Receiver cooperation in topology control for wireless ad hoc networks

1. 1858 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 4, APRIL 2015
Receiver Cooperation in Topology Control
for Wireless Ad-Hoc Networks
Kiryang Moon, Do-Sik Yoo, Member, IEEE, Wonjun Lee, Senior Member, IEEE, and
Seong-Jun Oh, Senior Member, IEEE
Abstract—We propose employing receiver cooperation in cen-
tralized topology control to improve energy efficiency as well as
network connectivity. The idea of transmitter cooperation has
been widely considered in topology control to improve network
connectivity or energy efficiency. However, receiver cooperation
has not previously been considered in topology control. In particu-
lar, we show that we can improve both connectivity and energy effi-
ciency if we employ receiver cooperation in addition to transmitter
cooperation. Consequently, we conclude that a system based both
on transmitter and receiver cooperation is generally superior to
one based only on transmitter cooperation. We also show that the
increase in network connectivity caused by employing transmitter
cooperation in addition to receiver cooperation is at the expense of
significantly increased energy consumption. Consequently, system
designers may opt for receiver-only cooperation in cases for which
energy efficiency is of the highest priority or when connectivity
increase is no longer a serious concern.
Index Terms—Ad-hoc network, energy efficiency, multi-hop
communications, network connectivity, receiver cooperation,
topology control, transmitter cooperation.
I. INTRODUCTION
THE wireless ad-hoc network has been receiving growing
attention during the last decade for its various advantages
such as instant deployment and reconfiguration capability. In
general, a node in a wireless ad-hoc network suffers from
connectivity instability because of channel quality variation and
limited battery lifespan. Therefore, an efficient algorithm for
controlling the communication links among nodes is essential
for the construction of a wireless ad-hoc network. In a topology
control scheme, communication links among nodes are defined
to achieve certain desired properties for connectivity, energy
consumption, mobility, network capacity, security, and so on.
In this paper, we propose topology control schemes that aim
Manuscript received February 23, 2014; revised July 24, 2014 and November
12, 2014; accepted November 12, 2014. Date of publication December 4, 2014;
date of current version April 7, 2015. Part of this work was presented at IEEE
WCNC, Shanghai, China, April 2013. This work was supported in part by
Basic Science Research Program through the National Research Foundation
of Korea (NRF) funded by the Ministry of Education (NRF-2010-0025062 and
NRF-2013R1A1A2011098). The associate editor coordinating the review of
this paper and approving it for publication was M. Elkashlan. (Corresponding
authors: Do-Sik Yoo and Seong-Jun Oh).
K. Moon, W. Lee, and S.-J. Oh are with Korea University, Seoul 136-701,
Korea (e-mail: keith@korea.ac.kr; wlee@korea.ac.kr; seongjun@korea.ac.kr).
D.-S. Yoo is with the Department of Electronic and Electrical Engineering,
Hongik University, Seoul 121-791, Korea (e-mail: yoodosik@hongik.ac.kr).
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/TWC.2014.2374617
to increase the energy efficiency and the network connectivity
simultaneously.
In a wireless ad-hoc network, two nodes that are not directly
connected may possibly communicate with each other through
so-called multi-hop communications [1], [2]. By employing
multi-hop communication, a node in a wireless ad-hoc network
can extend its communication range through cascaded multi-
hop links and eliminate some dispensable links to reduce the to-
tal required power. Various efforts have been made to study how
the links must be maintained and how much power must be as-
sociated with each of those links for optimal network operations
depending on the situation at hand. For example, Kirousis et al.
[3] and Clementi et al. [4] studied the problem of minimizing
the sum power consumption of the nodes in an ad-hoc network
and showed that this problem is nondeterministic polynomial-
time (NP) hard. Because the sum power minimization problem
is NP hard, the authors in [4] proposed a heuristic solution for
practical ad-hoc networks. Ramanathan and Rosales-Hain, in
[5], proposed two topology control schemes that minimize the
maximum transmission power of each node with bi-directional
and directional strong connectivities, respectively. When the
number of participating nodes is very large, it is crucial to
reduce the transmission delay due to multi-hop transmissions.
To maintain the total transmission delay within a tolerable limit,
Zhang et al. studied delay-constrained ad-hoc networks in [6]
and Huang et al. proposed a novel topology control scheme in
[7] by predicting node movement.
In [3]–[7], it was assumed that there exists a centralized
system controlling nodes so that global information such as
node positions and synchronization timing is known by each
node in advance. However, such an assumption can be too
strong, especially in the case of ad-hoc networks. For this
reason, a distributed approach has been widely considered [8]–
[11], where each node has to make its decision based on the in-
formation it has collected from nearby neighbor nodes. Li et al.
proposed a distributed topology control scheme in [8] and
proved that the distributed topology control scheme preserves
the network connectivity compared with a centralized one.
Because the topology control schemes in [3]–[8] guarantee only
one connected neighbor for each node, the network connectivity
can be broken even when only a single link is disconnected.
Accordingly, a reliable distributed topology control scheme that
guarantees at least k-neighbors was proposed in [9]. The result
in [9] was extended to a low computational complexity scheme
in [10], to a mobility guaranteeing scheme in [11], and to an
energy saving scheme in [12].
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2. MOON et al.: RECEIVER COOPERATION IN TOPOLOGY CONTROL FOR WIRELESS AD-HOC NETWORKS 1859
In [13], the concept of cooperative communications was first
employed in centralized topology control, where it was shown
that cooperative communications can dramatically reduce the
sum power consumption in broadcast network. Cardei et al.
applied the idea of [13] to wireless ad-hoc networks in [14].
Yu et al. further showed that cooperative communications can
extend the communication range of each node with only a
marginal increment in power consumption so that network
connectivity is increased in an energy efficient manner [15],
[16]. Because of these various advantages, the idea of coop-
erative communications has been widely considered in recent
studies on topology control to maximize capacity [17], improve
routing efficiency [18], and mitigate interference from nearby
nodes [19], [20]. The idea of cooperative communications in
these previous works [13]–[20] is realized in the following
way. First, a transmitting node sends a message to its neighbor
nodes (called helper nodes). After the helper nodes decode the
message, they (as well as the transmitting node in some cases)
retransmit the message to a receiving node, and the receiving
node decodes the message by combining the signals from
multiple nodes. Therefore, strictly speaking, only the concept
of transmitter cooperation has been employed, and receiver
cooperation has not been considered.
In this paper, we propose to employ the idea of receiver
cooperation in centralized topology control schemes, possibly
in combination with transmitter cooperation, to increase the
network connectivity in an energy efficient way. Consequently,
we propose two centralized topology control schemes, one
based solely on receiver cooperation, and the other based
both on transmitter and receiver cooperation. For comparison
with proposed schemes, we consider a cooperative topology
control scheme in [16] that is based solely on transmitter
cooperation. We show, through extensive simulations, that we
can improve both network connectivity and energy efficiency
if we employ receiver cooperation in addition to transmit-
ter cooperation. We conclude that the system based both on
transmitter and receiver cooperation is generally superior to
that based only on transmitter cooperation. We also show
that the system based solely on receiver cooperation is as
energy efficient as one based both on transmitter and receiver
cooperation despite a slight decrease in network connectivity.
Although the system based both on transmitter and receiver
cooperation achieves higher network connectivity than one
based only on receiver cooperation, we show that the additional
connectivity increase requires significantly increased energy
consumption. For this reason, system designers may opt for
receiver-only cooperation, if energy efficiency is of the high-
est priority or connectivity increase is no longer of serious
concern.
The remainder of this paper is organized as follows.
In Section II, we describe the channel model considered
throughout this paper. In Section III, we explain the topology
control scheme without cooperation that underlies the two
cooperative topology control schemes considered in this paper.
The two cooperative topology control schemes are then de-
scribed in Section IV. Furthermore, the performance of the two
cooperative topology control schemes are numerically analyzed
in Section V. Finally, we draw conclusions in Section VI.
II. SYSTEM MODEL
In this section, we describe the system model consid-
ered throughout this paper. We consider a network V ≡
{v1,v2,...,vn} consisting of n nodes that are assumed to be
uniformly distributed over a certain region in R2. The nodes
are assumed to communicate with one another by transmitting
signals over a wireless channel with given bandwidth W. We
assume that the physical location of each node does not change
with time.
To model a practical wireless channel, we assume that the
path loss PL(di j) between nodes vi and vj is given by
PL(di j)[dB] = PLd0
+10klog
di j
d0
+2loghi j +Xσ +c. (1)
Here, PLd0
is the reference path loss at unit distance d0 obtained
from the free space path loss model [21], and k denotes the path
loss exponent that represents how quickly the transmit power
attenuates as a function of the distance. The variables di j and
hi j respectively denote the distance and the randomly varying
fast fading coefficient between vi and vj. In addition, Xσ is a
random variable introduced to account for the shadowing effect.
We assume that hi j and Xσ vary independently from packet
to packet, but remain constant during each packet duration.
We assume further that h2
i j follows a χ2-distribution with two
degrees of freedom and Xσ follows a normal distribution with
zero mean and standard deviation σ. Finally, the variable c is the
offset correction factor between the mathematical model and
field measurement. We note that the values of PLd0
, d0, k, σ,
and c vary depending on channel scenario, urban or suburban
[22]. For given PLd0
, d0, k, σ, and c, when node vi transmits
a signal to node vj with power Pi, the received signal to noise
ratio (SNR) γi j(Pi) is given as
γi j(Pi) =
Pi
N0, jW
×100.1×PL(di j)
, (2)
where N0, j denotes the one-sided noise power spectral density
at vj. Throughout this paper, we assume that the maximum
transmit power of each node is given by Pmax.
As the final issue in the system model, we briefly discuss net-
work synchronization. Communication in a completely asyn-
chronous manner is impossible, or at least be very difficult to
achieve. In fact, synchronization can be a particularly important
issue in ad-hoc networks [23]–[25]. In this paper, we assume
that symbol level synchronization is maintained among par-
ticipating nodes. Although detailed synchronization techniques
are not the main focus of this paper, we briefly describe how
the issue of synchronization can be resolved with existing
methods. Synchronization techniques have been reported that
it can achieve time errors around 3 ∼ 7 µs. At such a level of
synchronization, it will become desirable to maintain symbol
duration longer than 50 µs, which corresponds to symbol rate
of up to 20 kilo-symbols per second. A symbol rate of 20 kilo-
symbols with rudimentary binary phase shift keying (BPSK)
modulation results in a data-rate of only 20 kbps, which is not
very high. However, we can employ multi-carrier techniques
such as orthogonal frequency division multiplexing (OFDM)
to increase the data rate while maintaining or reducing the
symbol rate. For example, if we employ an OFDM system
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Fig. 1. A pictorial representation of G = (V,E) with V = {v1,...,v8} and E = {(v1;v2)NN,(v1;v3)NN,(v4;v5)NN,(v4;v6)NN,(v4;v7)NN}.
with 512 subcarriers, the data rate can be increased to about
10 Mbps using a simple BPSK sub-carrier modulation scheme.
Consequently, even with existing techniques such as the OFDM
scheme and synchronization algorithms proposed in [25], it is
possible to maintain the symbol-level synchronization required
to implement the algorithms proposed in this paper.
III. NODE-TO-NODE TOPOLOGY CONTROL
In this section, we explain a topology control scheme, which
we refer to as the node-to-node topology control (NNTC)
scheme, that is based solely on node-to-node communication
links. To describe the NNTC scheme, we first consider the
concept of a wireless communication link between two nodes
and its related definitions. In this paper, a wireless link between
two nodes is said to exist if the received SNR exceeds a certain
threshold, meaning that the packet error probability is below a
certain level (corresponding to the threshold). More formally,
we say that there exists a node-to-node (N-N) link from node vi
to node vj if and only if
f (γi j(Pi)) ≤ ατ, (3)
for a certain transmit power Pi ≤ Pmax from vi. Here, f : R + →
[0,1] denotes the packet error probability function associated
with the given coding and modulation scheme and ατ is the
given threshold on the packet error probability, which we call
the error threshold hereafter. We assume that f is a monoton-
ically decreasing continuous function and that all the nodes
share the same packet error probability function f.1
When there exists a uni-directional N-N link from vi to vj,
the power Pi that satisfies (3) with equality, which we denote
by PNN(vi → vj), is called the minimum N-N routable power
of N-N link from vi to vj. We note that PNN(vi → vj) directly
follows from the definition that
PNN(vi → vj) =
N0, jW f−1(ατ)
100.1×PL(di j)
. (4)
If both the uni-directional N-N links from vi to vj and from vj
to vi exist, we say that there exists an N-N bi-directional link,
or simply an N-N link between the two nodes vi and vj that
1In many previous works on topology controls [14]–[17], (3) is equivalently
written as γi j(Pi) ≥ SNRτ ≡ f−1(ατ). However, to consider the receiver
cooperation scheme in a unified framework, we directly consider the packet
error probability function f.
we denote by (vi;vj)NN. The minimum N-N round-trip power
PNN(vi,vj) of the bi-directional N-N link (vi;vj)NN is defined
as the sum of the two uni-directional minimum N-N routable
powers, namely, as
PNN(vi,vj) = PNN(vi → vj)+PNN(vj → vi). (5)
We note that there are some situations in which two nodes vi
and vj can communicate with each other even if there is no N-
N link between vi and vj. For example, we consider the case in
which there are two N-N links (v1;v2)NN and (v1;v3)NN. In this
case, v2 and v3 can exchange a message through v1 even if there
is no N-N link between v2 and v3. To route a message through
multiple N-N links, all available N-N links should be known
to the nodes. To reduce the routing complexity, only some of
the existing N-N links are used for communications in practice.
By eliminating redundant links, we can simplify the message
routing protocol and save power consumed for exchanging
reference signals such as pilot and channel information [26],
[27]. We denote the set of N-N links to be used for routing by E.
Consequently, (vi;vj)NN ∈ E means that there exists N-N link
(vi;vj)NN and this N-N link is to be used for routing. Here, we
note that (vi;vj)NN /∈ E does not necessarily mean that there is
no N-N link between vi and vj. In graph theory, the combination
G = (V,E) of V and E is called a graph with vertex set V and
edge set E. In the remainder of this paper, nodes and links shall
also be referred to as vertexes and edges, respectively.
For a given E, if (vi;vj)NN ∈ E, vi is said to be a neigh-
bor of vj and vice versa. We denote by N(vi|E) the set
of neighbors of vi. For illustration, we consider the graph
G = (V,E) with V = {v1,v2,...,v8} and E = {(v1;v2)NN,
(v1;v3)NN,(v4;v5)NN,(v4;v6)NN,(v4;v7)NN}, which compactly
describes the situation in Fig. 1. In this example, v5, v6 and
v7 are neighbors of v4, therefore, N(v4|E) = {v5,v6,v7}. Here,
we note that v5 is not a neighbor of v7, however, it is possible
for v5 to send a message to v7 if (v4;v5)NN and (v4;v7)NN
are cascaded. Likewise, if vi and vj can send a message bi-
directionally using a single or cascaded multiple N-N edges, we
say that vi and vj are connected by N-N edges. The maximal set
of nodes connected by N-N edges in E is referred to as a cluster.
For notational convenience, a given cluster {vi1 ,vi2 ,...,vim } is
denoted by Ωmax{i1,i2,...,im}. For instance, in Fig. 1, there are
three clusters {v1,v2,v3}, {v4,v5,v6,v7}, and {v8}, which are
denoted by Ω3, Ω7, and Ω8, respectively. As shown in this
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Fig. 2. Steps to construct the edge set E for a given node distribution V. (a) Identification of all N-N links. (b) A typical example of a spanning forest of
GL = (V,L).
example, several clusters can exist for a given graph. We denote
the set of all clusters by V . We note that V = {Ω3,Ω7,Ω8} in
the above example.
We now describe precisely how the set E of N-N edges to
be used for routing in the NNTC scheme is constructed. For a
given node set V, the set L of all existing N-N links and the set
V of clusters defined by the graph GL = (V,L) are identified.
Next, the edge set E is defined as a subset of L such that the
graph G = (V,E) also leads to the same cluster set V as graph
GL = (V,L). Several candidate algorithms exist that can build
E such as breath-first search (BFS) [28] and depth-first search
(DFS) [29]. In this paper, we use the minimum-weight spanning
forest (MSF) algorithm that aims to build a sparse edge set
using the optimal average power required for network structure
construction [1], [8], [15], [16]. In the MSF algorithm, first a set
TΩ called a minimum spanning tree (MST), is defined for each
cluster Ω ∈ V . After obtaining all the MSTs, the set FV , called
the minimum spanning forest of V, is defined as the union of all
the MSTs, namely, as
FV =
Ω∈V
TΩ, (6)
which is defined to be edge set E in the NNTC scheme.
It now remains to describe how the MST TΩ is obtained for
each cluster Ω ∈ V . If Ω is a singleton, then TΩ is defined to be
the empty set /0. If Ω contains more than one node, to obtain TΩ,
it is necessary to consider the set L|Ω of all edges that connect
nodes in Ω. For instance, we consider the example depicted
in Fig. 2(a) in which the network consists of three singleton
clusters and nine non-singleton clusters. For a non-singleton
cluster Ω encircled by a red colored line, the edge set L|Ω is
defined as the set of all edges inside the red circle. We call a
subset T of L|Ω a spanning tree of Ω if and only if there are no
cycles (loops) in T and if any two nodes in Ω are connected by
edges in T. For example, the edge set of each cluster depicted
in Fig. 2(b) is a spanning tree of that cluster. Among all the
existing spanning trees of Ω, the one that leads to the minimum
edge-weight sum is referred to as the MST TΩ of Ω. Here, the
minimum N-N round-trip power PNN(vi,vj) of the N-N link is
used for the weight of each edge (vi,vj)NN ∈ L.
We note that transmission through the link in FV is not com-
pletely error-free, but has a packet error probability of ατ. How-
ever, in the following, we assume that the communication link
in FV is error-free, possibly with the help of an automatic repeat
and request (ARQ) scheme. Clearly, the repeated transmission
will consume additional energy. However, even with the sim-
plest ARQ scheme, the average required energy to complete a
successful transmission is increased from a single transmission
(with packet error rate ατ) by a factor of 1/(1 − ατ) [30]. We
note that the factor 1/(1 − ατ) is reasonably close to 1 if ατ is
chosen to be small, say, less than 0.1. Therefore, if ατ is suffi-
ciently small, the additional cost for error-free communication
is only a small fraction of the total cost and hence is negligible.
IV. COOPERATIVE TOPOLOGY CONTROL
We note that inter-cluster communication, namely, commu-
nication between nodes belonging to different clusters is not
possible solely through cascaded N-N links. To make inter-
cluster communications possible, [16] employed the idea of
transmitter cooperation in which multiple nodes in one cluster
simultaneously transmit the same message to a single node in
another cluster. In [16], to keep the additional complexity due to
the employment of cooperative transmission manageable, it was
assumed that a pair of nodes belonging to two communicating
clusters were pre-assigned so that communications between the
two clusters could only happen between these two nodes with
the help of nodes in their neighborhoods. We note that not
only the neighboring nodes around the transmitting node but
also the nodes around the receiving node can help to establish
inter-cluster communications. Consequently, in this paper, we
propose to employ receiver cooperation in which the inter-
cluster communication is regarded as successful if the receiving
node or any of the neighboring nodes succeeds in receiving the
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message correctly. If the neighboring nodes only around the
receiving node participate in the cooperation, the established
link between two clusters is referred to as the node-to-cluster
(N-C) link. Furthermore, if neighboring nodes around both
the transmitting and receiving nodes participate in the link
establishment, the inter-cluster communication link is called
cluster-to-cluster (C-C) link.
In this section, we describe two centralized cooperative
topology control schemes based on N-C and C-C links that
are referred to as node-to-cluster topology control (NCTC) and
cluster-to-cluster topology control (CCTC) schemes, respec-
tively. In each of these cooperative topology control schemes,
cooperative links are employed to connect the clusters obtained
from the graph G = (V,E) described in Section III. Conse-
quently, the network configuration defined in a cooperative
topology control scheme is described by four sets, namely, the
set V of nodes, the set E of edges used for routing in the NNTC
scheme, the set V of clusters defined by the graph G = (V,E),
and the set E of cooperative edges. For this reason, the network
configurations defined in the NCTC and CCTC schemes are
identified by GNC = (V,E,V ,ENC) and GCC = (V,E,V ,ECC),
respectively. Here, ENC and ECC consist only of N-C and C-C
edges, respectively.
A. NCTC
In this subsection, we describe how the network configura-
tion GNC = (V,E,V ,ENC) corresponding to the NCTC scheme
is defined. Given graph G = (V,E) and corresponding cluster
set V , the edge set ENC is obtained in three steps. First, the
set LNC of all N-C links connecting clusters in V is identified.
Next, for each N-C link in LNC, the weight of the link is
defined as the minimum power required to establish it. Finally,
the desired edge set ENC is defined as the MSF of the graph
GLNC = (V ,LNC).
To describe the NCTC scheme, we first define the node-
to-cluster (N-C) link. For more concrete understanding of
N-C link, we consider a simple example of receiver cooperation
between two clusters Ω3 = {v1,v2,v3} and Ω7 = {v4,v5,v6,v7}.
For illustration, we assume that the inter-cluster communication
link between two clusters is established if the error probability
is less than or equal to 0.1. We assume that the decoding error
probabilities at nodes v4, v5, v6 and v7 are, respectively, given as
0.3, 0.4, 0.8, and 0.9 when v1 sends a message with maximum
power. Consequently, node v1 and a node in Ω7 cannot estab-
lish inter-cluster communications between Ω3 and Ω7 through
N-N links. However, if any of the nodes in Ω7 succeed in
correctly decoding the message, the message can be routed to
any of the desired nodes in Ω7. If such receiver cooperation is
employed, communication fails only when all four nodes v4, v5,
v6, and v7 fail to decode the message at the same time. We note
that such a probability is 0.3×0.4×0.8×0.9 = 0.0864 < 0.1.
For this reason, we say that cooperative communication link
between Ω3 and Ω7 is established.
In the above example, all nodes in the receiving cluster try
to decode the transmitted message. However, if the size of the
receiving cluster is large, the routing protocol and maintenance
cost can become very burdensome. For this reason, we assume
that a certain receiving node and its one hop neighbors partici-
pate in the receiver cooperation. To be more precise, for a given
pair of clusters, a certain node is selected from each cluster
and the signal is assumed to be transmitted from either of these
two nodes and then received by the other node and its one-hop
neighbors.
We note that there exists a more aggressive method of re-
ceiver cooperation than the one described above. For example,
the bridge node can achieve a huge combining gain if the
helper nodes transmit observed soft information rather than
decoded bits. However, the transmission of the observed data
generally consumes large amount of energy and bandwidth.
Consequently, a sufficiently fine quantization must be con-
sidered to employ soft combining. Because this problem is
highly complex, we assume in this paper that the helper nodes
decode the message and deliver it to the bridge node. However,
considering the importance of this problem, serious research
employing soft combining schemes should be pursued.
For a more formal description, we consider two non-empty
clusters Ωl and Ωm from the given graph G = (V,E) defined in
the NNTC scheme. We formally define the concept of an N-C
link as follows.
Definition 1: Let vbl
∈ Ωl and vbm ∈ Ωm. Then, we say
that there exists a bi-directional N-C link, or simply, a N-C
link denoted by (vbl
,N(vbl
|L);vbm ,N(vbm |L))NC between Ωl
and Ωm, if and only if
∏
vr∈{vbm }∪N(vbm |L)
f γblr(Pbl
) ≤ ατ (7)
and
∏
vr∈{vbl
}∪N(vbl
|L)
f (γbmr(Pbm )) ≤ ατ (8)
for some Pbl
≤ Pmax and Pbm ≤ Pmax.
Here, L denotes the set of all N-N links described in
Section III. In other words, all one-hop neighbors of the re-
ceiving node are assumed to participate in receiver cooperation
regardless whether they belong to E. We note that the error
probability between helper and bridge node is assumed to
be zero, as mentioned in Section III. For a given N-C link
(vbl
,N(vbl
|L);vbm ,N(vbm |L))NC, nodes vbl
and vbm and sets
N(vbl
|L) and N(vbm |L) are called the bridge nodes and helper
sets, respectively.
In Definition 1, we note that the sum of the Pbl
and Pbm values
that satisfy (7) and (8) with equality is the minimum total trans-
mission power required to make round-trip communication
between Ωl and Ωm through (vbl
,N(vbl
|L);vbm ,N(vbm |L))NC.
Because the sum Pbl
+ Pbm depends on the choice of the N-C
link, it is natural to choose the N-C link that minimizes the sum
power Pbl
+Pbm . The minimized sum power shall be referred to
as the minimum N-C round-trip power and the corresponding
N-C link as the minimum power N-C link between Ωl and Ωm.
We denote by PNC(Ωl,Ωm) the minimum N-C round-trip power
between Ωl and Ωm.
We now describe how we establish communications between
Ωl and Ωm. First, let vbl
∈ Ωl and vvm ∈ Ωm be the bridge
nodes of the minimum power N-C link between Ωl and Ωm
and let Hl and Hm be the helper sets of the link. We now
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Fig. 3. Steps to construct the edge set ENC for the given graph G = (V,E). (a) Identification of all N-C links. (b) A typical example of a spanning forest of
GLNC
= (V ,LNC).
assume that a source node vs in Ωl − {vbl
} attempts to send
a message to destination node vd in Ωm − {vbm }. In this case,
vs sends the message to bridge node vbl
through cascaded N-N
edges, and then bridge node vbl
transmits the message to Ωm.
The message sent from vbl
is then decoded at bridge node
vbm and all the nodes in the helper set Hm. Because of the
definition of the N-C link, the message must be decoded, with
negligible failure rate, at least at one node in {vbm } ∪ Hm.
Because Hm consists only of the one hop neighbors of vbm , the
nodes that successfully decode the message can be determined
by vbm with little overhead. After determining the nodes that
successfully decoded the message, vbm delivers the message to
target destination node vd through the cascaded N-N edges.
Finally, we describe how the edge set ENC is constructed
in the NCTC scheme. First, the minimum power N-C link is
identified for each pair of clusters between which N-C links
exist. Let LNC denote the set of the minimum power N-C links
obtained as the result. For each (vbl
,Hl;vbm ,Hm)NC ∈ LNC,
the weight is then defined as the corresponding minimum N-C
round-trip power. After computing all the weights of LNC, the
sparse edge set ENC is defined as the MSF of GLNC = (V ,LNC).
Note that the MSF construction procedure described in
Section III can be directly applied here by substituting V and
L with V and LNC, respectively. In Fig. 3, the procedure is
illustrated. For instance, Fig. 3(a) indicates all the minimum
power N-C links between clusters by solid red lines and
Fig. 3(b) illustrates the shape of a typical spanning forest that
does not include any loops. Likewise, after finding all the
spanning forests of GLNC = (V ,LNC), the one that minimizes
the sum weight is defined as the MSF ENC. After obtaining
the ENC, the desired final graph GNC = (V,E,V ,ENC) for the
NCTC scheme is constructed.
B. CCTC
In this subsection, we describe the CCTC scheme and explain
how the network configuration GCC = (V,E,V ,ECC) corre-
sponding to the CCTC scheme is defined. We first explain
the concept of a cluster-to-cluster (C-C) link and the related
routing protocol with a simple example. We assume that source
node vs ∈ Ωl attempts to send a message to destination node
vd ∈ Ωm. In this case, vs sends a message through cascaded
N-N edges to a pre-defined bridge node vbl
. After receiving
the message, vbl
disseminates the message to the nodes in a
pre-defined helper set Hl. After decoding the message, vbl
and
vhl
∈ Hl simultaneously transmit the message to Ωm in the
next time frame. In Ωm, a pre-defined bridge node vbm and
the nodes in a pre-defined helper set Hm attempt to decode the
message with the multiple signal replicas from the transmitters.
If the maximum ratio combiner (MRC) [31] is employed at the
receiving node vr ∈ {vbm }∪Hm, the combined average received
SNR ¯γr at vr can be written as
¯γr = γblr(Pbl
)+ ∑
vhl
∈Hl
γhlr(Phl
), (9)
and the decoding error probability at vr is given as f(¯γr). To
establish the symbol combining in (9), the same signals from
the multiple transmitters should be received at the same time
as assumed in [13]. We note that problems related to time
synchronization were discussed in Section II. Similarly to the
case for N-C links, we say that the message is decodable, with
negligible failure rate, at least at one node in {vbm }∪Hm if
∏
vr∈{vbm }∪Hm
f(¯γr) ≤ ατ (10)
with small enough ατ, where f(·) denotes the common packet
error probability function for given received SNR, as defined in
Section II. If the inequality (10) holds, we say that there exists a
C-C link from Ωl to Ωm. Once the message is decoded at nodes
in {vbm } ∪ Hm, the message is delivered to destination node vd
through cascaded N-N edges to complete the routing procedure.
To maintain the C-C link power efficiently, it is necessary
to choose appropriately the node pair (vbl
,vbm ), the helper set
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(Hl,Hm), and the transmission power from each transmitting
node to minimize the power consumption. However, the com-
putational complexity makes such an optimization algorithm
hardly feasible not only in practical systems but also in sim-
ulation environments [14]. For this reason, it is widely assumed
that nodes participating in transmitter cooperation use the same
power [15], [16]. Consequently, we adopt the same assumption
when designing the CCTC scheme.
For a more formal description, we consider two non-empty
clusters Ωl and Ωm from a given graph G = (E,V). We define
the concept of a C-C link in the following definition.
Definition 2: Let vbl
∈ Ωl, vbm ∈ Ωm, Hl ⊂ N(vbl
|L), and
Hm ⊂ N(vbm |L). Then, we say that there exists a bi-directional
C-C link, or simply, a C-C link denoted by (vbl
,Hl;vbm ,Hm)CC
between Ωl and Ωm if and only if
∏
vr∈{vbm }∪Hm
f
⎛
⎝γblr(Pcl
)+ ∑
vhl
∈Hl
γhlr(Pcl
)
⎞
⎠ ≤ ατ, (11)
and
∏
vr∈{vbl
}∪Hl
f γbmr(Pcm )+ ∑
vhm ∈Hm
γhmr(Pcm ) ≤ ατ (12)
for some Pcl
≤ Pmax and Pcm ≤ Pmax.
Here, Pcl
and Pcm denote the common transmission powers
of transmitting nodes in Ωl and Ωm, respectively. For a given
C-C link (vbl
,Hl;vbm ,Hm)CC, the nodes vbl
and vbm are called
the bridge nodes and the sets Hl and Hm are called the helper
sets between Ωl and Ωm. Such terminology is the same for of
N-C links. However, in the case of C-C links, the nodes in the
helper set participate not only in receiver cooperation but also
in transmitter cooperation.
In Definition 2, we note that the total transmission power
minimally required to make round-trip communication between
Ωl and Ωm is given by (|Hl| + 1)Pcl
+ (|Hm| + 1)Pcm using the
values for Pcl
and Pcm that satisfy (11) and (12) with equality.
Here, |X| denotes the cardinality of set X. We also note that the
required total transmission power (|Hl|+1)Pcl
+(|Hm|+1)Pcm
varies depending on the choice of the C-C link. Consequently, it
is natural to choose the C-C link that leads to the smallest total
required transmission power. The smallest total required trans-
mission power and the corresponding C-C link are referred to as
the minimum C-C round-trip power and minimum power C-C
link between Ωl and Ωm, respectively. We denote the minimum
C-C round-trip power between Ωl and Ωm by PCC(Ωl,Ωm).
We now describe how the edge set ECC is constructed in
the CCTC scheme. We note that the procedure for obtaining
ECC is essentially the same as that for obtaining ENC. There-
fore, we describe it with brevity. First, the set LCC of all the
minimum power C-C links between clusters is identified. For
each (vbl
,Hl;vbm ,Hm)CC ∈ LCC, the weight is defined as the
corresponding minimum C-C round-trip power. After comput-
ing all the weights of LCC, the sparse edge set ECC is defined
as the MSF of GLCC = (V ,LCC). After obtaining ECC, the
desired final graph GCC = (V,E,V ,ECC) for CCTC scheme is
constructed.
Next, we briefly remark on the additional receiver processing
costs required for the NCTC and CCTC schemes. Compared
to the transmitter cooperative topology control scheme in [16],
additional decoding power is required in the NCTC and CCTC
schemes because of multiple-node decoding. This additional
decoding increases not only the power consumption, but also
the overall system complexity. Furthermore, each receiving
helper node should report the received message decodability
to the bridge node, which increases system overhead. There
are some analytical studies on receiving power consumption
[32], [33] and overhead [34] because it could be a critical issue
in the case of ad-hoc networks. However, we note that the
decoding power consumption and related overhead are heavily
dependent on the receiving strategy. For example, one can chose
a receiving strategy in which the receiving helper nodes decode
the message in the order of channel conditions until a successful
decoding node appears. In this case, the average decoding
power consumption and system complexity can be reduced.
In addition, the serach for the optimal receiving strategy is
highly non-trivial and requires serious and independent study.
However, despite its importance, in this primary effort on
topology control, we do not consider such issues any further
to keep the problem tractable.
Finally, we briefly consider the impact of mobility on the pro-
posed topology control schemes. Unfortunately, the proposed
schemes are basically inapplicable except when the mobility
is very low. When a node moves, three situations can happen.
First, in some situations in which only minor movement is
involved, there may be no changes in the network topology
except for the configurations inside the cluster to which the
moved node belongs. Second, in other situations, the cluster
to which the moved node originally belonged, must be divided
into more than one cluster. Finally, in still other situations,
some clusters could be unified into one cluster by the N-N
links newly defined by the node movement. In the first case,
the mobility problem is relatively simple. If the moved node is
not a bridge or helper node, the moved node could be simply
attached to the nearby cluster. On the other hand, if the moved
node is a bridge or helper node, the bridge and/or helper nodes
of the corresponding cooperative link are changed to one of the
alternatives among the pre-stored alternative bridge and helper
nodes. However, if there is no alternative bridge and/or helper
node or if the second or the third situation occurs, clusters and
cooperative edges should be redefined. In addition, if several
nodes move at the same time, the second and third situations
may happen more frequently and this is why the proposed
schemes are applicable only when the mobility is very low.
V. PERFORMANCE EVALUATION
AND NUMERICAL RESULTS
In this section, we analyze through simulations the per-
formance of the two proposed centralized topology control
schemes, namely, the NCTC and CNTC schemes, and compare
them to the NNTC scheme and cooperative topology control
scheme in [16] that is based solely on transmitter coopera-
tion. For convenience, we call the topology control scheme in
[16] the cluster-to-node topology control scheme (CNTC). To
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TABLE I
SIMULATION CONFIGURATION PARAMETERS
our best knowledge, the CNTC scheme achieves the highest
connectivity with a power requirement that is onl marginally
greater than other existing topology control schemes. In this
section, we show that the proposed NCTC scheme provides
better energy efficiency with marginal connectivity loss and the
CCTC scheme allows both better energy efficiency and higher
connectivity than the CNTC scheme.
A. Simulation Configuration
The system performance is evaluated through simulations in
this paper. Although analytic evaluation is generally more desir-
able, the performance of topology control schemes is very hard
to analyze. To the best of our knowledge, only some analytical
results have been obtained for the case of non-cooperative
communications among an infinite number of nodes [35], [36]
and previous studies [13]–[16] on cooperative topology control
schemes have only been evaluated through numerical simu-
lations. For this reason, we study the performance through
simulations. However, we provide partial analytical reasoning
whenever possible. Furthermore, to improve the value of the
results, we reflect practical situations as much as possible
in simulation configuration by employing channel parameters
based on actual field measurement [22] and the design parame-
ters in the 3GPP standard [37].
To describe the system configuration used for performance
evaluation, we need to specify the values of various parameters,
which we divide into two categories: channel parameters and
system design parameters. The channel parameters include
the reference path loss PLd0
, path loss exponent k, shadow-
ing random variable Xσ, offset correction factor c, and noise
power spectral density N0,i. First, we assumed that N0,i, i =
1,...,n, were identically given as −174 dBm/Hz, the noise
power spectral density at the room temperature. For the other
channel parameters PLd0
, k, Xσ, and c, we consider two sets
of values, given in Table I, that represent suburban and urban
scenarios [22].
The system design parameters considered in this section are
the number of nodes n, simulation area A, error threshold ατ,
packet error function f, and maximum transmit power Pmax.
Parameters n and A are closely related to the node density,
which determines the number of nodes participating in the
cooperation. Therefore, we varied n and A to observe how the
performance is influenced by the node density. The choice of
error function f depends on the error correction coding scheme
employed. In this study, we assume that a convolutional code
with a constraint length of two is used as the error correction
coding scheme with a packet length of 1,024 [38]. Hence, we
used the actual packet error rate obtained through extensive
simulations with the aforementioned convolutional code for the
packet error function f. For the choice of ατ, we used 10−2,
a value often adopted as the target packet error rate in many
situations. Finally, we assumed that the node power Pi is limited
by Pmax = 250 mW, and Pi is uniformly distributed over a
10 MHz bandwidth. Detailed values of the above channel and
system parameters are summarized in Table I.
B. Connectivity
To compare the level of performance achievable with the
proposed topology control schemes, we first consider a metric
called connectivity to measure the average proportion of nodes
connected to a node. Before proceeding with the formal defini-
tion of metric connectivity, we observe that the performance of
a given topology control scheme depends not only on the values
of n and A but also on the distribution of these n nodes over area
A. For this reason, we assume that n(≥ 2) nodes are randomly
and uniformly distributed over a given area A in the following
discussion.
To formally define connectivity, we first denote the set of
all nodes connected to node vi by R(vi). We note that the set
R(vi) depends on the choice of topology control schemes. For
instance, in the NNTC scheme, R(vi) is the set of all nodes
connected to vi by an N-N edge. On the other hand, in a
cooperative topology control scheme, R(vi) consists of all the
nodes that are connected through cascaded N-N and cascaded
cooperative edges. Therefore, the connectivity Γ (of a given
topology control scheme) is defined as
Γ =
1
n
E
n
∑
i=1
|R(vi)|
n−1
, (13)
where |R(vi)| denotes the cardinality of R(vi). Here, the ex-
pectation E[·] has been taken because the cardinality |R(vi)|
depends on how the nodes are distributed over a given area.
We note that R(vi)/(n − 1) is the proportion of nodes that
are connected to vi and hence Γ is the expected value of its
arithmetic mean. For notational convenience, the connectivities
of CCTC, NCTC, NNTC, and CNTC schemes are denoted by
ΓCC, ΓNC, ΓNN, and ΓCN, respectively.
In Fig. 4, the connectivity for various topology control
schemes is shown as a function of the number of nodes n
for three different areas and two different environments. Most
importantly, we observe that ΓCC ≥ ΓCN ≥ ΓNC ≥ ΓNN for
all values of n and A and for any environment considered.
We clearly see that either transmitter or receiver cooperation
improves connectivity. The fact that the CCTC scheme achieves
the highest connectivity is hardly surprising, hence what we
actually need to observe is how the NCTC and CNTC schemes
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Fig. 4. Connectivity as a function of the number of nodes for various topology control schemes in various communication environments. (a) Urban. (b) Suburban.
perform in comparison to it. In particular, since ΓCN ≤ ΓNC,
we conclude that transmitter cooperation is more effective than
receiver cooperation at achieving connectivity.
C. Power Consumption
So far, we have observed that the CCTC scheme achieves
the highest connectivity and that the connectivity gap between
the CNTC and CCTC schemes is not large. In fact, it is not
more than 8% in most cases. Consequently, it is possible to
say that the CNTC scheme is a good alternative to the CCTC
scheme if we consider connectivity only. However, the CNTC
scheme is not as efficient as the CCTC scheme in terms of
power consumption. Before proceeding with the analysis of
power consumption, we define ˆECC to be the set of cluster pairs
corresponding to the edges in ECC. In other words, (Ωl,Ωm) ∈
ˆECC, if and only if the edge set ECC contains the C-C edge
between Ωl and Ωm. In a similar way, we denote the sets of the
cluster pairs corresponding to edges in ENC and ECN by ˆENC
and ˆECN, respectively.
To quantitatively compare the power consumption of the
CCTC and CNTC schemes, we now consider the following two
quantities
¯PCC =
1
n
E
⎡
⎣ ∑
π∈ ˆECC∩ ˆECN
PCC(π)
⎤
⎦ (14)
and
¯PCN =
1
n
E
⎡
⎣ ∑
π∈ ˆECC∩ ˆECN
PCN(π)
⎤
⎦, (15)
where PCN(π) denotes the minimum C-N round-trip power
between the pair π of clusters, similarly to PCC(π) and PNC(π)
as defined in Section IV. We note that these quantities represent
the average power required per each node to establish cooper-
ative edges between clusters in ˆECC ∩ ˆECN. Consequently, by
comparing ¯PCC and ¯PCN, we intend to compare the power re-
quired for the CCTC and CNTC schemes to establish common
cooperative edges.
Before proceeding with the evaluation of ¯PCC and ¯PCN, we
first note that the two sets ˆECC − ˆECN and ˆECN − ˆECC of cluster
pairs are not necessarily empty. Because the CCTC scheme
employs receiver cooperation in addition to transmitter coop-
eration, it appears reasonable to expect ˆECC − ˆECN to contain
some sizable number of cooperative edges and ˆENC − ˆECC to
be empty. In fact, the average number of elements in ˆECC −
ˆECN reaches as much as 25% of that of ˆECC ∩ ˆECN in many
situations. However, interestingly, ˆECN − ˆECC is not necessarily
empty. This is because of the employment of MSF algorithm,
that removes some redundant links. In other words, in CCTC
schemes, some links used in the CNTC scheme are eliminated
by applying the MSF algorithms in some rare situations. From
our numerical analysis, we found that the average cardinality
of ˆECN − ˆECC sometimes reaches as much as 8% of that of
ˆECC ∩ ˆECN. However, in most cases, the set ˆECN − ˆECC is empty
and hence ˆECC ∩ ˆECN is the same as ˆECN.
Fig. 5(a) illustrates how the values of ¯PCC and ¯PCN change
as a function of the number of nodes n. We note that ¯PCC
first increases as n increases and then decreases after n reaches
a certain value. A similar tendency can be found in ¯PCN. To
explain this non-monotonic performance of ¯PCC and ¯PCN, we
define two quantities
FCC =
E ∑π∈ ˆECC∩ ˆECN
PCC(π)
E | ˆECC ∩ ˆECN|
(16)
and
FCN =
E ∑π∈ ˆECC∩ ˆECN
PCN(π)
E | ˆECC ∩ ˆECN|
, (17)
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Fig. 5. The average additional power required per each node to establish cooperative edges in CCTC and CNTC schemes. (a) ¯PCN and ¯PCC. (b) ¯PCN over ¯PCC.
to describe the average power consumed to establish a C-C link
and a C-N link, respectively. As a result, ¯PCC and ¯PCN can be
rewritten as
¯PCC =
1
n
·FCC ·N (18)
and
¯PCN =
1
n
·FCN ·N , (19)
where N = E[| ˆECC ∩ ˆECN|].
While we cannot provide fully analytical behaviors of the
quantities ¯PCC and ¯PCN, which is very difficult, it will be mean-
ingful to consider their qualitative behaviors. First, we note that
the quantities FCC and FCN are mainly affected by the distance
between clusters. It is natural to expect that the average cluster-
to-cluster distance will decrease with an increased number of
nodes n. However, the average cluster-to-cluster distance de-
creases as a very slowly varying function of n, particularly after
n reaches a certain critical value. This is because two clusters
are merged into one if the distance between them becomes too
close. As a consequence, FCC and FCN decrease very slowly as
n increases. For example, the minimum observed value of FCC
was only about 25% lower than the maximum observed value in
the simulation performed for an urban 2 × 2 km situation where
n ranged from 10 to 100. Because the quantities FCC and FCN
are relatively unaffected by the variation of n, the behaviors of
¯PCC and ¯PCN can possibly be accounted for by the behaviors of
the average number of elements N in ˆECC ∩ ˆECN, which, in fact,
varies very significantly as n varies. Let us observe, when the
node density is sufficiently low, that N increases as n increases,
since increased n results in an increased number of clusters
and then in an increased number of edges. However, when the
node density is high enough, adding nodes no longer makes the
number of clusters larger because the addition of nodes now
results in cluster unification. For this reason, N first increases
up to a certain critical value of n and then decreases again
as n grows further. However, it is very difficult to predict the
behavior of N in a fully analytical manner, since N depends on
too many factors such as node distribution, channel and fading
models, error probability function, and so on. As far as we
know, only a few analytical results [35], [36] have been derived
for non-cooperative communications with an infinite number of
nodes and none for general cases or cooperative environments.
We now discuss the simulation results of comparing ¯PCC and
¯PCN. Because FCC and FCN vary slowly as functions of n, the
variations of ¯PCC and ¯PCN are dominantly determined by 1/n
and N . When n = 10, N is almost zero since a very small
number of clusters exist and they are located too far away.
As n increases up to a certain value, the number of clusters
increases so that the chance of cooperative communication also
increases. In this region, N grows faster than n, therefore, ¯PCC
becomes larger. On the other hand, if n exceeds a certain value,
the number of clusters decreases, and eventually, it goes to one.
Therefore, N quickly converges to zero with growing n, and
this is why ¯PCC decreases. In Fig. 5(a), we next observe that ¯PCC
is always smaller than ¯PCN. To quantify the difference between
the two values, we illustrate the values of ¯PCN/¯PCC in Fig. 5(b),
where we clearly see that ¯PCN is about 10–100% larger than
¯PCC. From this figure, we clearly see that the CCTC scheme
requires significantly less power than the CNTC scheme to
establish the same cooperative edges.
Here, the question arises as to how the NCTC scheme
compares to the CCTC scheme in terms of power consumption.
First, we can compare the amount of power required for the
CCTC and NCTC schemes to establish common cooperative
edges. In a similar comparison in Fig. 5, we noted that ¯PCC
is significantly smaller than ¯PCN. However, in the case of the
CCTC and NCTC schemes, there is virtually no difference
between the powers required to establish common coopera-
tive edges. This is related to the assumption that the nodes
participating in the cooperative transmission use the same
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Fig. 6. The relative amount of power required to establish one more additional cooperative edge with the CCTC scheme in comparison with the NCTC and
CNTC schemes. (a) Urban. (b) Suburban.
transmission power as in CCTC scheme. Because of this con-
straint on the transmission power, only one node is selected,
even in the CCTC scheme, to transmit signals almost always
whenever the cooperative edge is contained in both ˆECC and
ˆENC. Therefore, it can be said that the NCTC scheme is almost
as efficient as the CCTC scheme in terms of power consump-
tion. Consequently, if the connectivity is of less priority than
the power consumption or if the situation is such that the
connectivities of CCTC and NCTC are almost the same values
because of a very high node density, the NCTC scheme can be
considered to be a good alternative to the CCTC scheme. This is
particularly so because the average power required to establish
a cooperative edge in ˆECC − ˆENC is significantly larger, in many
cases, than the power required to establish cooperative edge
in ˆENC.
To illustrate this, we consider the metric ρCC
NC defined as
ρCC
NC =
DCC
NC
KNC
(20)
in which
DCC
NC =
E ∑π∈ ˆECC− ˆENC
PCC(π)
E | ˆECC − ˆENC|
(21)
and
KNC =
E ∑π∈ ˆENC
PNC(π)
E | ˆENC|
. (22)
We note that DCC
NC denotes the power required to establish one
C-C link that can not be established in NCTC scheme and
that KCC
NC is the power consumption required for one N-C link.
Consequently, the metric ρCC
NC measures the relative amount of
power required to establish one more additional cooperative
edge using the CCTC scheme in comparison to the NCTC
scheme. In a similar manner, we define the metric ρCC
CN by
ρCC
CN =
E ∑π∈ ˆECC− ˆECN
PCC(π)
E | ˆECC − ˆECN|
÷
E ∑π∈ ˆECN
PCN(π)
E | ˆECN|
(23)
=
DCC
CN
KCN
(24)
to quantify the relative amount of power required to establish
one more additional cooperative edge using the CCTC scheme
in comparison to the CNTC scheme.
In Fig. 6, we plot ρCC
NC and ρCC
CN as functions of n. Here,
we first observe that the numerical values of ρCC
NC and ρCC
CN
are around 3 and 1.2, respectively, for all cases considered.
We note that, as mentioned in the explanation of Fig. 5, the
power consumed to establish a single cooperative link decreases
with growing n so that DCC
NC, DCC
CN, KNC, and KCN are all
decreasing functions of n. In addition, we note that the power
required to establish a cooperative link is mainly affected by
the number of transmitting nodes and the transmitting power
of each node. We also note that the cooperative link between
two clusters is established by only a small number of nodes
located near the boundary of each cluster, even when the cluster
size is very large. This means that the number of transmitting
nodes is almost constant, regardless of n. Therefore, the rate
of decreasing power consumption is primarily affected by the
transmitting power of each node, which is closely related to the
distance between clusters. Because the configuration of clusters
is identically given by the NNTC scheme, as n increases, the
decreasing rate of the power required to establish cooperative
links is relatively similar for all three cooperative schemes,
namely, the NCTC, CNTC, and CCTC schemes. For this
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reason, the ratios DCC
NC/KNC and DCC
CN/KCN remain roughly the
same regardless of the value of n.
We next observe that the values of ρCC
NC, plotted by solid pur-
ple lines, are always around three. This means that to establish
an edge that cannot be established in the NCTC scheme, the
CCTC scheme requires about three times the power required
to establish an edge in the NCTC scheme, regardless of the
scenario and node density considered. Combining this result
with the connectivity result in Fig. 4, we gain an important
insight into the system design. When n = 50, the connectivity
of the CCTC scheme is almost twice that of the NCTC scheme.
Therefore, a three-fold increase in power consumption could be
a reasonable choice if connectivity is of the highest priority.
However, when n = 100, by employing the CCTC scheme,
one would achieve 0.13% increase in connectivity, but three
times more power would still be required. Therefore, some
system designers may prefer the NCTC scheme to the CCTC
scheme, for instance, where power efficiency is of the highest
priority or connectivity increase is not an issue. In contrast,
ρCC
CN, plotted by dotted by the green line, is about 1.2 in all
cases. This means that only 20% more power is required to add
a new cooperative edge using the CCTC scheme that cannot
be established in the CNTC scheme. Consequently, one can
replace the CNTC scheme with the CCTC scheme without a
serious power consumption burden, regardless of node density.
VI. CONCLUSION
In this paper, we proposed to employ receiver cooperation
in topology control to improve energy efficiency as well as
network connectivity. In particular, we proposed two central-
ized topology control schemes, one based solely on receiver
cooperation, and the other based both on transmitter and re-
ceiver cooperations. For comparison, we also considered a
topology control scheme that is based solely on transmitter
cooperation. By extensive simulation, we showed that we can
improve both connectivity and energy efficiency if we employ
receiver cooperation in addition to transmitter cooperation.
Consequently, it is generally more desirable to employ both
receiver and transmitter cooperation than to employ transmitter
cooperation only. We also showed that the increase in network
connectivity by employing transmitter cooperation in addition
to receiver cooperation is at the expense of significantly in-
creased energy consumption. For this reason, we conclude that
the system based only on receiver cooperation could prove to be
a good alternative to one based both on receiver and transmitter
cooperation, if energy efficiency is of the highest priority or the
increase in connectivity is no longer of serious concern.
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Kiryang Moon received the B.S. degree in ra-
dio communication engineering and Ph.D. degree
in computer and radio communication engineering
from Korea University, Seoul, Korea, in 2008 and
2014, respectively. His current research interests
consist of diverse aspects of communications and
networking including wireless ad-hoc network, in-
formation theory, and cooperative communication.
Do-Sik Yoo (S’98–M’02) received the B.S. degree
in electrical engineering and M.S. degree in physics
from Seoul National University, Seoul, Korea in
1990 and 1994, respectively. He received the M.S.
and Ph.D. degrees in electrical engineering from the
University of Michigan, Ann Arbor, MI, USA, in
1998 and 2002, respectively.
Since September 2006, he has been a Faculty
Member in the School of Electronic and Electrical
Engineering, Hongik University, Seoul, Korea. His
research interests consist of diverse aspects of signal
processing, communications and networking including statistical signal pro-
cessing, spectrum sensing, coding and modulation, information theory, multiple
access and resource allocation, and wireless networking.
Wonjun Lee (M’99–SM’06) received the B.S. and
M.S. degrees in computer engineering from Seoul
National University, Seoul, Korea, in 1989 and
1991, respectively. He received the M.S. degree in
computer science from the University of Maryland,
College Park, MD, USA, in 1996 and the Ph.D.
degree in computer science and engineering from the
University of Minnesota, Minneapolis, MN, USA,
in 1999. In 2002, he joined the faculty of Korea
University, Seoul, Korea, where he is currently a Pro-
fessor in the Department of Computer Science and
Engineering, Director of the World Class University Future Network Optimiza-
tion Technology Center (WCU-FNOT), and Director of the Future Network
Center (FNC). His research interests include mobile wireless communication
protocols and architectures, RFID security and MAC protocols, cognitive radio
networking, data center network for cloud computing, and VANET. He served
as TPC for IEEE INFOCOM 2008–2015, ACM MOBIHOC 2008–2009, IEEE
ICCCN 2000–2014, and over 145 international conferences. He received the
Gaheon Academic Award from the Korean Institute of Information Scientists
and Engineers (KIISE) in 2011 and the LG Yonam Overseas Faculty Member
Award from LG Yonam Foundation in 2008. He was a recipient of the Korea
Governmental Overseas Full-Scholarship from 1993 and 1996.
Seong-Jun Oh (S’98–M’01–SM’10) received the
B.S. (magna cum laude) and M.S. degrees in elec-
trical engineering from Korea Advanced Institute
of Science and Technology (KAIST) in 1991 and
1995, respectively, and the Ph.D. degree from the
Department of Electrical Engineering and Computer
Science, University of Michigan, Ann Arbor, MI,
USA, in September 2000. He is an Associate Pro-
fessor with the Department of Computer and Com-
munications Engineering, Korea University, Seoul,
Korea. Before joining Korea University in September
2007, he was a Senior Engineer with Ericsson Wireless Communication,
San Diego, CA, USA, from September 2000 to March 2003. He was also a
Staff Engineer with Qualcomm CDMA Technologies (QCT), San Diego, CA,
USA, from September 2003 to August 2007. He served in the Korean Army
during 1993–1994.
His current research interests are in the area of wireless/mobile networks
with emphasis on the resource allocation for next-generation cellular networks
with the physical-layer modem implementation. While he was with Ericsson
Wireless Communication, he was an Ericsson representative for WG3 (physical
layer) of 3GPP2 standard meeting. While at QCT, he developed CDMA
modems in ASIC for base station (CSM 6700) and mobile station (Qualcomm
Interference Cancellation and Equalization, QICE). From 2008 to 2010, he
served as a Vice-Chair of TTA PG 707, the Korean evaluation group registered
in ITU-R, where he was in charge of performance evaluations of LTE-Advanced
and IEEE 802.16m systems, submitted as an IMT-Advanced technology in
ITU-R WP-5D. He received the Seoktop Teaching Awards from the College
of Information and Communication, Korea University, for outstanding lectures
in the fall semester of 2007 and spring semester of 2010. He was a recipient
of the Korea Foundation for Advanced Studies (KFAS) Scholarship from 1997
to 2000.
For More Details Contact G.Venkat Rao
PVR TECHNOLOGIES 8143271457