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401978-1-4799-5296-0/14/$31.00 © 2014 IEEE
PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014
A “Raised-Fractional-Power”
Wireless Transmitter Power Consumption ModelN. Zogovic, G. Dimic, and D. Bajic
Abstract—Wireless communications afford mobility and flex-ible network topologies of computer networks. However, theirenergy efficiency must keep improving. Since the major powerconsumer in a wireless transmitter is the power amplifier, energyefficiency can be improved by reducing transmit power dependingon the channel conditions and performance metrics. We proposea novel transceiver power consumption model for Class A, ABand B power amplifiers. It is a better fit than the existing affinemodel of the total transmitter power consumption, as a functionof the transmit power. In the model, we explicitly upper- andlower-bound transmit power.
I. INTRODUCTION
The energy efficiency (EE) of wireless communications
[bit/Joule] has become an important issue in wireless networks
[1], [2]. A major boost to EE can be achieved by adapting the
transmit power, i.e. power delivered to antenna, pt, to channel
attenuation change, because the dominant power consumer
in a transceiver is the transmitter power amplifier (PA) [2],
[3]. Since the control mechanism for pt is not clearly stated
in previous work [4]–[8], there is some ambiguous in EE
modeling from the perspective of communications protocols,
so we try to address the problem of modeling by considering
pt control mechanism focusing on component level, as defined
in [2].
The dominantly used wireless transmitter power consump-
tion model is an affine transformation pt → pTX, where pTX
is the total power consumption at transmitter [2], [9]. In other
models, it is typically assumed that pt is proportional to dn,
where d is the transmitter-to-receiver distance, and n ≥ 2, [9];
this comes from modeling the channel loss over a wireless link
L ∼ dn.
For most types of PAs, the PA efficiency increases with pt[7], [8]. In [8], it is proposed that pTX ∼ d−
n
m , where m is
the efficiency degradation factor. For simulated Class A and
C transmit PAs, m = 2.6 and 2.8 is obtained, respectively [8].
In [10], the model pTX ∼ √pt, with explicit bounds pt ∈
[pt,min, pt,max] and pt dependent on L, is proposed.
We reconsider the pt → pTX model, by analyzing possible
control of pt in the Class A, AB, and B, linear PAs. We
avoid using L and propose a transformation pTX (pt) ∼ ptwith
explicitly bound pt ∈ [pt,min, pt,max], where v ∈ [0, 1]. The
model verification using data of real transceivers shows that it
Nikola Zogovic and Goran Dimic are with the Institute Mihajlo Pupin,University of Belgrade, Belgrade, Serbia, e-mail: nikola.zogovic@pupin.rs,goran.dimic@pupin.rs.
Dragana Bajic is with the Faculty of Technical Sciences, University of NoviSad, Novi Sad, Serbia, e-mail: dragana.bajic@gmail.com.
This work was supported in part by grants TR32043 and III43002 of theMinistry of Education and Science of the Republic of Serbia.
Figure 1. Wireless transceiver block-scheme
approximates pTX (pt) more accurately than the affine model
does. Data fitting indicates that v > 1m
for m = 2.6 or 2.8. The
adapted model applies to any topology and any deterministic
or probabilistic model of L.
II. POWER AND ENERGY CONSUMPTION MODEL
A. Transceiver Power Consumption Components
Wireless transceiver consists of transmitter (TX) and re-
ceiver (RX) sections. Typical transmitter and receiver block
schemes are given in [11], reproduced here for convenience in
Fig. 1.
The following blocks make a transceiver: digital-to-analog
converter (DAC), radio frequency synthesizer (RFS), upcon-
version/downconversion mixer (mix), power amplifier (PA);
low-noise amplifier (LNA), baseband amplifier (BA), base-
band anti-aliasing filter (AAF), and analog-to-digital converter
(ADC). In equations below, p denotes power and suffixes de-
note the transceiver blocks. The total transmitter and receiver
power consumptions, pTX and pRX, are [11]
pTX = pDAC + pRFS + pmix + pPA (1)
pRX = pLNA + pRFS + pmix + pBA + pAAF + pADC.(2)
The purpose of transmitter PA is to amplify the signal to the
specified power level, pt, and feed it to the antenna. Hence, PA
power consumption, pPA, depends on the desired level of pt,
e.g. [12], and so does pTX, c.f. (1). The PA is the dominant
power consumer with a wide range of power consumption,
whereas power consumption of every other block is constant.
Thus, pRX in (2) is constant for any received signal power,
pr, e.g. [12]
402
Figure 2. A general scheme of power amplifier
pRX = const. (3)
B. A Simple Power Amplifier Power Consumption Model
Definition 1. The PA efficiency, ηPA, is
ηPA =pt
pPA(4)
It is desirable to have as large PA efficiency as possible, i.e.
ηPA → 1, with preserved linearity of the PA. The challenge
is that increased ηPAcomes at the expense of compromised
linearity of the amplifier. The PA efficiency vs. linearity trade-
off has led to evolution of several classes of power amplifiers,
such as A, AB, B, C, D, E and F, e.g. [13]. In Classes A, AB
and B, the output stage transistor of the PA operates in linear
regime thereby preserving input signal envelope (e.g. [13]).
We consider linear power amplifiers in Class A, AB and B,
with transmit power within range, pt ∈ [pt,min, pt,max].For a general scheme of PA see e.g. Fig. 15.1 in [13],
reproduced here for convenience in Fig. .
We describe a PA power consumption model using the
following simplifying assumptions, where VDD is the power
supply voltage:
1) PA output stage transistor conducts from 0 to VDD
output voltage.
2) The output stage transistor drain (or collector) volt-
age and current are vDS = VDS+IrfRL sin (ω0t) and
iD = ID + Irf sin (ω0t), respectively, where ω0 = 2πf0,
f0 is the signal carrier frequency, and T is the symbol
duration, T ≪ 1f0
. VDS, ID are bias voltage and current.
RL is the output resistance. Irf is the amplitude of the
current fed to the antenna.
The output transistor conducts if vDS (t) > 0 and iD (t) > 0.
The portion of an RF cycle that the output transistor conducts
is called conduction angle, 2φ. We show how setting of
VDS, ID, and VDD, shapes pPA (pt) and ηPA (pt).Class A PA (2φ = 2π) output voltage is vout =
−IrfRL sin (ω0t) and the power delivered to the antenna,
averaged over T , is pt =12I2rfRL. Hence,
pPA = VDDID, Irf =
√
2ptRL
. (5)
For Class A PA with variable output power:
Irf,min ≤ Irf ≤ Irf,max⇒ ηPA ∈ (0, 0.5). At the PA output
stage, pt is adapted by 3 approaches [13]–[15]:
1) Fix bias and supply voltage,
(VDS, ID) = (Irf,maxRL, Irf,max), VDD = Irf,maxRL.
(5) ⇒ pPA = const, so that (4) ⇒ ηPA ∼ pt.
2) Adapt bias, but fix supply voltage,
(VDS, ID) = (IrfRL, Irf), VDD = Irf,maxRL. (5)
⇒ pPA ∼ √pt, so that (4) ⇒ ηPA ∼ √
pt.
3) Adapt both bias, and supply voltage,
(VDS, ID) = (IrfRL, Irf), VDD = IrfRL. (5)
⇒ pPA ∼ pt, so that (4) ⇒ ηPA = const.
Class B PA (2φ = π) output stage consists of a turns-ratio-
n transformer and two push-pull configured transistors [13],
[14]. Averaging over T
pPA =2
πVDDIrf , pt =
n2
2I2rfRL, (6)
[13], [14]. In Class B ηPA ∈(
0, π4
)
, for Irf ∈(
0, VDD
n2RL
)
.
There are two approaches to adapt pt at the PA output stage
[13], [14]:
1) Fix supply voltage, VDD = Irf,maxn2RL. (6) ⇒ pPA ∼√
pt, so that (4) ⇒ ηPA ∼ √pt.
2) Adapt supply voltage, VDD = Irfn2RL, by varying Irf .
(6) ⇒ pPA ∼ pt, so that (4) ⇒ ηPA = const.
Class AB PA (π ≤ 2φ ≤ 2π) is a hybrid of Class A and Class
B PAs. There are two approaches to adapt pt at the PA output
stage [13]–[15]:
1) Adapt bias, but fix conduction angle and supply
voltage, (VDS, ID) = (−IrfRL cosφ,−Irf cosφ),VDD = 1
2πRLIrf,max (2φ− sin 2φ). Then
pPA = VDDID ⇒ pPA ∼ √pt, so that (4)
⇒ ηPA ∼ √pt.
2) Adapt bias and supply voltage, but fix conduc-
tion angle, (VDS, ID) =(−IrfRL cosφ,−Irf cosφ),VDD = 1
2πRLIrf (2φ− sin 2φ). Then pPA = VDDID ⇒
pPA ∼ pt, so that (4) ⇒ ηPA = const.
a) A simple pPA model: Taking into account power
consumption of PA and the approaches to adapt PA output
power, we propose
pPA = pPA +∆pPA
(
pt
pt,max
)v
;
v ∈ {0, 0.5, 1} , pt ∈ [pt,min, pt,max] , (7)
where pPA and ∆pPA are constants with unit of measurement
[W]. pPA accounts for minimum fixed PA power consump-
tion and ∆pPA accounts for variation of total PA power
consumption from minimum to maximum. v depends on the
approach to adapt PA output power. Ratio pt
pt,maxnormalizes
the argument of the (.)v
operation to the range[
pt,min
pt,max, 1]
,
while the normalized argument is a number with no unit
of measurement. In practice, pt power levels are discrete.
However, we assume that pt can be adjusted continuously,
which facilitates the analysis below.
403
C. Transmitter Power Consumption Model
Starting from (7) and taking into account (1), we develop a
transmitter power consumption model:
1) Total constant power consumption at the transmitter is
accounted for by the minimum total transmitter power,
pTX,min. It is analogous to pPA from (7) and corresponds
to the minimum transmit power, pt,min.
2) Total variation in the transmitter power consumption
is modeled by the difference between its maximum,
pTX,max, and minimum, pTX,min. It is analogous to
∆pPA from (7), and accounts for changes in pTX due
to changes in output power level, pt ∈ [pt,min, pt,max].3) Exponent v is in the range v ∈ [0, 1], rather than having
discrete values as in (7). This facilitates modeling of
the influence of various PA properties, which were not
accounted for in the simple model (7).
Definition 2. Transmitter power consumption, pTX, is the best
fit, in the least squares sense, of the curve between the points
of minimum and maximum total transmitter power, pTX,min
and pTX,max, respectively, depending on the transmit power,
pt ∈ [pt,min, pt,max]:
pTX (pt) =
pTX,min + (pTX,max − pTX,min)
(
pt − pt,min
pt,max − pt,min
)v
, (8)
where v ∈ [0, 1] is the fitting parameter. Alternatively,
pTX (pt) = p0 + ρx (pt)v,
p0 = pTX,min,
ρ = pTX,max − pTX,min, (9)
x (pt) =pt − pt,min
pt,max − pt,min
.
The definition of x (pt) in (9) enables existence of a
fixed point (pt, pTX) = (pt,min, pTX,min), irrespective of the
value of v. Ratiopt,max
pt,minis typically at least 20dB. Thus, the
difference pt
pt,max− x (pt) =
pt,min
pt,max· pt,max−pt
pt,max−pt,minis negligible
relative to pt
pt,max. Finally, pt ∈ [pt,min, pt,max] ⇒ x ∈ [0, 1].
D. Model Fitting for Real Transceivers
Table I provides transceiver power settings1. The first six
transceivers are suitable for low-power communications in
personal area networks (PAN) and WSN. The following two
transceivers conform to the IEEE 802.11 standard (WiFi). The
last two rows show power settings for two power amplifiers
for WiMAX transmitters.
The model (9) is fitted using nonlinear least squares, for
power law, to evaluate optimal v, using data provided in
manufacturers data sheets. Fig. 3 shows pTX (pt) curve fitting
for CC1101 transceiver and affine approximation (v = 1).
1Data sheets are available at the following URLs: for transceivers no. 1, 2,5, and 6 at www.ti.com; no. 3 at www.semtech.com; no. 4 at www.atmel.com;no. 7 and 8 at http://para.maxim-ic.com; and for power amplifiers 9 and 10at www.analog.com.
Table ITRANSCEIVER MODEL SETTINGS (FIXED)
Power in [mW].
No. Transceiver pt,min pt,max pTX,min pTX,max pRX
1 CC1000 0.010 3.16 25.8 76.2 28.8
2 CC1101 0.001 10.00 36.3 97.2 46.8
3 SX1211 0.079 10.00 39.6 84.8 9.9
4 AT86RF212 0.079 10.00 31.5 74.4 27.6
5 CC2420 0.003 1.00 25.5 52.2 56.4
6 CC2500 0.001 1.26 29.7 64.5 39.9
7 MAX2830 1.170 165.96 642.0 1335.6 173.6
8 MAX2831 1.000 237.14 588.0 1062.6 173.6
9 ADL5570 5.250 426.30 672.0 2310.0 -
10 ADL5571 25.000 741.31 1085.0 3650.0 -
0 2 4 6 8 100
10
20
30
40
50
60
70
80
90
100
pt [mW]
pT
X [m
W]
data
vopt
v = 1
Figure 3. CC1101 pTX (pt) curve fitting: vopt = 0.58
The relative fitting error on sample i is
epTX,rel (i) =pTX (i)− pTX (i)
pTX (i)100%,
where pTX is the true value (from data sheet), and pTX is
the value obtained by fitting the model (9). The mean and
root mean square of relative fitting error, on the set of NS
samples, are µpTX,e and σpTX,e, respectively
µpTX,e =1
NS
NS∑
i=1
epTX,rel (i) , σpTX,e =
√
√
√
√
1
NS
NS∑
i=1
e2pTX,rel (i).
Fig. 4 shows epTX,rel versus pt for CC2420, AT86RF212 and
MAX2831 transceivers for vopt and v = 1.
Table II shows vopt; as well as µpTX,e [%] and σpTX,e [%]
for vopt and v = 1. The rightmost column of Table II showspt,max
pt,minin [dB]. Ratio
pt,max
pt,minis at least 20dB for transceivers,
as claimed in justification of (9).
The presented results indicate the merit of the model (9). It
better fits real transceivers than the affine model (v = 1). The
proposed model is valid for a wide range of transmit power,
from PANs via WiFi to WiMAX.
Fig. 3 indicates that the curvature of pTX (pt) has non-
negligible influence on power consumption or performance.
For pTX (v = vopt) = pTX (v = 1), fixed at some value, the
404
0 50 100 150 200 250−20
0
20MAX2831
pt [mW]
0 2 4 6 8 10 12−20
0
20AT86RF212
ep
TX,r
el
[%]
0 0.2 0.4 0.6 0.8 1 1.2−20
0
20CC2420
vopt
v = 1
vopt
v = 1
vopt
v = 1
Figure 4. pTX (pt) curve fitting residuals for vopt and v = 1
Table IIFITTED AND DERIVED TRANSCEIVER MODEL PARAMETERS
vopt, err [%] v = 1, err [%]pt,max
pt,min
Transceiver vopt µpTX,e σpTX,e µpTX,e σpTX,e [dB]
CC1000 0.64 - 0.56 4.69 9.84 12.62 25.0
CC1101 0.58 1.06 4.68 9.87 11.67 40.0
SX1211 0.60 - 0.25 1.12 7.96 9.76 21.0
AT86RF212 0.77 - 0.36 3.36 4.67 6.92 21.0
CC2420 0.48 - 0.04 1.48 10.65 12.89 25.0
CC2500 0.55 - 0.55 4.23 7.82 10.54 31.0
MAX2830 0.80 - 0.14 0.73 3.37 4.10 21.5
MAX2831 0.67 - 0.30 1.95 4.34 5.64 23.8
ADL5570 0.72 - 1.01 3.04 7.96 9.95 19.1
ADL5571 0.69 - 0.78 3.47 10.46 12.16 14.7
curvature causes pt (v = vopt) ≤ pt (v = 1) because
pt (v = vopt)− pt,min
pt (v = 1)− pt,min
=
(
pt (v = 1)− pt,min
pt,max − pt,min
)1
v−1
≤ 1,
where equality holds at pt = pt,min or pt = pt,max. This
motivates analysis of the influence of v on energy efficiency
of wireless links, with adaptable pt.
III. CONCLUSION
We have proposed a novel transceiver power consumption
model, pTX (pt), suitable for adaptive transmission power
control. The model is obtained from an analysis of the
electronics of the power amplifier, as the dominant power
consumer in a transceiver. We have shown that the proposed
model is a tighter approximation of a real transceiver power
consumption than the affine model. The model explicitly
bounds pt ∈ [pt,min, pt,max].
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