
solve our JTRDS-SIC in this 15-node network, and the obtained
results are shown in Fig. 5. We observe that when is smaller,

10. QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3117
Fig. 5. Flow rates (under JTRDS-SIC) versus .
Fig. 6. Average number of active links per schedule versus .
the achievable flow rates are higher, and as increases, the rate
decreases. Clearly, when is small, the interference neighbor-
hood of a link gets larger (see Fig. 7); therefore, a link l will be
able to coordinate its scheduling/transmission with more links
in its interference neighborhood, i.e., INl. This implies that,
ultimately, each selected schedule may contain, on average,
more active links (see Fig. 6), which, in turn, implies better
spectrum spatial reuse in the network. However, it should be
noted that a larger interference neighborhood may result in
higher scheduling overhead to coordinate the selection of the
schedule. Now, conversely, a larger implies a smaller inter-
ference neighborhood, and as a result, most of the links in the
network will be located outside the neighborhood of a particular
link, preventing any effective coordination in the selection of
the schedule and resulting in lower attainable flow rates.
The flow rate continues to decrease until it reaches a mini-
mum value (at = 0.7) beyond which it starts to increase. This
can be explained as follows. When = 0.7, as we mentioned
earlier, the radius of the interference neighborhood is small (see
Fig. 7), and thus, fewer links may exist within the (INl − Al)
area. Fig. 8 indicates that almost 0 links within that area may
be active. However, according to the protocol, the value of
the tolerable interference assigned to links within that area
Fig. 7. Average radius of neighborhood versus .
Fig. 8. Average number of active links in different areas versus .
is set to (1 − )Imax
; given that almost no links are active
within that area (see Fig. 8), this tolerable interference value
is wasted and would have been better off allocated to links
outside this interference neighborhood (i.e., nINl), where
the other transmission links are located. As increases, the
value of (1 − )Imax
decreases, and more tolerable interference
(i.e., Imax
) is allocated to those links outside the interference
neighborhood of link l, and such links will attempt to schedule
their transmissions concurrently with link l. Fig. 8 shows that
as increases, more links outside the neighborhood are active
in the schedule and none of the links within the interference
neighborhood are. This explains the behavior of the traffic flow
rates shown in Fig. 5 where beyond = 0.7, the rates start
to increase. Fig. 6 shows the average number of active links
per schedule, and as previously explained, smaller indicates
better coordination to construct the schedule and, therefore,
more active links per schedule, hence better spatial reuse, and
larger yields lower spatial reuse.
Finally, we study the benefits of SIC by comparing the
performance of JTRDS-SIC with JTRDS, where in the latter,
nodes do not have any SIC capabilities. The results (individual
flow rates) are shown in Fig. 9, and we use a value of = 0.3.
The selection of = 0.3 is motivated by Fig. 7 where we show

11. 3118 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015
Fig. 9. Achievable flow rates (JTRDS-SIC versus JTRS ( = 0.3)).
that both methods have close average radius for the interference
neighborhood. Fig. 9 shows that flows achieve much higher
rates in a network with SIC capabilities (almost twice the rate
is achieved by most of the flows). To better understand, we
observe from Fig. 6 that the JTRDS-SIC method (when =
0.3) has a much better schedule length than that of the JTRDS
method; indeed, the schedule length (i.e., number of active
links per selected schedule) of JTRDS-SIC is almost twice that
of JTRDS. This shows that SIC is effectively managing the
interference in the network and promoting transmission con-
currence, leading to better achievable flow rates in the network.
VI. CONCLUSION
In this paper, we have studied the benefits of SIC in improv-
ing the performance of wireless networks. We considered solv-
ing an NUM problem in the context of cross-layer optimization
of the joint congestion control, routing, and scheduling problem
under the SINR interference model. Through dual decompo-
sition, we divided our design problem into a congestion con-
trol subproblem and a routing/scheduling subproblem. Given
the complexity of the scheduling subproblem, we presented
a decentralized method for solving the link scheduling prob-
lem. Our decentralized method benefits from the interference
localization concept to help neighboring links coordinate their
transmissions, taking into account SIC constraints, and without
causing sufficient interference that may corrupt ongoing sched-
uled transmissions. Our approach to solving the joint design
problem is completely decentralized. We have numerically
solved the cross-layer optimization, and we have shown that
our distributed resource allocation method achieves very close
results to centralized methods (e.g., our achieved results are
below 2% from the centralized P&C scheduling method, which
achieves 100% throughput performance, and we obtain similar
results to the centralized GMS). We also studied the benefits
of SIC, and we have shown that the flows in the network may
achieve up to twice the achievable rates in a network with-
out SIC. We have shown that networks with SIC capabilities
promote better transmission concurrence and, therefore, better
spectrum reuse.
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Long Qu received the B.S. degree in communica-
tion engineering from Zhengzhou University, Henan,
China, in 2010. He is currently working toward
the Ph.D. degree in communication and information
systems with Ningbo University, Zhejiang, China.
From December 2012 to December 2013, he was
a visiting Ph.D. student with Concordia University,
Montreal, QC, Canada. His current research interests
include cross-layer design in wireless communica-
tion systems and wireless network optimization.
Jiaming He received the M.S. and Ph.D. degrees
from Zhejiang University, Hangzhou, China, in 1993
and 1996, respectively.
He is currently a Professor with Ningbo Univer-
sity, Zhejiang, China. His research interests include
broadband wireless communication systems.
Chadi Assi (SM’08) received the B.Eng. degree
from the Lebanese University, Beirut, Lebanon, in
1997 and the Ph.D. degree from the City University
of New York (CUNY), New York, NY, USA, in
2003.
He is currently a Full Professor with the Concor-
dia Institute for Information Systems Engineering,
Concordia University, Montreal, QC, Canada. Be-
fore joining Concordia University, he was a Visiting
Researcher with Nokia Research Center, Boston,
MA, USA, where he worked on quality of service in
passive optical access networks. His main research interests include networks
and network design and optimization. His current research interests include
network design and optimization, network modeling, and network reliability.
Dr. Assi is on the Editorial Board of the IEEE COMMUNICATIONS SUR-
VEYS AND TUTORIALS, IEEE TRANSACTIONS ON COMMUNICATIONS, and
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He was a recipient of
the prestigious Mina Rees Dissertation Award from CUNY in August 2002 for
his research on wavelength-division multiplexing optical networks.