design principles for energy harvesting wireless

Design Principles for Energy Harvesting Wireless Communication Networks

Aylin Yener

[email protected]

Acknowledgment: NSF 0964364

Introduction

Ubiquitous

Mobile / Remote

Energy-limited

6/16/20142

Many sources

Abundant energy

Green

Energy Harvesting

Wireless Communications

Energy Harvesting Wireless Networks

Energy Harvesting Networks

Wireless networking with rechargeable (energy

harvesting) nodes:

Green, self-sufficient nodes,

Extended network lifetime,

Smaller nodes with smaller batteries.

A relatively new field with increasing interest.

6/16/20143

Some Applications

Wireless sensor networks

Greencommunications

6/16/20144

Harvesting Energy

Fujitsu’s hybrid device

utilizing heat or light.

Image Credits: (top) http://www.fujitsu.com/global/news/pr/archives/month/2010/20101209-01.html(bottom) http://www.zeitnews.org/nanotechnology/squeeze-power-first-practical-nanogenerator-developed.html

Nanogenerators built at

Georgia Tech, utilizing strain

6/16/20145

New Network Design Challenge

A set of energy feasibility constraints based on energy harvests govern the communication resources.

Main design question:

When and at what rate/power should a rechargeable (energy harvesting) node transmit?

Optimality? Throughput; Delivery Delay

Outcome: Optimal Transmission Schedules6/16/2014

6

One Energy harvesting transmitter.

Find optimal power allocation/transmission policy that departs maximum number of bits in a given duration T.

Energy available intermittently.

Up to a certain amount of energy can be stored by the transmitter BATTERY CAPACITY.

Throughput Maximization

[Tutuncuoglu-Y.’12]

6/16/20147

Energy harvesting transmitter:

Energy arrives intermittently from harvester Transmitter has backlogged data to send within a

deadline T. Stored in a finite battery of capacity

System Model

Ei

transmitter receiver

Energy queueData queue

Emax

Emax

6/16/20148

Energy arrivals of energy at times

Arrivals known non-causally by transmitter, Design parameter: power rate .

iE is

)( pr

E0

t

TE1 E2 E3

s1 s2 s3s0

System Model

6/16/20149

Notations and Assumptions

Power allocation function:

Energy consumed:

Transmission with power p yields a rate of r(p)

Short-term throughput: T

dttpr0

))((

)(tp

T

dttp0

)(

6/16/201410

Power-Rate Function

Transmission with power p yields a rate of r(p)

Assumptions on r(p):

i. r(0)=0, r(p) → ∞ as p → ∞ ii. increases monotonically in piii. strictly concaveiv. r(p) continuously differentiable

Example: AWGN Channel,

)( pr

Rate

Power

Nppr 1log

21)(

6/16/201411

Power-Rate Function

r(p) strictly concave, increasing, r(0)=0 implies

)( pr

Rate

Power

pppr in decreasing llymonotonica is )()tan(

Given a fixed energy, a longertransmission with lower power departs more bits.

Also, r -1(p) exists and is strictly convex

6/16/201412

Lazy Scheduling, El Gamal 2001

Battery Capacity:

Energy Constraints

(Energy arrivals of Ei at times si)

Energy Causality: nn

n

i

t

i stsdttpE

'0)( 1

1

0

'

0

nn

n

i

t

i stsEdttpE

')( 1

1

0

'

0 max

nn

n

i

t

i stsnEdttpEtp '0)(0)( 1

1

0

'

0 max , ,

Set of energy-feasible power allocations

6/16/201413

Energy “Tunnel”

cE

t1s 2s

0E1E

2EmaxE

Energy Causality

Battery Capacity

6/16/201414

Optimization Problem

Maximize total number of transmitted bits by deadline T

Convex constraint set, concave maximization problem

T

tptptsdttpr

0)()(..,))((max

nn

n

i

t

i stsnEdttpEtp '0)(0)( 1

1

0

'

0 max , ,

6/16/201415

Necessary conditions for optimality of a transmission policy

Property 1: Transmission power remains constant

between energy arrivals.

Proof: By contradiction

r(p)dtr(p(t)) dt(t)) r(p

elsetptttptttp

tp

,tttptp

* of concavity strict to due Then

Define

energy total given with ][0, some for Let

00

222

111*

2121

)(],[)(],[)(

)(

)()(

6/16/201416

Let the total consumed energy in epoch be

which is available in energy queue at

Then a constant power transmission

is feasible and strictly better than a non-constant

transmission.

Necessary conditions for optimality

],[ 1ii ss totalE

ist

],[, 11

iiii

total sstss

Ep

Transmission power can change only at is

6/16/201417

Property 2: Battery never overflows.

Proof:

pr(p)dtr(p(t))dt(t))pr(

elsetp

tptp

TT

in increasing is since Then

Define

time at overflows of energy an Assume

00

)(

],[)()(

Necessary conditions for optimality

6/16/201418


Property 3: Power level increases at an energy arrival instant

only if battery is depleted. Conversely, power level decreases

at an energy arrival instant only if battery is full.

Policy can be improved Policy cannot be improved

p(t)

p’(t)p*(t)

r(p(t))dt(t))dtpr(

6/16/201419


Property 3: Power level increases at an energy arrival instant

only if battery is depleted. Conversely, power level decreases

at an energy arrival instant only if battery is full.

Policy can be improved Policy cannot be improved

p(t)p’(t)

r(p(t))dt(t))dtpr(

p*(t)

6/16/201420


Property 4: Battery is depleted at the end of transmission.

Proof:

increasing is since Then

Define

p(t) after remains of energy an Assume

r(p)dtr(p(t))dt(t))pr(

elsetp

TTtptp

TT

00

)(

],[)()(

6/16/201421

Necessary Conditions for Optimality

Implications of Properties 1-4:

Structure of optimal policy: (Property 1)

For power to increase or decrease, policy must meet the upper or

lower boundary of the tunnel respectively (Property 3)

At termination step, battery is depleted (Property 4).

An algorithmic solution can be found recursively, see

[Tutuncuoglu-Y.12]

constant ,}{ ,0

)( 1nnn

nnn psiTt

itiptp

6/16/201422

Energy “Tunnel”

cE

t1s 2s

0E1E

2EmaxE

Energy Causality

Battery Capacity

6/16/201423

Shortest Path Interpretation

Optimal policy is identical for any concave power-rate function!

Let , then the problem solved becomes:

The throughput maximizing policy yields the shortest path through the energy tunnel for any concave power-rate function.

1)( 2 ppr

)(..1)(min0

2

)(tptsdttp

T

tp

length of policy path in energy tunnel

)(..1)(max0

2

)(tptsdttp

T

tp

6/16/201424

Shortest Path Interpretation

Property 1: Constant power is better than any other alternative

Shortest path between two points is a line (constant slope)

E

t06/16/2014

25

Alternative Solution(Using Property 1)

Transmission power is constant within each epoch:

KKT conditions optimum power policy.

NnEpLEts

prL

n

iiii

N

iiipi

,...,10..

)(.max

max1

1

}1,{)( ,N,iiepocht,ptp i

(Li: length of epoch i)

(N: Number of arrivals within [0,T])

6/16/201426

0

0

1max

1

n

iiiin

n

iiiin

EpLE

EpL

full is battery when only positive only 's

empty is battery when only positive are 's

Solution

Complementary Slackness

Conditions: nEpLE

nEpL

n

iiiin

n

iiiin

0

0

1max

1

n

nN

nj jjnp

positive a at decreases positive a at increases

1)(

1*

6/16/201427

(Water Filling-Goldsmith 1994)

Directional Water-Filling

[Ozel, Tutuncuoglu, Ulukus, Y., 2011]

Harvested energies filled into epochs individually

0 tO O O

0E 1E 2E

Water levels (vi)

6/16/201428



Constraints:

Energy Causality: water-flow only forward in time

0 tO O O

0E 1E 2E

Water levels (vi)

6/16/201429



Constraints:

Energy Causality: water-flow only forward in time

Battery Capacity: water-flow limited to Emax by taps

0 tO O O

0E 1E 2E

Water levels (vi)

6/16/201430

Example

31

0

20 E51 E

1s

p

12 E 93 E 74 E

2s 3s 4s

10max E

6/16/2014


Energy tunnel

and directional

water-filling

approaches

yield the same

policy

E

t0

0 tO O O

0E

OO O

0E

1E 2E 3E 4E 5E

1E 2E

3E4E

5E

6/16/201432


Energy tunnel

and directional

water-filling

approaches

yield the same

policy

E

t0

0 tO O O OO O

6/16/201433

Simulation Results

Improvement of optimal algorithm over an on-off transmitter in a simulation with truncated Gaussian arrivals.

6/16/201434

Extension to Fading Channels

[Ozel-Tutuncuoglu-Ulukus-Y.‘11]

Find the short-term throughput maximizing and transmission completion time minimizing power allocations in a fading channel with known channel states.

Finite battery capacity

6/16/201435

System Model

AWGN Channel with fading h :

Each “epoch” defined as the interval between two “events”.

)1log(21),( hphpr

0E 2E 3E 6E 7E

0 tx x x x

Fading levels

L1 L4 L7

h1h2=h3=h4

h5h6=h7

h8

0,..5,4,1 E

O O O O O

6/16/201436

TM Problem with Fading Transmission power constant within each epoch:

Maximize total number of transmitted bits by deadline T

Solution once again is directional waterfilling.,...,MnEpLEts

phL

n

iiii

M

iii

i

pi

10..

)1log(2

max

max1

1

}1,{)( ,M,iiepocht,ptp i

6/16/201437

n

M

ni iin h

p 11*

Directional Water-Filling for fading channels

0 tO O Ox

0E 2E 4E

Fading levels (1/hi)

Water levels (vi)

x

Same directional water filling model with added

fading levels.

Directional water flow (Energy causality)

Limited water flow (Battery capacity)

6/16/201438

Multiple EH Transmitters

How to allocate power when there are more than one energy harvesting transmitters sharing the same medium?

How do the network parameters affect the optimal policy?

Many recent multi-node models, e.g., MAC (and BC) [Ozel,Yang,Ulukus’11,’12], Relay [Cui, Zhang,’12], [Oner, Erkip’13], [Varan, Y.’13], …, Two-way Relay [Tutuncuoglu, Varan, Y.’13],…

6/16/201439

Interference and EH: Gaussian IC with EH Transmitters

E1[i]

Transmitter 1 Receiver 1

Energy queue

E1,max

E2[i]

Transmitter 2 Receiver 2

E2,max

1

1

a

b

2212

1211

ZXXbY

ZXaXY

[Tutuncuoglu-Y. ’12]

6/16/201440

,N, n,j

EipiEts

ipipr

j

n

ijj

N

i

121

][][0..

])[],[(max

max,1

12100

21 p,p

Sum-Throughput Maximization Problem:Find optimal transmission power/rate policies that maximize the total amount of data transmitted to both receivers by a deadline T=Nτ.

Problem Definition

6/16/201441

Claim:

Concavity of sum-rate

2121 ),( ppppr and in concave jointlyis

Given any transmission scheme achieving a sum-rate r(p1,p2), one can utilize time-sharing to construct concave sum-rate:

0,,10,)1(..

),()1(),(),,(

max),(

2

2121

21

21*

ppppptspprppr

ppr

ppr

jjjj

6/16/201442

Convex problem allows the solution to be found

using coordinate descent between and

Optimal Policy

Iterative Generalized Directional Water-filling(IGDWF):

constrained water-filling with generalized water levels:

nN

ni iip

n

n

prp

v

)()(

6/16/201443

][1 ip ][2 ip

Two-user IGDWF

44

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

GDWF for

User 1

6/16/2014

Two-user IGDWF

45

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

GDWF for

User 2

6/16/2014

Two-user IGDWF

46

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

GDWF for

User 1

6/16/2014

Two-user IGDWF

47

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

GDWF for

User 1

GDWF for

User 2

6/16/2014

Take-away

Multiple energy harvesting transmitters sharing the same medium: transmit policy of one depends on the others.

Care need to be exercised in iteratively finding the water-filling solutions.

Policies do depend heavily on the channels, some instances converge in one iteration and/or result in simplified algorithms, e.g., strong interference.

6/16/201448

Multiple EH Transmitters:The concept of Energy Cooperation[Gurakan-Ozel-Yang-Ulukus ’12]

Intermittent energy nodes may be energy deprived!

Relay can “receive”

the energy to forward

the data.

Energy cooperation

between nodes can be

very useful!

6/16/201449

Wireless Energy Transfer

Already present in RFID systems

New technologies like strongly coupled

magnetic resonance reported to achieve

high efficiency in

mid-range

Image Credits: (top) http://www.siongboon.com/projects/2012-03-03_rfid/image/inlay.jpg(middle) http://www.witricity.com(bottom) http://electronics.howstuffworks.com/everyday-tech/wireless-power2.htm

Transfer energy to a 60-watt bulb with 50 percent efficiencyfrom 6-feet & 90 percent efficiency from 3-feet (MIT).75 percent efficiency from two to three feet away (Intel).

6/16/201450

Wireless Energy TransferIn-body (in-vein) wireless devices

6/16/201451

Image Credits: (top) http://www.extremetech.com/extreme/119477-stanford-creates-wireless-implantable-innerspace-medical-device (bottom) http://www.imedicalapps.com/2012/03/robotic-medical-devices-controlled-wireless-technology-nanotechnology/

Poon, 2012

Energy Harvesting and Cooperating Models (EH-EC)

52

Time slotted model, N slots

with length T, indexed by i

K transmitters receive energy

packets of size Ej[i] at the

beginning of the ith time slot

][1 iE

][2 iE

1

2

][1 ip

][2 ip

Received energy stored in an infinite size battery

In slot i, node k transmits with power pk[i]

6/16/2014

EC-EH

53

In time slot ,transmitter sends transmitter an energy of with efficiency

Uni-directional energy transfer is a special case with

][1 ip

][2 ip

n

ik

K

jjkkjkjk

batk TipiiiEnE

1 1,,, ][][][][][

1

2

][1 iE

][2 iE

Harvested energy Received and sent energy

Energy used for transmission

1221

Kkjαα j,kk,j ,...,1,,0,0

i kj

][, ijk k,jα

Energy in node k’s battery at the end of the ith time slot:

6/16/2014

EC-EH

54

Energy Constraints:

Non-negativity of transmit power and transferred energy:

0][][][][][1 1

,,,

n

ik

K

jjkkjkjk

batk TipiiiEnE

NnKkjnnp kjk ,...,1,,...,1,,0][,0][ ,

Energy Causality: Energy required by transmission or transfer is available, i.e., harvested:

What is the sum-capacity of EC-EH-MAC and EC-EH-T(wo)-W(ay)-C?

6/16/2014

Sum-Capacity:

EC-EH-TWC

55

),,0(~ 2

21122

12211

kkN

NXhXY

NXhXY

N

21 1log211log

21 ppCTWC

S

p1

p2

][1 iE ][2 iE

1 21h

2h

1,2

2,1

6/16/2014

EC-EH-MAC

56

),,0(~

...2

11

NN

NXhXhY KK

:by and Normalize

k

k

hXXYY

h

','

2

K

kk

MACS pC

11log

21 Sum-Capacity:

R

p1

p2

...

pK

1h

2h

Kh

1

2

K

][1 iE

][2 iE

][iEK

1,2

2,1K,1

1,K

K,22,K

6/16/2014

Problem Statement

57

Nn,...,Kj,k

TipiiiE

npnts

ipipipCN

n

ik

K

jjkkjkjk

kjk

N

iKS

nnp jkk

,...,1,1

0][][][][

,0][,0][..

])[],...,[],[(1max

1 1,,,

,

121

][],[ ,

Find maximum achievable sum-rate by optimizing the energy transfer and energy expended for tx.

6/16/2014

[Tutuncuoglu-Y. ’13]

Simplifying the Problem

58

1) Optimal Routing of Energy Transfers:Use equivalent transfer efficiency values that reflect the optimal routing of energy transfers.

2) Procrastinating Policies:Restrict to a subset of policies that delay energy transfer unless transferred energy is used immediately

3) Decomposition:Solve energy transfer and power allocation separately

6/16/2014

Redefine effective efficiency values as

where is any feasible energy transfer path

Routing Energy Transfers

59

2,1 3,2

1 2 3

3,1 Energy can be transferred through multiple paths.

Optimal policy chooses the highest efficiency path.

Transferring and receiving energy simultaneously is suboptimal.

jeeeekeejk mm

,,,),...,(, ...max211

1

),,...,,,( 21 jeeek m

6/16/2014

Procrastinating Policies

60

Definition: A procrastinating policy satisfies

i.e., the energy received by a node is not greater than the energy required for transmission within that time slot.

In a procrastinating policy, a node does not transfer energy unless the receiving node intends to use it immediately.

Lemma: There exists at least one procrastinating policy that solves the sum-capacity problem.

Restrict search space to such policies

][][1

,, iTipK

kjkjkj

6/16/2014

Sum-Capacity Problem

61

Nn,...,Kk

TipiE

npts

ipipCN

n

ikk

k

N

iKSnpk

,...,1,1

0][][

,0][..

])[],...,[(1max

1

11

*

][

Define consumed powers

Sum-Capacity problem can be decomposed as

][][1][][ ,1

,, iiT

ipip kj

K

jkjjkkk

,...,Kkj

iTipits

iiT

ipCC

K

jjkkjk

kj

K

jkjjkkS

iS

jk

1,

][][,0][..

])[][(1][max

1.,

,1

,,][

*

,

Power Allocation Energy TransferSolved directly (single slot)Solved via IGDWF

6/16/2014

EC-EH-TWC

62

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

2]1[1 E 5]2[1 E

4]2[2 E 7]4[2 E

5.01,22,1

6/16/2014

EC-EH-TWC

63

T 2T 3T 4 T

4

0

T 2T 3T 4 T

3

9

12

0

8

6

2

6

v1

v2

2]1[1 E 5]2[1 E

4]2[2 E 7]4[2 E1]1[2,1

2]4[1,2

2]1[1 p 2]2[1 p 2]3[1 p 1]4[1 p

0]1[2 p

2]2[2 p 2]3[2 p

7]4[2 p

5.01,22,1

6/16/2014

EC-EH-MAC

64

Energy transfer direction is determined by

Power allocation problem is solved as if a single transmitter with energy arrivals

jkjka ,max

][][1

iEaiEK

kkk

T0 t2T 3 T 4T

i

nnE

1][

]1[E]2[E

]3[E

]4[E

6/16/2014

Simulations

65

Energy transfer from 3 to 1 is optimal after this point, allowing sum-capacity improvement

6/16/2014

104.011.02.03.01

][

,]10,0[~][],[,]1,0[~][

/10

,110,105,100

sec1,100

1,3

,

32

1

190

3

2

1

jk

mJUiEiEmJUiEHzWN

dBhdBhdBh

,TN

MAC

TWC-Simulations

66

Uni-directional energy transfer may be suboptimal in both

directions

5.0,5.0,]10,0[~][,],0[~][

/10

,100,100

sec1,100

1,22,1

2

1

190

2

1

aamJUiEmJEhUiE

HzWN

dBhdBh

,TN

6/16/2014

676/16/2014

Information Theory of EH Transmitters

So far, we have assumed

sufficiently long time slots and

utilized the known rate

expressions.

What if energy harvesting is

at the channel use level, i.e.,

each input symbol is individually

limited by EH constraints?

Tx

iE

Rx)( pRRate

iXENC

iE

DEC1 1 0 0 0 1

iY

686/16/2014

Energy Harvesting (EH) Channel:

[Tutuncuoglu-Ozel-Ulukus-Y.‘13]

The channel input is restricted by an

external energy harvesting process.

State: available energy

Has memory (due to energy storage)

Depends on channel input

Causally known to Tx (causal CSIT)

ENCODERiXW

Energy Harvesting

Energy Storage

Information Theory of EH Transmitters

ii YX

696/16/2014

EH Channel

ENCODERW

iE

DECODERW

CHANNELiX iY

iS

XYP |

ii SX

),min( max1 EEXSS iiii

(Ch. input constrained by state)

(State has memory)(State evolves based on ch. input)1max E

BATTER

Y

1,0iX

706/16/2014

Capacity with Zero Storage

Let , and encoder can use arriving energy, i.e.,

Memoryless channel with causal state, [Shannon 1958]

0max E

)()(max qpHpqHCpZS

ENCODER DECODERii YX

WW

iE

. 1,0,1,0,0

ii

ii

XthenEifXthenEif

716/16/2014

Capacity with Infinite Storage

2121

,1),(

qqqH

CIS

As , a save-and-transmit scheme proposed for the

AWGN ch [Ozel, Ulukus, 12] is optimal.

Any codeword with can be conveyed without error

maxE

pX ][


WW

iE

iSmaxE

726/16/2014

The Binary EH Channel

[Tutuncuoglu-Ozel-Y.-Ulukus’13]

Unit battery, Binary noiseless channel, Timing channel equivalent: encoding strategy; upper bound by

providing state info at the decoder.

ii YX 1max E


WW

maxEiE

iS

][

)()(max 1 )1(1

))1((

)( TE

tpTHC t Tq

qH

tpBEHC

t

t

T

736/16/2014

A tighter upper bound than [Tutuncuoglu-Ozel-Y.-Ulukus’13]:

A lower bound on i.e., the information leaked to the receiver about the harvesting process.

)|;( UTZI

New Results on BEHC[Tutuncuoglu-Ozel-Y.-Ulukus’14](will be presented at ISIT 2014)

Improved encoding scheme as well:

ZUNZUZUZU

V1)mod(

1

746/16/2014

New Results on BEHC

Asymptotically optimal achievable

rate

Improved upper bound on capacity

Capacity within 0.03 bits

756/16/2014

EH DMC with CSIT&CSIR[Ozel-Tutuncuoglu-Ulukus-Y.’14](will be presented at ISIT 2014)

The battery state is available causally at both Tx and Rx Input symbol , with consuming units

of energy.Xi {0,1,..., K}

Si

ENCODER CHANNEL DECODERiX iY

WW

maxEiE

iS

Information flows both through the physical channel and the battery state. (e.g., communication is possible without channel)

iS iS

Xi k k

766/16/2014

EH DMC with CSIT&CSIR

ENCODER CHANNEL DECODERiX iiYY 21

WW

),|,( )1(121 iiii yxyyp

Δ

)1(2)1(1 ii YY

ENCODER CHANNEL DECODERiX iY

WW

maxEiE

iS iS iS

)|( ii xyp

Original EH channel with

CSIT and CSIR:

Equivalent channel with

feedback:[Chen-Berger ‘05]

Feedback does not increase capacity Weissman, Goldsmith 2009

776/16/2014

EH DMC with CSIT&CSIR

Conclusion• New networking paradigm: energy harvesting nodes

New design insights arise from new energy constraints!

Realistic concerns, e.g. storage capacity, storage

efficiency impact transmission policies.

Multi-terminal scenarios need to be handled with care.

Cooperation with an energy harvesting relay or energy

cooperation brings additional insights and possibilities.

Information theoretic formulations are challenging but

promising to yield new insights.6/16/2014

78

Current Studies and Open Problems

Information theoretic limits, optimal coding schemes for energy harvesters

Operational principles of energy harvesting receivers

Impact of EH on signal processing PHY algorithms

Impact on network protocols

Efficient online schedules, simple practical implementations

Papers: 6/16/2014

79

http://wcan.ee.psu.edu/

design principles for energy harvesting wireless

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