Optimizing the Battery Energy Efficiency in
Wireless Sensor Networks
(Invited Paper)
Dongliang Duan1, Fengzhong Qu2 , Wenshu Zhang1 and Liuqing Yang1
1. Department of Electrical and Computer Engineering, Colorado State University,
1373 Campus Delivery, Fort Collins, CO 80523, USA.
2. Department of Ocean Science and Engineering, Zhejiang University,
Hangzhou, Zhejiang 310058, China.
Emails: [email protected], [email protected], [email protected], [email protected]
Abstract— In wireless sensor networks (WSN), battery energy
efficiency is a crucial issue since the sensor nodes in WSNs are
generally driven by nonrenewable batteries. In recent years, there
has been an increasing trend of incorporating special battery
characteristics into network protocol design and optimization.
This paper provides the overview of battery energy consumption
optimization for two specific communication tasks. To do that,
we introduce a realistic node model incorporating circuit power
consumptions and battery nonlinearity. Based on this model, one
can choose a more battery-energy-efficient modulation scheme for
the entire network. By a case study, we show that the modulation
selection depends on the internode distance. Then, for specific
communication links within the network, one can either use
single-hop direct link communication or multi-hop communication by utilizing intermediate nodes for information relaying. Our
analyses show that from the battery energy efficiency perspective,
the choice of relaying depends on the transmission distance and
the relay node position.
I. I NTRODUCTION
Battery energy efficiency is a critical factor in wireless sensor networks (WSN), since sensor nodes are typically driven
by nonrenewable batteries [1]. There are quite a few works
studying approaches to improve battery energy efficiency for
wireless communications in sensor networks (see e.g. [2],
[3]). However, the analyses in most of existing literature
adopt an ideal model without taking into account the extra
power consumptions due to circuit operations and battery
nonlinearity. In recent years, there has been an increasing trend
of incorporating special battery characteristics into network
protocol design and optimization (see e.g. [4], [5], [6], [7])
with the introduction of a more realistic sensor node model.
To optimize battery energy efficiency, we first select a more
battery-energy efficient modulation scheme for WSN and
then, for further optimization, we introduce the problem of
selecting between single-hop direct-link communication and
multi-hop cooperative communication utilizing intermediate
relaying nodes.
This work is in part supported by Office of Naval Research under grant
No. N00014-07-1-0868 and Chinese National Science Foundation under grant
No. 61001067.
To select a more energy-conserving modulation, the comparisons between energy efficiencies of modulation schemes
have been well studied (see e.g. [8]). However, these comparisons do not take into account the circuit operations of
the modulation schemes and the extra battery energy loss due
to battery nonlinearity. To illustrate the effects of these two
factors, here we present a case study on the battery energy
consumption comparisons of two modulation schemes, namely
frequency shift keying (FSK) modulation and pulse-position
modulation (PPM) which are considered to have identical
energy efficiency. Results show that due to the differences of
their circuit operation time and pulse energy distribution, these
two modulation schemes consume different average battery
energy, and the selection criterion relies on the internode
distance of the network.
To further improve the network battery energy efficiency,
it is well known that when relaying is utilized to split the
direct transmission from the source to the destination into
two or more hops, the total battery energy consumption is
expected to be greatly reduced, since the transceiver distances
are smaller than that of the direct link and the path loss is
thus significantly reduced [9]. However, when circuit energy
consumptions are considered, it is shown that relaying does
not always save energy (see e.g. [10], [11]). This gives rise to
an intriguing relay selection problem. However, considerations
of this problem in [10] and [11] are under some very limiting
assumptions such as linear relay node placement, identical and
fixed transmission energy at the source and relay nodes without
energy allocation optimization, and an ideal linear battery
model. Here, we adopt a more general setup by assuming
arbitrary relay node placement with a more realistic nonlinear
battery model. With this problem formulation, the relay selection criterion from a battery energy efficiency perspective
in explicit closed-form expressions are established. Results
show that the relay selection criterion depends on both the
transmission distance and the relative position of the relay
node with respect to the primary nodes. In addition, numerical
results are presented to show the battery power efficiency
improvement at different candidate relay locations and for
various scenarios.
This paper is organized as follows: the system model
together with the average battery energy consumption analysis
for a single pulse transmission are presented in Section II.
With this analysis, the battery energy consumption comparison
of M-FSK and M-PPM is presented in Section III and the
relay selection problem is solved in Section IV. Finally,
summarizing remarks are given in Section V.
II. S YSTEM BATTERY E NERGY C ONSUMPTION M ODEL
A. Node Circuit Operation and Battery Nonlinearity
To capture the actual battery energy consumption of the
sensor nodes, the circuit power consumptions are taken into
account with Pct and Pcr denoting transmitter and receiver
circuit power consumption, respectively. Also, the inefficiency
of the DC/DC convertor in the node circuit is denoted by a
factor η < 1 and the imperfectness of power amplifier (PA) is
described by an extra power loss factor α > 0.
Moreover, the real battery discharge process is nonlinear.
As introduced in [4], the nonlinear behavior
of the battery
Imax
Vi
discharge process can be captured by P0 = Imin
μ(i) f (i)di,
where P0 is the average power consumption of the battery over
a battery discharge process, V is the battery voltage, f (i) is
the density function of the battery discharge current profile
during time period of interest [tmin , tmax ], μ(i) is the battery
efficiency factor [12] and Imax and Imin are respectively the
maximum and minimum affordable discharge currents. To
facilitate the ensuing analysis, we define the instantaneous
power consumption at time t as P0 (t) = V i(t)/μ(i(t)).
Then, the average power consumption of the battery over the
discharge interval [tmin , tmax ] can be alternatively expressed
tmax
tmax
as:
V i(t)
dt ,
(1)
P0 =
P0 (t)dt =
μ(i(t))
tmin
tmin
where ω is a positive parameter.
B. Channel Model
The channel considered here is path-loss Rayleigh fading
channel with additive white Gaussian noise (AWGN). The
channel gain factor G(d) depends on the transceiver distance d
and is given by [13, Chapter 4]: G(d) = Ps /Pr = Ml G1 dK ,
where Ps and Pr are the transmitted and received power of
the signal, and the remaining parameters are defined in Table
I. Accordingly, the relationship between the average energy at
the transmitter E and the average energy at the receiver Er is:
E/Er = Ps /Pr = G(d) = Ml G1 dK .
(2)
C. The Average Battery Energy Consumption
As a preliminary, we will first analyze the battery energy
consumption for a single transmitted pulse.
C.1: Transmitter Battery Energy Consumption
With our realistic circuit and battery model, the actual
battery energy consumption for transmitting a single pulse can
be obtained as the following lemma with detailed proof in [6]:
TABLE I
γp
N OTATIONS
channel link margin
gain factor at d = 1
path-loss exponent
battery efficiency factor μ(i) = 1 − ωi
transfer efficiency of the DC/DC converter
extra power loss factor of the PA
transmitted pulse
2
Tp
p(t)
dt
Tp
0
Ep
E0
Pct
Pcr
pulse energy
average battery energy consumption
transmitter circuit power
receiver circuit power
Ml
G1
K
μ(i)
η
α
p(t)
0
|p(t)|dt
Lemma 1 The total battery energy consumption for transmitting a single pulse p(t) with duration Tp and energy Ep is
approximately:
E0t =
ωγp (1 + α)2 2 1 + α
Pct
Ep +
Tp ,
Ep +
2
Vη
η
η
(3)
with parameters defined in Table I.
In (3), η and α terms reflect the influence of the inefficiency
of DC/DC converter and the extra PA power loss, respectively.
The result in Lemma 1 shows that the total battery energy
consumption can be decomposed into three parts:
1) The first term in (3) refers to the excess power loss due
to the nonlinear battery discharge process. This term is
proportional to the square of the energy of the transmitted
signal. In addition, this term is only affected by the pulse
shape through a scaling factor γp . Notice that, though
γp can be mathematically interpreted as the “energy” of
p0 (t), it is not the actual energy consumption of a DC
battery with a constant voltage V . Instead, this scaling
factor γp is the result of normalization of the un-amplified
pulse waveform p0 (t) in order to ensure a constant pure
(without any circuit energy consumption) and ideal (without any battery nonlinearity) battery energy consumption
independent of the actual shape the pulse takes. Finally,
this term also depends on the battery parameter ω, which
captures the nonlinear feature of the battery;
2) The second term in (3) refers to the energy carried by the
transmitted signal. it would be exactly the energy of the
transmitted pulse if there were not effects of the DC/DC
converter (via η) and the PA (via α);
3) The third term in (3) refers to the circuit energy consumption. It depends on the power of the circuit and the
pulse duration Tp .
C.2: Receiver Battery Energy Consumption
At the receiving node, there is no PA but a low noise
amplifier (LNA) with nearly constant power consumption.
Thus, the current Ir = Pcr /(ηV ) where Pcr is the circuit
power consumption at the receiver. In general, Ir is very small,
so μ(Ir ) = 1−ωIr ≈ μmax = 1 [4]. The circuit of the receiver
needs to be turned on for the demodulation duration Td . Hence,
TABLE II
the total battery energy consumption of the receiving node is:
Pcr
Td .
(4)
η
Then, the total battery energy consumption can be obtained
as the summation of the transmitter and receiver battery energy
consumptions.
E0r =
S YSTEM PARAMETERS
ω = 0.05
K=3
V = 3.7V
D. Performance Criterion
α = 0.33
G1 = 27dB
Pct = 105.8mW
μmin = 0.5
Ml = 40dB
η = 0.8
100
80
dc (m)
In the process of battery energy consumption analyses, average bit-error-rate (BER) is adopted as the performance metric.
Thus, in all the comparisons, the average battery energy
consumptions to achieve the same target BER performance
(P¯e ) are compared for both the modulation selection and the
communication link selection problems.
Tp = 1.33 × 10−4 s
N0 /2 = −171dBm/Hz
Pcr = 52.5mW
60
40
20
−3
10
32
III. M ODULATION S ELECTION : A C ASE S TUDY
In this section, we will establish a framework for choosing the more battery energy efficient modulation in wireless
sensor networks, and will present a case study of modulation
selection between PPM and FSK to show the effects of circuit
power consumptions and battery nonlinearity on the battery
energy consumption analyses and obtain the selection criterion
expressed as a closed-form function of the internode distance.
With f = 1/Ts , M-FSK and M-PPM have identical
bandwidth occupancy and bandwidth efficiency as shown in
[4]. However, when the realistic system model is considered,
these two schemes are found to have different battery energy
consumption performances.
For M-FSK, the signal pulse transmitted for symbol m ∈
{0, 1, . . . , M − 1} is pF
m (t) = sin(2π(fc + (2m− 1)f )t), t ∈
[0, Ts ], where fc is the central carrier frequency and f is the
frequency spacing.
For M-PPM, all possible signals utilize the same pulse
shaper and the information is conveyed by signal pulse position. To compare with M-FSK, pass-band M-PPM is considered. Then, the basic pulse is pP (t) = sin 2πfc t with t ∈
[0, Ts /M ], where fc is the carrier frequency. Correspondingly,
P
the pulse transmitted for symbol m is pP
t − m TMs .
m (t) = p
To calculate the average battery energy consumptions
for these two modulation schemes, the pulse shape factors
γpF and γpP need to be obtained in the first place. AcF
=
cording
to Lemma 1 and Table I, for M-FSK: γp,m
Ts
2
2
2
[sin(2π(f
+(2m−1)f
)t)]
dt
c
Ts
Ts
2π
0
= Ts . Similarly,
2 = 2 / 2π
[ 0Ts |sin[2π(fc +(2m−1)f )t]|dt]
2
2
P
F
for M-PPM, γp,m
= T2π
= M 2π
Ts = M γp,m .
s /M
M-FSK and M-PPM have the same required energy at the
F
P
= Epr
= Esr , where Esr is the required
receiver, i.e., Epr
average symbol energy to obtain the target BER performance
P¯e . In Rayleigh fading channels, this value can be obtained
from the formula given in [4]. Then, according to our path-loss
channel model describe in (2), the transmitted pulse energy are
EpF = EpP = Ml G1 Esr dK .
At the receiver demodulator, the circuit works the same
amount of time to detect received signals. Thus, the receiver
circuit energy consumption for both M-FSK and M-PPM is
Pcr Ts .
−4
10
BER (P¯e )
16
−5
10
2 4
8
M
Fig. 1. Comparison results of M-FSK and M-PPM under Rayleigh fading
channel as a function of modulation size M and BER requirement. Below
the surface: PPM-advantageous region; above the surface: FSK-advantageous
region.
Substituting all these parameters into (3) and (4), the
difference between the average battery energy consumptions
of M-FSK and M-PPM is obtained as:
2π 2Ml2 G21 ω(1+α)2 2 2K M−1 PctTs
Esr d + 2
ΔE0FP= (1 − M )
Ts V η 2 log2 M
M ηlog2 M
2K
= k2 d + k0 ,
(5)
2π 2 M 2 G2 ω(1+α)2 2
< 0 and k0 =
where k2 = (1 − M ) Ts Vl η21log M Esr
2
M−1 Pct Ts
M 2 η log2 M > 0. Thus, it is obtained that
1
2K
Proposition 1 There is a critical distance dc = − kk02
such that when the internode transmission distance d < dc ,
M-PPM consumes less battery energy than M-FSK and vice
versa.
The critical distance and the advantageous operation region
for both FSK and PPM are plotted in Fig. 1 with system
parameters given in Table II.
The comparison between M-PPM and M-FSK presented in
this section shows that the slight nonlinearity of the battery
is actually not negligible. If no battery nonlinearity were
considered, then we would expect that M-PPM is always
preferred since it costs less transmitter circuit power consumption. However, the comparison result shows that M-FSK is
preferred when internode transmission distance is sufficiently
large since M-FSK has a lower pulse amplitude thus higher
battery discharge efficiency.
IV. C OMMUNICATION L INK S ELECTION : R ELAY OR N OT
R ELAY ?
A. Single Relay Node Cooperation
In this paper, we only consider the case that a single relay
node is utilized to assist the communication. The primary
R
d
=
1
,
θ 1d
S1
Fig. 2.
d2
P1
=θ
2 d,
P2
S2
d, P̄e
Communication with possible single relay node assistance.
communication nodes are the source node S1 and the destination node S2 . Then a relay node R exists as shown in
Fig. 2. The relay node R can show anywhere in the twodimensional space. There are two candidate links for the endto-end communication from S1 to S2 , namely the single-hop
direct link S1 –S2 and the two-hop relay link S1 –R–S2 . We
denote the distance of S1 –S2 as d, the distance of S1 –R as
d1 = θ1 d, and R–S2 as d2 = θ2 d. Straightforwardly, θ1 and
θ2 satisfy conditions θ1 , θ2 > 0 and θ1 + θ2 ≥ 1. The linear
relay node placement is a special case with θ1 + θ2 = 1.
Without loss of generality, we adopt a simpler modulation
scheme, namely baseband binary phase-shift keying (BPSK)
for analysis simplicity. Under the Rayleigh fading channel with
coherent detection at receiver, the average BER at high signalto-noise ratio (SNR) is approximated as [14, Chapter 3]:
N0
,
(6)
Pe =
4Er
where Er is the signal energy at receiver. In addition, for the
relaying link, Decode and Forward (DF) relaying protocol is
considered first. It is shown later that DF and Amplify and
Forward (AF) protocols are identical at high SNR.
B. Total Battery Energy Consumption for Direct Transmission
Considering baseband BPSK modulation over the Rayleigh
fading channel, γpB = T1p according to Table I. Substituting (6)
into (3) and (4), the total battery energy consumption of the
direct transmission S1 –S2 , denoted as ED , can be expressed as
an explicit function of the direct-link transmission distance d
and the target BER P̄e :
ED = l 2
where l2 =
(Pct +Pcr )Tp
.
η
d2K
dK
+
l
+ l0 ,
1
P̄e2
P̄e
Ml2 G21 ω(1+α)2 N02
,
16Tp V η 2
l1 =
Ml G1 (1+α)N0
,
4η
(7)
and l0 =
Notice that ED can be regarded either as a
quadratic function of P̄e−1 for a given S1 -S2 distance d, or
as a quadratic function of dK with some desired P̄e .
C. Total Battery Energy Consumption for Relaying Transmission
When the relay link is deployed using the DF protocol, the
relay node R first demodulates the signal from the source and
then forwards the remodulated signal to the destination. Therefore, the relay link S1 –R–S2 can essentially be separated into
two decoupled links S1 –RD and RF –S2 , each having received
pulse energy Epr,i and transmission distance di = θi d, for
i = 1, 2. As a result, the total battery energy consumption for
the S1 –R–S2 link can be simply expressed as the summation
of the energy consumption of the two decoupled links.
Due to the inversely proportional relationship between the
received pulse energy and the average BER given in (6),
the energy distribution among the source node and the relay
node is exclusively determined by the average BER of the
two decoupled links, denoted by P1 and P2 respectively. The
overall average BER for the relay link can be tightly upper
bounded using P1 and P2 as P̄e ≤ 1 − (1 − P1 )(1 − P2 ) =
P1 + P2 − P1 P2 . In practice, the desired BER is usually
small (P̄e ≤ 10−3 ), which means P1 + P2 P1 P2 and
therefore P̄e ≈ P1 + P2 . The latter will be considered as the
error performance constraint for the relaying transmission in
the sequel, and the total battery energy consumption can be
rewritten in terms of P1 as
2K
K
d
d1
d2K
dK
2
2
ER (P1 )=l2 1 2 +
+
+l
+2l0 , (8)
1
P1
P1
P̄e − P1
(P̄e − P1 )2
with constraint 0 < P1 < P̄e . Obviously, in this expression it is
seen that with relaying, an extra l0 battery energy consumption
term is introduced which is caused by the extra circuit energy
consumptions of the relay node.
Now the energy optimization problem is introduced: given
the relay location d, the relative position of the relay node with
respect to the primary nodes captured by θ1 and θ2 , and the
objective overall objective BER performance P¯e , an optimal
energy allocation strategy should be adopted to obtain the S1 –
R link BER performance P1 to minimize the total battery
energy consumption ER (P1 ); that is,
ER = min ER (P1 ), subject to 0 < P1 < P̄e ,
(9)
P1
where ER (P1 ) is given by (8).
It turns out that the first-order term in the total battery
energy consumption ER (P1 ) formula for the relay link in
(8) dominates the total energy consumption within the BER
range of 0 < P1 < P̄e . Therefore, those second-order terms
can be temporarily discarded during the energy allocation
optimization process with negligible effect on the optimality.
After removal of the second-order term, the first-order total
battery energy consumption
K becomes
d1
dK
2
1
ER (P1 ) = L1
+
(10)
+ 2L0 .
P1
P̄e − P1
To find the P1 for minimization, taking the derivative of
ER1 (P1 ) with respect to P1 and setting it to zero, it is obtained
that:
K
2
K
K 2
d2 − dK
(11)
1 P1 + 2d1 P̄e P1 − d1 P̄e = 0 ,
which is a quadratic equation in terms of P1 . Note that
the root of this equation only depends on the distance ratio
d2 /d1 = θ2 /θ1 and the overall target BER P̄e . It has nothing
to do with the battery consumption formula coefficients L1
and L0 . The quadratic equation has well-established simple
root expressions. Within the range of 0 < P1 < P̄e , (11)
always has a single positive root, and the suboptimal P1 can
be obtained as:
K
(θ2 /θ1 ) 2 + 1
and P2so = P̄e − P1so =
P̄e ,
−50
(θ2 /θ1 )
(θ2 /θ1 )
K
2
K
2
+1
−40
P̄e .
It is already shown in [7] that the total energy consumption
with this suboptimal P1so approaches that with the theoretical
optimal solution to Eq. (9).
Substituting P1so back into (8), the total battery energy
consumption ER for the relay link S1 –R–S2 can be obtained
2 K
2K
L2 K2
as:
K
K
2
ER =
θ
θ
d
+
θ
+
θ
1
2
1
2
P̄e2
2
K
L1 K2
θ1 + θ22
+
dK + 2L0 .
(12)
P̄e
With this result, the next question to be addressed is: in
order to achieve higher battery energy efficiency, whether or
not, and under what conditions, should the relay link S1 –R–S2
be chosen rather than the direct link S1 –S2 .
D. Relay Selection Criterion
To compare the direct and relaying transmissions in terms of
the battery energy efficiency, the difference of the total battery
energy consumptions between the direct and the optimal
relaying transmissions, denoted as ΔE DR , is evaluated. The
sign of the difference will reveal the more efficient one: direct
link outperforms the relay link if the difference is negative,
and vice versa.
ΔE DR can be readily obtained by taking the difference of
(7) and (12):
ΔE DR(θ1 , θ2 ) = ED − ER
2 K
K
K 2
L2
K
K
2
2
θ1 +θ2
d
=
1− θ1 +θ2
P̄e2
2
K
K
L1
+
1− θ12 +θ22
dK −L0 , (13)
P̄e
−30
−20
0
10
20
30
40
50
−50
−40
−30
−20
−10
0
x (m)
10
20
30
40
50
(a)
−60
−40
 EDR=0
−20
relay zone
0
20
40
no−relay zone
60
−60
−40
−20
0
x (m)
20
40
60
(b)
−100
which is a quadratic function of dK . The constant term is
negative. This is resulted from the fact that the relaying
transmission consumes more distance-independent transceiver
circuit energy than the direct transmission. As a result, the
relay selection criterion can be obtained as following:
 EDR=0
−80
−60
−40
−20
y (m)
Proposition 2 For a relay node with distances θ1 d and
θ2 d apart from the primary nodes, choose direct link if
ΔE DR (θ1 , θ2 ) < 0; otherwise, choose relay link.
The numerical results for primary nodes located at
(−d/2, 0) and (d/2, 0) using the system parameters in Table
II are presented in Fig. 3. These figures show the relay
and no-relay zones. Also, we can see that the nearer the
relay node is to the center of the primary nodes, the more
battery energy can be saved (darker as shown in the figure).
Thus, within the curve ΔE DR (θ1 , θ2 ) = 0 is the batteryenergy saving area. Comparing Figs. 3.(a)-(c), we can see
that as the distance between the primary nodes increases,
the battery-energy saving area enlarges. For example, when
d = 100m, relay node place anywhere cannot reduce the
total battery energy consumption; while when d = 200m,
nearly any relay node between the primary nodes can be
no−relay zone
 EDR<0 everywhere
−10
y (m)
1
y (m)
P1so =
relay zone
0
20
40
60
no−relay zone
80
100
−100
−50
0
x (m)
50
100
(c)
Fig. 3. The position of the relay node: inside the curve, choose relaylink communication; outside the curve, choose direct-link communication.
The solid dots are the primary nodes. (a) d = 100m. (b) d = 150m. (c)
d = 200m.
the DF transmission, all the analyses for DF also hold for AF.
In other words, the two relaying protocols are equivalent in
terms of the relay selection over Rayleigh fading channels at
high SNR.
 =
1 2
x=0, y=y
80
max
60
40
1=1−2
x=x
, y=0
y (m)
20
max
0
−20
−40
−60
−80
−80
−60
−40
−20
0
x (m)
20
40
60
80
Fig. 4. The ellipse to approximate the energy-saving area for d = 200m.
Solid curve: the energy-saving area calculated by numerical computing;
dashed curve with stars: the elliptical approximation.
utilized for better battery energy efficiency. This is because
while the extra circuit consumptions caused by relaying is a
distance-unrelated constant, relaying can reduce more energy
consumptions for combatting the channel fading in longerdistance communications.
Interestingly, the energy-saving area can be approximated by
an ellipse as shown in Fig. 4. With current coordination setup,
2
2
the expression for the ellipse can be written as: xx2 + yy2 =
max
max
1, where the parameters xmax and ymax can be calculated by
taking two special points on the curve with θ1 = 1 − θ2 and
θ1 = θ2 , respectively. Thus, in real applications, one can just
check whether there are any relay nodes within the elliptical
area to utilize the cooperative communication for better battery
energy efficiency.
E. AF and DF Equivalence in Our Scenario
For the AF protocol, the relay amplifies what it receives
from the source, including the noise, and forwards to the
destination. With two links S1 –R and R–S2 , the AF relaying
transmission follows the same total battery energy consumption formula as the DF case as illustrated in the following:
Denote the SNR for the two links as ρ1 = Epr1 /N0 and
ρ2 = Epr2 /N0 . Using the AF protocol, the received signal
at the destination essentially involves two parts: useful signal
Epr2 · ρ1 /(ρ1 + 1) and noise Epr2 /(ρ1 + 1) magnified at the
relay node. Therefore, the overall SNR for the relay link S1 –
R–S2 is ρ = (Epr2 ·ρ1 /(ρ1 + 1))/(N0 + Epr2 /(ρ1 + 1)). Taking
the reciprocal of ρ, it is obtained that 1/ρ = (1/ρ2 ) · ((ρ1 +
1)/ρ1 )+1/ρ1 ≈ 1/ρ1 +1/ρ2 , where the approximation comes
from the fact that the practical desired is small and thus only
the medium to high SNR, i.e. ρ1 1, is considered. Due
to the relationship in (6), the average BER constraint for the
AF relaying transmission is obtained as the following: P̄e =
P1 + P2 , which is identical to that in the DF case. Since
the AF relaying transmission shares the same battery energy
consumption formula and BER performance constraint with
V. C ONCLUSIONS
In this paper, we introduce a realistic node model to
optimize the system energy efficiency in wireless sensor
networks (WSN) by taking into account both circuit power
consumptions and battery nonlinearity. Under this model, we
first choose a more battery-energy-efficient modulation scheme
for the entire network and then, we select either single-hop
direct-link or multi-hop relay-link communication to further
reduce the total battery energy consumption. For modulation
selection, new understandings on the battery energy efficiency
of modulation schemes are facilitated by our case study of
comparing M-FSK and M-PPM, which are traditionally considered as identically energy efficient, and it is found that the
selection criterion relies on the internode transmission distance
of the wireless network. For communication link selection,
the multi-hop transmission is shown to be not always more
battery energy efficiency and the criterion for selecting singleor multi-hop transmissions depends on both the transmission
distance and the relative position of the relay node with respect
to the primary nodes.
R EFERENCES
[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey
on sensor networks,” IEEE Communications Magazine, vol. 40, no. 8, pp.
102–114, August 2002.
[2] S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-constrained modulation
optimization,” IEEE Trans. on Communications, vol. 4, no. 5, pp. 2349–
2360, September 2002.
[3] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity
in wireless networks: Efficient protocols and outage behavior,” IEEE Trans.
on Information Theory, vol. 50, no. 12, pp. 3062–3080, December 2004.
[4] Q. Tang, L. Yang, G. B. Giannakis, and T. Qin, “Battery power efficiency of PPM and FSK in wireless sensor networks,” IEEE Trans. on
Communications, vol. 6, no. 4, pp. 1308–1319, April 2007.
[5] F. Qu, D. Duan, L. Yang, and A. Swami, “Signaling with imperfect
channel state information: A battery power efficiency comparison,” IEEE
Trans. on Signal Processing, vol. 56, no. 9, pp. 4486–4495, September
2008.
[6] D. Duan, F. Qu, L. Yang, A. Swami, and J. C. Principe, “Modulation
selection from a battery power efficiency perspective,” IEEE Trans. on
Communications, vol. 58, no. 7, pp. 1907–1911, July 2010.
[7] W. Zhang, D. Duan, and L. Yang, “Relay Selection from a Battery Energy
Efficiency Perspective,” IEEE Trans. on Communications, vol. 59, no. 6,
pp. 1525–1529, June 2011.
[8] J. Proakis, Digital Communications, 4th ed. McGraw-Hill, New York,
February 2001.
[9] S. Lakkavalli, A. Negi, and S. Singh, “Stretchable architectures for next
generation cellular networks,” in Proc. of the Intl. Symp. on Advanced
Radio Tech., 2003, pp. 59–65.
[10] J. Song, H. Lee, and D. Cho, “Power consumption reduction by multihop transmission in cellular networks,” in Proc. of Vehicular Tech. Conf.,
vol. 5, 2004, pp. 3120–3124.
[11] K. Schwieger and G. Fettweis, “Power and energy consumption for
multi-hop protocols: A sensor network point of view,” in International
Workshop on Wireless Ad-hoc Network, IWWAN 2005, vol. 1, 2005.
[12] M. Pedram and Q. Wu, “Battery-powered digital CMOS design,” IEEE
Trans. on VLSI Systems, vol. 10, no. 5, pp. 607–607, 2002.
[13] T. S. Rappaport, Wireless Communications: Principles and Practice,
2nd ed. Prentice-Hall, 2002.
[14] D. Tse and P. Viswanath, Fundamentals of Wireless Communications.
Cambridge University Press, 2005.