On the Homogeneous Transmission Power under the SINR Model
Evangelos Spyrou and Dimitris Mitrakos
School of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Egnatia Street, Thessaloniki, Greece
evang_spyrou@eng.auth.gr, mitrakos@eng.auth.gr
Keywords: Transmission Power, Packet Reception Ratio, Signal-to-Interference-and-Noise Ratio, homogeneous, Clear
Channel Assessment.
Abstract: Power control is quite important in the field of wireless sensor networks. Many works adjust transmission
power in order to either achieve significant improvement on packet reception or to save energy. Even though
the use of non-homogeneous transmission power utilisation benefits is evident in the literature, we study cases
where the use of homogeneous transmission powers across parts of the network may accomplish high Packet
Reception Ratio. We show examples of the above and provide experimental results that show that reception
of packets may be high in appropriate topologies or parts of the topology, with the use of the same transmission
power level. We evaluate two topologies with and without the use of Clear Channel assessment to present our
point.
1 INTRODUCTION
Wireless sensor networks (WSN) are going to the
second decade research, as shown by Breza, Martins,
McCann, Spyrou, Yadav and Yang (2010). The main
reason behind this trend is the plethora of civil and
military applications that require the gathering of data
and their successful wireless transmission within a
large terrain. WSNs consist of small wireless devices
that measure physical phenomena such as
temperature, pressure, humidity, or the position of
objects.
The distributed nature of WSNs, where devices
exchange information with others within their
transmission range, can be quite useful. However, this
very advantage is the main drawback of WSNs. The
nature of the radio employed by the devices is shared
by all participants in the transmission range; hence,
the issue of interference is addressed. It is intuitive
that simultaneous transmission might result in drop of
packets, since the communication medium suffers
from interference. Such a phenomenon is evident
with the use of graph-based models.
This has a direct impact on the network capacity
and throughput. In order to face the problem of
interference, we can address the issue of adjusting
transmission powers. Successful adjustment of
transmission powers result in a smaller set of
interferers; hence, an increase of network throughput.
It is imperative that we use the most appropriate
interference model to attempt to tackle this problem.
We utilize the physical SINR model by Gupta and
Kumar (2000), where interference is continuous and
decreasing polynomially with distance from the
sending device. We will provide the reader with a
formal description of the model at a later section of
the paper.
Briefly outlining the model, the receivers
successfully receives a message if the ratio of the
signal strength of the sender and the sum of
interference signals by devices, transmitting at the
same time, is larger than the hardware-defined
threshold. The denominator of the ratio also includes
ambient noise. The speed that the signal fades
depends on the variable called the path-loss exponent
α, dictated by Rappaport (1996), which takes the
value ranging from 2 - 6 according to environment of
the transmission. The accumulative nature of
interference provides a fruitful domain of research.
Only recently have some theoretical guarantees been
provided for SINR-based algorithms.
Power control is an important field in the field of
wireless networks, since it can control the
performance of the network. Furthermore, it may
increase the number of receivers for a given sender,
as well as tuning interference. However, power
assignment has a significant impact on the complexity
of the problems addressed by algorithms. In the
29
Spyrou E. and Mitrakos D.
On the Homogeneous Transmission Power under the SINR Model.
DOI: 10.5220/0005889000290035
In Proceedings of the Fourth International Conference on Telecommunications and Remote Sensing (ICTRS 2015), pages 29-35
ISBN: 978-989-758-152-6
Copyright
c
2015 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
literature, power assignment is distinguished between
uniform and non-uniform settings. As implied by the
two different approaches, uniform assignment sets the
same transmission power to all nodes. On the other
hand, in the non-uniform assignment, senders operate
on different transmission powers offered by the
communication medium.
Moscibroda, Wattenhofer, and Zollinger (2006)
as well as Moscibroda, Wattenhofer, and Weber
(2006), show that uniform power assignment exhibits
performance disadvantages as opposed to a non-
uniform one. However, cases where power control
approaches outperform uniform power assignment
schemes position the nodes in an area of exponential
size in the number of nodes. These schemes require
transmission power levels that differ by a factor
exponential in the number of nodes, as shown by
Avin, Lotker and Pignolet (2009). A uniform power
control has a number of advantages due to it being
simple.
Some of them include the lower cost of
transmitting at the same transmission power. The
simplicity of decision making implies lower cost,
since devices do not need to decide their power level
depending on factors, such as interference. In
addition, Avin C., Emek Y., Kantor E., Lotker Z.,
Peleg D. and Roditty L., (2009), showed the
convexity of reception zones of senders using a
uniform scheme. This is not the case for the non-
uniform scheme.
In this paper, we will build upon the results of
Moscibroda, Wattenhoffer and Weber, (2006) that
show that senders may transmit simultaneously and
messages will be received without collision due to
interference. We show that simultaneous
transmission of messages is feasible even with the use
of uniform transmission powers, which depends on
the distance of the interfering nodes with the
receivers.
2 RELATED WORK
There is a significant difference between the graph
based and the SINR models. Early works investigate
the SINR model based on the assumption of nodes
being uniformly distributed in the plane, such as
(Behzad and Rubin, 2003), (Grönkvist and Hansson,
2001). The complexity of these solutions, however,
gave way to computationally efficient approaches,
which provide guarantees that use SINR effects.
These solutions include scheduling (Moscibroda and
Wattenhofer, 2006) and topology control
(Moscibroda, Wattenhofer, and Weber, 2006).
Since then, a plethora of research has been
undertaken in scheduling (Calinescu and Tongngam,
2011), (T. Tonoyan, 2013), (Fan, Zhang, Feng, Zhang
and Ren, 2012), (Halldórsson and Mitra, 2012), as
well as topology control (Lou, Tan, Wang and Lau,
2012), (Bodlaender, Halldórsson and Mitra, 2013)
under the SINR model.
In (Halldórsson, Holzer, Mitra, and Wattenhofer,
2013), the authors explicitly investigate the power of
the non-uniform transmission power. On the other
hand, in (Avin, Lotker, Pasquale, and Pignolet, 2009)
valuable information is provided on the employment
of uniform transmission power. This is close to our
work, with the difference that we aim to show
different cases of uniform transmission powers
utilization under the SINR model. In (Whitehouse,
Woo, Jiang, Polastre and Culler, 2005), the authors
consider a scheme of collisions and not failures that
make explicit the utilization of the capture.
Furthermore, we provide the reader with some
early works regarding throughput increase in wireless
networks. In (Biswas and Morris, 2005),, the authors
propose a routing and MAC layer protocol, which
aims to the maximization of throughput. Also, a
scheme that surpasses graph-based models is
suggested in (Katti, Rahul, Hu, Katabi, Medard, and
Crowcroft, 2006).
3 PROMISSING EXAMPLES OF
UNIFORM TRANSMISSION
POWER
Initially we assume that the nodes are randomly
distributed on a unit plane. Moscibroda, Wattenhoffer
and Weber, (2006) showed that doubling the
throughput is feasible when we employ non-uniform
transmission powers in a 1-D setting. We consider a
2-D scenario where devices transmit with uniform
transmission powers. We consider a network of
devices, where a transmission from a device is
successful if the receiver can decode the message.
This occurs when
, where P is the signal
strength, I is the sum of interferences from other
devices and N is the ambient noise. Denote as the
hardware-dependent ratio.
Furthermore, under the physical model of
propagation, the signal strength P is modeled as a
polynomially decreasing function depending on
distance between the sender-receiver pair of devices.
Denote this as
and the aforementioned
function as
where α is the path-loss exponent
Fourth International Conference on Telecommunications and Remote Sensing
30
ranging from 2 to 6 according to the setting of the
network (e.g outdoor, indoor).
We assume that the path loss exponent α = 3, the
SINR threshold β = 3 and the background noise N =
10nW. Note that the values above are reasonable for
practical wireless sensor scenarios, as presented by
Son, Krishnamachari, and Heidemann, (2006). We
denote
as the SINR ratio of node xi when
node xj is transmitting. Hence the power of node xj is
the signal and the powers of the other nodes
transmitting simultaneously are considered as
interference. Obviously, a transmission is successful
if
.
Consider the example that is given in figure 1. We
observe that the distances between the transmitting
and the interfering nodes are greater by
approximately a factor of 2. This is that the
interference distance is twice as great as the
transmitting distance.
Figure 1: Nodes Transmitting Simultaneously with
heterogeneous distances.
If we obtain the SINR values of the two
transmission pairs we have the following:
and
.
This shows that both messages transmitted go through
in the case of simultaneous transmission. The values
exceeding the SINR threshold hold even if nodes
transmit with the minimum transmission power. Note
that using any graph-based approach trying to send
the two messages in parallel will fail because,
intuitively, the medium between the two receivers can
only be used once per time slot.
4 MULTIPLE NODE
INTERFERENCE
The main issue with the utilization of the SINR model
is the fact that it can get very complicated,
constituting it intractable in terms of the protocol
designer. In known network topologies, transmission
power increase results in node degree increase, which
implicitly means that the number of interferers
increases as well. This may assist in the decrease of
the packets decoded in the network; hence, a decrease
in the PRR. Y. Gao, J. C. Hou, and H. Nguyen,
(2008), p.3 introduce the term "interfering node",
which is given by (1).
(1)
Where
is the distance between the sender i and
the receiver j. Also,
is the distance between the
interfering node k and the receiver j. This essentially
provides the node, whose interference results in the
packet to be dropped by the receiver. The authors also
provide the term interference degree, which they
show that it might not be minimized by using the
minimal transmission power assignment.
Note that a node can be interfering with the
transmission of packet and the packet may still be
received. Hence, interference degree is the number of
nodes that collide or interfere with a transmission that
may result in a successful transmission or not.
Following the interference degree, it is useful to
provide the reader with some notes on the potential
number of interferers. Earlier in the paper, we
assumed that the nodes are randomly distributed;
hence, the number of interferers is a random variable.
Nodes that are receiving in slot s-1 are transmitting in
slot s, thus, interfering with nodes receiving in slot s.
We refer the MAC layer slots as slots. We use the
work of Vakil and Liang, (2006), p.4, to indicate that
the number of interferers is given by (2)
(2)
where
is the number of nodes within the
transmission range r of node i, which have been
On the Homogeneous Transmission Power under the SINR Model
31
receiving in slot s and transmitting in the current slot.
Also,
is the number of permissible sources –
transmission ranges - in slot s. There is a difficulty in
obtaining the number of interferers, since the
calculation of inter-node distance is required and is
quite difficult to obtain accurately. The parameter,
which can be utilized in order to obtain the distance,
is the Received Signal Strength Indicator (RSSI)
value (Xu, Liu, Lang, Zhang and Wang, 2010), which
may differ significantly from its actual value if the
two nodes are not within Line-Of-Sight.
Figure 2: Multiple Nodes Transmitting Simultaneously
with heterogeneous distances
We will continue our examples shown in the
previous section of the paper, in order to show a case
where the packets in the presence of multiple
interfering nodes get decoded simultaneously. We
have to mention that the intuitive action of the
transmitting nodes in figure 2 is to reduce their
transmission power in order to minimize the
interfering nodes; hence, to increase the probability of
decoding the packet successfully. However, the case
we examine in the particular figure shows that even
with a high transmission power, simultaneous
reception of the packets is feasible, provided that the
interfering nodes are at a quite larger distance than the
transmitter-receiver pair. Note that all the nodes are
transmitting with transmission power of 0dB.
Specifically, the SINR ratio between nodes x1 and x2
with nodes x5, x6 interfering is
,
which is higher than the SINR reception threshold.
Similarly, for nodes x3, x4 when nodes x7 and x8 are
interfering the SINR is
.
Hence the packet is received successfully.
5 EXPERIMENTAL RESULTS
We decided to put some of our examples to a test
reflecting some of the examples we carried out. We
are considering a network of 15 nodes running for 30
minutes on the Indriya testbed (M. Doddavenkatappa,
M. C. Chan, and A. L. Ananda, 2012). Note that there
will be 108000 messages transmitted to all the nodes
in the network, since every node is transmitting 4
packets per second. The devices in Indriya are
employed with the Chipcon CC2420 radio, which
uses the modulation and encoding specified by the
IEEE802.15.4 standard.
We carefully selected two scenarios; one, where
the nodes are connected but in a sparse manner and
another that the nodes are in a dense area. We
employed a form of synchronization, where the nodes
transmit at the same time. Note that the transmission
power, with which the nodes transmit is the
maximum, 0 dB. The metric we utilize is the Packet
Reception Ratio (PRR) and the number of successful
receptions on the network. First, though, we provide
the reader with the relationship between the SINR and
the PRR.
SINR is the Signal-to-Interference-plus-Noise
Ratio (SINR) of the transmission from node k to node
j, which we denote as γk,j , which is given
by
(3)
where
is the channel gain between the interfering
node t of node j. The Bit-Error-Rate (BER) for the
CC2420 (Fu, Sha, Hackmann and Lu, 2012, p. 3),
which we denote as ξ is
Fourth International Conference on Telecommunications and Remote Sensing
32
(4)
and finally, for any link
, PRRk,j
denote as Pk,j - can be expressed by
(5)
where is the packet length in bits. As dictated in
Zhao and Govindan (2003), at the physical layer,
packet reception experiences variability by the
existence of a grey area within the communication
range of a node. Receiving nodes in this grey area are
susceptible to unstable packet reception.
Furthermore, the grey area is almost a third of the
communication range in certain environments. The
grey area also exhibits temporal packet reception
variation.
Physical layer coding schemes exist capable of
masking some of the variability of packet reception.
The 802.15.4 standard uses a 32:4 DSSS chip-to-bit
encoding. Because the CC2420 uses soft chip
decision, there's no real concept of a "bit error."
Instead, it effectively calculates the closeness of each
chip to 0 and 1 and then chooses the symbol sequence
which is closest to the soft chip decisions.
Figure 3: Mean PRR with and without CCA of dense
topology
In most scenarios a high SINR means high PRR.
We performed two experiments; in the first setting the
nodes use the Clear Channel Assessment (CCA), in
order to sense the channel before they proceed to a
transmission of a packet. In the case that the channel
is busy, the node performs an exponential back-off
and attempts to transmit again. In the second scenario,
using the same configuration of nodes, CCA is being
disabled. Our intuition is that we will find a difference
in the performance of the two settings in the sparse
case. As for the dense configuration, we believe that
the CCA enabled setting will outperform the CCA-
disabled one. This is due to the examples in the
previous section, that the nearest interferer will block
the transmission.
Figure 4: Mean PRR with and without CCA of sparse
topology
In figure 3, we observe that for the dense scenario,
disabling the CCA significantly affects performance.
In fact, the difference between the CCA- enabled and
CCA-disabled is approximately 20%. Furthermore,
we investigated the number of the received messages
received by all nodes in the network configuration.
Our findings show that the CCA-enabled setting
achieved 15,3% more messages received than the
CCA-disabled setting. This is natural since, the
messages transmitted by the CCA-disabled network
are being dropped, since the channel is not sensed
first, due to the density of the configuration.
Thereafter, we studied the performance of the
same two settings for a sparser configuration, where
the interferers have a greater distance from the
receivers. In figure 4 we can see the mean PRR
obtained for both settings. We note that the mean
PRR is similar, which does not give us enough
information on which settings accomplishes the best
performance.
Table 1: Received messages of sparse topology
with/without CCA
Configuration
Received Messages
With CCA
54864
No CCA
53244
Table 1 provides information of the received
messages across the network. We observe that the
number of the received messages of the configuration
with the CCA disabled reaches the number of
messages of the CCA-enabled one. This is due to the
fact that when CCA is disabled, provided the sparsity
of the configuration, interferers and transmitters pass
On the Homogeneous Transmission Power under the SINR Model
33
messages at the same time, without performing a
backoff, which may result in packet drop. On the
other hand, even in the sparse configuration, nodes
sense the channel's state first; hence they delay in the
transmission of their packets.
6 CONCLUSIONS
In this paper we showed that utilizing uniform
transmission powers may result in increase of PRR.
This is dependent on the distance between the
receiver and the interferer. We studied two settings,
one with CCA enabled and the other with CCA
disabled. We have seen that in a sparse configuration,
using the CCA-disabled setting results in the network
reaching the quality of messages reception of the
CCA-enabled setting; thus, exhibiting a similar PRR.
On the other hand, in a dense configuration, the CCA-
enabled setting outperforms the one where CCA is
disabled.
The use of the aforementioned results implies the
necessity of spatiotemporal optimization and stability
of wireless sensor networks. That is, WSN power
control optimization methods may employ the careful
selection of receivers to indicate whether a network
should use uniform or non-uniform transmission
power settings in specific regions. Furthermore,
depending on the network density as well as the
network neighbor and interference degrees, the
network protocol designers, may find that CCA is a
holding back factor of the network throughput
increase. This may be valid in outdoor topologies
where the signal is not affected by factors, such as
Wi-Fi devices (Wu, Stankovic, He and Lin, 2008).
At this point, we have to mention it would be
interesting to experiment with nodes when distances
are fixed, according to the examples discussed
previously. Furthermore, since the Indriya testbed is
spread across different rooms, another interesting
experiment would be to test the topological
configurations under Line-Of-Sight, where the path
loss exponent does not fluctuate. These experiments
may provide us with useful insight regarding the PRR
and rate of transmission.
Finally, this approach may indicate the fact that
interference may not be high enough to require
lowering the transmission power level of a node, even
if the transmission power used is high. This may give
a helpful insight on the behavior of the network PRR
in a two-hop neighborhood.
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