Idea Consumption Factor and Power-Efﬁciency Factor A Theory for Evaluating the Energy Efﬁciency...

7/28/2019 Idea Consumption Factor and Power-Efciency Factor A Theory for Evaluating the Energy Efciency of Cascaded Communication Systems

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 32, NO. 12, DECEMBER 2014 1

Consumption Factor and Power-Efficiency Factor:A Theory for Evaluating the Energy Efficiency of

Cascaded Communication SystemsJames N. Murdock, Member, IEEE and Theodore S. Rappaport, Fellow, IEEE

AbstractThis paper presents a new theory, called the con-sumption factor theory, to analyze and compare energy efficientdesign choices for wireless communication networks. The ap-proach presented here provides new methods for analyzing andcomparing the power efficiency of communication systems, thusenabling a quantitative analysis and design approach for greenengineering of communication systems. The consumption factor(CF) theory includes the ability to analyze and compare cascadedcircuits, as well as the impact of propagation path loss on the totalenergy used for a wireless link. In this paper, we show severalexamples how the consumption factor theory allows engineers tocompare and determine the most energy efficient architecturesor designs of communication systems. One of the key conceptsof the consumption factor theory is the power efficiency factor,which has implications for selecting network architectures orparticular cascaded components. For example, the question ofwhether a relay should be used between a source and sinkdepends critically on the ratio of the source transmitter power-efficiency factor to the relay transmitter power-efficiency factor.The consumption factor theory presented here has implicationsfor the minimum energy consumption per bit required toachieve error-free communication, and may be used to extendShannons fundamental limit theory in a general way. This workincludes compact, extensible expressions for energy and powerconsumption per bit of a general communication system, andmany practical examples and applications of this theory.

Index TermsPower Consumption, Energy Efficiency, PowerEfficiency, Millimeter-wave, Wireless, Cascaded circuits, Capac-ity, Relay channel.

I. INTRODUCTION

COMMUNICATION systems today, including both wire-

line and wireless technologies, consume a tremendous

amount of power. For example, the Italian telecom operatorTelecom Italia used nearly 2 Tera-Watt-hours (TWh) in 2006

to operate its network infrastructure, representing 1% of Italystotal energy usage [1]. Nearly 10% of the UKs energy usage

is related to communications and computing technologies [1],

while approximately 2% of the USs energy expenditure isdedicated to internet-enabled devices [2]. In Japan, nearly 120

W of power are used per customer in the cellular network

Manuscript received: April 15, 2012, revised: October 12, 2012. Portionsof this work appeared in the 2012 IEEE Global Communications Conference(Globecom).

J. N. Murdock is Texas Instruments, Dallas, TX (e-mail:[email protected]). This work was done while James was a student atThe University of Texas at Austin.

T. S. Rappaport is with NYU WIRELESS at New York University andNYU-Poly,715 Broadway, Room 702, New York, NY 10003 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/JSAC.2014.141204.

[1]. Similar power/customer ratios are expected to hold for

many large infrastructure-based communication systems. [2]

estimates that 1000 homes accessing the Internet at 1 Giga-

bit-per-second (Gbps) would require 1 Giga-Watt of power.

All of these examples indicate that energy efficiency of

communication systems is an important topic. Given the trend

toward increasing data rates and data traffic, energy efficient

communications will soon be one of the most important chal-lenges for technological development, yet a theory that allows

an engineer to easily compare and analyze, in a quantitativefashion, the most energy efficient designs has been allusive.

Past researchers have explored analytical and simulation

methods to compare and analyze the power efficienciesof various wireless networks (see, for example, works in

[3][4][5][6][7][8]). In [3], researchers explored the energy

efficiency in an acoustic submarine channel and illustrated

how the choice of signaling, when matched to the channel,

could approach Shannons limit. In [4], researchers considered

a position-based network routing algorithm that could be

optimized locally at each user, in an effort to reduce overall

power consumption of the network, but were unable to derive

convenient and extensible expressions for power efficiency

that could be generalized to any network. In [5], energy

consumption was compared to the obtainable data rate of end-users, and an analysis technique was used to determine energy

efficiency through the use of distributed repeaters. In [6], anovel bandwidth allocation scheme was devised to optimize

the power consumed in the network while maximizing data

rate, but the analysis was not extensible to a cascaded systemof components, nor could it be easily generalized. [7] illus-

trates how cumbersome and complicated the field of energy

conservation can be in ad-hoc networks, at both the link and

network layers (e.g. the individual wireless link, as well as the

network topology, where both have a strong impact on energy

utilization). In fact, a recent book, Green Engineering [8],illustrates the importance, yet immense difficulty, in providing

an easy, generalized, standardized method for analyzing and

comparing power efficiency in a communications network.

Despite the extensive body of literature aimed at energy

efficient communication systems, we believe this paper is thefirst to present a generalized analysis that allows engineers

to provide a standard figure of merit to compare the power

efficiency (or energy efficiency) of different cascaded circuit

or system implementations over a wide array of problem

domains. The analysis method presented here is general,in that it may be applied to power efficient circuit design,

0733-8716/14/$31.00 c 2014 IEEE

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2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 32, NO. 12, DECEMBER 2014

transmitter and receiver design, and also to various network

architectures such as relay systems (the relay problem in [5]

is validated using the CF theory in this paper).

This work has been motivated by the need to have a

compact, repeatable, extensible analysis method for comparing

the power efficiency of communication systems and networkdesigns. In particular, as cellular communication networks

evolve, the base station coverage regions will continue to

shrink in size, meaning that there will be a massive increase

in the number of base stations or access points, and relays

are likely to complement the base stations over time [9].To accommodate the demand for increased data rates to

mobile users, we envisage future millimeter-wave (mm-wave)

communication systems that are much wider in bandwidth

than todays cellular and Wi-Fi networks. These future systems

will use highly directional steerable antennas and channelbandwidths of many hundreds of MHz thereby supporting

many Gigabits per second data rates to each mobile device

[9] [10][11][12]. As such systems evolve, small-scale fading

in the channel will become much less of a concern, and more

attention will need to be placed on the power effi

cient designof handsets and light weight base stations and repeaters thatuse wideband channels and multi-element phased arrays with

RF amplifiers. The theory presented here aims to aid in the

design of these wideband wireless networks and devices. Asshown in this paper, the CF framework gives communication

engineers a methodology to analyze, compare and tradeoffcircuit and system design decisions, as well as network archi-

tectures (e.g. whether to use relays or small cells, and how

to trade off antenna gain, bandwidth, and power efficiency in

future wireless systems) [9][10][11][12].

In this paper, we provide fundamental insight into the

required power consumption for communication systems, and

create an-easy-to-use theory, which we call the consumptionfactor (CF) theory, for analyzing and comparing any cascaded

communication network for power efficiency. In Section II

we present the consumption factor framework for a homo-

dyne transmitter [12]. Section III generalizes the concept

of power-efficiency analysis, which is fundamental to the

consumption factor framework, for any cascaded communi-

cation system. Section IV provides numerical examples of thepower-efficiency factor used in the consumption factor theory.

Section V presents a general treatment of the consumptionfactor, based on the power-efficiency analysis of the preceding

sections. Section VI demonstrates a key characteristic of the

power-efficiency factor i.e. that gains of components that

are closest to the sink of a communication system reducethe impact of the efficiencies of preceding components. In

Section VII, we use the consumption factor framework to

develop fundamental understandings of the energy price of

a bit of information. We use our analysis to demonstrate how

the consumption factor theory may be applied to designing

energy efficient networks, for example by helping to determine

the best route to send a bit of information in a multi-hop

setting to achieve the lowest energy consumption per bit.

Section VIII provides conclusions. The key contribution of this

paper is a powerful and compact representation of the powerconsumption and energy consumption per bit of a general

communication system. The representation takes the gains

Fig. 1. Block diagram of a homodyne transmitter used to demonstrate thepower-efficiency factor and consumption factor (CF).

and efficiencies of individual signal-path components (such

as amplifiers and mixers) into account. A second key result is

that, in order to align the goals of lower energy per bit and

higher data rates, it is advantageous to design communication

systems that require as little signal power as possible, solow, in fact, that ancillary power drain (e.g. for cooling, user

interfaces, etc.) dominates signal power levels. While this mayseem intuitive, the CF theory proves this, and provides a

tangible, objective way of comparing various designs while

showing the degrees to which communication systems must

reduce ancillary power drain, but must also seek means of

reducing required signal levels even more dramatically than

the ancillary power drain. By making every bit as energy

efficient as possible, we show it is possible to greatly expand

the number of bits that can be delivered for a given amount

of energy. Means of achieving this goal include the use veryshort link distances (such as femtocells) at millimeter-wave

frequencies for future massively broadband wireless systems.Earlier, less developed versions of the consumption factor were

presented in [13].

I I . CONSUMPTION FACTOR FOR A HOMODYNE

TRANSMITTER

We define the consumption factor (CF) for a communication

system as the maximum ratio of data rate to power consumed,

or equivalently as the maximum number of bits that may

be transmitted through a communication system for every

Joule of expended energy. A study of the consumption factor

requires a careful analysis of both the power consumptionand data rate capabilities of a communication system. In this

section, we will provide a simple analysis for a homodyne

transmitter as illustrated in Figure 1, to motivate the theorypresented here. We consider a homodyne transmitter because

this topology is attractive for many massively-broadband sys-

tems due to its low cost and low complexity [12]. We will

generalize our analysis in Section III to be applicable to a

general cascaded communication system.

The homodyne transmitter in Figure 1 is comprised of

components that directly handle the signal, such as the mixerand power amplifier, in addition to components that interact

indirectly with the signal, such as the oscillator. Components

that interact directly with the signal are designated on the

signal path, while components that are not in the path of the

signal are designated off the signal path.



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MURDOCK and RAPPAPORT: CONSUMPTION FACTOR AND POWER-EFFICIENCY FACTOR: A THEORY FOR EVALUATING THE ENERGY EFFICIENCY... 3

A key component of the consumption factor framework is

understanding that the efficiency of each signal path compo-

nent may be used to relate the ancillary or wasted power

of each component to the total signal power delivered by that

component. For example, the efficiency of the power amplifier

is used to find the partial power required to bias the amplifier(which is not used, or wasted, in terms of providing signal path

power) as a component of the total signal power delivered tothe load. We define the efficiency of the power amplifier,PA,

and of the mixer, MIX ,:

PA =PPARF

PPARF + PPANONRF

(1)

MIX =PMIXRF

PMIXRF + PMIXNONRF

(2)

where PPARF is the signal power delivered by the power

amplifier to the matched load, and PMIXRF is the signal power

delivered by the mixer to the power amplifier. PPANONRF and

PMIXNONRF

are the power levels used by the power amplifier,

and mixer, respectively, that do not directly contribute todelivered signal power. Using (1) (2), we find:

PPANONRF = PPARF

1

PA 1

(3)

PMIXNONRF = PMIXRF

1

MI X 1

(4)

The second key step in the consumption factor analysis results

from the realization that the signal powers delivered by each

component in the cascade, PPARF , and PMIXRF , may be related

to the total power delivered by the communication system,

through the gains of each signal path component. As shownin Section III, this formulation for a cascaded systems power

efficiency is reminiscent of Friis classic noise figure analysis

technique for cascaded systems [24]. Using (1)-(4), we nowfind the delivered RF power to the matched load, PRADIORF ,

in terms of the signal power from the baseband signal source

and the various gains stages as:

PRADIORF = PBBSIGG

MIXGPA (5)

PPANONRF = PPARF

1

PA1

= PRADIORF

1

PA1

(6)

PMIXNONRF =PMIXRF

1

MIX1

=PRADIORF

GPA

1

MIX1

(7)

where PBBSIG is the signal power delivered by the baseband

components to the mixer, and GMIXand GPA, are the powergains of the mixer and power amplifier, respectively. Equation

(5) simply states that the power delivered to the matched load

is equal to the power delivered by the baseband components

multiplied by the gain of the mixer and of the power amplifier.

Note that we have implicitly assumed an impedance matched

environment. Impedance mismatches may be accounted for byincluding a mismatch factor less than one in the gain of each

component.

The total power consumption of the homodyne transmitter

may be written as:

PRADIOconsumed = PRADIORF + P

PA

NONRF + PMIXNONRF

+ PBB + POSC (8)

where PBB is the power consumed by the baseband com-

ponents and POSC is the power consumed by the oscillator.

The term PRADIORF is the total signal power in the homodynetransmitter delivered to the load. Using equations (5) through

(7) in (8), we re-write the total homodyne power consumption

as:

PRADIOconsumed = PRADIORF

1+

1

PA1

+

1

GPA

1

MIX 1

+ PBB + POSC (9)

PRADIOconsumed =PRADIORF

1 +

1PA

1

+ 1GPA

1

MIX 1

1

+ P

BB

+ P

OSC

(10)

From (10), the factor1 +

1

PA 1

+ 1

GPA

1

MIX 1

1

plays a role in the transmitter power consumption analogous

to that of efficiency. In other words, this factor may beconsidered the aggregate efficiency of the cascade of the

mixer and power amplifier. In Section III we will generalizethis result and define this factor as the power efficiency factor

for an arbitrary cascaded system (where the cascade may

be either a cascade of components or circuits, or may eveninclude the propagation channel).

Now that we have formulated a compact representation

of the power consumption of a homodyne transmitter, we

must determine the maximum data rate that the transmittercan deliver in order to formulate the consumption factor of

the transmitter. To do this, we assume that the transmitter is

communicating through a channel with gain Gchannel to a

receiver of gain GRX having noise figure F with bandwidth

B. We assume also that the transmitter matched load is

replaced by an antenna with gain GANTTX . The signal power

used by the receiver in the detection process,

PRX , is given by:

PRX = PRADIORF G

ANTTX GchannelG

ANTRX GRX (11)

where GANTRX is the gain of the receiver antenna, and GRX

is the gain of the receiver excluding the antenna. We willassume an AWGN (Additive White Gaussian Noise) channel,for which the received noise power at the detector, Pnoise, is:

Pnoise = K T F B GRX (12)

where K is Boltzmanns constant (1.38x1023 J/K) and T is

the system temperature in Kelvin. The SNR at the receiver

detector is therefore:

SN R =PRADIORF G

ANTTX GchannelG

ANTRX GRX

K T F B GRX(13)

The SNR is related to the minimum acceptable SNR at the

output of the receiver, SN Rmin, as dictated by the modulation



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Fig. 2. An example of the use of the power-efficiency factor to find theconsumption factor of two different cascades of a baseband amp, mixer, andRF amp.

and signaling scheme, through a particular operating margin

MSNR:

SN R = MSNRSN Rmin (14)

The minimum power consumption occurs when MSN R isequal to 0 dB (i.e. MSNR = 1). Solving for P

RADIORF , we

find:

PRADIORF,min =SN RminK T F B

GANTTX GchannelGANTRX

(15)

where we now denote PRADIORF as PRADIORF,min to indicate that

this power level corresponds to the minimum acceptable SNR

at the receiver. The minimum power consumption for the

transmitter is found using (10) and (15) as:

PRADIOconsumed,min =

SNRminKTFBGANTTX GchannelG

ANTRX

1 + 1PA 1 + 1GPA 1MIX 11

+ PBB + POSC (16)

The maximum data rate Rmax at the receiver is given interms of the SNR and the bandwidth according to Shannons

capacity formula if the modulation and signaling scheme are

not specified. If these are specified, then we find the maximum

data rate in terms of the spectral efficiency of the modulation

and signaling scheme sig (bps/Hz):

Rmax = Blog2 (1 + SN R) , General Channel

Rmax = Bsig, Specific Modulation Scheme (17)

The consumption factor, CF, for the homodyne transmitter isthen found by taking the ratio of (17) to (16):

CF =Rmax

PRADIOconsumed,min(18)

CF =Blog2 (1 + SN R)

SNRminKTFB

GANTTX

GchannelGANTRX

1+

1

PA1

+ 1

GPA

1

MIX1

1 + PBB + POSC

(19)

We will assume a standard log-distance channel gain model:

Gchannel = P Go + 10 log10do

d [dB] (20)

Fig. 3. Higher values of power consumption off of the signal path com-ponents result in higher values of SNR needed to maximize the consumptionfactor (CF).

where P Go is the close-in free-space path gain (usually a

large negative number in dB) received at a close-in referencedistance do, d is the link distance ( d >do), and is thepath loss exponent [10][12][19][20]. Two examples for CF

using equation (18) and (19) are shown in Figures 2 and 3.Figure 2 shows how the consumption factor of a 60 GHz

wireless communication system varies as the efficiency of the

power amplifier or the mixer are changed, and indicates that

the efficiency of the power amplifier is much more important

in terms of maximizing the overall system efficiency than the

mixers efficiency. The key lesson from this example is that the

efficiencies of the devices that handle the highest signal power

levels should be maximized in order to have the most dramatic

effect in maximizing the consumption factor. Figure 3 shows

the impact of changing the minimum required SNR at thereceiver. Note that we have assumed an SNR margin of 0 dB.

The figure indicates that higher levels of power consumption

by non-signal-path devices such as the oscillator result inhigher levels ofSNR to maximize the consumption factor. The

figure also indicates an optimum value ofSNR to maximize theconsumption factor. This optimum value depends critically on

the amount of power consumed by devices off the signal path.

Note that in these figures, we have assumed the efficiency and

gain of the mixer are equal. This assumption will be explained

in Section III, where we will find that the gain and efficiency

of an attenuating device are equal (similar to Friis noise figure

analysis). Note that we have used a logarithmic scale in Figure

3 to allow for easy comparison between the different curves.

III. GENERAL CASCADED COMMUNICATION SYSTEMWe will now generalize the consumption factor to provide

a framework for analyzing a general cascaded communication

system.

The consumption factor is defined [18] as the maximumratio of data rate to total power consumption for a commu-

nication system. To determine the consumption factor, we

must first determine a compact representation of the power

consumption of a general cascaded communication system.

Consider a general cascaded communication system as shown

in Figure 4 in which information is generated at a source, andsent as a signal down a signal path to a sink. Signal path

components such as amplifiers and mixers are responsible



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Source

. . .

Sink

. . . . . . . . . .

Signal Path Devices

Non-Signal Path Devices

1 2 N

1 k M

Fig. 4. A general communication system composed of components on andoff the signal path.

for transmitting the information signal to the sink. Non-

signal path components include voltage regulation circuitry,

displays or cooling components that do not participate directly

in the signal path, but do consume power. The total power

consumption of the cascaded communication system in Figure

4 (ignoring the source and sink) may be written as:

Pconsumed = Psig +

Nk=1

Pnonsigk +

Mk=1

Pnonpathk (21)

where Psig is the sum of all signal powers of each component

in the cascade, Pnonsigk is the signal power used by the kth

signal path component but not delivered as signal power tothe next signal-path component, and Pnonpathk is the power

used by the kth component off the signal path. To evaluate

(21), we must consider each component on the signal path

separately. The efficiency of the ith signal path component

may be written as:

i =Psigi

Psigi + Pnonsigi(22)

Where Psigi is the total signal power delivered by the ith stage

to the (i + 1)th

stage, and Pnonsigi is the signal power used

by the ith stage component but not delivered as signal power.

This is a very general representation of efficiency that may be

applied to any communication system component. A similar

measure of efficiency, the PUE (Power Usage Effectiveness),is already used to measure the performance of data centers,

and is the total power used for information technology divided

by the total power consumption of a data center[14].

Let us consider (22) applied to an attenuating stage, such as

a wireless channel or attenuator. Fundamentally, an attenuator

should consume only the signal power delivered to it by

the preceding stage (i.e. the consumption factor theory treatsattenuators as passive components that do not take power from

a power supply). The signal power delivered by an attenuator

to the next stage is a fraction of the signal power delivered to

the attenuator. Therefore, if the ith stage is an attenuator, then

the efficiency of an attenuator, atten, as given by (22) is:

Psigi = GattenPsigi1 (23)

Pnonsigi = (1 Gatten) Psigi1 (24)

atten =GattenPsigi1

GattenPsigi1 + (1 Gatten) Psigi1= Gatten

(25)

where Gatten is the gain of the attenuator, and is less than

one. Thus, we have shown that atten = Gatten for a passivedevice or channel.

The total power consumed by the ith stage on the signal

path may be written:

Pconsumedi = Pnonsigi + Paddedsigi (26)

where Paddedsigi is the total signal power added by theith component, which is the difference in the signal power

delivered to the (i + 1)th

component and the signal powerdelivered to the ith component. We can sum all the signal

powers added by the components on the signal path (fromleft to right in Figure 4) to find:

Ni=1

Paddedsigi = PsigN Psigsource (27)

where Psigsource is the signal power provided by the source,

and PsigN is the signal power delivered by the Nth(and last

stage) signal-path component. Adding (27) to the signal power

from the source, we find that the total signal power in thecommunication system is equal to the signal power delivered

to the sink (in other words, the signal power delivered by the

last stage is equal to the sum of all signal powers delivered

by each component in the cascade):

Psig = PsigN (28)

From (22) the total wasted power of the kth stage (i.e. power

consumed but not delivered to the next signal path stage) may

be related to the efficiency and total delivered signal power

by that stage:

Pnonsigk = Psigk 1

k 1

(29)

Also, the signal power delivered by the kth stage may be

related to the total power delivered to the sink by dividing by

the gains of all stages after the kth stage, (i.e. to the right of

the kth) thus yielding:

PsigN= Psigk

Ni=k+1

Gi (30a)

Pnonsigk =PsigNN

i=k+1 Gi

1

k 1

(30b)

where Gi is the gain of the ith stage. We can therefore

compute the total power consumed by the communicationsystem as the power consumed by the source which is assumed

to equal the signal power delivered by the source, and the three

additional terms that represent the power consumed by the in-

path cascaded components, and the power dissipated by the

non-signal path components:

Pconsumed = Psigsource +

Ni=1

Pconsumedi +

Mk=1

Pnonpathk

(31a)



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Pconsumed = PsigN

1 + 1PsigN

Mk=1

Puknonpathk

+N

k=1

1N

i=k+1

Gi

1

k 1

(33)

H1cascadedsystem =

1+

1N 1

+

1

GN 1

N1 1

+ . . .+1

GN . . . GM+1 1

M 1

+1

GN . . . GM 1

M1 1

+ . . .1

Ni=1

Gi

1

1 1

1

(38a)

H1subsystem2 = 1+

1

N 1

+

1

GN

1

N1 1

+ . . . +

1

GN . . . GM+1

1

M 1

(38b)

H1subsystem1 = 1 +

1

M1 1

+ . . .

1M1

i=1Gi

1

1 1

(38c)

H1cascadedsystem = H1subsystem2 +

1Gsubsystem2

H1subsystem11

(38d)

Hcascadedsystem =Hsubsystem1Hsubsystem2

Hsubsystem1 +Hsubsystem2Gsubsystem2

(1Hsubsystem1)(39a)

limHsubsystem11

Hcascadedsystem =Hsubsystem2 (39b)

of the product of the channel gain with the receiver gain. Inthis case, we find that the overall power-efficiency factor is

approximated by:

Hlink GRX GchannelHTX (42) (42)

This is an important result of this analysis. In particular, it

indicates that in order to achieve a very power-efficient link,

it is desirable to have a high gain receiver and a highly

efficient transmitter. This can be understood by realizing that

a higher gain receiver reduces the output power requirements

at the transmitter. Eqn. (42) indicates the great importance

of the transmitter efficiency. Note, however, that the receiver

efficiency is still important, as from (39b) it is clear that the

receivers efficiency is an upper bound on the efficiency of the

overall link.

IV. NUMERICAL EXAMPLES

To better illustrate the use of the consumption factor theory,

and the use of the power-efficiency factor, consider a simplescenario of a cascade of a baseband amplifier, followed by

a mixer, followed by an RF amplifier. We will consider two

different examples of this cascade scenario, where different

components are used, in order to compare the power effi-

ciencies due to the particular specifications of components.

Assume that for both cascade examples, the RF amplifier is acommercially available MAX2265 power amplifier by Maxim

technology with 37 % efficiency[15]. In both cases, the mixer

is an ADEX-10L mixer by Mini-Circuits with a maximum

conversion loss of 8.8 dB[16]. In the first case, the baseband

amplifier (the component furthest to the left in Figure 4 ifin a transmitter, and furthest to the right if in a receiver)is an ERA-1+ by Mini-circuits, and in the second case thebaseband amplifier is an ERA-4+ [17], also by Mini-Circuits.The maximum efficiencies of these parts are estimated bytaking the ratio of their maximum output signal power to their

dissipated DC power. As the mixer is a passive component,its gain and efficiency are equal. Table 1 summarizes the

efficiencies and gains of each component in the cascade. Using

(35), the power-efficiency factor of the first scenario is

Hscenario 1 =1

10.37+

116.17 10.361+ 10.3616.17 10.1165 1

= 0.2398,

whereas the power-efficiency factor of the second scenario is

Hscenario 2 =1

10.37+

116.17

1

0.361

+ 10.3616.17

10.18361

= 0.2813.

Therefore, we see that the second scenario offers a superior

efficiency compared to the first scenario, due to the better

efficiency of the baseband amplifier, but falls far short of

the ideal power efficiency factor of unity. Using differentcomponents and architectures, it is possible to characterize and

compare, in a quantitative manner, the power-efficiency factor



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TABLE IAN EXAMPLE OF THE USE OF THE POWER -EFFICIENCY FACTOR TO COMPARE TWO CAS CADES OF A BASEBAND AMP, MIXER, AN D RF AM P.

Component Gain Ef ficiencyExample 1MAX2265 RF Amp 24.5 dB (voltage gain of 16.17) 37%ADEX-10L Mixer -8.8 dB 36%ERA-1+BB Amp 10.9 dB 11.65 %Example 2MAX2265 RF Amp 24.5 dB 37%

ADEX-10L Mixer -8.8 dB 36%ERA-1+BB Amp 13.4 dB 18.36%

and consumption factor (see subsequent sections) of cascadedcomponents.

As a second example, consider the cascade of a transmitterpower amplifier communicating through a free-space channel

with a low-noise amplifier at the receiver. Let us assume that

the cascade, in the first case, uses the same RF power amplifier

as in the previous example (MAX2265), while the LNA is

a Maxim Semiconductor MAX2643 with a gain of 16.7 dB

(6.68 absolute voltage gain) [18]. We will assume this LNA

has 100% effi

ciency for purposes of illustrating the impactof the PAs efficiency and the channel (i.e. here we ignore the

LNAs efficiency, although this can easily be done as explained

above). For a carrier frequency of 900 MHz, now consider

the cascade for a second case where the MAX2265 RF poweramplifier is replaced with a hypothetical RF amplifier device

having 45% power efficiency (a slight improvement). Assume

the link is a 100m free space radio channel with gain of -71.5dB. Since the propagation channel loss greatly exceeds the

LNA gain, (42) applies, where HTX is the efficiency of the RFamplifier, so that in the first case using the MAX2265 amplifier

(37% efficiency), the power efficiency factor of the cascaded

system is 173.5e-9, while in the second case (using an RF

Power amplifier with 45% efficiency), the power efficiencyfactor is 211.02e-9. The second case has an improved power-

efficiency factor commensurate with the power efficiency

improvement of the RF amplifier stage in the receiver. These

simple examples demonstrate how the power-efficiency factormay be used to compare and quantify the power efficiencies

of different cascaded systems, and demonstrate the importance

of using higher efficiency RF amplifiers for improved power

efficiency throughout a transmitter-receiver link.

V. CONSUMPTION FACTOR

We now define the consumption factor, CF, and operating

consumption factor (operating CF) for a general communi-

cation system such as that in Figure 4, where CF is defined

as:

CF =

R

Pconsumed

max

=Rmax

Pconsumed,min(43)

operating CF =R

Pconsumed(44)

where R is the data rate (in bits-per-second or bps), and Rmaxis the maximum data rate supported by the communication

system. Further analysis based on only maximizing R or

minimizing Pconsumed is also pertinent to system optimizationin terms of consumed power and carried data rate. For a very

general communication system in an AWGN channel, Rmax

may be written using Shannons information theory accordingto the operational SNR and bandwidth, B:

Rmax = Channel Capacity = Blog2 (1 + SN R) (45)

Or, for frequency selective channels [3]:

Rmax =

B0

log2

1 +

Pr (f)

N(f)

df

= B

0

log21 + |H(f)|

2Pt (f)

N(f) df (46)

where Pr (f), Pt (f), and N(f) are the power spectral densi-ties of the received power, the transmitted power, and the noise

power at the detector, respectively. H(f) is the frequencyresponse of the channel and any blocks that precede the de-

tector. Note that equations (45) and (46) make no assumptions

about the signaling, modulation, or coding schemes used by

the communication system. To support a particular spectral

efficiency sig (bps/Hz), there is a minimum SNR required

for the case of an AWGN channel:

SN R

MSNR= SN Rmin = 2

sig 1 (47)

The operating SNR of the system, as well as the operating

margin of the operating SNR ( denoted by MSNR which

represents the operating margin above the minimum SN Rmin)may be used to find the consumption factor and operating

consumption factor expressed in terms of the systems power-efficiency factor H:

CF =B log2 (1 + SN R)

Pnonpath +

SNRMSNR

PnoiseH

(48a)

CF =B log2 (1 + MSNR(2

sig 1))

Pnonpath + (2sig 1 )PnoiseH

, (48b)

and (49) where we have made use of (34) and the fact thatthe signal-power available to the sink, PsigN is related to the

noise power available to the sink, Pnoise and the SNR at the

sink:

PsigN = Pnoise SN R = K T FB GRX SN R (50)

And where the right hand equality in (50) holds for an AWGNchannel. K is Boltzmans constant (1.38x1023 J/K), T is the

system temperature (degrees K), F is the receiver noise factor,

and B is the system bandwidth.

There is an important implication of the consumption factorthat relates to the selected cell size and capacity of future

wireless broadband cellular networks. To see this, consider



9/16


Operating CF =Blog2

SNR

MSNR+ 1

Pnonpath + SN R

PnoiseH

(49a)

Operating CF =Bsig

Pnonpath + MSNR (2sig 1) PnoiseH

(49b)

two limiting cases illuminated by the consumption factortheory. In the first case, we assume that the signal path

power consumption is the dominant power drain for a link,

as opposed to the non-path power. This may be the case,

for example, in a macrocell system in which a base-station

is communicating to the edge of the macrocell, and the RFchannel requires more power to be used in the RF amplifier

to complete the link than the power used to power otherfunctions. In this case, the consumption factor equation (48a)

is approximated by:

CF HB log2 (1 + SN R)

SNRMSNR

Pnoise

. (51)

For an AWGN channel, we find that the consumption factor

is relatively insensitive to bandwidth if the signal-path power

dominates the non-path power:

CF Hlog2 (1 + SN R)

SNRMSNR

K T F GRX

. (52)

Equation (52) indicates that for such a link we can increasedata rate by increasing bandwidth, but that unless the signal

path components are made much more efficient (i.e. the system

power-effi

ciency factor is made closer to 1), then as data rateincrease we will require approximately the same energy per

bit. In other words, if transmission power is the dominant

cause of energy expenditure, then there is little that canbe done to drive down the energy-price per bit through an

increase in bandwidth. There are two problems that arise: A)

efficiency improvements in inexpensive IC components are

becoming harder to achieve due to performance issues when

supply voltages are scaled below 1 volt, which is approx-imately the supply voltage used by many present-day high

efficiency devices, and B) with the exponential growth in data

traffic that is occurring today, unless the energy cost per bit can

be reduced exponentially, we face an un-tenable requirement

for increased power consumption by communication systems.The upshot of (52) is that for conventional cellular systems, all

signal-path devices, and particularly the RF power amplifier

the precedes the lossy channel, and other components that

precede lossy attenuators, must be made as power efficient as

possible, thus suggesting that modulation/signaling schemes

should be chosen to support as efficient an RF amplifier aspossible.

Consider the second limiting case of equation (48a), in

which the non-path power dominates the signal power. In

this case, we are assuming that items such as processors,displays, and other non-signal path components (typical of

smart-phones and tablets) dominate the power drain. We find

from (48a) that in this case:

CF B log2 (1 + SN R)

Pnonpath. (53)

Eqn. (53) indicates that wider-band systems are preferable

on an energy-per-bit basis provided that signal-power can be

made lower than the total power used by components off the

signal path. This situation is clearly preferable to the first case

as it indicates that by increasing channel bandwidth (say, by

moving to millimeter-wave spectrum bands where there is atremendous amount of spectrum [3][12][13]), we also achieve

an improvement in the consumption factor, i.e. a reduction inthe energy cost per bit. Interestingly, this indicates that the

goals of massive data rates (through larger) bandwidths and

smaller cell sizes combined together can be used to achievea net reduction in the energy cost per bit. As an increase in

bandwidth also enables an increase in data rate, this limiting

case allows us to simultaneously increase both data rate and

consumption factor: i.e. our goals for more data and more

efficient power utilization in delivering this higher speed data

are aligned. This is not to say that we should increase non-

path power to the point that equation (53) holds. Rather, we

would desire to decrease the required signal path power to

the point where (53) holds. If the non-path power can be

reduced, but the signal power can be reduced even faster, then

we arrive at the ideal situation of improving power efficiencywith a move to higher bandwidths and greater processing

and display capabilities in mobile devices. To achieve thisgoal, it is likely that link distances will need to be reduced

as bandwidths are increased. The goal of making the signal

power as low as possible so that the non-path power dominatesmay at first be counter-intuitive. However, realize that in

order to have as many bits as possible flowing through a

communication system it is advantageous to make each bit

as cheap as possible. In order for (53) to apply, we require:

Pnonpath >

SN R

MSNR

Pnoise

H(54)

Recall the form of the power-efficiency factor of a wirelesslink given by (41). We will model the channel gain as:

Gchannel =k

d(55)

Where d is the link distance, is the path loss exponent,

(which equals 2 for free space), and k is a constant. Using

(55) in (41) and (54), we find (56). And by isolating distance,

we find

d

SN R

MSNR

Pnoise

H1RX +

1

GRX

d

k 1

+

d

GRX k

H1TX 1

(56)

and when further simplifying, we see

d < GRXHTXkPNPMSNR

PnoiseSN R

1

HRX (58)and, finally, solving for distance, we see that

d 1 to ensure that by increasing bandwidthwithin a given bound, we do not violate (59):

d ln (2) NoC

HTX

PNPGRX +NoCln (2)

1GRXHRX

(78)If we model the channel gain as (55), we find:

k

d>

ln (2) NoC

HTX

PNPGRX + NoCln (2)

1 GRXHRX

(79)and (80). If PNP

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