Wireless Sensor Network, 2010, 2, 168-172
doi:10.4236/wsn.2010.22022 y 2010 (http://www.SciRP.org/journal/wsn/). Published Online Februar
An Energy-Efficient Access Control Algorithm with
Cross-Layer Optimization in Wireless Sensor Networks
Zhi Chen, Shaoqian Li
National Key Laboratory of Communication, University of Electronic Science and Technology, Chengdu, China
Received July 20, 2009; revised October 25, 2009; accepted November 17, 2009
Abstract
This paper presents a wireless sensor network (WSN) access control algorithm designed to minimize WSN
node energy consumption. Based on slotted ALOHA protocol, this algorithm incorporates the power control
of physical layer, the transmitting probability of medium access control (MAC) layer, and the automatic re-
peat request (ARQ) of link layer. In this algorithm, a cross-layer optimization is preformed to minimizing the
energy consuming per bit. Through theory deducing, the transmitting probability and transmitting power
level is determined, and the relationship between energy consuming per bit and throughput per node is pro-
vided. Analytical results show that the cross-layer algorithm results in a significant energy savings relative to
layered design subject to the same throughput per node, and the energy saving is extraordinary in the low
throughput region.
Keywords: Wireless Sensor Network (WSN), Cross-Layer Design, Energy Efficient, Energy Consumption
per Bit, Throughput
1. Introduction
Wireless sensor network (WSN) consist of a large num-
ber of small, low data rate and inexpensive node that
communicate in order to sense or control a physical phe-
nomenon. Most of the applications proposed for WSN
depend on node designs that minimize complexity and
energy consumption [1]. This is because WSN node bat-
tery replacement will be difficult due to deployment in
remote locations or in difficult environment. Even when
nodes are accessible, their low cost may make it more
efficient to simply replace the entire node rather than just
its battery.
Opportunities for minimizing WSN node energy con-
sumption exist at all layers of the protocol state. Many of
the proposed WSN routing algorithm account for energy
consumption in some fashion [2]. Considerable work has
also been performed on minimizing energy consumption
at the medium access control (MAC) layer [3,4]. Energy
can also be saved at the physical layer by optimizing
parameters such as modulation scheme and number of
transmit antennas [5,6].
While working with individual protocol layers will
help to conserve WSN energy, it has been shown that
cross-layer optimization of the entire protocol stack will
result in the greatest savings [7]. However, computing
this optimal design and implementing it across a WSN is
difficult due to the strict complexity constraints imposed
on the WSN nodes. As a result, researchers have started
to investigate simplified cross-layer energy conservation
solutions that are more suited to low complexity WSN
devices [8–10].
In [8,9], promising results have been presented for
minimizing WSN energy consumption using across-layer
power control algorithm that accounts for link layer and
physical layer behavior. This approach balances the en-
ergy consumed by the physical layer hardware with the
energy consumed by frames retransmitted as part of an
automatic repeat request (ARQ) error recovery scheme.
The basic idea is that lowering transmit power decreases
physical layer energy consumption but a transmit power
that is too low increases the energy wasted on excess
ARQ retransmissions. As a result, an optimal transmit
power exists that achieves a compromise between these
two effects. One drawback to the work presented in [8,9]
is that the physical layer model used in both papers as-
sumes only thermal noise in the radio channel and does
not include multiple access interference (MAI). When
the SNR is high, the MAI effect on the BER can’t be
This work is supported in part by Key Projects in National Science &
Technology Program under Grant 2008ZX03005-001

Z. CHEN ET AL.169
ignored, so the optimized transmit power level presented
in [8,9] would not be the actual optimized value.
Based on the work of [8,9], a new power control algo-
rithm that accounts for MAI and MAC layer behavior is
proposed in [10]. The contribution of [10] is that the
MAI effect on physical BER is taken into account, and
an accurate queuing system is used to model for ALOHA
MAI. Although how physical layer reliability is affected
by the MAI is considered, the parameter designs of MAC
layer, such as transmit probability, are not involved in
the cross-layer optimization in [10]. Meanwhile, the
comparisons of energy consumption alone are not suffi-
cient, because the energy consumption per bit is always
relative to the throughput per node. So the trade-off be-
tween the energy consumption per bit and the throughput
per node should be taken into consider.
The contribution of this paper is to present a new
cross-layer access control (CLAC) algorithm that ac-
counts for power control of physical layer, access control
of MAC layer, and ARQ behavior of link layer. Using
the CLAC algorithm, a significant energy savings rela-
tive to layered algorithms can be achieved subject to the
same throughput demand.
2. The System Model
A star network topology is assumed where each sensor
node transmits its send information to a sink node. Al-
though the star network showed in Figure 1 is very sim-
ple, it could represent a complicate mesh network where
the routing algorithm forms clusters with all nodes in
cluster transmitting to a central node designated as the
cluster head.
In the link layer, the ARQ mechanism is adopted. For
the simplification of analysis, the overhead of packet
header and CRC in front channel, the error and delay in
back channel are all ignored.
In the MAC layer, slotted ALOHA is selected as the
Figure 1. A star topology for WSN.
random access protocol. Each sensor node has the nodes
transmit signals in the same frequency band, and the
band width is. Each node transmits information at a
fixed rate of . The signal transmit power and the noise
power are denoted by and
B
R
PN
P
respectively, and
hence the transmit SNR N
P
P
i
. We assume a
Rayleigh block fading channel for every sensor node in
every slot. The fading gain for user in the time slot
is denoted by and is assumed to have unit vari-
ance. The fading is also assumed to be independent
across users and slots, so can be used to define the
fading gain for sensor node in any time slot. The sink
node employs single user decoding to decode informa-
tion from sensor nodes. By that we mean the sink node
decode one sensor’s codeword assuming ever other sen-
sor node’s signal as noise. In order not to be constrained
with a special modulate scheme, outage probability
t
()ht
i
i
i
h

is used to describe the transmitting error. The outage
probability of sensor nodes transmit in a slot is [12]. k
2
1
2
2
SNR
1Pr log1
SNR 1
k
i
i
h
RB
h






 



 











 (1)
When the fading coefficients are i.i.d. Rayleigh with
unit variance, then



1
21
1exp 2
SNR
RB
R
kB





 


(2)
From (2), it is obviously that the outage probability

is relative to SNR and . In this scheme, the throughput
is given by
k




1
21
SNR, 1exp2
SNR
RB
kRB
kRR 




 


(3)
The sensor node has small bulk and simple functions,
most of the energy is consumed by the signal trans-
mittting, so the circuit energy consumption is ignored in
our analysis. The energy consumption per bit involves
the energy consumed by the physical layer signal trans-
mitting and the energy consumed by link layer frames
retransmitting. The energy consumption per bit with the
scheme of SNR and is given by k
 

1
21
SNR,1exp 2
SNR
RB
kRB
EkPR PR 



  
 
(4)
The number of sensor nodes transmitting in a slot k

Z. CHEN ET AL. 170
is relate to the transmits probability , the throughput
and energy consumption per bit can be computed by av-
eraging
p


SNR,k  in (3) and


SNRE,

k

in (4) by
[12]. The results are given as follows
k


1
1
SNR,(1 )SNR,
21
21 exp
SNR
N
kNk
k
RB
N
RB
N
ppp
k
pppNR











 


k

(5)
 

1
SNR,(1 )SNR,
21
21exp 2
SNR
N
kNk
k
RB
N
RB RB
N
Ep ppE
k
ppPR







 
 

k
(6)
3. Cross-Layer Access Control Algorithm
According to (5) and (6), the optimization problem of
minimizing energy consumption per bit can be described
as follow, subject to the throughput demand

, the op-
timal transmit power level and transmit probability
should be decided to achieve the minimal energy
consumption per bit . This is a nonlinear program-
ming problem with constraints, the straightforward solu-
tion is much complicated, which is not suited to low
complexity WSN devices. Therefore, a simplified opti-
mization algorithm should be developed for sensor
nodes.
P
p
E
The partial derivative of function


SNR,Ep with
respect to argument is computed as p




1
SNR, 21
21exp 2
SNR
21
21 21exp2
SNR
RB
N
RB RB
RB
N
RB RBRB
Ep ppPR
p
Npp PR




 



 


(7)
According to (7),


SNR,E
p
p
is a monotonic in-
creasing function of . Similarly, the partial derivative
of function


SNRE,p with respect to argument
is computed as
P



 
21
SNR, 21 exp2
21
212exp 21
1
RB
NN
R
BRB
RB
N
RB RB
RB
N
N
P
Ep ppPR
PP
pp P
PP
RP




 



 








(8)
According to (8), there exists an optimal solution of
to achieve the minimal P 

SNR,Ep
. By solving the
Equation


SNR, 0
E
p
P



, the optimal solution of is
given by
P


21 orSNR2
RB RB
N
PP 1


 , 
(9)
It is obvious that is independent of the value of P. P

In the same way, by solving the partial derivative of
function


SNR, p  with respect to arguments
and P, it is found that
P


SNR, p  is a monotonic in-
creasing function of , and there exists an optimal so-
lution of P to achieve the maximal . The
optimal solution of P is given by
P

SNR, p 


1
12
RB
pN 
 (10)
Note that is independent of the value of .
p
P
Substituting and using relevant optimal value
and in (5) and (6), we get the cross-layer opti-
mized throughput and energy consumption per bit as
follows
P p
P
p

1
11
1
12
N
RB
ReN








 (11)



1
221
RBN RB
N
N
Pe
ENR


 (12)
The low energy consumption performance of this
CLAC algorithm is analyzed by comparing with the tra-
ditional layered access control (TLAC) algorithm in
which the transmit power and the transmit probability is
determinate independently.
In TLAC algorithm, the power control balances the
energy consumed by the physical layer and the link layer,
therefore, the Equation SNR 21
RB
 is satisfied still.
The difference of TLAC from CLAC is that the transmit
probability is independent of the value of SNR. The
throughput and energy consumption per bit in TLAC
algorithm are given by
P


11
21
N
RB
pppNRe 



 (13)

21 212
N
R
BRB
N
ppeP
ER

 

RB
(14)
4. Comparison of Layered and Cross-Layer
Approaches
Because there exists the trade-off between the throughput

Z. CHEN ET AL.171
and energy consumption per bit, the plot of energy con-
sumption per bit versus the throughput can compare the
energy saving performance of CLAC and TLAC fairly
and clearly.
In order to generate this plot, some assumptions must
be made about the parameters of the WSN. It is assumed
that the WSN consist of 16N

sensor nodes. A data
rate of , a noise power of
and a frequency bandwidth of are chosen
for the physical layer. A transmit probability
20kbpsR110dbmw
N
P
20kHzB
116p

is used for TLAC. The resulting energy consumption per
bit versus the throughput plot is shown in Figure 2. The
upper curve denotes the TLAC algorithm and the lower
curve denotes the CLAC algorithm.
Figure 2 shows that CLAC consumes less energy per
bit than TLAC at the same throughput demand. In the
high throughput region, two curves are close to each
other. The SNR increase along with the increase of
throughput, the MAI has more evident influence on BER
than noise. This evident influence of MAI result in that
the transmit probability designs can ignore the value of
SNR, so the performances of two algorithm are close. On
the other hand, CLAC have significant energy savings
relative to TLAC in the low throughput region. The SNR
decrease along with the decrease of throughput, the ef-
fect of noise on BER is obvious, so it is very necessary
for the transmit probability variety according to SNR.
Another interesting phenomenon can be found in Fig-
ure 2. For CLAC, the energy consumption per bit de-
creease as the decreasing of throughput, but the energy
consumption per bit for TLAC trended to be constant as
the decreeasing of throughput. The reason is that the
transmit probability for TLAC dose not change along
with SNR, the multiple access channel capacity is not
used adequately, and the decreasing of SNR and the de-
creasing of data rate have canceling effect on the energy
consumption per bit.
05 10 15 20 25
-400
-350
-300
-250
-200
-150
-100
-50
0
50
Throughput (kbit/s)
Energy/bit (dBJ)
CLAC
TLAC
Figure 2. Energy consumption per symbol vs. throughput
per node.
It also emphasized that the cross-layer optimizes access
control is indispensable for low throughput WSN.
5. Conclusions
This paper presents a WSN access control algorithm.
Based on slotted ALOHA protocol, this algorithm in-
corporates the power control of physical layer, the
transmitting probability of MAC layer, and the ARQ of
link layer. In this algorithm, a cross-layer optimization is
preformed to minimizing the energy consuming per bit.
Analytical results show that the cross-layer algorithm
results in a significant energy savings relative to layered
design subject to the same throughput per node. At the
same time, the cross-layer algorithm has low complexity
of implementation, and it is suitable to the low energy
consumption and low complexity WSN devices.
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